ll!!! If ill." THE CYCLIC PATTERN OF HEIGHT GROWTH FROM BIRTH TO MATURITY By Reuben Robert Rusch AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Teacher Education Year 1956 Approved _ ABSTRACT The purpose of this study was to determine the individual cyclic pattern of heicnt growth from birth to maturity. Although much research has been done with cross-sectional height data, there is relatively little evidence showing the individual'pattern of height growth ever even short periods of the growth process, and even less evidence to show the individual pattern from birth to maturity. Fels Research Institute, Yellow Springs, Ohio, provided the longitudinal height measures Which were used. Of the cases they had available the serial measurements of 46 girls and 31 boys met the criteria of completeness chosen for this study. The straight line that best fitted the data was individ~ ually determined from the serial height measures taken at six month intervals. The measured heivhts were then compared to this straight line. The individual data and its straight lin of best fit were plotted on separate graphs. To determine the cyclic pattern objectively and mathematically, the equations of the straight line were solved for each time that height was actually measured. ”he difference between the measured heights and the result of solving the straight line equations was termed a deviation. If the recorded meaSure was aeove the straight line, that is greater than the magnitude represented by the straight line, the deviation was considered positive, if it was below the straight line, it was considered negative. 1 2 The deviations were then analyzed to determine the numter of cycles of height growth, according to three criteria for determining cycles. In general, a cycle was considered to be characterized by increasing Upward movement followed by decreasing upWard movement. A definite cyclic pattern of height growth from birth to maturity was found in all cases. There were differences in the patterns of height growth of boys and girls although the patterns of most boys as well as girls showed either three or four cycles. In all cases the cycle occurring immediately after birth was the most pronounced. The rate of growth was most rapid after birth and gradually decreased for the next two or three years. Almost all cases exhibited a distinguishable curve or cycle at what might be considered the time of adolescence. This pattern was, howeVer, less obviously curvilinear in some cases. The individuality of the cyclic patterns of height growth was shown eSpecially during the period between the beginning cycle and the adolescent cycle. During this period of the growth process the rate changed more frequently in some cases than it did in others TGSultiUL in a greater number of cycles. It was concluded that the general cyclic pattern of height growth for the Various individuals snowed many.similarities, al- I thounh unique characteristics were found, especially bethcn infancy and adolescence. Capyrightod b I Reuben Robert Busch 1958 THE CYCLIC PATTERN OF HEIGHT GROWTH FROM BIRTH TO MATURITY By Reuben Robert Rusch A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Teacher Education Year 1956 ACKNOWLEDGMENT The writer wishes to express his appreciation and gratitude to all those who have assisted in making this study possible; particularly to Dr. A. R. DeLong for his interest, patience, and helpful criticisms. Dr. Thanks are also due to S. Garns, Head of the Physical Growth Department at Fels who has not only made the measurements available for this study but has also contributed valuable suggestions. 11 TABLE OF CONTENTS Page LIST OF TABLES O O O O O C O O I O O O O C 1v LIST OF FIGURES . . . . . . . . . . . . . . V CHAPTER I INTRODUCTION . . . . . . . . . . . . 1 Statement of the Problem . . . . . . . 8 Importance of the Study . . . . . . . 9 Definition of Terms. . . . . . . . . 13 II REVIEW OF THE LITERATURE . . . . . . . . 14 III LONGITUDINAL ANALYSES FROM BIRTH TO MATURITY. . 34 MGLhOd o o o o o o o o o o o o o 38 Iv ANALYSIS or THE DATA. . . . . . . . . . h? V SUMMARY, CONCLUSIONS, AND IMPLICATIONS. . . . 14? Conclusions . . . . . . . . . . . 148 Implications . . . . . . . . . . . lu9 APPENDICES. . . . . . . . . . . . .- . . . 152 BIBLIOGRAPHY . . . . . . . . . . . . . . . 199 iii --¢—~ Table II III LIST OF TABLES Page Summary of the Data . . . . . . . . . 50 Where Cycles of Height Growth Begin . . . . 141 Physical Trauma and Their Affect on Height Cycles. ... .. .. . . . . . . . . . 145 iv Figure 1. 10. ll. 12. 13. lb. 15. LIST OF ILLUSTRATIONS Variation in Rate of Individual Height Growth . Height Growth of a Single Individual Using the Data of Montbeillard Similar to the Figure Presented by Scammon . . . Case 75F, A Comparison of TWO Methods of Finding the Straight Line of Best Fit Case 75F, A Comparison of Two the Straight Line of Best Fit Case 75F, A Comparison of Two The Straight Line of Best Fit Case 25F, Height Measures and Of Beat Fit 0 O I O O 0 Case 28F, Height Measures and or Best Fit 0 O O O O 0 Case 37F, Height Measures and of Best Fit . . . . . . Case 59F, Height Measures and of Best Fit . . . . . . Case 66F, Height Measures and or Best Fit 0 O O O O 0 Case 67F, Height Measures and of Best Fit . . . . . . Case 72F, Height Measures and or B831: Fit 0 l O 0 o 0 Case 75F, Height Measures and 0f Beat Fit 0 O C . O 0 Case 76?? Height Measures and of Best Fit . . . . . . Case 82F, Height Measures and Of Best Fit 0 o o o o 0 Methods of Finding Methods of Finding the the the the the the the the the the Straight Line Straight Line Straight Line Straight Line Straight Line Straight Line Straight Line Straight Line Straight Line Straight Line Page 28 39 H1 43 51 53 54 55 56 57 58 59 60 Figure 16. 17. 18. 19. 20. 21. 25. 26. 29. 30. 31. LIST OF ILLUSTRATIONS —- Continued Case 83F, Height Measures and the Straight Line or Best Fit . . . O O O O O Q O O O 0 Case 88F', Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . Case 94F“, Height Measures and the Straight Line or Best Fit 0 O C O O O O O O O I 0 Case 96F, Height Measures and the Straight Line Of Beat Fit 0 C . I O . O C C C C O . Case 97F, Height Measures and the Straight Line or. Best b‘it O O . O O I O O O C O O 0 Case 111F*°, Height Measures and the Straight Line or Be St Fit 0 O 0 O O O O O O O O O 0 Case 117F, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case lZOF, Height Measures and the Straight Line or Best Fit 0 O O O 0 O o o a O 0 o 0 Case 126F, Height Measures and the Straight Line Of Beet Fit 0 O I I O I O O O O O 0 I Case 127F, Height Measures and the Straight Line or Best Fit 0 I O O I O O O I C O O 0 Case 137F, Height Measures and the Straight Line or Best F‘it l O O I O O O O O I I l I Case 140F, Height Measures and the Straight Line Of Beet Fit 0 C C O C C O O C . O O 0 Case 1U2F, Height Measures and the Straight Line or Be at Fit 0 O I C C C C C . O O . . Case lhuF, Height Measures and the Straight Line Of Beat Fit C O O O C C C C O O C C 0 Case lh5F*, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case146F*, Height Measures and the Straight Line Of Beat Fit . . . O O . C U C C O O 0 vi Page 61 63 64 65 66 67 68 69 7O 71 72 73 74 75 76 Figure 32. 33. 3h. 35. 36. 37. 38. 39. #0. H1. #2. 43. an. “5. 46. 47. LIST OF ILLUSTRATIONS -- Continued Page Case lHBF, Height Measures and the Straight Line Of Beet Fit I I I I I I I I I I I I I 77 Case 150F, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I I 78 Case lSlF, Height Measures and.the Straight Line of Best Fit . . . . . . . . . . . . . 79 Case 165F, Height Measures and the Straight Line Of Best Fit 0 o o o o o o I I O O 0 o 80 Case 17OF, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . 81 Case 171F*, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I I 82 Case 176F, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I I 83 Case 179F, Height Measures and the Straight Line or Be at Fit I I I I I o o o o I o o 0 81+ Case 183F, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . 85 Case 185F*, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . 86 Case 188F, Height Measures and the Straight Line Of Be St Fit I I I I I I I I I I I I I 87 Case 19lF, Height Measures and the Straight Line or Be at Fit I I I I I I I I I I I o o 88 Case 193F, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . 89 Case ZONF, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . 90 Case 205F, Height Measures and the Straight Line Of Beat bflit I I I I I I I I I I I I I 91 Case leF, Height Measures.and the Straight Line Of Beet Fit I I I I I I I I I I I I I 92 vii Figure #8. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. LIST OF ILLUSTRATIONS —— Continued Case 214F, Height Measures and the Straight Line Of Beet Fit I I I I I I I I I I I I I Case 217Fo, Height Measures and the Straight Line of Beat Fit I I I I I I I I I I I I Case 220E, Height Measures and the Straight Line Of Boat Fit I I I I I I I I I I I I I Case 221F, Height Measures and the Straight Line Of Best Fit I I I I I I I I I I I I I Case lOM*, Height Measures and the Straight Line Of B081: Fit I I I I I I I I I I I I Case N9M, Height Measures and the Straight Line Of Be at Fit I I I I I I I I I I I I Case 54M“, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I I Case 55M°, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case 71M*°, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case 74M, Height Measures and the Straight Line or Best Fit I I I I I I I I I I I I Case 77M, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case 78M, Height Measures and the Straight Line Of Beet Fit I I I I I I I I I I I I I Case 81M, Height Measureseand the Straight Line Of Beat Fit I I I I I I I I I I I I I Case 8hM*, Height Measures and the Straight Line or Be St Fit 0 o o a o o o o I o o o 0 Case 92M, Height Measureszand the Straight Line Of BeSt Fit I I I I I I I I I I I I I Case 98M*, Height Measures and the Straigit Line Of BeSt Fit 0 o o o o o o o o o o o 0 viii Page 93 94 95 96 98 99 100 101 102 103 105 106 107 108 Figure 6e. 65. 66. 67. 68. 69. 70. 71. 75. 76. 77. 78. 79. LIST OF ILLUSTRATIONS -- Continued Case 102M*°, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . Case 112M, Height Measures and the Straight Line or Best Fit I I I I I I I I I I I I Case ltho, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . Case 135MO, Height Measures and the Straight Line or Best Fit I I I I I I I I I I I I I Case 138M, Height Measures and.the Straight Line of Best Fit . . . . . . . . . . . . Case 141M*, Height Measures and the Straight Line Of Beat Fit a o o I o a o o o o o o 0 Case 153MO, Height Measures and the Straight Line Of Be at Fit I I I I I I I I I I I I I Case 154M, Height Measures and the Straight Line Of Be at Fit I I I I I I I I I I I I I Case 156M, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case 157Mo, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . . Case 16OMO, Height Measures and the Straight Line of Best Fit . . . . . . . . . . . . Case 167240, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I Case 174M0, Height Measures and the Straight Line Of Beat Fit I I I I I I I I I I I I Case 177M, Height MeasureSEind the Straight Line Of BeSt Fit I I I I I I I I I I I I I Case 180Mo, Height Measureszand the Straight Line Of Beet Fit I I I I I I I I I I I I Case 183M*°, Height Measures and the Straight Line of Beet Fig I I I I I I I I I I I I I ix Page 109 110 111 112 113 114 115 116 117 118 123 124 Figure 80. 81. 82. 83. 8h. 85. 86. 87. 88. LIST OF ILLUSTRATIONS -- Continued Case 186M, Height Measures and the Straight Line Of Boat Fit I I I I I I I I I I I I Case 189M0, Height Measures and the Straight Line or Best Fit I I I I I I I I I I I I Case 197M0, Height Measurcszand the Straight Line or Best Fit I I I I I I I I I I I I Cycles of Height Growth, Girls . . . . . . Cycles of Height Growth, Boys . . . . Cycles of Height Growth, Girls . . . . . . Cycles of Height Growth, Boys . . . . . . Cycles of Height Growth, Girls . . . . . . Cycles of Height Growth, Boys . . . . . Pase 125 12? 13h 135 136 138 139 CHAPTER I INTRODUCTION The approach to precision of measurement, description, and analysis of data in the eXact sciences such as physics and chemistry has been followed at a later date by similar advances in the social sciences. The analytical balance, microsc0pe, and electron Inicroscope are examples of the improvement of instruments for rneasurement in the exact sciences. Likewise the sliding <1alipers calibrated in millimeters,the Baldwin square, and JG-ray apparatus are examples of almost equally precise measuring iristruments used in human growth and development research, a fixeld considered as belonging to the social sciences. Mathematical equations have been devised that describe thus results of repeated experiments in the exact sciences. SJJnilarly in the social sciences mathematical equations have been used to describe the growth of individuals and of groups. \‘ lNathan Shock, "Growth Curves," Handbook of EXperimental yygflholo , ed. by S. 8. Stevens (New York: Wiley, 1951). Pp. CL.§E€H§K 2 Even the important change from metaphysical alchemy to chemistry and the numerous implications that this change has brought about has a parallel in importance in the social sciences. This equally important change, occuring years later, is the change from the cross-sectional to the longitudinal approach in the collection, analysis, and interpretation of data. Nowhere in the area of the social sciences has this change in approach been better demonstrated than in the com— ,paritively recent research literature concerned with human gzpwth and development. In describing observation of phenomena. objectivity 41nd the law of the single variable have been of utmost impor- tancs among the exact scientists for some time. Many authors anuang the social scientists have shown their awareness of the necessity of objectivity in experimentation and the reporting 01' these results. However, the law of the single variable Seems foreign to most of the writers who have conducted cross- Sectional studies in the social sciences. Courtisz is one of true few who has shown his awareness of the law of the single Variable or as he puts it ”the court of last resort in science. " HE! has conducted some important individual longitudinal research or! school children which was governed by this law. \ .— 2 A. S. A. Courtis, Towards A Science of Education (Ann Pboer: Edwards Browt'ners, 19517. p. f 3 In the area now designated as child growth and develOp- ment, Stewart3 is frequently given credit as one of the first to realize some of the advantages of the longitudinal approach. He was one of the first to conclude that the pattern shown by averaging the growth of a group of children had little relation— ship to the pattern of individual growth.)+ Hence, since these conclusions of Stewart there has been a shifting of emphasis in the research relating to child gwowth and deve10pment. Former studies which sought to ziscertain the relation between two variables measured in a Zlarge group of children at a given time are being replaced by :3tudies of the growth process made by many cumulative observa- ‘tions of the same child or children. The shifting of emphasis in the collection of data is Slxawly being realized. Social scientists are now collecting OtDJective longitudinal measurements on individuals over a period of time. They are constantly striving to devise experi- ‘nerits in which the law of the single variable is operating. In the analysis of the data, this change or shifting 01‘ emphasis is even more gradual. For purpose of analysis these \ W 38. F. Stewart, "Physical Growth and School Standing of Boys," Journal of Educational Psychology, 7:414—1426, 1916. u Ibid.. p. ”26. L1. scientists have grouped the data according to sexes and some other phenomena such as the menarche and then proceeded to analyze the group pattern with regard to the pOpulation mean or some other similar average. Thus since social scientists have followed the letter of the law in the collection of information, but not the Spirit of the law in the analysis of this information, comparatively little has been discovered about individual longitudinal grOWth. One of the schools of thought which has made this 'transition in point-of-view as well as in the statement of the general principle is the organismic school. This theory for eexplaining growth of the whole individual, is based on the nuost recent individual longitudinal research. Supported by Ccnartiss, Millard6, Olson7, and othersa’g. the organismic ‘ 58. A. Courtis, "Growth and Development in Children," égvances in Health Education, Proceedings of Seventh Health .anaference, Ann Arbor, Michigan, 1933 (New York: American Cilild Health Association, 193“). 6Cecil V. Millard, ghild Growth and Development (Boston: D. C. Heath and 00.. 1951). 7Willard C. Olson, Child Development (Boston: D. Heath and Co. . 19u9). C. 0 8Arthur R. DeLong, "Longitudinal Study of Individual hiildren," Michigan Education Association Journal, November, 1951 , p. 113. 9Thomas P. F. Nally and A. R. DeLong, "An Appraisal of 3 Method of Predicting Growth,” Child Devdo ment Lab. Publication. er‘ies II, No. 1, (East Lansing, Michigan, 19325. 5 concept interprets all aspects of develOpment in respect to a life pattern.lo Thus the part that time plays in the develOp- ment of the individual is recognized. The majority of the modern writers in the child development area seem to feel that most growth is cyclic in nature.11’ 12’ 13’ 14’15 One of the most convincing reports 10Cecil V. Millard, Child Growth and Deve10pment, Op. cit., p. 1+. 11Raymond N. Hatch, Ggidance Services In The Elementary School (Dubuque, Iowa: Wm. C. Brown, 195i), p. 10. 128. A. Courtis, "What is a Growth Cycle?', Growth, 1 3C. V. Millard, "The Nature and Character of Preadolescent Growth in Reading Achievement," Child Development, Vol. 11. No. 2, 1940. in H. P. Stoltz and L. M. Stoltz, The Somatic Development J Adolescent Boys (New York: MacMillan, 1951). pp. 112-113. 15 S. A. Courtis, Maturation Units and How to Use Them (Ann Arbor: Edward Brothers, 1950). PP- 179-180- 6 of cyclic growth of the human body is the statement of Shuttleworth: . . . . First, all twenty—two dimensions exhibit two major growth cycles consisting of accelerating and decelerating phases. Second, the growth phases of the first cycle are initiated at different ages and are of different durations such that the growth trends of the twenty-two dimensions are not synchro- nized. Third, the growth phases of the second cycle, in respect to a given menarcheal or M G - age group, are initiated at approximately the same ages and are of similar durations such that the growth tfgnds of the twenty-two dimensions are synchronized. In spite of the accumulation of data to support the ideas of cyclic growth and in spite of the use of the term by many writers, there has been relatively little attempt made to eXplain the specific constitution of a growth cycle. Courtis,l7’18 one of the proponents of the organismic concept vflhose studies have most rigorously followed the law of the Single variable, has not only defined empirically the term (chle, but has devised a mathematical method for describing growth within a cycle. This mathematical description of growth 13 built on the Gompertz discovery19 and assumes a law of grOWth.2O ‘ 16Frank K. Shuttleworth, "The Physical and Mental Growth (if Girls and Boys Age 6 to 19 in Relation to Age at Maximum (krowth,' Monographs ofijthe Society for Research in Child Develop- .EEEQE, Vol. XIV, No.2, Serial No. 50, 1939. p. 221. "What is a Growth Cycle7", Op. cit. to Use Them, 17S. A. Courtis, 188. A. Courtis, Maturation Units and How ~20 . Cit.’ p. 179-180. 19Benjamin Gompertz, EpilosOphical Transactions of the al Society of London for the Year MDCCCXXVLPart:;, Printed {Ecnx 4y"W: Nicol, St. James, Pall Mall, Printers to the Royal Society, MDeccxv 203. A. Courtis, Maturation Units and How to Use Them, Mn 13- 2. 7 , Nally23, Kowitzzu, Rusch25’26, Millard21, DeLongZZ Greenshieldsz7, and others28 have demonstrated that the Courtis29 technique adequately describes individual longitudinal growth. Although this description of growth is reasonably accurate and mathematical, certain procedures for determining the exact equation require the Judgment of the writer of the equation. 21 C. V. Millard, "The Nature and Character of Preadolcscent Growth in Reading Achievement," Child Development, 0p. cit. 22Thomas P. F. Nelly and A. R. DeLong, "An Appraisal of a Method of Predicting Growth," Child Development Laboratory flblication , op. cit. 23Thomas P. F. Nally, "The Relationship Between Achieved (}rowth in Height and the Beginning of Growth in Reading." Lhnpublished Ph.D. thesis, Michigan State Colhage, 1953. 2“Gerald T. Kowitz, "An EXploration into the Relation- 8k11p of Physical Growth Pattern and Classroom Behavior in Eluementary School Children." Unpublished Ph.D. thesis, Michigan State College , 1951+. 25Reubcn R. Rusch, "The Relationship Between Growth in Hexight and Growth in Weight.” Unpublished Master's thesis, Mischigan State College, 1954. 26Reuben R. Rusch, "Center of Gravity and the Law of GrI‘owth." Unpublished paper as part of requirement for Educa- ti on 521+. 27C. M. Greenshieldso "The Relationship Between Consistent IQ Scores, Decreasing IQ Scores and Reading Scores Compared on TWO DeP‘felopmental Bases." Unpublished Master's thesis, Michigan State University, 1955. 28Lillian Larner, "A Comparison of Growth in Height with GIWthth in Achievement." Unpublished paper in partial fulfillment 01- 13he requirements for the course Education 524, April 12, 1955. 29$. A. Courtis, Maturation Units and How to Use Them, ' cit., passim. O 8 One of these judgments is the determination of just where the individual cycles of growth occur.‘ Statement of the Problem Many of the implications and advantages of the longi- tudinal approach are in the process of being realized. Some of the first authors collected longitudinal data on the growth of children and treated the data according to the then standard cross— sectional methods. Thus even using longitudinal measure- ments , because of the treatment of the measurements, facts about the growth of individuals were hidden and much still I‘Dmfificiris to be discovered --— discovered only when longitudinal data are treated in an individual longitudinal manner. Mathematical equations have been used advantageously ’2 '1 t9 de scribe individual growth within a cycle.vov31:34u33.34 \ Gr- 30C. V. Millard, "The Nature and Character Of Preadolesccnt owth in Reading Achievement," Child DevelOpment, 9p. cit. 3. 31Thomas P. F. Nally and A. R. DeLong, "An Appraisal Of Me thod Of Predicting Growth," C_hild DevelOpmcnt Laboratory W211; 9.2. 01.13.. 2 G 3 Thomas P. F. Nally, "The Relationship Between Achieved POWth in Height and the Beginning of Growth in Reading, " OpI cit. 33Reuben R. Rusch, "Center of Gravity and the Law of C'I‘OWth." op, cit. 3“C. M. Greenshields, "The Relationship Between Consistent 1Q Scores, Decreasing IQ Scores and Reading Scores Compared on TWO Developmental Bases," op. cit. “G. Holmgren, R. Rusch, and L. Barron have worked out a mathematical method for determining the maximum of each individual cycle. Using this method all equation writers are able to write identical equations. 9 In this method. we have seen demonstrated a technique for analyzing individual longitudinal data in terms of the individuals contin- uou a growth pattern. It is the purpose of this study to determine the individual pattern of height growth from birth to maturity and in so doing to give indication as to where cycles of height grOWth occur. Importance of the Study A great variety of material supposedly dealing with the growth and develOpment of children has been accumulated and nume rous concepts and theories have been postulated in an attempt to analyze and eXplain the data and hence, growth. Until the past 30 years, most of the measurements collected and analyzed were of the cross-sectional variety. Stewart35 was the first to provide evidence that showed that cross-sectional studies do not yield the same results as longitudinal studies. DeLong36 in using the Holt Data to compare the longi- tudirial and cross-sectional method Of analysis showed that the re was a significant difference in the results of a cross~ Sec”lienal and longitudinal study of similar children. He \ 355. F. Stewart, ”Physical Growth and School Standing 0f Boys," Journal of Educational Psychology, op; Cit. . 6 3 Arthur R. DeLong, "The Relative Usefulness of Longitudinal and Cross-Sectional Data. " Paper presented at a meeting of the Michigan Academy of Science, Arts, and Letters. March 26, 1955, p.9. 10 points out that the two basic assumptions of the cross- sec tional approach are: . . , . when group scores are used individual differences average out, therefore the measure of central tendency is representative Of the group. . . . . When a statistical interpretation is made cross-sectionally about how grOWth Occurs, the assumption is made “13% individuals hold their posi— tions in their group.‘ DeLong's study proceeds to show that the individual does not hold his position in the group and that the measures Of central tendency describe only a very small portion of the group and for only a very short period Of time.’ Thus we see rational and conclusive evidence to illustrate that [1] cross- Sectional and longitudinal studies do not yield the same results, and [2] that the basic assumptions made when inter- pret 1mg cross-sectional data to show growth are in error. Since the individual does not hold his position in the group and since the measure of central tendency does not describe the growth of any individual for any period of time, norms based on grouped data do not represent any individual's growth pattern. For example, since according to Olson39 the average height for a group of six year Old boys is 52.9 inches and for a group of \ 371bid., p. 5. 7. 38Ibid., p. 9 39Willard C. Olson and Byron 0. Hughes, "Manual for the Description of GrOWth in Age Units," University of Michigan, Elementary School, Ann Arbor, Michigan, 1950. ll seven year Old boys it is 5b.? inches we have no bases for concluding that any six year Old boy in that group is exactly 52. 9 inches or any 7 year old boy in that group is exactly 54.? inches. And we have even less reason to believe that any six year Old will grow exactly 1.8 inches or the difference between 54. 7 and 52.9 inches in the next year. Therefore the rates as represented by the norm have no relationship [as far as showing growth is concerned] to individual growth rates. Stoddard reports the same conclusion when speaking of mental growth. "NO generalized growth curve can describe the pattern for a Single individual.“ The growth equations that are written using the Courtis Techn iqueu'l assume a law of growth but use the longitudinal measurements available on a single individual to provide the bases for the equation, and hence for the individual grOWth curve . This Technique)+2 also assumes, on the basis of much evidence, that growth is cyclic and hence the equations are Written for each individual in terms of his cyclic pattern 0 f- 8 Pthh. \ .1 wGeorge D. Stoddard, The MeaninLof Intelligence (New Ork: The MacMillan CO., 19937. p. 179. h 18. A. Courtis, Maturation Units and How to Use Them, .329 . cit., p. 10“. Ibid. 12 Cross-sectional studies revealed nothing about individual to,“ growth. Most longitudinal studies reported grouped longitudinal data and were carried on over a limited period of time. To date there has been no true longitudinal study of the height growth of boys and girls from birth to maturity repOrted in the literature. No author has attempted to accumulate a sampling of cases of boys and girls with measures from birth to maturity, and to analyze the data on an individual cyclic bases- Thus there is a limited amount of evidence from which t30 conclude about the number and magnitude of individual growth cycle 8 over the entire growth period. Even among the proponents of the organismic school of growth there is not complete agreement as to exactly where growth cycles occur and the writers of the equations have set up <11 fferent criteria for writing the equations that describe the grthh procegg.u5'46 Thus it seems reasonable to assume, that since most equation writers compared some aspect of growth to he 1ght growth, it would be advantageous to them, as well as to Others who use other methods to describe and compare serial \ ”3 L Arthur R. De Long, ”The Relative Usefulness Of ongitudinal and Cross-Sectional Data. " Op. cit. “S. F. Stewart, "Physical Growth and School Standing of Boys," Journpg]; of Educggional Psychology, Op, cit. ufiCecil V. Millard, Child Growth and Development, op, cit., p. 65. “68. A. Courtis, gtgturation Units and How to Us; Them, 02- cit., pp. 190-141. 4 « ...- 13 ginavvth of the individual, to have added information about the cym:].ic pattern of height growth from birth to maturity. Definition of Terms y_: m x +26: “The graph of this rational and integral equation of the first degree having tn? variables is always a straight line." g; The lepe of the line.“8 b; The intercept on the y axis.“9 x and : The independent and dependent variables.50 rate: Increase per unit of time. gzglg; Increasing upward movement followed by decreasing upward movement.* Trauma: An experience of such.magnitude that it might possibly affect the pattern of growth. \ (I3 “7W. Wells and W. W. Hart, Progressiye Second Algebra Oston: D. C. Heath and 00., 193“). p. 31. #8 Raymond W. Brink, A First Year of College Mathe— Yfigglcs (New York: I), 'ppleton - Century Company: Inc. u ugIbid., p. 26. 50 Ibid., p. 27 * This definition is to be held tenatively until such a time when an empirical definition can be derived from the data. CHAPTER II REVIEW OF THE LITERATURE An abundance of information has been accumulated on the growth of height, and several authors at different times historically have accomplished exhaustive reviews of the lit- ere.t:1,1re.51’52’f'3 Therefore, only a sampling of the studies need ‘to be reported in this review in an attempt to give an overview of the literature dealing With height. Almost all of the earlier anthropometric research was or a cross-sectional variety and told us little about the \ l 5 Howard V. Meredith, "Physical GrOWth of White Children - A Review of Axnerican Research Prior to 1.900," Mono- we of the Society for Research in Child Development, Vol.1. No' 2 o 1936. 52 I W. M. Krogman, ”A Handbook of the Measurement and unterpretation of Height and Weight in the GrOWing Child,” Ono ra he of the Society for Research in Child Development, V01. XIII, No. 3. V SBReview of Educational Research, Vol. III (April, 1933); v01. v1 (Feb., 1936); Vol. IX (Feb..l939); Vol. XI (Dem. 1941); 13%. XIv (Dec, 19%); Vol, xx (Dec.,1950), and Vol. XII (Dec.. 2). 11+ / 15 individual growth of children. Dickson published some of the first of the cross-sectional material on height in this country.51+ My next table is a very interesting one, giving the measurements, weight, etc. , or the young gentle- men of the Virginia Military Institute at Lexington; for which, I am indebted to one of their body, Mr. Hart, to whom I thus make my acknowledgements. One hundred and fifty names are set down ~150. Of these the average height is . . . 5 ft. 09 in. It is presumed that they are all Virginians. The tallest is 6 feet, 04 inches; age, 21; of Irish and Scotch descent. The shortest is 5 feet, 03 inches; age, 15; of Scotch and French descent. . . . Under the Rev. Dr. Buist's care, in Laurens, ( South Carolina) there are 83 young girls between the ages of 5 and 18 - one young lady is set down at 21. From 12 to 21 years of age there are 52, whose éixrerage age is 14 years and 1 month. or these, the average height is . . . . 5 feet, the average weight is . . . . 100 1/5 lbs. Under 12 years - some mere children — there are 31 young girls. Of these, the average age is about . . . . . . . . 9 years the average height is . . . . . . . .14 ft., .01 1/16 in. .57 11/12 lbs. the average weight is . . . . . . . Three of them were born in Texas, one in Alabama, one in Georgia, the rest are South Carolinians. In this study of Dickson's the information was grouped aecoI‘ding to sexes, and mention was made of the ethnic and environmental backgrounds of the people involved, thus a beginning was made in understanding some of the variables Operating in research. Samuel Henry Dickson, ”Some Additional Statistics of Height and Weight," Charleston Medical Journal and Review, 1858, 13, No.4, p. 500- 16 This publication demonstrates in a historic manner the progress that has been made since that time. Even to a person who, today, is still somewhat cross-sectionally oriented, the errors and improvements needed in a study of this type must be obvious. In terms of a cross-sectional frame of reference the children were not grouped according to age level. We have no evidence to indicate the amount of clothing, shoes, etc. that was worn when the measures were taken. No recognition was given to the known fact that children grow heavier and taller as they get older cronologically or with the passing of time. The children were, however, dealt with more adequately than if all had been lumped into a single group. Bowditch,55’56 in the 1870's and 80's collected cross— sectional data on several thousand school children (boys and girls) over a period of time. From these measurements he made conclusions as to the relationship of weight and height and by averaging the heights of groups of boys and girls he drew average growth curves. Since he recorded measurements over a period of time, Bowditch can be identified as one of the first 55H. P. Bowditch, "Comparative Rate of Growth in the Ewfl Sexes," Boston Medical and Surgical Journal, 1872, 10, 3 -435. 56H. P. Bowditch, “The GrOWth of Children," Eighth Annual Report of Magsachusetts State Board of Health, 1822. Pp. xxv;_E98, pp. 273-32h. 17 to accumulate short term longitudinal data on groups. Further, he should be given credit for realizing that group grthh is not straight line but curvilinear or even cyclic. Since he drew average growth curves on the accumulated short term longi- tudinal measures, he did not get an adequate picture of individ— ‘ ual growth differences. Another of Bowditch's conclusions was the important contribution,which he supported by evidence, that growth is most rapid during the earliest years of life. From this state- ment it seems logical to conclude that he also realized that the growth rate is not constant. 57 In 1881 Peckham reported an investigation in the public schools of Milwaukee on 5,107 boys and 5,130 girls ranging in age from four to 19 years. Colored children and those physically deformed were not included. Peckham's exclusion of racial groups and those not classified as normal was a good beginning in the realization that a reduction in variables leads to more useful results. These findings he then compared with the corresponding values for Boston children as reported by Bowditchss’ 59 and concluded that Milwaukee 57Geo. W. Peckham, "The Growth of Children,“ Sixth Annual Report of the State Board of Health of Wisconsin, 1881. Pp. lxxxiv, lu6, p. 28-73. 58H. P. Bowditch, "Comparative Rate of Growth in the Two Sexes," Boston Medical and Surgical Journal, op. cit. 59H. P. Bowditch, "The Growth of Children,“ Eighth Annual Report of Massachusetts State Board of Health. l8ZZ,op.cit. 18 children were taller than Boston children because the pepulation 60 of Milwaukee was less dense than that of Boston. His conclusion thus implies that environment affects physical growth. Apparently there was some realization of the wholeness of growth - the idea that one aspect of growth affects another - on the part of Tarbell,61 since in 1881 he reported a growth study of the stature and body weight of idiotic and feeble minded children. From this study he concluded: I. Idiotic and feeble-minded children are shorter and lighter than public school children throughout the age period from six to nineteen years. Beyond sixteen years the inferiority of the feebleminded children is well marked. 2. Growth of the two sexes of feeble-minded children follows a similar course to that of the two sexes of public school children except that the adolescent acceleration is delayed about two years. Thus, on the average, feeble-minded girls appear to exceed feeble— minded boys in stature and body weight during thg age interval from about fourteen to seventeen years. 2 Tarbell thus presented some of the first evidence to show that there is some relationship between mental and physical growth -- between height and weight,and intelligence. The first published height norms in the United States of England seem to be those presented in 1887 at the International 60Geo. W. Peckham, "Various Observations on Growth,“ Seventh Annual Report of the State Board of Health of Wisconsin, 1882. Public Document No. IE, p. 61. 61G. G. Tarbell, ”On the Height, Weight, and Relative Rate of Growth of Normal and Feeble-minded Children," Proc. Assoc. Med. Officers. American Institutions for Idiotic and Feeble-minded Persons. (Philadelphia, Pa.: Lippincott, 1883), 'Eb. 188-189. 621bid., p. 188. 19 63 Medical Congress held in Washington. Stephenson, presented tables giving averages for stature, annual absolute increases in stature, average for body weight, and annual absolute in- creases in body weight, all at yearly intervals. Stephenson's norms provided a partial picture of how the average of a group of children grew and not a representation of the pattern of growth of any one child. In 1891, Greenwood,64 analyzing some height and weight data collected in the public schools of Kansas City, organized the material into what later became common groupsings: [1] race, and [2] date of collected information. He found that for all groups studied, girls exceeded boys in both stature and weight at 13 and in years. Hence, evidence was established for what has been interpreted by some as the adolescent Spurt. Further evidence of the difference in rate of growth among boys and girls at adolescence and of the nature of this 63Wm. Stephenson, 'On the Rate of Growth in Children," Trans. International Meeical Congress, Ninth Session,gWashington, m 2,, nus—1+9. 64L. M. Greenwood, "Heights and Weights of Children," Twentieth Annual Report of the Board of Education of the Kansas CityfiPublic Schools, Kansas CityLMissouri 1890-1891, (Kansas City, Missouri: Electric Printing Co., 1891), pp. 192. 20 growth was contributed by Bowditch.65 In 1891, he presented a further analysis of the data collected in Boston. He applied Galton's method of percentile grades to the Boston data and drew curves of the measurements of a given sex. These curves showed marked differences between the sexes during the adolescent period. Stewart,66 in a study showing the relationship of school standing and the physical growth of boys was one of the first in the area of human growth and development to demonstrate that he was consciously aware of the idea that individual growth might be different from group growth. This idea is shown in the organization of his study. The first part of the study deals with average heights and average weights of groups of boys of different school grades. The second part is a study of the individual records of twenty-nine boys whose physical measurements are complete for four or more successive years. Th2 third part is a summary of the points suggested. 7 And it is in the following questionable conclusions of Stewart that we find some of the first empirical evidence to show that cross-sectional and longitudinal analysis do not 65H. P. Bowditch, "The Growth of Children, Studied by Galton's Method of Percentile Grades." Twenty-Second Annual Report of the State Board of Health of Massachusetts, Public Document N0. 31”, 1391, pp. 17“'—79"'.5220 668. F. Stewart, "Physical Growth and School Standing of Boys," Journal of Educational Psychology, op. cit. 67Ibid., p. ulh. 21 yield the same results. It is here that we see that cross- sectional data may yield confusing and contradictory evidence about individual growth and hence from the conclusions of cross—sectional studies we gain no information about how individuals grow. 1. When we consider averages of groups of the same age, the group one year ahead of the normal grade averages both heavier and taller than the group of the normal grade. In some cases the group one year below the normal averages both heavier and taller than the group of the normal grade. 2. When individual curves and correlations are considered without reference to the size of the boy or to his stage of development, it is difficult to see any relation between physical growth and school standing. 3. When individual curves and correlations are considered, together with the size of the body at fourteen years of age and his stage of development, the following are suggested: a. Heavy or tall boys of early development rank better than light boys of early or medium deve10pment. b. Light boys of late deve10pment rank better than light boys of early or medium development. Short boys of late development do not rank high. 0. Boys of medium size or of medium period of development are hard to classify, though a majority of the? appear to be doing school work of medium rank. 8 Since Stewart's study, DeLong69 showed that there was a significant difference in the results of a cross-sectional 68Ibid., p. u26. 69Arthur R. DeLong, "The Relative Usefulness of Longitudinal and Cross-Sectional Data," op. cit. 22 and a longitudinal study of similar children. He then explained that the two basic assumptions made when using cross-sectional data to show growth are incorrect. These two incorrect assumptions are: . . . when group scores are used individual dif- ferences average out, therefore the measure of central tendency is representative of the group. . . . When a statistical interpretation is made cross—sectionally about how growth occurs, the assumption is made fiaat individuals hold their positions in their group. Figure 1. has been designed to show that analyses of cross—sectional studies do not illustrate the true pattern of individualggrowth. Line A represents the height growth pattern of one six year old boy and line B the height growth pattern of another six year old boy. The broken line represents the average of the measurements of the two boys at all times. According to Figure 1. the average height of the group of boys at two years is 33.8 inches and at three years it is 36.9 inches. The ayerage rate of growth between two and three years is 3.1 inches. It is obvious from the individual patterns that the averages do not describe the grOWth pattern of either individual, since neither boy A nor B is 33.8 inches at two years or 36.9 inches at three years and certainly neither of the boys grew 3.1 inches between the ages of two and three. Since DeLong71 found that this was also true when large numbers _ HEIGHT IN INCHES 23 38 -L A 37 “h // 36 er- 3 35 _, B an 4- Average - - _ _ 33 ~- A 32 4e : : w :— + : 20 28 30 34 36 40 AGE IN MONTHS Fig. 1. Variation in Rate of Individual Height Growth7a 72Willard C. Olson and Byron 0. Hughes, "Manual for the Description of Growth in Age Units," op. cit., p. 22. 24 of children were involved, it seems quite rational to conclude that cross-sectional studies reveal little about individual growth. Many studies somewhat following the basic pattern used 73’74'75 Most of the by Stewart followed in the literature. authors made some improvement in objectivity, design, or technique of analysis. 76 devised a method of graphically Bayer and Gray plotting growth of children from one to 19 years. The chart showed the relation of the individual to the average of a group. Burgess77 presented a similar chart using percentile curves. 73Ethel Abernethy, "Relationship Between Mental and Physical Growth," Monggraphs for Society of Research in Child vaelopment, Vol. 1, 1929. 71+H. Gray and T. G. Ayres, Growth in Private School Childrgp (Chicago: University of Chicago Press, 1931). 75H. Gray and A. M. Walker, "Length and Weight," Ameripan Journal of Physical Anthropology, 1921, 4, 231-8. 6 7 L. M. Bayer and H. Gray, "Plotting of a Graphic Record of Growth for Children Aged One to 19 Years," American Journal of Diseases of Children, 1935, 50, l#08-17. 77 M. A. Burgess, "The Construction of Two Height Charts," Journal of American Statistical Association, 1937, 32, 290-310. 25 Wetzel78’79 devised a method of plotting the relationship of height to weight in such a manner that normal growth was straight line. This method has since been discredited.80 More recently Sontag and Reynolds81 have used the standard deviation to develop what they call a standard score. On the composit sheet many aspects of growth can be compared to one another and to the average and the distribution of a group. Olson and Hughes82 have developed growth ages in months for physical growth (dental, carpal, height, weight, grip etc.) similar to the growth ages that some authors have gotten on mental tests. According to this technique the individuals 78Norman C. Wetzel, 2pc Treatmgnt of Growth Failure in Children (Cleveland: N.E.A. Service, Inc., 19E8). 79Norman C. Wetzel, "The Motion of Growth --Theoretical Foundations," Growth I, April, 1937. 80Stanley Marion Garn, "Individual and Group Deviations from 'Channelwise' Grid Progression in Girls," Child Develgpment, Vol, 23, No. 3, September, 1952. 81 L.W. Sontag and E. L. Reynolds, "The Fels Composite Sheet: A Practical Method for Analyzing Growth Progress," Journal of Pediatrics, 19u5, 26, 327-35. 82 Willard C. Olson and Byron 0. Hughes, "Growth of the Child as a Whole,” Child Behavior and Development, ed. by Barker, Kovin, and Wright (New York: McGraW-Hill Book Co, 1993). 26 specific growth age is dependent upon the age of the average of a group of children who measure approximately the same, but differ Widely in cronological age. In spite of these studies, little individual longitudinal data on the entire growth period was collected. In 1932 when analyzing the growth curves of six adolescents Boaz concluded: The general growth curve of man has long been known, but we have little evidence in regard to the growth of individuals who ultimately reach various statures. For this purpose it is necessary to follow the individual growth from childhood to the adult stage. Some material of this kind has been collected but not Snough to give an adequate insight into the phenomena.8 The same dilemma was again presented in 1951 by Shock when discussing individual growth curves, ". . . measurements of individual over the entire growth period are extremely rare.'8u It might be added that individual longitudinal analyses of the measurements are even more rare. Scammon85 give Gueneau de Montbeillard credit for being the pioneer investigator in the individual method,for accumulating individual measurements from birth to maturity. Montbeillard measured the growth in height of his son from 8 3Frank Boaz, "Studies in Growth," A Journal of Human Biology, 1932, h, p. 307. I; 8 Nathan Shock, "Growth Curves," Handbook of EXperi- mental Ps cholo , ed. by S. 8. Stevens (New York: Wiley, 1931), p. 335. 85R. E. Scammon, "The First Scriatim Study of Human. Growth," Ameriegnpgpurnal of Physical Anthropology, X: No. 3. 1927. p. 333. 27 birth until he was nearly eighteen years. These measurements were taken semi-annually or more frequently, and are reported and analyzed in an individual manner by Buffon in "Histoire Naturelle." According to Scammon, Buffon noted two important findings regarding growth. Of these the first is the observation that stature tends to decrease during the day and with prolonged exertion, and that this loss is regained with rest. The secondaés the recognition of a seasonal difference in growth. Figure :1 shows the data of Gueneau de Montbeillard presented in a manner similar to that of Scammon.87 From this graphic presentation Scammon says: It will be noted that the curve shows the typical four phases which most modern students have observed in the postnatal growth in stature of man, and which are characteristic of the growth of so many parts of the body. There is a period of rapid growth during infancy and early childhood; a middle period, extend- ing from three to nearly thirteen years, in which growth is slow but constant; a marked period of pre- puberal acceleration, from about thirteen and one- half to fifteen yearsaaand a period of slow terminal increment thereafter. The straight line in Figure 2: extending from the measurement at three years to the measurement near 13 years 861bid., p. 333. 87 Ibid., p. 333. 88Ibid., p. 331. HEIGHT IN CENTIMETERS 190‘ 28 J. L I .L L ;.14.4 02 u 6 810121l+1618 AGE IN YEARS Fig. 2. Height Growth of a Single Individual Using the Data of Montbeillard Simi ar to the Figure Presented by Scammon. 89 Ibid., p. 333. 29 has been added by the author to show the error in Scammons analysis. If the rate from three to nearly thirteen were constant in terms of increase in inches per unit time the growth pattern from three to thirteen would be a straight line. Since the growth pattern based on semi-annual measure- ments is obviously not straight, the rate, in terms of the definition given must be changing. Hence the idea that height growth is in four phases 90 or two cycles as suggested by Scammon and supported by 91 Shuttleworth and others needs further analyzing on an in- dividual longitudinal bases using frequent measurements on the same individuals from birth to maturity. The cyclic nature of growth among plants and animals has been known for some time, but it is only comparatively recently that the cyclic growth of man has been recognized. The idea that cyclic growth can be described by a mathematical formula is a concept that has received sporadic attention for 93 ' 9 the past century, Verhulst,92 Mitscherlich, Robertson, 9OIbid.. p. 331. 91Frank K. Shuttleworth, "The Physical and Mental Growth of Girls and Boys Age 6 to 19 in Relation to Age at Maximum Growth," Monographs of Society for Research of Child Development, op. cit. ' 928. A. Courtis, Maturation Units and How to Use Them, op. cit., pp. 179-180- 93Ib1d.p PP. 179-180. 9h Ib1d~o' ppo 179-1800 3O Thurstone,95 Pear1,96 Reed,97 Brody,98’99 Spellman,100 and and more recently Courtis101 and Bayleyloénn: some of the persons who have published formula on growth curves. Each of the writers has a different formula, assumes that there are a different number of cycles in the growth process, and believes these cycles occur at somewhat different times. Ibid., p. 179—180. 96R. Pearl and L. J. Reed, "Skew Growth Curves," Proceedings of the National Academy of Science, XI, 1925,16-22. 97Ibid. 98 S. Brody, Growth and Development, III Growth Rates Research Bulletin,(University of Missouri, College of Agriculture: Agriculture EXperimental Station, Bulletin 97), January, 1927. 998. A. Courtis, Maturation Units and How to Use Them, op. cit., pp. 179-180. 102 Nancy Bayley, "Predicting Height of Children," A paper presented at the annual meeting of the Society for ‘Research in Child Deve10pment, 1955. 31 The most pepular individual growth curve now being used to describe the grOWth of human beings is the S. A. 103 Courtis adaptation of the Gompertz function. The Gompertz discovery, according to Courtis, describes the law of grQWth and has wide application in the social and biological sciences. Windsor compared mathematically the popular logistic curve and the Gompertz curve and concluded: The Gompertz curve and the logistic possess similar preperties which make them useful for the empirical representation of growth phenomena. It does not appear that either curve has any substantial advan- tage over the other in range of phenomena which it will fit. Each curve has three arbitrary constants, which correspond essentially to the upper asymptote, the time origin, and the time unit or "rate constant." In each curve, the degree of skewness, as measured by the relation of the ordinate at the point of in- flection to the distance between the asymptote, is fixed. It has been found in practice that the logistic gives good fits on material showing an in- flection about midway between the asymptotes. No such extended experience with the Gompertz curve is yet available, but it seems reasonable to eXpect that it will give good fits on material showing an inflection When about 37 per cent of the total growth has been completed. Generalizations of both curves are possible, but here again there appears to be no reason to eXpect any markfid difference in the additional freedom provided.10 10 38. A. Courtis, Maturation Units and How to Use Them, op. cit. 10h C. P. Winson, "The Gompertz Curve as a Growth Curve," Proceedings of the National Academy of Science, 18: p. 7, 19320 , 32 105 Since this comparison was made, however, Millard, 06 108 109-110 111 DeLong,1 Nally,107 Kowitz, Rusch, and Greenshields have shown the extent to which the Gompertz curve adeQuately describes growth. All of these writers have compared some aspect of growth to growth in height. They have followed a plan outlined by Courtis in writing the equations and in 1050. V. Millard, "The Nature and Character of Pre- adolescent Growth in Reading Achievement," Child Development, Op. cit. 106Thomas P. F. Nally and A. R. DeLong, "An Apprasial of a Method of Predicting GrOWth," Child Develgpment Laboratogy Publication, _2. cit. 107Thomas P. F. Nally, "The Relationship Between Achieved Growth in Height and the Beginning of Growth in Reading," Unpublished Ph. D. thesis, Michigan State College, 1953. 108Gerald T. Kowitz, "An Exploration into the Relation— ship of Physical Growth Pattern and Classroom Behavior in Elementary School Children," Unpublished Ph.D. thesis, Michigan State College, 1954. 0 1 9Reuben R. Rusch, "The Relationship Between Growth in Height and Growth in Weight." Unpublished Master's thesis, Michigan State College, 1954. 110Reuben R. Rusch, "Center of Gravity and the Law of Growth." Unpublished paper as part of requirement for Educa— tion 524. 1110. M. Greenshields, "The Relationship Between Con- sistent IQ Scores, Decreasing IQ Scores, and Reading Scores Compared on Two Developmental Bases." Unpublished Master's thesis, Michigan State University, 1955. 33 determining the number of cycles.112 However, over the latter procedure there seems to be considerable conflict,ll3.114 Equation writers have eXpressed their concern as to just where cycles occur. Since individual longitudinal height data from birth to maturity has not been analyzed in an individual longitudinal way, and since the occurrence of individual cycles of height growth has caused some conflict among modern researchers, the related problem, the individual cyclic pattern of height growth was chosen for this study. 1128. A. Courtis, Maturation Units and How to Use Thgm, op__. -913..- 1131b1d.. pp. 140-141. 114 Cecil V. Millard, Child GrOWth and Development (Boston: D. C. Heath and 00.. 19517. p. 65. CHAPTER III LONGITUDINAL ANALYSES FROM BIRTH TO MATURITY In order to show the individual longitudinal pattern of height growth from birth to maturity, it was necessary to have height measures that covered this period of growth. One of the largest collections of data available in the world is at Michigan State University. However, none of their material covers the complete period from birth to maturity. Letters were sent to several of the leading Child DevelOpment Labora- tories in the United States, asking whether they had this type of information and whether itivas available for this longitudinal analysis. One hundred per cent reaponse was received to the letters, but few places reported having any available data that was this complete. Fels Research Institute, however, replied that they had this information on approximately 300 children and that the information would be made available for analysis. The Fels program from which the data for this study was obtained was begun in 1929. Families from which these children come, live locally or in nearby towns and communities. They enroll the child early in the pregnancy of the mother and all mothers are voluntary participantS. About a dozen new families are admitted to the study annually to replace the 34 35 children who drop out when they reach physical maturity or for some other reason such as the family moving out of that region. The main factor in the selection of the families is the proba- bility of long residence in this area. According to Reynolds: The group as a whole is a fair cross-section of the white population of Southwest Ohio and the children belong to that large and almigt undefinable class known as "normal" children. The Fels program is a long term, integrative multi— disciplinary study of grOWth and development of these children, from fetal life through maturity. Thus the skills and contri- butions of such disciplines as anatomy, anthrOpology, bio— chemistry,g;enetics, pediatrics, nutrition, physical growth, physiology, psychology, psychOphysiology, psychiatry, and sociology are used in conducting the seriatim deve10pmenta1 study. The department of physical growth is one of several divisions of the Institute. It is responsible for the collec- tion of data and for research in the areas of body structure, growth progress and health. Fels children (as those in the study are called) visit the physical growth laboratory at regular intervals, where the procedures include medical and dental examination, health and nutritional history, body measurements and observations, nude photographs, and a compre- hensive series of roentgenograms of various parts of the body. 115Earle L. Reynolds, "The Distribution of Subcutaneous Fat in Childhood and Adolescance," Monographs of the Society for Rpsearch in Child Development, Vol. XV. Serial No. 50, No. 2, 1956, p. 12. 36 At this same visit, these children also take part in the programs of such other departments as psychology, psycho- physiology, biochemistry, etc. The subjects were nude when the height and crown—heel measures were taken. The standing height measures were taken with a wall mounted instrument that uses a sliding arm on a scale calibrated in millimeters. A scale calibrated in milli- meters with a sliding arm fastened to the table was used to take the crown-heel measures. The subject lay horizontally on a table when these measures were taken. A trained physical anthropometrist took these measures of the children. The child was placed in exactly the same position each time he or she was measured thereby reducing the error of measurement due to the technique employed. Theinstruments used for measurement cannot readily be moved and were located in one room. Thus there was a minimum amount of error that can be attributed to the instruments. It is impossible to take standing height measures of a child who can't stand. Therefore, until the child was several years old no attempt was made to measure his standing height. Instead the child was placed horizontally on the table and the crown-heel length was measured. At a later age, when both measures were taken, in most cases, this crown-heel length showed that the children were somewhat longer than they were tall. After the child was about six years old, crown- heel measures were no longer taken. Standing height measures were then taken as long as the child remained in the study. 37 The Fels Children were given a number when entering the study. The first person to enter the study was given number one, the tenth person, number ten, etc. Hence, it is usually true that the smaller the number of the case, the more height measures there were available on that subject (many of these being after maturity) since some subjects were followed until they were 2“ years old. The numbers assigned by Fels to identify the children and allow them to remain anonymous were used to identify the child in this study. However, an F (for female) was added to the number if the case was a girl and an M (for male) if the case was a boy. All cases that could meet the following criteria were selected frdm the Fels group for use in this study. 1. There had to be continuous height measure- ments from birth to maturity taken at semi- annual intervals from within the first three months of life to maturity (as determined by two belOW). Cases were not chosen if more than two years of continuous measurements were missing in the total pattern of height growth from birth to maturity, or a total of two and one-half years of measurements.* 2. As an indication of maturity, the roentgen- ograms were used. For this purpose the epiphyses of the humerus had to be fused.** 0f the 300 Fels Children, the data on 31 boys and 46 girls met the above criteria and hence were used in this study. ”These cases where one to three of the semi-annual meas- ures are missing are identified in this study by a * before the case number. **The author was taught to make this judgment by S. Garns, the head of the Physical GrOWth Department at Fels. 38 Method In order to show the true individual continuous pattern of cyclic height growth from birth to maturity, a mathematical method was used to determine the pattern of growth. This method made applicable by Holmgren and Busch was originally devised to help different people write similar mathematical equations when using the Courtis Technique to describe growth. In essence, the straight line of best fit is determined math- ematically by the individual data and then the plotted measure- ments are compared to the straight line. In applying this procedure to the Fels data the following steps were taken. 1. A criteria was set up for determining height maturity. This was done for two reasons: [A] Garns has shown that growth in standing height continues after skeletal growth is complete and height growth is a composflmeof many measurable growth aspects. [B] By including continuous measurements after the height measurements have stopped increasing. the slope of the straight line decreases or becomes farther away from the increasing height measures. Thus it becomes increasingly difficult when examining the graphs empirically to determine where the cycles of height growth occur. Figure 3. shows how the straight line becomes further from the data during the years when the child is growing if measures be- yong height maturity are used in determining the _ _ StI‘H:J!Lt line H .3 ‘451'..’ “9771- >. annual measures ‘. mufirLty 3 Equation is y = .5;,sw K 4 70.1 B :2 — u — ~ — Slrai“ht line found by usinw semi— g 190 “ annual meusiree beyond maturity .. Equation is y = .4457} X + Tl,OO h A 180 -_ . . . Lets ire UCLJWl 1t sures g 170 ~— 160 n / U) / 33 ’ / Q E B E U 2 H B m (5 H {:3 m Place where measure— ments of standing Height replace measurements taken with subject in Horizontal position .' s so 1 4 50 i 2 5 i l I i I i : I O 20 no 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 3. Case 75F.A_Comp risen of Two Methods of Finding the Straight Line of Best Fit. #0 straight line of best fit. This criteria for height maturity was: the individual six month interval measurements must increase by one or more centimeters per year. When this failed to happen the individual was considered mature for purposes of using the meas— urements for determining the straight line of best fit. In several instances the available measures did not show that the subject had reached height maturity according to this definition of height maturity. In these cases the last continuous height measureivas considered the point of height maturity. These individ~ ual cases are identified by a ° sign before the case number. 2. Measures other than those taken at six month intervals from birth to the above criteria of height maturity were eliminated.for purposes of determining the straight line of best fit. There were an abundance of measures available the first several years of life, but after about the age of six, height measures were only taken semi-annually. By using more measurements per unit for one part of the growth period than for another part of the growth period, the period from which more measurements were used for a given unit of time would have more of an influence in determining the line of best fit. An example of this is shown in Figure 4. >} J3 «4 $4 , m _____"_* Straight line Foind by uzing sem1_ g annual measures to maturit‘ equation > is y 2 .530h# + 70.13 p 1‘40 d].- it” ~ - — — - Straight line found by usi.e all data H to maturity equation is y : .filSQQ X + 56.92 E .r 180 -_ . . . . . Dots are actual measures 170 —- 160 i lib -_ m I. (—7] 1 E4 U40 ..- a Q a D Z 120 -L H E.‘ A m 6 110 -_ .‘-—4. z: 100 _ Place where measure~ ments of standing Height 90 replace measurements taxen with subject in Horizontal position 80 _ 70 - x I ‘30 .4... 50 : 4. 5 i t i : i i r i : O 20 no no 80 100 180 1&0 160 180 200 220 AGE IN MONTHS Figure 4. Case 75?. A Comparison of Two Methods of Finding the Straight Line of Best Fit. 42 Figure 5, again using Case 75F, was constructed to show a comparison of two straight lines of best fit lising two slightly different amounts of data to deter— mine these lines. This was done because a few cases had several semi-annual measurements missing, but not enough to eliminate them from the study according to the criteria of selection, described previously in the selection of Fels children for this study. The straight line of best fit represented by the unbroken line in Figure 5. Was determined by using semi-annual measure- ments from birth to maturity. A period of one and one-half years of measurements, picked at random, were not used from the same data when the other straight line (as represented by the broken line in Figure 5.) of best fit was determined. The negligible affect of small amounts of missing data on the straight line can be seen from examination of this figure. 3. The mathematical eXpression of this straight line of best fit y = m x + b was next determined. In this equation m equals the slope of the line and b is the Starting point when x (time in this instance) equals zero (at birth); y equals the magnitude of the measure- ment. A. m for this equation of height growth was de— pgxy -£X£j termined by the equation m = i nzx2 - (2301 31x7 irid‘ liga2 foxnu‘ cw"lsirnr eeriw :? aynuul measures to maturity T iswatio, is y = .5QUdh K + 70.13 ‘ . p l _ ._ , , m — - ~ ‘ ~ :traixnt line :ouud by using seni~ 2 lEO ._ annual measures to maturity. Cmi‘tlng u 3 o“ {no semiuannual measures or a '3 l 1/2 year period. figuntion is 8 16‘0 ~~ = .2317: x + v.75 u: / , _ , Pots are actual measures :70 -_ l‘O —— ‘ . Q Q ‘ ‘lL’r‘J L —4-—. m ) x 9 L4 :1] lug .0... 2 H E-4 Z N m 130 __ o z f—i 110 __ e r $ 5 g 110 -_ 100 .. Place where measures ments of standing Height 90 q replace measurements taken With subject in Horizontal position 80 -- 7O _ 60 «nu-u“ 1 ill 50 l 1 1 I l I l : g ' I I l I 0 2O 40 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 5. Case 75F. A Comparison of Two Methods of Finding the Straight Line of Best Fit. 4L» In this equation for finding m, n equals the number of height measurements at six month intervals, x equals the time of measurement in months and y equals the height measurement in centimeters. B. b for the general equationcif height growth was determined by the equation b == 2.3.211 " 5m n 2x2 -(.£x)2 Again in this equation as in the equation for finding the slop of the line, n equals the number of height measurements at six month intervals from birth to maturity, x equals the time of the measurement in months and y equals the height measurement in centimeters. C. In order to determine the slepe m and the starting point b of the straight line that would best fit the height measurements from birth to maturity, the Specific functions of the equations for finding m and b had to be determined. These specific functions were: 2x2 The sum of squares of each time measurement. (£102 The sum of the times of the measurements, squared. 2xy The sum of each time, times each measure, squared. fix The sum of the times. i y The sums of the measurements n The number of measures. 45 D. These function were then found and substituted appropriately in the equations for finding the slope and the starting point. The two equations are then solved. This provided the slope and starting point of the general straight line equa- tion or the straight line that best fits the data. a. In order to graphically present the individual straight line of best fit and the data, two times were chosen that were appropriate for the graph and the equation was solved for y, or the measurement at the chosen times. The straight line was then drawn on the graph of the data through the values of y corresponding to the times chosen. This line represents all the points that would be found by solving the equation for all times. 5. The data were then compared by examination, since they were plotted on the same graph, to this straight line of best fit to determine the number of cycles of height grOWth from birth to maturity. All measurements were included on theggraph to determine the cyclic effect. 6. In order to show the graphic data in an objective mathematical manner, the general straight line equation y = m x + b was solved for each time that corresponded to the time when a height measurement was taken on the 46 child. The actual measurement was then compared math- ematically to the straight line measurement. At all times the straight line measurement obtained by solving the equation was subtracted from the actual measurement at that time. The differences between these measures were eXpressed in terms of a plus or a minus number of centimeters. A plus number of centimeters indicated that the actual measurement is greater than (or above on the individual graph) the straight line measurement and a minus number of centimeters indicated that the actual measurement was below the straight line at that point of time. Thus the increase and decrease in centimeters and the change in sign of deviations (the difference between actual measurements and straight line representation) showed the curvilinear nature of individual height growth from birth to maturity and hence the cyclic pattern of height growth in a completely individual, objective, mathematical manner. CHAPTER IV ANALYSIS OF THE DATA The Fels data for the purpose of this study was found to be the most complete available. Height measures were taken at the Fels Research Institute semi-annually (more frequently during the early years) from birth to maturity. Considerable patience and.accurate measuring instruments were used in securing these horizontal and standing height measures. However, more frequent height measurements on these children would have contributed considerably to a study of this type. Analysis of this data on an individual longitudinal bases has revealed much about the individual cyclic pattern of growth. However, some cycles appear to be only a year or less in length. Whether this is due to seasonal difference inggrowth rate or to the diurnal variation has yet to be established on an individual longitudinal bases. Measurements at six month intervals are not frequent enough to give us a true picture of seasonal cyclic growth. Long bone growth has been shown to be more rapid during one season than another and since long bone growth is one of the morphological components of height growth it seems reasonable to hypothicate that during certain seasons height growth may be more rapid than during other seasons. Ln 48 No attempt is made at Fels to check the diurnal variation in height growth. An attempt is made, however, to measure all children in the mornings so that the diurnal variation of the morphological components of height, if such a factor exists, may be influencing the height measure a constant amount. Certainly there is no place in the world where there are as many accurate, continuous, height measures on such a large number of children from birth to maturity as there are at Fels. More frequent measurements on the same children would be needed, however, to provide the material from which a similar analysis of seasonal cyclic growth and diurnal variation could be made. Some of the data concerned with the height measures of the girls and boys are found in Appendices A and B. The cases are listed in Column One according to the number assigned by Fels. Column Two represents the total number of height measures of that boy or girl. Column Three is the age to the nearest tenth of a month at which the first height measure was taken and Column Four is the age to the nearest tenth of month at which the last height measure was recorded. Column Five shows the periods, if longer than six months, during which there was no recording of height growth measures. Column Six is the age of height maturity (according to the previous definition of height maturity). Column Seven is the age in months and tenths of a month at which time con- tinucus standing height measures were recorded for that child. 1+9 A summary of the material presented in Appendices A and B is shoWn in Table I. The group means and the range of scores show the similarity between the groups of boys and girls in the total number of measures, the age of the first and the last measure, and the age when permanent height meas- ures were begun. The age of height maturity,which is the only factor in this table resulting from individual growth, shows that boys as a group reach height maturity at a later chronological age than do this group of girls. However, analysis of Appendix B provides an example of a boy Who reaches height maturity before 173.6 months of age or the mean for the group of girls. Many boys are shown by Appendix B to reach height maturity before the chronological age of 197.9 months or the top age of height maturity of one girl in this group of girls. Thus Appendices A and B and Table I illustrate that although boys, as a group, reach height maturity at a later chronological age than girls taken as a group, there are many individual boys Who reach height maturity at an earlier chronological age than do some girls. The plotted height measurements of each child and the straight line that best fits the data are shown in Figures 6. through 82. The vertical line drawn at approximately 72 months of age represents the time at which the measurements were changed from horizontal position measures to standing height measures. Therefore, all dots to the left of that line, 50 unless otherwise indicated, represent the length of the subject and all measures to the right of the line represent the standing height of the boy or the girl. TABLE I SUMMARY OF THE DATA EEEE—Charac- Girls N = 3677 _fl Boys N = 31 teristics Mean Range, Mean Range Total No. of Measures 53 -34-60 56.5 #8-60 Age of Last lst Meas. .6 0-2.5 .5 0-3.0 Age of Last Measure 218.7 178.7 — 288.6 229.0 192.0-288.l Age of Ht. Maturity 173.6 150.3 - 197.9 199.9 168.2—216 Age Perman- ent St. Ht. Measures Begin 1+0.5 26.0 - 78.0 38.6 28.0- 69.0 it Obviously the standing height of a child could not be measured until the child has learned to stand. The Fels measures of length were discontinued when the subject was somewhere between the age of six and ten years. Hence, a time had to be selected when, for ourposes of this investigation, the horizontal position measures would no longer be used and standing height measures would take their place. For almost all subjects there was recorded, continuous standing height measures from the age of six on to maturity. Therefore, six ERS IMET E4 EN 1,) IN HEIGHT __ strum: 111*» f0. n my mlv r semi~ f: :13.“le ‘neaSmes :3 wa’ul t, '2" Equation is — so15“ \ + no.7g 3 4,; c: 3 s are ac"al n :sures E <- M A1 a «1 OJ <0— :1: qt— _ . uk- a- Place where measure- ments of standing Height - replace measurements taken with subject in Horizontal position ‘1!- —§ 2 __1 : : : 5 l + : : : . . O 20 40 6O 80 100 120 140 160 180 200 220 Figure 6. Case 25F. AGE IN MONTHS Height Measures and the Straight Line of Best Fit. dTEHS HEIGHT IN CENTIM' 115 105 straimrt line is found by using semi— g erudisl PPinlPfiS to wmfix;rit5' 3 Equation 18 y = .6456? X + 75.90 p m >1 Zwvts '«re xactnial, méwisurmas +3 .. I: m H 5‘3 Place where measure- ments of standing Height replace meaSurements taken with subject in Horizontal position 75 65 55 n 1 1 1 I J 3 5 0 2ro do 6'0 8'0 1'00 1'20 MO 160 AGE IN MONTHS Figure 7. Case 28F. Height Measures and the Straight Line of Best Fit, Straight 1i1e is found by using semi» nnnun? meisurvs to maturity Equation is y = .5w30w X + 58.2s Maturity +3 .31 Dots are actual measwres m RS ENTIMhTE H U HEIGHT IN ii ‘7 _;1 115 105 95 85 75 65 45 Place where measure— ments of standing Height replace measurements taken with subject in Horizontal position w‘i (1) :1; -L. O\ AGE IN MONTHS Height MeaSures and the Straight Line of Best Fit. : : .L 80 100 120 220 7): 9 ___7-___1____ StréiL-rilt line is Found .,y 11513;! 3577-11“ '1; wniuil measures ti maturitv 5 {aviation 18 y : 53(1)} X 4' O7 ‘0 .35 ii. 131') __ :‘0’8 211“” [wins]. measures : @ ‘7R __ L 1'5 H— l ‘ ‘ 155 as 1M5 ._ n t 5’? 135 __ a 1’" r‘ {‘5’ 145 —} 4.2 r“! :4 ___fi._~_ Strulgnt line found by using semi— 2 annual measures to naturity 2 Elquatlfln is y = .5755?) X + 70.29 >7 {-3 , . . . Dots are actual meaSures a; 1&5 4" .r—q g 175 ~- 165 ~ 155 ‘- m {1: fr? 1&5 ....— g '7‘ E: 135 ‘" m o E 125 ar— e a g llS “ m m 105 -— I 95 » Place where measure- ments of standing Height 85 - replace measurements taken with subject in Horizontal position 75 - 65 —- - 55 -= 1+5 : : a : : ! 5 5 5 J. O 20 MO 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 24. Case l26F. Height Measures and the Straight Line of Best Fit. z p E _m_*___ Straight line found by usina‘ semi— 23 annual meRSures to maturity 2 Equation is y = .59930 X + 62.74 E m 185 %_ . . . . . Dots are actual measures 3 175 - 165 -— 155 -~ Q 145 “ j E E 135 ' H E :3 125 ._ (3 H 115 ~— Ea E {3 105 a- m 95 -— Place where measure- ments of standing Height 85 - replace measurements taken With subject in Horizontal position 75 - 65 - 55 -- a. l I l I L 45 5 5 l 2 5 1 ~ I l I i l ; o 20 no 60 80 100 v 120 140 160 180 200 220 § AGE IN MONTHS Figure 25. Case 127F. Height Measures and the Straight Line of Best Fit. u v 4 iaht Maturitf Straiant line found 3y usin: semi— annual meaSurrs to maturity {Quation is y = .N7317 X + 68.75 m, . . . . . ofis are actual measures lop —_ m m l7E ~~ 165 a— 155 -— a u 1“5 ‘— m K) 2 125 — H E“ g 115 —— H [1) LI: 105 +- 95 -- Place where measure— ments of standing Height 55 __ replace measurements taken with subject in Horizontal position 75 -— ' 65 __ I. 55 ~_; 45 ‘ ; : . : e l : .' : ; : 1 O 20 b0 60 80 100 120 140 160 180 200 220 AGE IN MONTHS J p. rurn 26. Case 137F. Height Measures and the Straight Line of Best Fit. ETERS 7' ,l “1% GEN IN HEIGHT 115 105 b5 75 65 55 ”5 h 4.) H g 5 fl ____ Straight line found by using semi— * annual measures to maturity g Equation is y = .99881 X + 77.83 3 Q, 4 Dots are actual measures 5 T- -4r- Place where measure- ments of standing Height 4 replace measurements taken With subject in HoriZontal position " 3 ' ‘ i i i ! ; 1! o 20 no 6'0 80 100 120 1Lm 160 180 200 220 AGE IN MONTHS Figure 27. Case lNOF. Height Measures and the Straight Line of Best Fit. ' ENTIIJL 11111515 ‘ L/ T I“; HEIlHT 95 85 75 65 55 1+5 Straight line found by using semi- annual measures to ma*urity equation is y = .37085 X + 08.93 Dots are actual meaSures Maturitv AGE IN MONTHS Figure 28. Case leF. Height Measures and the Straight Line of Best Kit. + _ Place where measure— ments of standing Height - replace measurements taken with subject in Horizontal position I l l l I , I l I L I I I I l I l I_ I y I I I O 20 no 60 80 100 l20 140 160 180 200 220 Straight lin~ found uy using semi— annual measures to mutwrity {quation is y = .5002? X + 09.95 +3 .r—l S4 2" p CU a 4,; ,C? b: 4—4 0) LE / Cots are actual measures ins ~~ 175 ~— 165 d~ “II 155 i_ lufi -— m m 4.1 5; 1.35 —— E E; g 125 —— D H 115 -I e m (‘5 ’3 105 ~— 95 ~— Place where measure— ments of standing Height 85 « replace measurements taken with Subject in Horizontal position 75 65 q- 55 —3 1+5 I I I I I I I I l O 20 NO 60 80 100 120 140 160 180 AGE IN MONTHS y\) \0 Figure . Case luuF. Height Measures and the Straight Line of Best Fit. m #3 ’ -l -______ itraim t ane inane 0y using semi— 2 u rwlnl IhEIIsurh>s to Inai‘;rf t3’ : Euwition is y 2 ,‘3wol X + 72.62 2 4: 1’, Dots are actual measures 9 «IL “ "'— -r-1 (D m l”S ‘— c O ‘ 165 .— 155 _ 1M5 4— ' m I: ,J o E- P 3 ljj “ .//- :4 / 1.25 -- . / 3 ‘ /// z . h/ “ 115 —~ . " /‘/ PI o // i ‘ .‘ /// H // 7d 1(DS “ r// L // v ‘//r/ Place where measure— ments of standing Height replace measurements taken with subject in Horizontal position 65 -— -‘ 55 ——' #5 I f i l i i i i i i O 20 40 60 80 100 120 140 160 180 200 AGE IN MONTHS Figure 30. Case lb5?*. Height Measures and the Straight Line of Best Fit. a 4.: ”£1 ____-_m, Straisnt line found by using semi- 5 annual measures to maturity g Aquatiin is y = .5052? X + 68.82 H 4,3 Q 185 __ . Dots are actual meeSures .3 :33 17f) -I> .. iéj —~ . 153 -~ 1&5 » m E q; 135 ~— 2 T 125 «- D ‘4 115 ~- EA :1: (D e; 105 __ E 95 —_ Place where measure- ments of standing Height 85 ~ replace measurements taken with subject in Horizontal position 75 - 65 __ 3 55 '4'; 1+5 : I i : i I I l l I 4 o 20 no 60 80 100 320 140 160 180 2’00 220 AGE IN MONTHS Figure 31. Case lhéF“. Height Measures and the Straight Line of Best Fit. 5* ___r"w_ Strairhi lire found ry using semi— 2 annual measures to maturity 3 Rouation is y = .53160 X + 74.19 g 21 1ft Dots are actual measures p 4.",‘1 -" A: u H (D -i m i/S r / // ' ‘ 165 "‘ / b . 1" //' DJ /./ ~ :3 *5 ‘ ‘ [—4 {I} / E: 135 -- o P; E O 125 __ 2 H S: 115 -— a W :3 105 s 95 ._ . Place where measure- ments of standing Height 85 - replace measurements taken with subject in Horizontal position 75 - 65 -- . 55 «c 45 I I I I I % I I I I I O 20 no 60 80 100 120 luO 160 180 200 220 AGE IN MONTHS Figure 32. Case leF. Height Measures and the Straight Line of Best Fit. % 4.7 - \ H __‘_~_‘” Straight line lound Ly using semi- ; annual measures to maturity, F Equation is y = .54355 X + T9.?3 2 lots are actual measures E i u 16:) ~'- H (D m 1/5 ~- 165 -b . i u c . ' I o 155 ‘- lb5 __ m CS 9 l -_ g 55 E 25 12 q- I I 5 U f: 115 __ a 3% H 105 —_ [11 m 95 ._ ‘ .' Place where measure- ments of standing Height 85 ~ replace measurements taken with subject in HoriZontal position 75 « 65 -I- 55 'j' I u5 I I I I I I. I I I I .I O 20 40 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 33. Case lSOF. Height Measures and the Straight Line of Best Fit. HEIGHT IN CENTIMhTERS It) 5 115 105 95 85 75 65 55 45 $traight Edna Cl An 1018 are Line Found by using semi~ annual measures to fiqurity is y = .575e7x + 85.9;; actual reasurts ht bfat‘ul’j t 2,7 Figure 34. Case 151F. AGE IN MONTHS Height Measures and the Straight Line of Best Fit. «4 CD m +- " Place where measure— ments of standing Height - replace measurements taken with subject in Horizontal position I 9 I I I II I I I AI 0 20 40 60 80 100 120 160 180 200 220 HEIGHT IN CENTIMETEHS 185 1 :25, 125 115 105 95 85 75 65 55 45 ___ it: 1*ht Lir» *wu5‘ y us‘ ~ sewi- axnuul mewsur s to maturity ; mquation is y : .iglv; X + 71.25 ‘q r h . Dofe an: actual firm‘unefi g , a +4 '1) m Place where measure— ments of standing Height replace measurements taken with Subject in Horizontal position Irity n l 1 l l L n l I l I l I l I l 20 40 60 80 100 120 140 160 AGE IN MONTHS Figure 35. Case 165F. Height Measures and the Straight Line of Best Fit. ;>, p _~ifi-,.” Straight line found by using semi- 2 annual measures to maturity 3 Equation is y =.53333 X + 71.52 i 185 # Dots are actuml measures g "-4 a? 175 “ 165 - 155 ~— 2 145 - 9 7;} 135 -- L‘“ 3 6’ 1135 "- 2 0—1 B 115 “ E r: . § 105 “ 95 -~ ‘ Place where measure- ments of standing Height 85 —. replace measurement taken with subject in Horizontal position 75 - 65 -_ ' 55 -~. 1+5 1 1 I l l _ [L i : I : I l I l I O 20 40 60 80 100 120 140 160 180 200 AGE IN MONTHS Figure 36. Case 170F. Height Measures and the Straight Line of Best Fit. m p w L ___,,m“, Slraifht line found Ly using semi- 3 annual measures to maturity 5 Equation is y = .00525 X + 71.25 p c 185 1 . . . . . Dots are actual measures ,fi 0.) m 175 « Q ‘ \ O . ' 165 I ‘ . 155 * m o: 10,5 ‘- a ' ,E‘; 5? 1% —— m D 1. 1:25 - g B . E 115 ““ L m m 105 _- 95 "“‘ . v\ p- -’ Place where measure ments of standing Height 85 renlnce measurements I taken with subject in Horizontal position 75 65 fl .‘ 55 --. 45 I i i I t i i I I I I O 20 40 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 37. Case l7lF“. Height Measures and the fltraight Line of Best Fit. 82 I HEIGHT IN CENTIMETERS 125 115 105 95 85 75 65 55 45 Straight line anrnual megmvire Equation y = found oy using 8 to maturity .50857 X + 73.39 semi— Do‘ (. are actual measures Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity 20 Figure 38. Case 176F. 60 80 100 120 AGE IN MONTHS ] I l I 140 160 180 éoo Height Measures and the Straight Line of Best Fit. RS CEXTIMbTm HEIGHT IN 125 115 105 95 85 75 65 55 45 Streishf linw found uy using semi- annual measures to maturity equation is y = .5557% K + “0.7? (aturity .Po's are notwel measures E 2L C1) :1": Place where measure— ments of standing Height replace meavurement taken with Subject in Horizontal position I n . 1 1 J I l n 1 J l I I l | F I F] I 29 no 60 so 100 120 1&0 150 180 200 220 AGE IN MONTHS Figure 39. Case 179F. Height Measures and the Straight Line of Best Fit. Straigrt lin: TCund by using Semim annual measures to maturit" LV EQuqtion is y = .57;17 X + 58.15 'ofs are BCtUfll men ures Height Maturity NTIMETERS CE IN HLIGHT 135 125 115 105 95 85 75 65 55 Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position fl ”*Two measures at the same date 1" CD4- 0 N— O O N N O o 20 no 60 80 160 120 140 160 AGE IN MONTHS Figure 40. Case 182 F. Height Measures and the Straight Line of Best Fit. turity _ Straight line found by using semi- annual mesSures to mwiurity w iiquatjmi is y = .5337/ X+ “(3.99 2? H 155 __ Bots are actual measures -§ r1 Q) m 17,) ~— 165 "" . o o ' . A 155 w m 14 1 (I: 5 m E4 11] >: 135 -- H a 2 m , r) 125 "‘" I L ‘ // O . //// ,E‘ 11:) “' v /// II: // C5 . /,. I“! ‘ / La , ,/ a: 10f, .. //,/ // o ‘ / 95 ... ' /3 +J w ‘4 LI :5 +3 C3 :5: p 1: EL -r-( Q) I: Figure #3. Case 191F. Height Measures and the Straight Line of Best Fit. I I l . 1 60 80 100 120 AGE IN MONTHS 140 160 180 'mvss £1: CENTIM -u IN 125 115 85 75 65 55 45 we H m 1 ,7 ,. A. ”11:; g (1)1“ ,1 It” TE 1)? 1’ .1“; 1 ”7‘1 1 1x1 .7) fly usin; semi— s to maturity — '3290 X + 73.1; Do 8 are actual measures Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity \ Figure at, Case 193F. Height Measures and the Straight Line of Best Fit. l I 80 106 120 AGE IN MONTHS O-.. HEIGHT IN CENTIMETEHS 95 85 75 65 55 45 is . , L __~fi__‘_"‘ ntzrala‘lt 1.:ne I UUIL‘ :y XISIILY scrni~ 5 n nual measure: To_mwturity q triation is y : .oéiefi X + 71.20 2 p n Lots are actual mtesures a H 5 O ‘ ‘ Place where measure~ ments or standing Height replace measurement taken with subject in Horizontal position I L 1 1 I L 1 l l l I f T T l l V I 20 b0 60 80 100 120 140 160 180 AGE IN MONTHS Figure 45; Case EObF. Height Measures and the Straight Line of Best Fit. ‘IMETERS CENZ HEIGHT IN 125 115 95 85 75 65 55 45 y 4.) 2‘ 3 Straight line found by usini semi— Q annual measures to maturity 2 Lquatiom is y = ,6A195 x + 7i,76 E m Dots are actual meaSures '3 3 Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position I 1 l 1 1 I 4' I 5 : g 5 20 40 60 80 100 120 1&0 160 180 200 220 AGE IN MONTHS Figure #6. Case 205?. Height Measures and the fitrgigfit Line of Best Fit. |\ HEIGHT IN CENTIMETHHS H (‘1 \ n 175 165 125 115 105 95 85 75 65 55 1+5 strairht lino found by using semi- annual measures to maturity Equation is y = .55an X + no.8 (n Lots are actual mes ures Height Maturity Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position l l l l l l l I I y - I I 26 no 60 80 100 '120 7 7 Mo 160 180 200 AGE IN MONTHS. - Figure #7. Case 211F. Height Measures and thezfitr‘ A glut Line of Best Fit. 220 E85 HEIGHT IN CENTIMET P] Q?) Ln 105 95 85 75 65 55 45 C h. H n .J ‘ots are actual measures traiiht line found by using semi— nnuel measures to maturity quetion is y = .531b9 X + 63.71 Hsturity Height Place where measure~ ments of standing Height replace measurement taken with subject in Horizontal position H £3 E a, :3 H E: 5:15 “cam 001: : : ! ‘ :3 : i 5 i ’i 20 #0 60 80 100 160 180 200 220 AGE IN MONTH;' Figure 48. Case ZluF. Height Measures and the;fi*"5 ”Line of Best Fit. L HEIGHT IN CENTIMHTEHS 185 115 105 95 85 75 65 55 45 Straight li annual mvasu hquation is ...“...— ....-- .L “D S Dots are actual tound by using semi— to maturity .57h55 X + 66.73 {7.62181} {‘0 8 Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position I ,, ‘7’ I l Height Maturity Figure #9. Case 217FO. l ,. _ . . I I so 100 120 iuo 160 AGE IN Memes; Height Measures and thegofitr “Eight Line of Best Fit. .4»- IN CENTIMHTERS HEIGHT 125 115 55 45 Straight annual measures to maturity Equation is y = .5322} X + 79.78 “OTB are lire found by using semi— actuul measures Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position Maturity {.3 .C "Oi; *4 G.) if. l I 20 40 l , 7 J 80 106 126 AGE IN MCNTfis q i I ‘ l IUO 160 180 200 Case 220r. Height Measures and thewstnsigfie Line of Best Fit. HEIGHT IN CENTIMETEHS Straight line found by using semi- annual measures to maturity Equation is y = .58?l2 X + 68.52 Dots are actual measures ments of standing taken with subject AGE IN NO Figure 51. Case 221F. Height Measures and Place where measui'“ replace measuremenf Hori zontal posit io; ’ >2 .3 f 3 p c! 22': p £1 bi H (D (E 200 220 Straight line foun' by using semi— annual measures to maturity my Equation is y = .5;59O X + /;.75 Height Maturity actual measures Dots are '__ o O a 175 h 165 A— 155 “ [D (I: E} iu5 -» :3 z E A 2: 155 " (2.] O 123 .— HEIGHT IN F H \J'1 95 ~- Place where measure- ments of standing Height 85 « replace measurement taken With Subject in Horizontal position 65 ~- : : : : : , +7 ~ 5 .L ! : 4, o 20 no 60 80 100 1'20 140 160 180 200 220 AGE IN MONTHS - I Figure 52. Case lOM*. Height Measures and the $tra; it Line of Best Fit. I . 7‘.__ _,..,, -7, Straisht line found by using semi~ annual measures to maturity Equation is y = .55224 X + 75.60 Cots are actual measures 175 -- ' 165 <* 155 ~ 116 .. 135 0 125 ‘ 115 “ 105 “ 95 ‘ Place where measure— ments of standing Height replace measurement 85 ' taken with subject in Horizontal position 75 4 65 -_ f 55 ~-' #5 : f a : e i : % : O 20 40 6O 80 100 120 140 160 180 AGE IN MONTHS Figure 53. Case 49M. Height Measures and the Straight Line of Best Fit. HEIGHT IN CENTIMETERS 105 95 85 75 65 55 45 Straisht line found Dy using semi~ annual measures to maturity Equition is y = .5oln0 X + 71.?? th Maturity pots are actual measures Hei Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position 1 l 1 ‘ I" . : l . 20 no 60 80 100 126 146 160 180 200 AGE IN MONTHS) Figure 54. Case 54M*. Height Measures and the Stra éft Line of Best Fit. ‘Q. i 220 Straight line found by using semi— annual measures to maturity equation is y = .55139 X + 71.90 Height Maturity A 185 “ . . . Dots are actual measures HEIGHT IN CENTIMETERS Place where measu ments of standing replace measureme; taken with subjec Horizontal positii l I l i { I I I O 20 40 60 80 100 lUO 160 180 200 220 AGE IN Figure 55. Case 55M0. Height Measures anfi'tf< HEIGHT IN CENTIMETEHS 175 165 155 1&5 125 115 105 95 85 75 65 55 45 _..— Straight line round by using semi~ annual measures to maturity Equation is y = .56120 X + 76.40 . . . . . Dots are actual measures .- Place where measure— ' ments of standing Height replace measurement taken with subject in Horizontal position l 1 1 , . l —>- Height Maturity ; , . I _7 . 20 Q0 60 80 100 120 AGE IN MONTHS Figure 56. Case 71w.O Height Measures and the; Straight Line of Best Fit. .’ '6 K I 140 V 160 180 HEIGHT IN CENTIMETERS 195 175 145 135 125 115 105 95 85 75 65 55 45 Straight line found by uSinr Hemi~ annual measures to maturity fQuation is y = .5072? X + 7~.05 . . . . . Dots are actual measures Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position >. +3 .74 $4 3 +3 m E p Q m H m :11 AGE IN MONTHfi Figure 57. Case 71m. Height Measures and the straights Line of Best Fit. \ ..L- ' ‘ 4H n 4 1 I l , A4 I 1 11 I l I l I [ r I l l I a O 20 MO 60 80 100 120 140 160 180 200 220 102 Q: I :3 E 1 Al] ENTIM~ {1 \J HEIGHT IN 185 105 95 85 75 65 55 45 Straight line found by usinz semi— annual measures to maturity Equation is y = .5099? K + 69.59 Dots are actual measures Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity \ 20 to 60 Figure 58. Case 77M. so 100 I 120 140 léo AGE IN MONTHS Height Measures and the Straight Line of Best.Fit. NTIMETERS was oh i HEIGHT ID 185 125 115 105 95 85 55 “5 straight line “0 annual measures :quation is y = . . . . Dots are actual und Dy using semi— to maturity .317011 E; + 70,30 measures Place where meaSure— replace measurement taken with subject in Horizontal position ments of standing Height i l Maturity x Height Figure 59. Case 78M. '80 100 AGE IN MONTHS I 140 160 180 200 Height Measures and the Straight Line of Best Fit. TEES HEIGHT IN CENTIME 165 155 M5 135 125 105 95 75 65 55 U5 Straifint line annual measures Equation is y Hots are I a o 0 o fruind :Jy ilsins: semi- to maturity = .53959 X + 77.64 actual measures Place where measure— ments of standing Height replace measurement taken with Subject in Horizontal position ; : : i e ! }~ : ! 0 20 b0 60 80 100 120 140 160 AGE IN MONTHS Figure 60. Case 81M. Height Measures and the Straight Line of Best Fit. m +3 ...-.1 p :5 p ___ __ Straight Line found by 1131“»: semi- £5 annual measures to maturity p Equation is y = .537b7 X + 70.07 if; fl 185 «e . . . . . Dots are actual measures g 175 -- 1.455 ._ 155 " m 145 0 £11 a e 5:) ’ ~— Z 135 H (L. 2 m 125 *- L) 2 H B 115 E g 105 _- m 95 -- ' Place where measure- ments of standing Height 85 — replace measurement taken with subject in Horizontal position 75 — 65 -- ..' 55 7' 45 : : : ¥ : :- ' ' 5 1 . 1 o 20 no 60 80 100 120 1&0 160 180 éoo 226 AGE IN MONTHS Figure 61. Case 84M“. Height Measures and the Straight Line of Best Fit. .r“. S HEIGHT IN CENTIMETER Straight . . . . . lots line found by using semi~ annual measures to maturity Ecuation is ' = .55155 K + 73.35 , 3 actual measures Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity 65 if 55 " u5 : i i i i 5 f i i i 4, O 20 40 60 80 100 120 140 160 180 200 220 Figure 62. Case 92M. AGE IN MONTHS Height Measures and the Straight Line of Best Fit. HEIGHT IN CENTIMETERS 105 95 85 75 65 55 45 n :3 4.3 S ___i_._. Straight lino frunn by using semis 7 annual measures to fiaturity E Equatien is y T .569 s X + 71.51 .3 CD A . . . . . Dots are actual measures ”Zr .1 " Place where measure— ments of standing Height — replace measurement taken with Subject in Horizontal position : : : : : s l 3 % : 1 20 40 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 63. Case 98M”. Height Measures and the Straight Line of Best Fit. TERS m .1. HEIGHT IN CENTIM 185 125 115 105 95 85 75 65 55 45 Straight line annual measures Hquation is i found by us n: semi— to maturity .51351 X + 69.07 . ~ots are actual measures Place Where measure— ments of standing Height replace measurement taken with subject in HoriZontal position «5) 4.3 H 54 :5 3,) CU .q‘ .e.‘ p E N H @ CE i : ; 1 iii % ! i ! : ee+ o 20 No 60 80 100 120 140 160 180 200 220 Figure AGE IN MONTHS 64. Case 102M*0. Height Measures and the Straight Line of Best Fit. turity _ Strairht line found by using semi— annual measures to maturity m Equation is y = .NQMQO K + 69.90 E 8 Bots are actual measures g] 185 w H <1) m 175 4—. \ / 165 "" . . I 155 " ./’ m /// . 5 1a; ' E E 135 e 2 g 125 2 H a g 115 I H , s 105 1 l 1 Place where measure- ments of standing Height replace measurement~ taken with Subject in Horizontal position 55 ~¥ N5 5 4 5 : l 3 : i i l 1 O 20 4O 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 65. Case 112M. Height Measures and the Straight Line of Best Fit. Straight line found by using semi~ annual meaSures to maturity Equation is y .46550 X + 72.02 Height Maturity V— 16g " . Dots are actual measures 175 — 165 + 155a— m 145a- m 1,3 E E 135‘— H E4 0 12-) '— 2 H , B 115*— m w E m 105-- 95 -~ Place where measure- , . , ments of standing Heigh 85 v// replace measurement taken with subject in 75 __I/ Horizontal position 65 -- 3 55 ':' “5 : . 1 : : :i— i : : ' 20 L0 60 80 100 120 140 160 180 200 AGE IN MONTHS Figure 66. Case llMMO. Height Measures and the Straight Line of Best Fit. HEIGHT IN CENTIMETERS l?5 165 155 115 105 95 85 75 65 55 “5 Straight l‘ne found by usin¢ semi— annual measures to maturity Equation is y = .53052 X + 77.15 Dots are actual measures Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity l 1 l l I v I I 20 MO 60 80 100 AGE IN MONTHS Figure 67. Case 135MO. Height Measures and the Straight Line of Best Fit. CENTIMETARS HEIGHT IN 105 ‘ 85 “ 75 ‘ 65 _ 55 - Straight line found by using semi- annual measures to maturity :quation is y : ,59050 X + 7u.79 Dots are actual measures Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position Height Maturity 45 V, l I 720 40 50 80 100 120 140 160 180 AGE IN MONTHS Figure 68. Case 138M. Height MeaSures and the straight Line of Best Fit. TEES L] ‘4 U v ha I [:3 IN C HEIGHT 185 f a \) "J‘, 105 95 85 75 65 55 45 Straight annual measure Equation . Dots are 111"“? is y fOthi by {iSlYLT semis s to maturity : .57119 X + 71.45 actual measures Place where measure- ments of standing Height replace measurement taken with subject in Horizontal position l I l l Height Maturity ‘F Figure 69. 80 100 120 AGE IN MONTHS Case 1M1M*. Height Measures and the Stfigight Line of Best Fit. _ Straight line Towns oy using semi» annual measures to “itmrity , ‘ 1,77 . r /r~ :quution 18 y : .149);3 .( + 77.0/ . . , . Tots are actual measwres 185 -— 175 ‘— 165 «— 155 ~- m 1&5 —— m {L} E3 135 ~— 2 H Ea 5‘ 125 —- ‘0 2 H 54 11:) .1.— m C? H Eé 105 95 —— Place where measure— ments of standing Height 85 _ replace measurement taken with subject in Horizontal position 75 ~- 65 _- o 55 -~ ? “5 ’ i 5 3 1 s 3 3 O 20 no 60 80 100 120 140 160 AGE IN MONTHS Figure 70. Case 153M0. Height Measures and the Straight Line of Best Fit. HEIGHT IN CENTIMETERS 185 125 115 105 95 85 55 45 >3 4,: H 94 5 4.3 ’33 *3 H .p _-__-,_- Strsizht line founu uy usinu semi— annual measures to maturity g Equation is y = .53450 X + 70.3/ 3‘ G) ‘_ . flats are actual measures 53L//// .1— \ I1- 4— N... Place where measure— ments of standing Height - replace measurement I taken with subject in Horizontal oosition I I I I I I I I I l I I I I ' I I I l l ‘r l *1- O 20 40 60 80 100 120 1&0 160 180 200 220 AGE IN MONTHS Figure 71. Case 154M. Height MeaSureS and the Straight Line of Best Fit. 116 r .l \1 kn F" 'J\ U1 145 135 125 115 105 95 85 75 65 55 45 Straicht line founfl by using semi- annual measures to maturity iquation is y = .53398 X + 73.69 Dots are actual measures Place where measure~ ments of standing Height replace measurement taken with subject in Horizontal position I I .L I 4. : I I ' 1 1 20 no 60 80 100 120 ‘ 140 160 180 2'00 255 AGE IN MONTHS Figuie 72. Case 156M. Height Measures and the Straight Line of Best Fit. HT HE 135 125 105 95 55 45 4 U) ‘Paijht annual TYII?r'IsIIPe S J : vquation is y y\ mots F1 1“? (iCC‘Hll line found LV using semi~ to mulurity .50106 X + 70.92 measures Place Where measure- replsce measurement taken with subject in Horizontal position I I AL ments of standing Height V t Maturity Heish Figure 73. Case 157M0, I l 80 100 120 AGE IN MONTHS Height Measures and the Straight Line of Best Fit. 3 V >3 4.) :I 5 , _ i itrsi:fli liIu‘ FO'MnA my tiSlns‘ semi— # erg gal measures to maturity p .. . , in M In I, m :Jquatim‘; is y : ._‘)-'w:j/’~J A + 174.42 H G) .1 m 155 -— . . . . . Dots are actual measures I I I . / // . l 175 —— . O 155 — , 155 - 2 145 -— m [—1 m E I __ I-—I 1*) s z s t 125 __ / 2 H E 115 ~— (‘1 H 3'1 .I.‘ 105 -_ 95 —— Place where measure- ments of standing Height 85 — replace measurement taken with subject in Horizontal position 75 - ‘I 65 —~ .' C 55 ‘2 us I I I I I I I I I I I O 20 MO 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 7a. Case 160MO. Height Measures and the Straight Line of Best Fit. Straiaht line found my using semi— annual measures to maturity Equation is y = .situs X + 73.02 Height Maturity Dots are actual measures 185 +— 175 h b 155 r 155-* 1&5 —- Q g] 135 .— Q E 125 *- 5 C) E 115 4 B 5% fi 105 -- E 95 —' . Place Where measure- ments of standing’fleight 85 — replace measurements taken with subject in Horizontal position 75 s 65 __ ‘3 55 -.j 55 I I I I I I I I I I I O 20 40 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 75. Case 167M0. Height Measures and the Straight Line of Best Fit. 1‘ .I ‘0- ‘x ' .\ IMETERS \J'm TGHT IN CEI \—u '4. .4 H F“ RD ‘J\ 155 iu5 125 115 105 55 us a +3 ...-I F4 5 —. . . I I . p _<-“_ straisht line round my using semi- g annual measures to maturity A Eouatioh is y = .H9505 X + 77.59 fi 3) . Pets are actual measures g -v- II} _.L— Place where measure— ments of standing Height — replace measurement taken With subject in Horizontal position : g I I I : {I | 1| I J o 20 no 60 86 160 120 140 iéo 180 £00 2éo AGE IN MONTHS Figure 76. Case i7uMO. Height Measures and the Straight Line of Best Fit. I (:3 ;T “NTIM .1 4—! ‘f‘{ is ’5, 7 , . a , . . I: A ». hi "IQ 3tfei£hfi Linn :ouno o3 aeint seniu : ~—__A A- . .x : 7 (I nnnuwl mexspres to ma.mrity fl. ‘ ,I f p [Histion is y : .54904 K + /u.7o :3 A, w H . . . o’5 are A“* n1 measI“ s m in: T 7L2); -I— I.V b ‘ . ' l7 —— a .’ I 1' ’i 1):) .... 5 1:5 .... C 1h) __ r 13) HEIGHT IN 115 " 105 ~- 9 -... 5 ' Place where measure— ments of standing Height 85 _ replace measurement taken with subject in Horizontal position 75 ~ 55 -— 5 55 -w #5 I I I I I I I I I I I 200 l o 20 no 60 80 100 120 140 160 180 220 AGE IN MONTHS Figure 77. Case 177M. Height Measures and the Straight Line of Best Fit. 105 95 85 55 45 straight lire found my using semi- aniuel me sures to maturity squation is y = .5U719 i + 73.60 Heiqht Maturit 1 50’s are actuui meenu‘ Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position J I I l I L I 1 l v I T l l 0 20 no 60 80 1350 120 I 140 3.60 AGE IN MONTHS Figure 78. Case lBOMO. Height Measures and the Straight Line of Best Fit. CENTIMETERS IN HEIGHT *J {\IAI 45 I'Iz'xnunl measures ~3Quation is y : :re nctunl If} nglSLlIVC? S fitrnizht line founu by using semi— Place where measure- ments of standing Height replace measurement taken with subject in Horizontal oosition Height Maturity ‘ I I I I I I I I I 4% 20 40 6O 80 100 120 140 160 180 200 220 Figure 79. Case 183M.*O AGE IN MONTHS Height Measures and the Straight Line of \ Best Fit. ) atroipht line found by usine semi— annual measures to maturity Lqustiox is y : .57b55 K + 70.58 > 4,5 .r—I S—d 3 4.) (31 i 4.) *v. + I a.» , r (\"V\ c I: 1w; __ I ")1? HI 8 riCtuIIl ”Head-5.176 a 31L \V/ " .14 175 —— 16“ ~- 155 ‘- 145 —_ U) H 135 -- 22 H E , :3 125 *- D Z 4 H 115 _I_ E a: do *3 105 -— :11 95 “' . Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position 45 I I, I I I" .‘ I . O 20 NO 60 80 100 120 140 160 180 200 AGE IN MONTHS Figure 80. Case 186M. Height Measures and the Straight Line of Best Fit. TEES GENUINE; HEIGHT IN 75 65 55 45 >7 +2 H E ___._-‘_‘ Streipnf lint Boone 3y using semi» 5 annual measures to maturity g Equaticn is y = . 2143 K + 7u,33 M 4.3 A {1 ‘0“9 a e actual measures fig 4- CD I: or Place where mea3ure- ments of standing Height — replaee measurement taken with subject in Horizontal position I l I l l #L I I I l I r I | , I I I I I I I j 0 20 NO 60 80 100 120 140 160 180 200 220 AGE IN MONTHS Figure 81. Case 189MO. Height Measures and the Straight Line of Best Fit. HEIGHT IN 85 75 65 55 45 StraiJrT line found By using semi— annual measures Equation is y = pots are actual v to Jalurity .51551 X + 78.73 m€:'a,SUl‘E? S \\\\ Height Maturity I Figure 82. Case 197MO. AGE IN MONTHS Height Measures and the Straight Line of Best Fit. . / Q // ‘- /// Place where measure— ments of standing Height replace measurement taken with subject in Horizontal position I I I I I I I I I I I O 20 no 60 80 100 120 1&0 140 160 200 220 128 years or 72 months was the time selected to change from one measure to another. Allowance for this change was made in the analysis of the cyclic pattern. The longer vertical line on Figures 6. through 82, drawn at a later chronological age represents the time of height maturity of that boy or girl. Figures 6 through 82 are drawn according to the same scale. Thus the figures can be superimposed on one another and apparent similarities and differences in the cyclic patterns can easily be discovered empirically and then sub— stantiated or refuted by the mathematical magnitude and Sign of the deviations (Appendices G and H). The plotted pattern of each individuars height shows that arOWth is very rapid at birth and gradually decreases. This conclusion from the figures is substantiated by the change in magnitude of the deviations as shown in Appendices G and H. The true growth pattern in all cases starts below the straight line representation of growth and crosses the line at approximately 18 months. In almost all cases the true EIrOWth pattern aaain falls below the straight line representa- tion of growth. In some eases the true growth pattern aaain rises above the straight line representation and falls below this straight line (see Figure 6).. In other cases the true pattern of growth rises toward the straight line, but does not rise above it (see Figure 10). 129 Thus in some cases there is a more distinguishable curve or cycle beginning at approximately 138 months than there is in other cases. Figure 53, Case H9M, is a good example of such a pronounced change in rate of growth at about the time when other adolescent changes could be expected to occur. Figure #1, Case 185F, is an example of little change in the height growth rate at about the time when adolescent change could be eXpected to occur. These cases were chosen as representative of two extremes on a continuum. Most of the cases fall somewhere in between these examples, but all of them have individual distinguishing characteristics that make no two curves exactly alike -- though they are sometimes similar. The individual straight line equation constants for girls and boys reapectively are found in Appendices C and D. The rates for girls range from .4731? to .66595 centimeters a month with the mean rate for the group being .56600. The rates for boys range from .h8550 to .66158 centimeters a month with a mean rate of .5#16u for the group. The starting point of the straight line is in every individual case (see Figures 6. through 82) above the birth length of the child. Appendix C shows that the range of incipiencies for girls according to straight line growth is from 63.71 to 77.83 centimeters. Likewise the range of in- cipiencies of the hypothecated straight line growth for boys Shown in Appendix D is from 69.7 to 78.73 centimeters. The group mean for girls is 70.53 centimeters and for boys 73.31 centimeters. I}! ’ ..— I H - m”, ‘39:.."1 I As". $1“. . "- - t_ I “5333-15. 8 130 The amount of the deviations of actual growth from straight line growth at six month intervals for every individ— ual case ale shown in Appendices E and F. The algebraic sum of these deviations in addition to showing the pattern of growth with.reSpect to straight line growth servesas a check on the accuracy of the straight line equation. The straight line of best fit was determined mathematically by the measure— ments taken at six month intervals from birth to height maturity. Therefore, by solving the equation for height at the time of the measure and subtracting this value from the measure algebraically, the sum of the differences should theo- retically be zero if the equation is accurate. In rounding off the figures for purpose of multiplication in solving the equation, an error of up to .l of a centimeter could theoreti- cally occur for each measure. Thus if there were 25 measures at six month intervals used in finding the equation and if all of these happened to be rounded in the same direction the algebraic sum would be 2.5 centimeter, (either plus or minus depending upon the direction of rounding) and the equation would still be correct. The cyclic pattern of height growth (as determined by the deviations of the measures from the straight line) from birth to maturity are shown in Appendices G and H. The straight line of best fit was determined mathematically by the measurements taken at six month intervals. To determine the cyclic pattern of growth the equation found was solved for sf“ *6 1‘35; J.‘ ‘ ' l r M-. ‘- F9"??? gm; an. 1.111 . 5 ' A II '8 131 all times for which a height measure was recorded. This dif- ference in centimeters between the actual measure and the straight line measure for every case is represented in Appendix G for the girls and in Appendix H for the boys. A plus sign indicates the measure was greater than the straight 1.; ! line and a minus sign means the measure was below the straight :. r5 '5 line. In all cases the rate of the straight line was math- I' L"?~x:! L1- ‘4' t {-51}. ematically positive. The line was further from the base at ‘1 “,1 ..TV' 0 ‘53:}...3. , _ ’3 the end of growth in height than at birth (see Figures J through 82). This is as would be expected from a straight line of’ best fit derived from growth data. Thus we have the growth plotted not only with respect to time, but also related to its own straight line of best fit -- a line that is slanted when compared to either the time or size axis. In order to now determine objectively and mathematically the number of cycles of height growth it was necessary to have a working definition of a cycle. A cycle was considered to be 1 characterized by increasing upward movement, followed by de- 3reasing upward movement With reapect to the straight line of >est fit. This type of movement over time could readily be etermined by the deviations. A cycle was considered to have nded only after an increased deviation showed that the next Icle began. The end of the cycle was then marked '. The results of this analysis are summarized in Figures and 81+. Twenty out of #6 girls as shown by Figure 83. have NM‘ ‘\ NUMBER OF GIRLS 12 10 Fig. 7—211 _1_ 132 83. *u 6 7 8 9 10111213141516 NUMBER OF CYCLES Cycles of Height Growth, Girls 133 :her eight or nine cycles of height growth according to this finition of a cycle of height growth. Similarly Figure 81+ owa that: 13 of the 31 boys have seven or eight cycles of ight growth according to this definition of cycles. It seems that according to most physical anthropologists he error of height measurement is at least .5 of a centimeter. herefore the individual deviations presented in Appendices G .nd H were analyzed again to determine the cyclic pattern of is ight growth in which differences were considered only if they were greater than .5 of a centimeter. These individual cycles are marked " in Appendices G and H. Figures 85 and 86 summarize the results of this analysis. It can readily be seen that by using this added criteria in the definition of cycles we find that for both boys and girls there are fewer cycles of height growth. From the age of 72 months to maturity the plotted data represent standing height measures rather than horizontal position measures. Since the horizontal measurement of body length is usually greater than standing height, the analysis of the number of cycles of height measures to this point could have included an extra cycle. Hence the data (Appendices G and H) were further analyzed according to the second definition (see page 131) of cycles. This time if the end of a cycle occurred at the time when standing height measures began, it was omitted from consideration as a cycle. Further, as seen by GXamination of Figures 6. through 82, there were a few times ‘91. {if :‘b‘ :1 1:: 5. mun-'1'- 5'33”: 1 7‘45?“ 'u’ 1.11211 NUMBER or Boys 12 10 131+ Tl 1 23 us 67 8910111213311-11516 NUMBER OF CYCLES Fig. 84. Cycles of Height Growth, Boys NUMBER or 0.1an 16 14 12 10 135 Jrfsr rtgrv NUMBER OF CYCLES Fig. 85. Cycles of Height Growth, Girls NUMBER OF BOYS 136 16 1h 12 10 123b567°89 NUMBER or CYCLES Fig. 860 ‘ Cycles of Height Growth, Boys 137 when a standing height measure was included among the horizontal position measures and there was one case where a horizontal position measure was included among the s tanding height measures. This was done on the Figures 6. through 82, and in the analysis because these were the only measures available at that date and it seemed better to include the measure. These type of measures could also appear to increase the number of cycles of height growth. Hence if one of those measures constituted the end of the cycle according to the second criteria for determining cycles -- it was not considered a cycle. The number of cycles of height growth according to this third working definition of cycles are shovm for each individual in the last column of Appendices G and H. The summary of these findings for girls and boys are found in Figures 87 and 88. Fifty-six per cent of the girls are found to have either three or four cycles of height growth from birth to iaturity. An equal number of these girls were in each of the we cyclic categories. The next largest number of girls, 3 per cent, had two cycles of height growth from birth to ,turi ty. Thus 76 per cent of the girls experienced either a, three, or four cycles of height growth. Forty-five per cent of the individual boys (as compared 26 per cent of the girls) measures showed four cycles of wth. The next largest number of boys, 19 per cent, showed 8 cycles of height grthh. Thirteen per cent of the boys 11, with} ’ ‘u 1. fan a :‘fil‘i VIHTT‘EWI’ N17." 1.42; 3‘, 4 NUMBER OF GIRLS 16 14 12 10 P0 138 Mean 3- 7 Standard Deviation Range 1 ~ 7 1 2 3 u 5 6 7'8 NUMBER op CYCLES Fig. 87. Cycles of Height Growth, Girls l.#31 NUMBER OF GIRLS 16 14 12 10 139 Mean h.2 Standard Deviation Range 2 - 7 1 23 #5 6 78 NUMBER or CYCLES Fig. 88. Cycles of Height Growth, Boys 1. 385 11K) measures indicated three cycles of height growth. Thus 78 per cent of the boys measures showed either three, four, or five cycles of height growth. The range in the number of cycles for the group of girls is one to seven cycles. The range for boys is similar -- two to seven cycles. a; The mean number of cycles for the group of girls was Lia 3.7 with a standard deviation of 1.431. E The mean number of cycles for the group of boys was t 4 4.2 and the standard deviation was 1.385 cycles. A test of significance showed that the means of the two uncorrelated groups Was significant well above the .01 level of confidence. For purposes of understanding the individual pattern of height growth, it is not only important to know the number of cycles from birth to maturity, but also the time when the cycles begin and end. Table II, which is a summary of the information found in Appendices G and H, shows where the cycles »f‘ height growth begin,* according to the second criteria for i eta—mining cycles. From the table, it can be readily ascertained that :63 age where the greatest number of cycles began for the ”This point in time could Just as correctly be thought as the time when a cycle ended, since the mark Was placed t he last deviation that exhibited decreasing upward movement her than at the first deviation to exhibit increasing upward ament. V, 'l lul‘. .{l 114: I . ill [I'll , llil TABLE II WHERE CYCLES OF HEIGHT GROWTH BEGIN .Age 1J1 Number of Children Having the Beginning Months of a Cycle at this Time Girls 7 Boys T ’. V. {7 stag. ' .‘ J 1 l g? f. L‘ g. 1‘ g. ,. E 1’ 3 —-_‘. omvmmpumwo I\. N U‘Ol-JmHkmeQf‘Jl—‘HOttONNOl—‘ONOOONOOI‘JHOCHOOHOOOOOO \OONWUHwHtl-‘ONUNEHWHNOOOHOU‘OOHHNHHOOHOHOi—‘OOOO 142 TABLE II -— Continued ng in Number of Children Having the Beginning Months of a Cycle at this Time Girls Boys 1 1? 78 84 9o 96 102 108 11H 120 pm 132 um NM 1% 1% 162 um rw 180 1% r% we TOTAL 128 110 V . " r‘ t ' Ll -fiag t I ‘1 l ' ‘ 'nahtgrlfng-gnmCflI‘Q-G Kin?!" ;‘ ...-l oooooowmuppmmmupHuumm 00Hoommmmpwu0HpouHut Q4 girls was 138 months. Fourteen girls or 30 per cent of the group began a cycle at that age. Twenty-six girls or 57 per ’4 cent of the group began a cycle between 132 and 1hh months. The age at which the largest number of boys began a cydhaof height growth was 72 months. However, this may appear to be a cycle only because 72 months was the age where mostcn'the measures (for purposes of continuous analysis) vmrecflmnged from crown-heel length to standing height and it is @flmrally accepted that crown-heel measures are greater than 143 standing height measures taken at the same time. At 162 nunnths, the second largest number of boys, eight, or 26 per cent, began a cycle of height growth. Between 156 and 168 znonths 15 boys or #8 per cent of the group of boys began a height cycle. Six of the boys eXperience a new cycle after 162 months, the.age at which the last girl GXperienced a cyclic change. There are 25 changes in cycles among the boys after 138 months, the time when the largest number of girls began a new cycle, whereas there were only 11 changes in cycles for the group of girls after that time. If these last cycles are then labled the adolescent cycles, Table II shows that the adolescent cycle of height growth in many individual cases occurs at a later date for boys than it does for girls. In an attempt to seek explanations for the variations among individuals in the numbers of cycles of height growth from birth to maturity, the health examination records were used. Four of what might be considered the more serious physical traumauiwere selected, these are: scarlet fever, wh00ping cough, appendicitis, and an appendectomy. The dates of these traumamifor each individual were then compared to the date at which the cycles of height growth occurred (according to the second definition or a height cycle). If the trauma occurred six months previous to the beginning of a cycle, an x.was placed to the left of the number representing the month of occurrence of the cycle (see Appendices I and J). If the 3' ET ”'3 ‘7) fiat-‘5‘"- 5 “7- P'— :-':-‘:"He§» ‘1‘ "; hu— -. Vi}. “-WVV' l! — I. _ E E l g)! 141» trauma occurred up to six months after the beginning of a cycle, an x was placed to the right of the figure that repre- sented in months the date the cycle occurred. A summary of these findings is shown in Table III. Seven of the girls and three of the boys had scarlet fever. or the seven girls, in two instances the scarlet fever followed a cycle by six months or less. In five cases the scarlet fever did not occur within six months of a cycle. In one of the three cases of scarlet fever among the boys the diseasefollowed a height cycle by six months or less. The other two cases of scarlet fever did not occur within six months of the beginning of a cycle. Twenty-five of the girls and six of the boys had whooping cough. In six instances among the girls and in two instances among the boys this disease proceeded a cycle by six months or less. In three instances among the girls and in one instance among the boys the disease followed~ a ieight cycles by six months or less. In 16 cases among the wenty—five girls who had whooping cough and in three cases I“ the six boys who had whOOping cough, the disease did not :cur within six months of the beginning of a height cycle. Two of the girls and none of the boys had appendicitis. one case the appendicitis attack followed a cycle by six 1ths or less. Two of the girls and one of the boys underwent an rendectomy. In one case, a girl, the appendectomy preceeded eight cycle by six months or less. I “'I . me. i :4 -4r' ‘ “WW. .... ‘55.“? I ‘. ‘fil "lg": “fi’tfljim’ I“ .u,‘ .— ‘a‘y . ‘ 1.”. 145 N m o 0 0H m n ma Adeoe H o o o H N msouomocmamd o H m H o m massaged? m H o n 0 mm QwSOD mcHQoonz . m - mHoh d o m .hm>om pmHAwom d aepoao.oz ammomwae we macho eaoao e on m on a: mcHn : H mmcoz woman a amuw< .oz m50H>oam .02 moms insooo masons ma5wmuH3 Ha cooaooom m on a: wcHa o manna: msHa cookowo o assume we ampssz Innooo masons 195000 masons no sepslm whom mHAHG 685699 fl! 4‘ mmaomo BmUHmm zo Homhh¢ mHmmB nz< hmpCH Space npxam mco macaw momma mmeOfiwnHt m.mmHIN.mmH N.mmalm.mma m.mmanm.maa o.mm a.maa m.~aaum.aoa “.maa a.a a: maaao¢ 0.0m m.maa m.azm-m.oam m.H:m o.m mm mum 0.0m o.ama :.H:Nam.oam :.H:~ o.m mm moo 0.0m «.mma m.mo aam m.mma o.a on mam. m.mm m.aaa m.aamuoom a.naum.m m.aam o.a mm mom. o.am m.moa m.oam- mam m.oam o.H mm smm m.o: m.ama «.mam o.a on mmm m.o:m-m.mam :omam.mma . o.mm o.moa a.omum.m n.oam o.a am eon: H.N: a.mma m.oamu mam m.Q:m o.a om emu o.mm H.:na H.o:mum.oam H.ozm o.H mm awn H.Homno.oam o.mm m.ama o.o:msm.mam H.Hom m.a om saw o.mwmum.aam o.ma «.maa m.a:~-m.aa~ o.mwm o.H mm mow m.momna.mam o.m: 3.0ma :.m:mum.aam m.mom m. an mam o.mmmum.omm o.Hm o.moa N.ommum.oam o.wwm m.m m: mam m.ammum.aom H.0o m.oma m.:mmum.oam m.amm a.m am mam o.no o.mma m.mam o.a m: mmm .QHWOQ .mwmz pflwdmm hum—”859d: mpCOEmhfimwwz .mdmz wand .mwmz.pmH mohfimdmz omdo wcaucmpm unmeasumm ow¢ pzmdmm codndxm mo om< no mwd Mo om4 mo no mw< .02 Hence mAme .mA4DQH>HQZH mo mmHm<=szIIpmpCa Space npxam on» mo msap mnp pm maaxowa mam moMSmon owns» swap macs poc 9:9 mac opmnz momma mmpdoaocH * 0.0m a.aom m.m:aum.oma a.oam a. mm Saaat o.om o.oma m.oam o co 2mma o.on o.mam o.mam o om :nmao 0.0m o.wam m.mmmuwam m.mmm :. mm zaaao o.mm o.:om m.mmmum.nam w.mmm o aw xmaa m.w:mnmam o.mm m.mma mamum.mma m.mam o.a on zNoao¢ m.a:mnmam a.mm 3.5ma :.mmasmma n.a:m :. mm :mm: o.mm m.mma d:mum.mam a.a:N o.a mm ZNm 3.0:Nsoam 0.0: m.ama mmum : mm 3.0:N o.a mm 23m: n.3m m.mow n.0am o.a om Sam N.N: m.mwa mamna.mam o.m:m o.a ow 2mm m.:mmuw.mmm 3.3m :.oam m.mmwua.oam m.:om a. co 2mm N.ozmnm.wam m.omm-m.oam o.n: a.ama m.amauoma m.omm a.a mm Zane: o.w: n.mam momsm.wam o.mmm o.a mm ammo m.omaum.ama m.ma o.mma a.amnmm m.mam o.a as man: w.womun.mmm 2.3m c.0wa m.mmmumam m.mom m.m om 2m: a.mmmsm.mmm m.mmmnoam m.mmaum.maa 0.0m w.mma Nauw. a.mmm .m. m: 20H: 0.3m m.mo~ ~.oamumam m.oam a.a mm 23m .cawmm .mmox pnwaom mpapzpm: mpaosomSmmmz .mwoz puma .mdmz.pma momsmwmz omwo weaucmum pqmcwsmmm mw< unwamm cognagm mo ow< no mwd no owd mo mo om< .oz aapom maom .maammama92a mo mmamazzsm--4m«m emaamm m XHszmm< 156 'Il a.mm o.mma o.mma o om Sumac o.om o.mma o.mma a. mm :mwao 0.0m m.moa m.mma 0 mm zmma o.om o.aom m.amum.am o.:om m. mm 2mmao: o.om a.aom a.ammuaom m.amm 0 mm momao m.mm m.mma m.oam 0 mm Emma m.aa m.oam n.oa~ o on zamao 0.0m a.ama :.ma~ 0 mm zmoao m.mm o.oam o.oa~ o co somao m.mm m.mam m.mam 0 mm sumac o.mm m.mom o.mam o co zmma a.wm a.aom m.mam a. co zama m.mn. m.mam m.mam o co 2mmao .cawom .momz unmaom mpapSpw: upcmsoASmamz .mmoz puma .mwmz.uma momzmemz ammo wcavcmpm pcocmsnom mm< unmaom commaxm no mw< mo ow< mo mw< no mo mma .oz aapom 'Illtlvl UmSCdQCdo II m NHszmmd 157 APPENDIX C STRAIGHT LINE EQUATION CONSTANTS, GIRLS Case Rate Incipiency 25F .50150 70.76 28F .6056? 70.40 37F .593éu 68.2“ 59F .53833 67.90 66F .49195 72.01 67F .H9079 74.99 72F .56010 71.70 75F .49858 70.09 *76F .60050 72.36 82F .58302 67.15 83F .55660 69.89 *88F .58372 73.72 *90F .57151 69.59 96F .5135? 69.05 97F .52768 66.06 *OlllF .57231 71.34 117F .56568 72.67 lZOF .58760 72.14 126s .57566 70.29 127F .59930 62.74 137F .0731? 68.75 140F .59681 77.83 1u2F .57085 68.93 luup .5002? 69.95 *1u5F .53661 72.62 *1u6F .60522 68.82 148? .53180 70.19 150? .59356 69.23 151F .57887 68.92 165F .59293 71.25 l7OF .53303 71.52 *171F .60526 71.28 176F .608b7 73.39 179F .55578 70.77 182F .5931? 68.15 *185F .5537? 68.99 188F .57998 79.78 191F .56630 71.11 193F .55290 73.12 204E .66595 71.20 205F .60195 72.76 211E .56663 68.88 210E .5318? 63.71 0217F .57885 68.73 220E .63223 72.78 2217 .58212 68.52 MEAN .56600 70.53 RANGE .07317-66595 62.74-77.83 158 APPENDIX D STRAIGHT LINE EQUATION CONSTANTS, BOYS Case Rate Incipiency *loM .55590 75.78 09M .55224 75.60 “54M .56160 71.77 055M .55139 71.90 *071M .56120 76.40 70M .5062? 70.05 77M .5090? 69.59 78M .6170» 70.30 81M .53959 77.84 *BuM .5376? 70.07 92M .66158 73.25 *98M .56974 71.51 *0102M .51351 69.07 112M .09498 69.90 o1141M .08550 72.02 0135M .52052 77.15 138M .59050 74.79 “141M .57119 71.45 0153M .09523 77.6? 150M .53480 70.37 156M .53328 72.69 0157M .50166 70.92 0160M .50270 72.22 0167M .51646 73.02 o170M .09865 77.59 177M .5090“ 74.76 °180M .50719 73.60 *0183M .55010 73.48 186M .57835 70.88 0189M .52143 74.33 0197M .51861 78.73 MEAN .50160 73.31 RANGE .08550-.66158 69.0? - 78.73 ._l___.____i_________ —-———-— fi 37.“ 160867114 1.“. 91018004004111.5094 785801 1% GIRLS APPENDIX E DEVIATIONS OF ACTUAL GROWTH FROM THE STRAIGHT LINE AT 6 MONTH INTERVALS 32 W H?8..L3211%lk&&&&&&L .L22LL.L. .Lii&mmnm .—..+++++++++++++++_-....++++—..._—.. .r 82049322835968843795913234390fi417:269 2 6952 2%kk5k432433LL .....1368LiWLkWO 7 11 1112223 ....++++++++++++++++++_++.._......... .F 334101604604014859399851 8874343 321344 .W 1L6L22345k54434kkaaLLL..0....lLk68mMU __.-+++++++++++++++++++_ _._+___-.—_— .F 8233288906871438390381082923911255 5616 ,6 693L1112433343333121 .12&&23245 913692 ,6 1 11112 ._.++++++++++++++++++-..._-._._-_-__- .F 934 417445450408858818432724223241048 9 652022&&2&l33232LLLL....LLL..Lli&1%WL .5 1 1112 ... ++++++++++++++++++_....+..__._... F 3246916867736736216270886583911319366 7 L82LL23K12LZ ...... L&%2L .25801%&&8&5% a) 1 111222333 .-.+++++++++++++.+++++++....._.._.... .r 129 406634954794630493245784770647176 ... ............. ...... ...OC....... . _% N620 45555332111 11 1 l3ZRMNRM%fi%”W ...+++++++++++++_.-_+++-_...__-.__-_ F 8276331115853149039745504347 614409003 5 482 .23333323L22L2K1 . 1.....ZK6RLMSQ n2 1 1112 ..._++++++++++++++++++_..+++_..:._... . e sm06284062840 0628 406 92840628M062840628406 m af 112334456 :67 899 0012233 556678899011 u CT 11111111111111111222 S Algebraic 1@ APPENDIX E -- Continued o""1111" 788677910108665967 3 519 M72 .LLLlll33LLLLL. L LIL ...+++++++++++++++ + +++ - 4 1 -14.5 9W 907325081312507787057469/014 1.4.9 ooooooooooooooooooooooooooo 6 Mm4 1L4454554432211 251211 13& _ ..._+++++++++++++++....-...... 9w .....++++++++++++++ .....++++.._. *94F OOOOOOOOOOOOOOOOOOOOOO O O O C O C C O O 2321.. 123.“.3232323121 123311 45825 1 11 18539755136063908003“183.406 7710 n .....++++++++++++++_.._...—_._._ 20194124587411229283563163150116623 283 234LML3MMLMMLLL.. . ..LLL9L5836 2 11122 ....+++++++++*+++++++-..+._.......— 1“ near 73 U95312255i5655432L....1.. 368R ....+++++++++++++++....++.._._ 82F 11 8 8L1LLL1LLii533LL .L 368& .._++++++++++++++++++__+++.__.. *76F 11 007021384414128977183176844400 ...+++++++++++++++.._.._..._. n4. 9m613uu5£555uh~w221 1221.13 9w”. . . + Case Time 0628 .40 28.40 1123:405 84 628406284062840628406 900122334556678899011 11111111111111111222 &m Algerbraic 161 APPENDIX E -- Continued ”a’mm.apltl“|t‘r'rwhut. ...-I ’ w. 5142259228314301075766196540 1620974.1 5 .0...... 0.0 0.... O. 00000 I M“ fl74 1224M455134322L1 12LL0LLM68HUU 1 ....++++++++++++++++++...._. ......_. _ .F 608830761965919689439428247980979199 3 OOOOOOOOOOOOOOOOOO 00.00.0000... 0 a2 973 3334544422221 1 11 135 147137 4. 1 1.1.1222 1 ...+++++++++++++++..___.+...._._.._. _ w. 2002 3971687815116267 866576752556221 nu ML6LOL3M5566MiiiML3L .0... 24&14&1470 0 4 21 1112223 1 .... +++++++++++++++++.+........_... w. 53065291005736188502715968060441.3532 3 .....OIOOOOOOOOOOOO. 000000000 00.0100. 0 wu fi94 2334455544422221 1122321 2359fl 1 .__.++++++++++++++++++............... . w. J3202326131517883JJ0477727 3953985224 7. 6.6.LL34444M41n2. .. .LL2.L .2.L 360.3503693603 0 2 1 11122223344 1 .._++++++++++++.....+++............._ . 6J6293228047528J1341422111128J2207656 8 .Ho 000000 00.00 0000000000000 I 0 AV 95L33MM333322LLL 112L221122 L4703583 2 .1 11112 1 ...+++++++++++++++_......+++....._... + w. 10153869728081781565 7956474997247496 3 000.00.00.00 000000 O. 0000000000 O... O 0 907311345656554443210 12333469369259 “2 11 111222 1 .._.++++++++++++++++ ......._..__..._ . w. 0745745557666631881946565547965199841 2 O .0.... O ..... .0 O a! 005LLL3M5566MM33L22 L .L3581571481 .1 21 1112223 1 ....+++++++++++++++++._......__...._. + e e 8 m06 :284 :284 8240 62840628M062840628406 m a 1 1123:445 778990012233 556678899011 nu T 11111111111111111222 S Algebraic 1% APPENDIX E -- Continued 37 .1”... REL. Errhmufml. ..d-.l.c......! .1 F 4173.136.803.88099§.63148 1484/0 595.89.01.34. I4 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 1922344455443111. L11011 12 258L5936 7 2 11122233 fl ...+++++++++++++++... +4+.. .....__.. + LIF 629617350489303645740193171445 53653 1 I I I I I I I I I I I o I I I I I I I 0 L6 2LMMLLMMLLL1L.11LLL .2M602582 7 2 11112 F1 ...+++++++++++++++.._...._._.._.___. + F 5594774920302716757834214014458643695 3 .5 38L LLLM5LLLMLLLLL...LL2LLMLLLLLLLLL6 6 .2 . 11122233 1 ...4+++++++++++++++++..........__.._.. 2 F 2540528194478992569207258461729338580 1 ..... I I I I I I I I I I I I I I 1 97LLLLLLM44412LL LLLl LL 1L79368250 5 1 111223 1. ...++++++++++++++.._...++++.......... . F 782654099850169675304355785333 946263 2 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 962 1354444532L1 . 1121 1 1369147046 5 1 111222 1 ....4+++++++++++++._....+++._....._._ + F 468 901384580457904763381860984505418 oIo oIIIIIIIoIIIIIIIIIIIooIIILIIIIII ”% $910L44555653332 1 1.122221 1369HMNm 0 1 ... ++++++++++++++++1_......___.____.. ,w 821444658434 423739 7 8 32214165356 3 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I .4 65213344444L 11 24814704815 1 1 11122233 I _._+++++++++ +...._ _ + ___._...... . W J0J31J30 J994 J8J0058873376558661999 1 I I I I I I I I I I I I I I I I I MW fimL .LLLL 6LLMMLLL2. l. 1 112222358m u. ...+++++ +++++++++++_....._......__ . e e s m06284 062840 :2840 628406284062840628406 m a 1 112 :3445 :7789 900122334556678899011 u C T 11111111111111111222 S A1gebra1¢ 35582235146224436398J7J664.29JJ8J MB APPENDIX E —- Continued F oooooooooooo 4 LLL .L4445555LLL lLLLL L L4.LLL O 2 1112 2 ...++++++++++++++._____________. F 93140975746920130791611077 0535212 ” mméLLLLMM555L5LMMLLLL 1 012M68HM 1 _._.++++++++++++++++++_... _____._ F 4969471054106618451527936564979294 % flLM.LLMLL5LLMLMLLLL . L .L3LLEUH 1 ____+++++++++++++++++_____+_______ F 902181641348529315JJ81940115244939 ................ I ......I ..I.. % &R3 355775553321L LLlllll 1L5THUN l ...+++++++++++++++_._____.+_._.___ W .422602190 66835763179 2317755647806 IIIIIIII IIII IIIIII IIIIIIIIIIIII w M73 13444 5423L1211 0 1256NMM * ....+++++ +++++++++++ +++++______._ F 472433073635841246JJ76731110665 09 IIIIIIIIIIIIIIIIIIIIIIII I. I I. 2 551234433332 1 .LL11 135L1 24 8 1 1 22 1 _._+++++++++++.+.__.___+++...__ .— 912/022.4.8882830lO)Q/I4«1.h~ph~.31..976863h~ 910610 F .......................... 9 971133L333432211LLL .Llll 1LM71259 7 1 1111 1 ___+++++++++++++++++_...._._..__.__ F 8160668J648397386J44484745968050173 IIIIIIIIIIIIII I I I I I I 6 104113LLM5M5LLLLLL 1211 26L2L9L5O 0 7 21 111223 1 ___.++++++++++++++._+++++._.______. e B 0628406284062840628406284062840628406 m a 11233445667789900122334556678899011 u C 11111111111111111222 S Algebraic M4 APPENDIX E -- Continued 3785629206930673552525294269778 1 m MLL..LLLMMMLMLLLLLL..LLLLLLLMRW . 2 ....++++++++++++++++......._... + F 2333042210650399111481234602J14 9 m fl82 LM44554MLLLLL . L333l 58NMM 2 ....++++++++++++++_++++++__._.. + W 0253640372111330713159399771144 1 a m7LLLM5MLMMML2 .L...1 2 .1L.LL6 o ...+++++++++++++++......++++... . F 61313321895744015116898239 8426 6 .H N61L24M444MLLLL. .321122L48HHM 2 ...++++++++++++....+_...._...._ + F 94348765L83832599573662042.4 7400 0 C . C O C O C O O C . .. O C C. O C C C C C O C C O I O O C C n M73 12445465422 1 11211 2347M“ 1 2 ..._++++++++++++++__..._._..__. . F 44230959866417509444491198004115 4 A” H95123M455555444321 LLLLLL57NMWfl 2 ....++++++++++++++++..._-......_ . e e 11 a m062840 062840 62 840628406284062840628406 m a 1 1123 34456667 789900122334556678899011 u C T 11111111111111111222 S Algebraic WM 77647985012?.192n471392907505522:4 9.4632 ooooooooooOoooooooooo ..... a... .0000 M72 112234443444421 3232 13 83604 22 ....+++++++++++++++++._....++....&d.. WM 6634892536345445800935162226597159558 . . . . C . . . C . . C C O . . C . . C . . . . . . . . . . @531. 1122341433233L11 . . 1. 14&% .....+++++++++++++++++++...__..___._. Wm 6637834.732501890360670297536557141008 NH5L 33344454344333211 1222 25% .._.+++++++++++++++++++..__._+++.._ °*71M .LL .44.54555444uu32 .LL24433 259L4 1 ....+++++++++++++++++++++++++ ...d. MS APPENDIX F HHS DEVIATIONS OF ACTUAL GROWTH FROM THE STRAIGHT LINE AT 6 MONTH INTERVALS M I O l O O O O 0 O O O I I O O O O O O O O O O O O ..... fi MB3 312%323132233331221 L .121 2473 o .._..+++++++++++++++++++.___+++++.__. W 9282309163885 34521386283830 8148608 fl U83 121114444 lillaLJL2L1M1L .L&i&Lu 1 ....+++++++++ +++++++__..._. +__.__. M 8689595457751079111443328021734307182 m4; ”Hum 234.555554.4.32.22 L334.4.L .L .annhmMMM/mm. 1 .._++++++++++++++++_....._.++.._._._. W 2 316489546672663754733577 020806083 u & 5 2423lmkallaz..L.aaall kl&.1i%uu o . ._++++++++++++++__._.... +++....._ e 1 a 062840628406284062840628W062840628406 m a 1123344566778990012233 556678899011 u C 11111111111111111222 S Algebraic 166 APPENDIX F -- Continued % 173111746586615698573244930473369395 2 O. O ..... O O U 5n842 1345565665545444221.11L 458 o ._.._.+++++++++++++++++++.._......... _ W 0624310448083652583659123106677573469 1 000000000 .OOOOOOOOOOOOIO- O n MB4 123333433223222LL 1222 1 135 o ._._++++++++++++++++++++._._._++++._. + w 3444691725273315902945666765858351 2 6 n NBML.24344544354.232. .L23421 AK. L4 8n ._._+++++++++++++++++_..._._++++.._.. . M W 6283191782839919619872579525452985 3 1 ........ 0.... 000...... O 0 fl U72 L2232333233L22 LLL13331 4 9 0 ...+++++++++++++++++......_...+++. . + M 26725234447497094584759121654722 702 1 % M7212333132322322LLL .allkl MU * ...+++++++++++++++++++......_++. .... _ M 8.092045744037725355500993977400007772 7 2 853&11%45565444.2LL. L343L ...L69l60k82 9 1 112223 _.__++++++++++++++._.._.+++__......._ + M 606760610650 57122795 288099665187034 1 .......... O... O M N95LL3355445 43333LLL0 .LL232 3 NR” * ..._++++++++ ++++++++ ....._......... + M 0666 307795378349896480134313118212 28 6 000000000000 I. 0.. 0 & WN830L34556766666544422 L24322247 RU .... +++++++++++++++++++......._.._.. . e e s m06 2840 62840 62 :40 628406284062840628406 m a 1 1123 :445 677899 00122334556678899011 u C T 11111111111111111222 S Algerbraic .It! 167 APPENDIX F -- Continued M...l..l.flw"...... . i11...: .....u .I2. $21...» gulf—kt}.ny 916210/00037695255185118569228996 51 8 m 1 M %M%LLL355655LLLLLLL.L..LLLL..LLL LL m . o ....+++++++++++++++++.......++++ .. ; + W 3393765121553649041421892842 48906348 4 m &82.12344434LLLLLLL.L 11LL0LLL2.217 O ___++++++++++++++++++.._.... ++++-.._ - W J266009825503283333311400370632749602 U Q93.3LL56555LLILLL....122334L .LLL..L4 0 O _.__++++++++++++++-_+..__..__—++++—__ M JJ1J494588510665712267J702J23JJJ51949 1 % 4.n3LL23444565iklllLL.. L3L .LLL .L367HU 1 .._.+++++++++++++++++..._..++++....._ + M 1J27485840300986955839738375878467016 W N85LL.233556MML3L11L211 2L2. 1L4LNR 0 1 ...._+++++++++++++++++++............_ W 4JJ4101137073J7680912J4J1754240J08456 4 ............. ... ....Q . U ””63 23455664555454433LLL LLLL23579 0 .....+++++++++++++++++++++.......—... _ m 274717699343653349547 7237JJ7JJJ09 2 M H94 222334453113LL21L L LLL .L468RN 4 ....+++++++++++++++++ .+++++....._ . M 0J8160157821519411835J26328J74J6- 5930 3 w 38 124lMl44i34LLLL... .LLLL.. .LL .mmmfl 1 ...+++++++++++++++++...._...+......__ . e e 8 m06 2840 :284 :40 628406284062840628406 w a 1 112364456 7899900122334556678899011 C T 11111111111111111222 S Algerbraio 1% APPENDIX F -- Continued °197M Vggg:at;.-;g gay _...L..u.E...twnyrévE~c§4I til ... 983187821112500934500473663659604 O O O O O O O O O O WN4L 23455664564543332 23445443 ....++++++++++++++++4+_....._...+ flLLL.LLL45LLL333LLLL.. ....... . . 556 133.4 75.4.4574 96 97.4 58.“. 1737870.“. 26 9 8 ....++++++++++++++++++._..+++..... OOOOOOOOOOOOOO O C O C O O O O 0 $82 al.35555n41432121 lZZBbuQ/l 693.4 1 11 3J41151480121998561105J425244 4209 _._.++++++++++++++._.._...+.._.... IOobw7nO.8n/279859w§6208560307/Oosgnvo737u.1562 000000000000 O O C C O O . mmuz BuuufiJ/On/ouuuhwafizfiJle .12331 _...+++++++++++++++++++....._.+_._5 o180M °*183M 186M O189M 68527716523445369146130882595830120 N741L24L556LLLLLLLLLL.LLLLLL3 L1 2L _...+++++++++++++++++.._....._+++_. 365393193989J5605103847677JJJ54J 12 .......... O O O O O o o o 593 13445u55h~w32233321 12332211 502 2 ll .._+++++++++++++++++++....-...-..._. 0174M 177M 5R73 1345566555555543221.LL3355543L2 87.4377214782796660221672583433110.1148 _..._++++++++++++++++++++........... Case Time 0628 :4 %:8h~. :6 7406 no 102 108 1% 1% 8% 628.4062 3 5667889 11 1111111.. 150 um 204 210 as Alge rbrai c %m 169 APPENDIX G THE CYCLIC PATTERN 0F HEIGHT GROWTH AS DETERMINED BY THE DEVIATIONS FROM THE STRAIGHT LINE, GIRLS Age 1:! Month 0 1 2 3 h 5 6 Case 25F —1#.8 — 8.2 28F -18.1 -13.3 ~ 9.2 - 6.2 37F -1103 " 8.2 " 802 59F -16. 9 -1203 - 708 ‘ 503 66F '16. 8 “In-5 ‘11-? "' 906 - 902 67F ~21. 3 ~19.0 ~16.6 ~14.3 ~11.3 72F ~16.8 ~15.1 ~12.2 ~10.5 ‘ 9.2 75F ~15. 3 ~12.8 ~10.9 ~10.5 - 7.9 - 7.7 ‘ 76F .19. o -150, -114.“ -1302 ‘1109 '1000 83F -17.0 -16. 2 -1n.5 -12.u -11.9 - 9.57 * 88F -22.2 ~16. 7 ~18.8 -10.3 ~ 8.0 * 94F ~12.1 ~ 3.8"' 96F “1503 - 90b 97F ~1H.9 ~10.0 °*111F -16.7 -12.5 -12.3 -1o.o - 8.9 - 7.8 117E ~20.0 ~16.7 ~lu.5 ~14.? ~13o5 ~10.7 120F -19.1 -16.1 -13.9 -12.0 -1o.u -1o.o 126F “19.6 ‘1“09 -1200 "' 90h "’ 702 "' Sou "" 505' 127p “1605 ‘1505 “13.5 "' 607 " 603 137F ~72.5 ~18.9 ~16.3 ~14.2 ~12.1 ~10.7 ' 9.3 luOF -2u.2 -19.9 -17.6 -16.2 —1u.o ~12.u -11.o 142F ~19.6 ~14. 9 ~11.7 ~10.0 ~ 9.3 ~ 7.0 1H4F ~21.5 -16.2 ~14. 5 ~10. 9 ~10.1 ~ 8.8 - 7.1 *lusF -22.2 -18.2 -17.0 -15. h -12. u -1o.1 -1o.o *1u6F ~16.8 -15.h -11.8 - 9. 7 - 7. 3 - 6.1 - 5.2 IHBF -23.“ -2003 -1905 -16. 1 ”1308 ”13.1 "' 906 15°F -19.7 -17.0 ~1h. 5 -13.6 -12. 2 -1o.h 151F -1902 -1608 -130 8 ”1300 " 9.0 - 8.1 "’ 705 165F ~23.5 ~18.1 ~16. 0 ~1u.u ~12., ~ 8.5 170F -21.6 -17.5 -13.6 -12.6 -1o.o - 7.9 ~ 6.2 *171F ~21.“ ~19. 2 ~18.“ ~14.0 ~11.8 ~10.2 ~ 9.1 176F ~21.8 ~19.0 ~17.l ~14.9 ~13.0 ~11.2 ~10.1 179? -1909 -1602 ”1305 ‘1006 " 8.“ - 7.6 "' 701 182E -']-50L‘V - 9.“ - 705 - 701 -' 507 .1855. -18.“ “lac? -1301 -10. 7 "' 903 " 707 - 7.2 188F -22.9 -18.8 ~16.9 ~1u. 6 -13.6 -12,u -12.o 193F ~20.9 ~18. 7 ~16.1 ~13.6 ~12.2 ~11.3 20hr ~20.3 ~15. 9 ~13. 2 -10.5 - 8.9 ~ 7.1 - 6.5 205? -21.u -17. 3 -13. 7 -1o.7 ~1o.7 - 9.“ 211? -1809 -1701 “13. 6 -1105 -1003 "' 8.0 " 70L} ZluF ~17.6 ~14.1 ~12. 5 ~11.1 ~ 8.6 ~ 6.9 ~ 6.1 02173 -2000 -16. 8 -1208 “12.0 - 807 - 707 - 702 22°F .21.? -170 5 ~14.8 ”1207 ”1003 "' 905 " 803 221F -1703 -1143“ -1201 -1001" - 909 - 805 '- 707 gpgflLsa 1 6§%%§%awfi§'ta—a5aaaa—arrfarIa“165465f5rfirfiffii'fiiarggf ' 'Where cycles occur according to first criteria. "Whnnn nvn1nn nannr according to second criteria. - Lanna“. m» ...: .I...4......r. .. ......vfi II‘I.6.4I?!'(‘ 10 " 503 b 4 143 2 9016175015575 471 7 694 2 I I I I I I I I I I I I U 4 4 255 322L222L2 L3 2&4 1 2 _ . ... . ....._.___.._ ... . ... . 7.94.434 04 23 5.27.8 16.20.0.8.U.5 £249976.22226. 5233538 I I I I I I I I I I I I I I I I I I I ”M 22223653 55 2542 7LL46343 1212 241L334 2531122 ........ .. .... ........ .._.__...__. ....... O 1 1 0 I I I I 1 7 4 6 4 1 _ _ . . 86 90643 30 046158112 63936289115203139 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 43 25763 46 3147435 4 34136224456264223 __ ~...—._+........__~.__._.— 1% .4 183.50.6—J1n/o I I I I 3536QM73657 _-...-.-_ 5 .4 _ abu6695803918829883 .nI/onw730.n/.R.Nn/.9n/.3 5&Rw3259m57n/o37n6562hW/mhwo 5.8.7nlo3/O.5235n4. .......-..._..-...-_.____._._ APPENDIX G -— Continued 0 08557 7 39 6 58 1 0 I I I I I I I I I I I I 5 83769 5 56 6 52 4 6 _ ...__ . __ . _. _ . 502 402785 8818 162 357.15 30711 I I I I I I I I I I I I I I I I I I I I I I I I I 7 58m 97336m 7386 746 N5888 86356 ... ...... .... ... ..... ...__ mn S E t FFFF FFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF en 5879fl7256fiT84671706770245680150169258134514701 &% So 2235667778889991122234444445567777888990011122 TY AM 1111111111111111111111112222222 OC . u. M o. . . o T m n «w I 5 0260 3 1078770439 13563855350 88419531 2 _ 1H APPENDIX G ~~ Continued 2 1 11111.L1 2.111L.&l.L0 121 + +++ . +..+++_+++ +++++++++++ _+..++++ 3 9 T 9 I I I a. 0 1 + _ _ .8 $ 6 1M1 40 353 5529628234 0463064619483413 5 .1 10 12. L1 11 LiiL 1.. L0 1 2LL&...L.L.L1 _ + ... +. ... ._++_.+.++ ++++.++.+_.+..++_. 7 26 6 1 8 3O 1 1 .1 0 +. + +. .+ N I I 6 0 37 08 381 O 310 3633424927598495 526 I II II III I III IIIIIIIIIIIIIIII III .1 2 2 41 14 1 2 1 12 1 12 11 . .. ._ +.. + .+. +.++++.++......_ +.. :5 5W543195 14 735 3032fl7807k44817 18895WW3140 IIIIIIII II III IIIIIIIII’IIIII IIIIIIIIIII 11 3 1232 32 34013312 11 1 3 2113 31 12 ..._._.+ _. ... +_...._._+_++.+ ........+_. 4 0 23 4 9 2 7 9 7 1 2 3L . 3 . k L 1 _ __ . . _ . . _ .mh S E .ueFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF ena5879$W2562384671706770245%80150169258134514W01 AW So32235667778889991122234444 45567777888990011122 TY AMnu 111111111111111111111111222£222 DC I .. M .. I . o T 3O . n .. . l. 0 . 1 q I... .8. ... ....8.a.t...|_lk Ct {H.511}. .vr .. 8 I 8 8 8 8 3.011... 1301015217557.483332305540“ “(773623.217964973h.“ 2 $422 LalkaalLLLaakalzlallklliamllMLiKLkl24443 ++++ +++++++++++++++++++++++++++++++++++++++++ Av AllaLaL1MlZML LLLMlaLLkakall&%llklk&1kl l 2 +++++++++++++ ++++++++++++++++++++++++++ + 7999n|munl793 ”.3. ozwmuvnvh062756047w31oozw0u6216 019 Mm lL&LL.Ll Lk la.llaLlLlllallalalkalaLklal l. ++++++++ ++ ++++++++++++++++++++++++++++ ++ “ u 8 172 APPENDIX G -- Continued —- Mm &.L&L. L1&L&..LLLLllelLllLLlLLlLllLlLLlAL&&&. ++++++ +++++..+++++++ ++++++++++++++++++++++++ 3 2 u 8 8 8 8 811149 95 043681375865048746254257889 199 a 2 LIL .L L L&&&.&.L&&L&L12 3112 .1 21 ++++++ ++ ++_++++++++++++++++++++_+++ +++ 35w P 6 8 I I I I I I M“ 111 1 1 +++ + + + mh s +u FF FFFFFFFFFFFFFF FFFF F F FF FFFFFFFFFFFFFFF E en 58W96725623846717Wfl7702W5$8W15W169258134514701 u% 80 2235667778889991122234444445567777888990011122 TY AM 1111111111111111111111112222222 00 v I. m 9* I I o T ..- 48 r, , .. . . o . Er...l8n‘wx...k.n.c I‘I.'I-nru¥ll.brf . 13 404874335131057810112 889920068301571838710 35 24543545M45535434455M M5MM55543347545554354 ++ +++++++++++++++++++++ +++++++++++++++++++++ 45 88 u 8 88 u 8 '8“8 8964448794624 66460 60 021648148084 2 2M113M31555M3 111M1 44 M53M5M4M1MM1 5 +++++++++++++ +++++ ++ ++++++++++++ + 42 I 8 8 8 8 8 8 8 8 8 8 1/00849026851u5581592/00 Win/62053919580879.“ ASK/95132 2 3522244354543443443444445454544453347544444443 ++++++++++++++++++++++++++++++++++++++++++++++ é; ” 88 8 88 '8 8 9388919005878 969957655266632697658336 25321M31111M1 2MM1M11M11MMMM541M1MM143 +++++++++++++ ++++++++++++++++++++++++ N3 36 16678W2®35925509562299793610143584016173562 2 35323342432423M233443332544535MM13MM1M34444 M +++++++++++++++++++++++++++++++++++++++++++ + APPENDIX G -- Continued 061 07324 189 @6025W747287392261F423P8 9 0 9 WW 351 11M11 11L 2114.M1212MM4.M1MMMM1M111& 1 5 2 +++ +++++ +++ ++++++++++++++++++++++++ + + + u 888 “8 813923103938 9205347237880 45774331321 w” 253324121111 1111111113111 11111111111 4 ++++++++++++ +++++++++++++ +++++++++++ 1h 8 t eFFFFFFFFFFFFFFFFFFFWFFFFFFFFFFFFFFFFFFFFFFFFFF ME .;u85879672562384671706 70245680150169258134514701 L 26 a2235667778889991122234444445567777888990011122 Tm AMnu 1111111111111111111111112222222 0 I II m II I I 0 TC “9“ N4 APPENDIX G -- Continued _ 2.....1: I .2 ...... ....fii..- 5 0465322459250396772.6.0.537.2 w, 1 4453556434536623561161641 + +++++++++++++++++++++++++ 53574W149348 86WW9775P9M17709835568092487153 IIIIIIIIIIII IIII IIIII % 123344455643 3662356455354464453245555553445 1 ++++++++++++ +++++++++++++++++++++++++++++++ 1 983443736 262258258369052 M. 2 241115642 31111M6M1111545 6 ... +++++++++ +++++++++++++++ 89748014148W 11m684158639351M38882364166635169 w 232335435153 453653456455464454444355555564444 1 ++++++++++++ ++++++++++++++J++++++++++++++++++ 85 12381039 40224294W50794 84 m“ 24 11114113 61111111536111 11 4 ++ ++++++++ ++++++++++++++ ++ 5475663146D8 0317203069824M8M043486 1444689206 W. 11221M1M1111 1M1111M11MM6M14.4.111113 15515M4414 5 ++++++++++++ ++++++++++++++++++++++ ++++++++++ “8 n 8 8 8 8 328 419751693 34728622? 05672831 8 m# 252 4543551M3 2151MM115 M1MM1M1. 4 3 I++ +++++++++ +++++++++ ++++++++ ... Mn 3 t eFFFFFF F FF F FFF FFF F B an a587967mm)“.mwawwW17wwwwmwwwwwwmfiwlawmselnwwiuvw1 pf 26 a223566777888999112223 444445567777888990011122 Tm AMnu 1111111111111111111111112222222 O I I M II I I 0 TC TH APPENDIX G -- Continued ...“...dfl "v .. _ “For.” 1W.» Fwy. b I"“ .4v.....hoo‘..t‘. . - - - -II n - 906803901918090 164502455743977144013199471312 % 11 L22L1 ..LllL 221221 .L. 1 1 111 22 1 1 4 1 +.++++++.++++++ ++..++.++_+..+.._+.+.++.+..._+ 3315997071220077853556970305655303635573451115 M 2 .111L2 .2L1121 11.L13.21 1.LL 12 .1 22 2 .L 1 1 +.+++++++*+++++++++.+++++_++.+++++.++++.++.+++ 06v83538747919868113818002W7574664461406991715 to I... 0000000 00000000.. %, 2 .L11111 22L11111.L11L11 21 LL .2134 31 12 3 at..._++++++++++++++++_+++++_++++++++.+++++++.§++ W4688849943202W9185881612476206589273831091093 % 1?.9341222343321341.11111.1LL2LL2L.LL11.1 113 3 ++++++++++++f++++++ .++++++++++++++++++++++ .+++ II - . 49J0348188229075378815908 59913939159114550397 M A1L .111111111111111L.11111 1LL11L11 1215L421 13 2 ++++++++++¢++++++++++++++ ++++++++.+++++++++++ ' ”fl. ' ' | - 1774418924113106612761132 46970971432604724JJ6 0.00.0.0... O O 0.000.... ”W 2L .1111111113442452 45214 1221213213335111L111 6 +++++++++++++++++++++++++ ++++++++++++++++++++ 3460106417116156685138944 01823096885622134100 .0C..........C..........C ......OOOOCCICCOCOOO W. 12 3443243542442452244234 33143322 23453541324 6, +++++++++++++++++++++++++ ++++++++++++++++++¢v+ Mn 8 .ueFF FF F FFF FFF E 2:“a58WW67H$6W384QWHWW®WWWflWfiMWWHWWHQWflWWHWWflHW7O1 &% 26 a2235667778889991122234444445567777888990011122 TY AM:u 1111111111111111111111112222222 NC I II m II I I o I. ‘1! 150 375798..”5bw17h30314 5u1785u5/IO 88h.07h.5817157h~..n5.29n/./O.2 O O C O ...... O C C O C C O . O O O .32L&. .L.L 3162 21 2123 1 L .2323L .2 +......+.+...+_ ..+._.... .++...._++_......+.. #5622 318816b16 5612662678178418461106769h39um M L .L20 1 112 2132 1 2 .L3L.11..L. ..L .&.L3 1 ..__. +..+++... ._._.++._+.++..++.++..._._.¢+. n m-.1 . u u - - an-“ fiflfiJfiJiLfifiMJJfiflflfi5179fifi93 8&513h7733h306102939 b w 1 1 2 1 3 11112 1 1 2 22111 1111212 31 1 1 .++._.+..++....+..._..... _.+._++_++..._....+. - - -nnum -uu . . 528k0534716388615927582137352291h9729910128322 R ..&.L..&&.L .3L53..&LL.L...LLLLLLLL..L.. L3LL232 1 .++..+.........+_..+.+.........++_.+........+. N6 53081810167017.45/IOJ271I“10.7.. 337-41.. 8.3/0. 1717969915 APPENDIX G —- C ntinued % .Lh 1 22 2122 .L2 .OL .2LLLOLLLOL .LLLLL.1L 1 ++++.++........+...++ .+. ..... +.. ....._..+. -u . nun - u - h971899036h5427 # “4779689640308h3798263h68582 m ..a..L.LL...L.. .02 ..... LLLL2.LL..L.L.LLL12. 2 1 +_+++++..+_+... + .+++.+._.._+..+__+.++.....+. h [1| .‘ n/..M.. 2 3395:489333 5334/an. 26378370 ZBuuMbw Ada/2518:4116 1M5 “mi Month 11 .LLLL1.0.L.LLLL2L1 1 11 1 .L .L .LL .L3L.. +.+++++..+.+. .+++..++_++.+..+.._+_+.++.+.+.++ eFF FF F F FF F F FF F FFFF eSBW96W2Wfl2FWh6W1WO®WWWZHWWWWHWWHQWWEWR3WWWH701 1223566777888999112223uhh4h45567777888990011122 C 1111111111111111111111112222222 . .. M 0. 0 9 o 3 NWM. CYCLES 177 APPENDIX 0 -- Continued 2 041452785456 99 940835909604343816 8341 0..0..0....0 .. 0.000. 00.00000... ..00 9 986816788808 70 760928765094622122 0531 1 22 1 1 1121 1 1112 11 2 1121221 1111 ...._...._.. .. ........_.._._.... .... 6 463223JJ892604J 12 291571115936J500 792225 00000 0.0.0.0000... 0 .0.... 8 6ML59M555475558 53761444376139089L 611831 122 1 11111 11 2 11 1 1111111 11 22 ............._. ............._.... ...... 0 4013644848411565572342966441989951544958106448 8 ML935LL321M2236ML9M3 .LLL2M3995655LL57L657M6680 1 21 1 11111 11 2 11 1 1 11 1 1111 11 ......_.............._............_..._....... 4 1712134JOJ2JJ43 695545016J832JJJ096647351024JJ ...... .0000... 0 ...-.... . 7 2751418L98L98 .3 8610 891LLL673MLL47255464L33M6 1 11 1 2 1 1 11 1111 1 ............_.. .......................__..... 8 6JJ294040250719 JJ8J0J8 82J3J44J84652950444J6J 00000 000.. ....0 0 0 6 .40 2 6 5686511 54 .5LM5OL8 .339L98L51332407LL0M 1 11 1 11 1 1 .....+.+.....+. ....... ........_...._......._ 2 7434379945459441742366905203144 63055409078129 .000000000. . . ..... 6 .08 .3 .3 .336322 433232231LMLLL6 6L3 .L119748 .8L 2 1 1 1 +..+...+..._.+....+ ........_.. ...._......+.. 6 488228304JJJ641 4711077453656JJ6961716 204JJ06 ........ .0. 0000-..... 0 .000... 2 .4444.4n4..21 ”1 22222 22122 .2 22 1 22222222 2 .. . ..+_.. mmeFF ...—.++....__+_+-._.+__ ens58WFFFFFFFFF I _ 8 967.25 FF am2223526vwwwwww%mmmmwwwwmmwppp22222 s 223 68 F O 1 44 01 F .0 Ml1111111MMMU5fimn%W2fiflmflFFFF FF E .. 111111888994514W01 L # lulllm011122 TC 222222 O! 178 APPENDIX G -- C_ontinued Age in? i Number Month 198 204 210 216 ' " of Cycles 5588 257 -11.9 48, o ~18.o -2o.3 12 5 L1 28? -31.7 -36. 1 -39.7 413.6 10 3 3 37F -28.9 --32. 3 -35.6 -39.6 8 u a 591“ -11.1 -18. o -17.4 -21.8 12 6 6 661" -13.5 -16. 6 -19.1 -22.6 11 7 7 67F - 8.1 -10. 3 -1u.u -15.u 1o 6 6 75? -12.o -111. 1 -—17.3 -2o.2 8 6 6 " 76F -19.1 ~25. 7 ~30.3 -33.6 7 3 3 82F ‘2108 '2503 ”28.2 “3205 6 5 5 8315' ~23.5 -27. 5 -30.6 -33.8 8 2 2 * 885' -23.2 -26. 3 -32.9 8 1+ u " 94F 9 5 u 96F -1o.5 -13. 9 -16. 6 -19. 8 4 3 3 97F -13.9 -17.o -19.5 -22.8 1+ u 1+ °*111F 7 1+ 4 1175‘ -21.9 ~24.8 -28.4 -31.7 7 3 3 1205' -19. 7 -22.u -25.9 -29.6 8 3 3 12617 -13. 7 -15. 6 -18.5 -23.6 12 5 5 127? -33. 5 ~36. 2 410.2 ~43.1+ 9 3 3 137p " 303 " 50 5 " 903 “11.2 8 ’4' 1" 14OF -21.6 -2u. 2 -27.2 -30.1 7 a L1 1421? -21.1 -23. 9 -27.9 6 u 1:, 141m - 8.9 ~11. 7 —13.u -17.1 11» 7 7 “14517 - 8. 9 -1o. 9 10 5 5 *1461? -2125 -28. 3 -31.5 -35.6 8 6 6 148F -11.5 ~1u.t+ -17.1 -20.8 14 6 6 1501? -17.6 -2o.2 -2L+.6 -26.3 7 2 2 1515' -18.8 -22. 5 ~25.8 -30.0 7 3 2 1651“ —25. 3 --29. 6 -32.9 ~36.5 11 1 1 1701? -15. 6 ~18. 5 -22.3 7 2 2 '1715' :25. 9 ~29. 3 -33.3 ~36.u 6 3 3 176? -25. 7 -30. 3 ~32.3 7 5 1+ 1791? -15. ~19. 0 5 3 3 1825' -22.0 -2L1. 9 8 3 2 “18517 -112, o -16. 6 10 4 u 188F -17.9 7 4 u 191? L» 2 2 1931-" ~14. 2 8 3 3 041-" 7 3 3 05F 3 2 2 LlF 7 3 3 145' 5 3 3 L7F‘ 6 4 1+ 205' 5 2 2 ZIP 6 2 2 2 0002020 2 2 24202 0.0 : 0.02: 2.22: 2.02: 0.22: 0.22: 2.22: 22220 2.2 0.0 : 0.0 : 2.02: 2.22: 0.02: 0.02: 0.22: 22020 2.2 0.0 :_ 0.2 : 2.22: . 2.02: 0.02: 0.22: 2002 0.2 2.02: 0.22: 2.02: 2.22: 2.22: 2.22: 0.02: 20020. 0.0 0.2 : 2.2 : 2.02: 2.22: 2.22: 2.02: 0.22: :0020 2.2 0.2 : 0.02: 2.22: 2.02: 2.22: 0.22: 0.02: .2222 2.22: 0.22: .2.02: 2.02: 0.02: 0.22: 0.02: 22220 2 .02: 2 .22: 0 .02: 2 .22: 2 .22: 2 .22: 2.22: 22020 2 0 0.0 : 2.2 : 0.02: 2.22: 2.02: 2.22: 0.22: 20020 2.2 : .2.02: 0.02: 0.22: 0.02: 2.02: 0.22: 22020 2.2 ...0.22: 2.2 : 2.02: 0.02: 0.02: 2.22: 0.22: 22002 0.0 .0.0 : 2.0 : 0.02: 2.02: 2.22: 0.22: 2.22: 3202 0.02: 0.02: 0.02: 0.22: 0.02: 0.02: 2.22: :0020 2.0 2.2 : 0.22: 0.22: 0.22: 0.22: 0.02: 2.22: 22220 0.0 0.0 : 0.2 : 2.22: 0.02: 0.22: 0.02: 0.02: 2002 2.22: 0.02: 0.22: 0.02: 0.02: 2.22: 2.02: 00020 0.0 : 2.2 : 0.22: 0.02: 2.02: 0.02: 02220 2.0 : 0.02: 0.02: 2.22: 2.22: 0.02: 0.02: :222 2.2 : 2.0 : 0.2 : 2.22: 2.22: 0.22: 2202.0 2.0 : 2.02: 0.22: 0.02: 2.02: :02 c 0.0 .. 0.2 .. 0.2 ... 2.2.2.. 2.22: 0.0.2: :22 0.2 : 0.2 : ...0.02: 0.2 : 0.02: 0.22: :20 .. 0.22: 2.02: 2.22: 2.22: 0.22: 0.22: :20 2.0 2.2 : 2.0 : 2.02: 2.22: 2.02: 2.02: :02 0.0 0.0 : 2.0 : 0.22: 2.22: 0.02: 0.02: :22 0.22: 0.22: 2.22: 2.22: 0.02: 0.22: :22 0.2 2.22: 2.22: 2.02: 0.02: 0.22: 222 to 0.2 0.0 : 0.02: 2.22: 2.02: :00 o 2.0 : 2.0 : 2.02: :20 c 0.22: 0.02: 0.02: 2.02: 0.22: :22 N.le :02 t 0000 0 0 +2 I n N 2 o 2:21 0200 . 0 Wm QHZHZNWBWZHA gflHémm EB 20mm CA W APPENDIX H - Continued 1% O “(D m m N . .. O O H N (“H m + II I ' \O .0...-... 0.... o 0 0.0.00. H H 33H W H NI-I-‘fI-‘I I—l Hm I-IN NN Il"'.'|l ||I+| U IIIIII'. 8 C - 33HHMWNH3 \OHChr-l ONmmmWHWNWW NHCDCD m o o o o o o o o o o o o o o o o o o c o o o o o H N0N :dNNm N 5 0 H0MNN'M2H MNKM H IIIIIIIII I+II IIIIIIIIIII IIII ; 3 0 m 2 3 2 2 2 H 0 H N N 2 2 d H I I I I I I I ; ; - m 2 NO\ 000 HON 00 In 202 2 200 00 O O O O I I O O O O O O O 0 O O O I I H N MN 2m 0Hm mN 02m N 0mm Nm N I II II III II I III I III II c. - - - - N mwmzH M0002202NN02MNH0m0imm2i0m H mdMM2 MNmmdNN$50 50fimdNéfifié£Nn£ H IIIII IIIIIIIIIIIIIIIIIIIIIIIII ; 2 n o m m m o H o o o o o o o H H m 0 a m w m a I I I I I I I o 4? 2H: 0 0N222mHHmo20 :H'V‘m—Ico =H\ O I O O O O O O O O O O I O O I O I O I O O O C H 0 2w: 0 NdN2a220mmza 02:00 00 I III I IIIIIIIIIIII IIIII I: m 2mN¢m0NH omomeflidwNmmm m 00 O I O O I O O O O O O O O O O I O O 0 I O I O 0 0 m0mmmm:2_2m0nm:2:0200mm 0 m2 IIIIIIII IIIIIIIIIIIIII I II 5.0 0 pozzzzzzzzzzzsz 2222:2322 :zsxzx: 0 onmomde22deNmN52anmd02oE22om0m2 d8 tm:«Hamm2222mmmmoHHMMdmmnn0022mmmmm BM 42b HHHHHHHHHHHHHHHHHHH 00 t to; t #3 co to 0000 03 00 a mam .' 28 la - 'O :- . m o22® 2:0 QONnNn2Hadm20mNamn2m 5 2H'H 242 §22&'N2222522'242222 m + ++:+ +++ ++++I+++++++++++++++ % I- 22NMH0Nmon on:omo:mm0m20mm:dom H'N'HHHHNH MNHN66'°H5NH KHNNNH H +++:++++++ +++I+++++++++++++++ 2M . u - - ' \OWMHQQQN \OOWHOMHWHH-iQ’ONHNQNmr-Inm dNéfi'°°°02222'22N2'22fi22'22'2" 2 +++::+:+ ++++++:++::++++:++++++ 23 I-l Bfib-fi-‘IWNQOMNH-‘JNOMMWNHQOO \nlfid‘ APPENDIX B - Continued a '4. . . . . . . . .H. . .N.(V.H. .4 .AH. .AN.H. r; . . + :+:+:++++:+:++II+++I:++ +I+ “N n \0 H5 ° H ++ + + o -- g - O O . C . . . . . . . . . . . . C . . Q . . O 8 N H HHO HHOMNHHH HN OMHH H + I 'lll +I I+I|I+|*'I+ I+ll H O\ H + 8 s I a: I: .- Ho~m®m2d¢02NNnddHH232m MN MNQHHH g NHH'dHNH’HfiH'fiNH H HN NN m I+IIIIIIIII++III+IIII +I +IIIII 5: 0 u no 2: 22:22:: 2 S 22: :2 S o a 0§§§22§§0222022§2EE2§020§22§§§2§ is,” wo0Hzmm2222mmmmoHHmmzmmmm0022mmmwm a“ «z HHHHHHHHHHHHHHHHHHH 00 t #02 t :3 co to 0000 0% co 9 .51 1% d - . 04; \O“\OmeW-L‘TCDOHFOHHBONNHWNnNW-d' um mm:HNndmmdmmmménmmmdm0nmnm ++ ++++++++++++++++++++++++++ 1+8 .08 VM0MNmno2oéimNd02mm3mNNo2mmm®mH «mmm dNNMWWMN:M#MMmm203mem3Adm 3 +++++++++++++++++++++++++++++++ 45 C. - - - - :0dm:ONmm0N00NN0zm00202moommom I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 02MMH2mNd¢mMN2mm323mzmz 0000:: In: ++++++++++++++++++++++++++++++ 2223020022232222022000202202222 mmmmHMHNiWéMMMMMéM£MdW3W333393d +++++++++++++++++++++++++++++++ NM“ 3 43 8 u u - I- 8 com:Hmnm0an0nm20man0N0:HNHO02¢2 . C . . C . . . . . . . . . . . . . . . . . . . . . . C . . :mMMNMH JadmnmNN2mmmz0m2mmadaém +++++++++++++++++++++++++++++++ APPEND IX H - cohtinued 36 mmmfld’d’NmOWWMHHOBr-IWHWJQWWNHHN H-fl'CD N3 ("(\1 HMI-I HMM-fl' MNSMHMNMNMJ' manafidmmm +++++++++++++++++++++++++++++++ 3h ' ' - -- - C - - . . . . . . . . . . . . . . . . . . . . . . . . . . C . . . ++++++++++++++++++++++++ ++++++ 32 - 8 o 8 q. n '- . NBCD QiWOBmHmHm339mW®WEH®N®®OH00 “<04“; M NNF§6;F:03NN NNNr-IM oMCJCGMC‘WM-‘fflm I++++++++++++++++++++++++++ +++ \ 30 :0 41m - - - - 8 - - ammmmodemHHo 0020002M22mm2 M'HHHHKNNN': N'NiNmeNdfiNN I++++++++++I+ +++++++++++++ 1 ‘++ Month Age in Case Wm WM Wm &M 177M 186M 9M 197M *um “9M * 54M ° 55M 0* 71M *mm 92H *%m O”102m 112M Olluu °135M 138M *1u1M °153M lshn 156M 0157M 0160M 0167M °17uu 0180M °*183M 018 O mmm CYCLES 183 2 “ifigéfivzl‘mfi‘t‘iczdd$fi°flfi°€~9fi§9~ew3¥m w«mndem2wnémnmN0wam:mmMMdeHm0 2 +++++++++++++++++++++++++++++++ - ; - - ; a -s 0°fi 333339333333333?333333333939 [\ m3 N“mammddNMMNm-tmmdmimv‘IMMMd’Nmm 3 I ++ ++++++++++++++++++++++++++++ ; ; 2 - ; -; ;:;;- -- - 2 313N3fi315 §33333333993339933353 o-H33m33m30 :NNdmmmmzzmnmmmamdmmn m +++++++++ +++++++++++++++++++++ M OMNNF‘N fiNd’HijI—IOW‘J‘ 0\ g 3 5 500502 0&805050200 d a + ++++++ +++++++++++ + 5 p :- - g 0mmmoodmn 3:8230Hm20Hom0222 NnN " 3 222222222 02222022000220000 220 2 { +++++++++ +++++++++++++++++ +++ -- 2- a- : :2 i 33§31993399333393333 Q \o m mzaNd200mmmz0d20n0mm 2 m + + ++++++++++++++++++++ APPENDIX H 8 - ' - u - 3 - - \ONQBWWMNWWONQ NOCDN4TO (fitnmxn2Na3mand'r-I . . I O C . . . . . . I . I . . C . . C C O . . O . O C C C . .3m3m33m2020Nnm22230mmmmm0m00:p0 m +++++++++++++++++++++++++++++++ 8 - - NWWNNOQNQJMNNWNQONWO‘Q O o .5 222220222222222202222 2 2 +- +++++++++++++++++++++ + :12mmMN0Hm023Nnmmmn2ommHnmmNmo:H :idaNédNdfiimfifiififiidnfiifiidfiifimmfim m -t++++++++++++++++++++++++++++++ a 212:::: : : :::: : :::::::: : cygde§25H§§§NNdm§H§§§2o2é2om0§2 #3 PI “M22220 mmOHHmm3000m0022mmwwm a» * HHHHHyHHHHHHHHHHHHH 00 I too I I3 00 o 0000 oo oo 9 t 1% 18h . = - VNNQWCRO“OK\H®O\H(\\ON:T\O ®M1\00\U‘\V\\O®\Od b-C's 0 I O o o o o O 0 O O I O O O O I 0 N31“. N Hr-l HN &J H°J&'44 J :H HI++|+I+IIHI++| ++IIII+IIHII R ' O - - MMNOWNHOON¢¢WOHITN :rtxaodoooommommatx . . . . C . . . . . C . . U . . C C . C . C . . . . NMNHN' MN m HH J: NH.H N H m. lll+++‘fl+lllll++l++llll+ll+lll 126 momodmonomo OWNWONW MQNHHHB3MOW\d—‘3 (GAFJCGAJFI 0&030 OF; C 0.3. O “qr-z O O 0 0C; 0 Cd(\: 0“; III++++I+ I+II++I ++|III++I+I++ 1% - - ‘ . . . C . . . . . . . C . O O . . . . . . C . C . C . . O . O -H N-a’HH 3Hm H3" HF‘N HHMI—IHHC‘J m II++++++++|+|+++|+++++++++++I++ Continued 11h I I 0 I 8 :3mmammmwmnzwmmunnamNMdnHmmoamo O O O O O O O O 0 I O O O O O 0 O I I O O O O 0 0 O O O I I O H Haamaazaaa a: HdN dNHNHHM II++++++++|++++++++++I++++++|++ um “\HHQNOOM$RM®QNMW®W®WNF\H® NOdOH-fl’ UN ' mm56fi&éa'é°d§fi mid§ &édddd'&d u+++++++++n++++++++++u++++++|++ APPENDIX H HR - D I 8 g '- uammmwoammmnaomwamomam:Hmaamom: mmm:mmzmmaamm&:aammmaammnmm §$ +++++++++++++++++++++++++++++++ 96 90 mr-IWBEMCDNO\N;\3\O aRO\H4'E)6\l\C'\OU‘\BU\O\CO‘-fi0\r\ c6mmfiifi§5dda§§mmd§£3Nmé&&mddfié&fi '+++++++++++++++++++++++++¢+++++ C t c- all g, - \oodmmom33Hmamnmozmmmmmmncowommm c6&mmm$fiaodm&Jdfin&mnfimadfln&&£&di +~+++++++++++++++++++++++++++++r T Age in Month Case =222222222222222225222222222222§ cygzmaaumadmwmmdmm Mdmmomzuommm r4 numummmmmmoaammahmmnomummmmwm HHHHHHHHHHHHHHHHHHH t: to: t #3 co to 0000 o; oo 3 CYCLES TOTAL 192 185 OOJ333W¢NCDO CON“\L\O\\G\OO\OU'\-do HMHWOO‘d’ fi&&'&&'difig 'J'°di&&fid& ifi'&§fi' III+IIIIIII +|+IIIIII++ II+III+ 186 : mmao HammaommmmmmmmdmmmmoaoHmoo . . O . I C . I I O . O . C . . . . . . C I . C I :HH wwmg' '4 mHHHHNNJmHH &mm lll+ +IIIIII+++IIIIll+++ll+lllI 180 oiwoamm:Hmommmummmowwmmm;:naamm &4°&fi'°fi&'&'°d'°&'é 'JJ&64"6J5 +I++++IIIII++++II+II++++II++III 174 mm mammmamommmNMdemmmémawmmmam I I I I I I I I I I I I I I I I I I I I I I I I I I I I m an HN o- N HHH H HNWN m J +| +++IIIII+I+III+II+I++IIIIIII 3. =3 8 on mmmwmmm:ddmwmnmmmmo mmmmmaow APPENDIX H - Continued {(3 " '2 '2 '2 '22.: '22 '22 3:20 '2222 '22 ++ ++II+IIIII+II++II+I +IIIII+I - ; :2. ; ; ; ;:E: - N fi?fl€99fifi%§fiffi9ifi%iffi€222%fifii29 ‘3 HN 3N 3N :MHNH H NHdN mm3m : +II+II+IIIIIIIII+II+IIIIIIII+I 156 x: : NI“\\OL\C'\NU'\I“\O\K\\ON\OO OQNWBMNfiNfimeN®F\ I I I I I m NN mm NMNNH H maaamd d III+IIIII+IIIIIIfIIIIIIIIII++I 150 8 8'- 3- 8 -8 mommommo:ommmmammmmmmmmmmmmmmmm IIIIIIIIIIIIIIIIIIIIIIIIII.IIIII maaaam NHN mm:a NH NNMHNHNJNH m IIII+IIIIIIIIIIIII+IIIIIIIIIIII #4 8 = - 8 . {\COMCDINb-NU‘IMCDMNOwaOWfi r-ICDOONVDIDLNGDUNNO‘RO o o u o o o o c o o o o o o o o o o o o a o I o o a I I o o Md!“ r-Ir-I m H Nam r-IN H MNr—IN r-INHMc-IN I I l I+ I I I ’I I'l’ I I I I + I + I I I I I+ I I I I I I Age in Month Case 2222222222222222222222222222222 omdmadmwadmwmNimmam30uouénomwmn Admnmmmmwmmmodamninnmmmwmmmmwmm HHHHHHHHHHHHHHHHHHH I #02 t :3 co to 0000 02 oo 4 TOTAL CYCLES 186 .wfipmpaho uncoom on mcfiumooom havoc mmaomo @2923: .wapmpfino pmpdm 0p mcfidpooow Laooo mm202o $2023. .wmaomo wcficfiEAopod you mfinmpapo uncomm 0p wcfiopooo¢o 2 2 w 2mmao N N N How I Smmflo 2 2 m m.2HI 2oma W m m N.\. 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L vodcdpcao II b XHszmm< ”a v 197 NmH ONH mm :m 2 ma \1H90uouucomm< mandodccmaq< nmsoo wcdnooss pw>oh poanmom cm 20 H moH mm mm SmmH Nsopomucomm< mapaoa6cmmg< swdoo wndnoonz Am>om pwaudom HBOpomuzomm¢ mfipfiofiucman< nwsoo mafiaoo£3 ho>oh pmthom owH hammmmmmmmmfl mauaoaccmug< nwsoo wcamoozz Am>om pmaumom NQH dHH NOH no «.63 hmmwmmmmmmmfl mdpfiofiuqmoq« swzoo wcaqoosx hm>mm pmaudom NQH mm mm zmwa Hmmuooccmmmd mflpfiofiuzmaa« nwdoo madmoonz nm>om umanwom :aw Nu MH MN m :0 H Macaomuqmmmfl meHOfiochn< swsoo wcdmoon3 Am>mm umapwom wHoho a adsoHHOh no 09 m30d>mhm unpcoz w manna: monogasooo no mm< cum wasmna 0Hoho mo Hapoe masque no moumnnsooo mopdoaUCH omwo Susana unwaom weapoogg< mapdmmom agapodm Umdndpcoo II b Xanmmm¢ 2 El! . ‘ 198 me mm Smma maopooUComm< mapHOHochR¢ smsoo wcdmoosz no>ob pmapoom ::H meH hEopomocoaa¢ mdpfiofiocmma< nwsoo mnfigoons ho>om poflnoom \II» QMH :m mm : SowH mEopooocomm< mdpflodocmooo nwzoo mcamoosz no>om poanmom macho o mcazoaaom A o 09 mg 0H>ohm mnpcox 0 Canvas monoanOoo no om< Una assays mmaoho ho Hdpoe Gauche no cosmhudooo mopdoaocH ammo spzono psmmmm mcapommu< handmmom muopoom doflcdpcoo II h NHszmm< BIBLIOGRAPHY Abernethy, Ethel. 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