"‘1?

DESIGN. CONSTRUCTION. AND '
CALIBRATION or A SIXTY-INCH
INTEGRATING SPHERE PHOTOMETER
THESIS FOR THE DEGREE OF M. 8.
Walter Alfred Had-rich

I932 '

 

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DESIGN, CONSTRUCTION, AND CALIBRATION
OF A SIXTY-INCH

INTEGRATING SPHERE PHOTOIETER

A Thesis
Submitted to the Faculty
of
iichigan State College
of

Agriculture and Applied Science

by

welter Alfred Hedrich
Candidate for the Degree
of

master of Science

June 1932

 

{HESAS

ACKNOWLEDGMENT

The writer is indebted to the members of the Department
of Electrical Engineering and Engineering Sheps for their
worthy seeperation in this project. He also wishes to express
his gratitude to members of the Department of Mathematics
whose services have been invaluable in the preparation of the
theoretical treatment of the subject. For the generous
Opinions, advice, and criticisms contributed by Dr. J. E.
Powell and Dr. I. S. Kimball of this department I am partic—

ularly grateful.
ly gratitude is especially due to Professor L. S. Foltz

of the Department of Electrical Engineering for helpful

criticisms and generous attention in checking the manuscript.

'0 A. H.

 

ENIII II“. - , h ., IIIINAJIWIIIIA

CONTENTS

Introduction

General Considerations

Theoretical Considerations

Design and Construction, with Photographs

Photometric Uses and Methods

Calibration

Page

10

57

68

80

 

c. “€3.1"35rw i»?!-fi.'.§fl_ I .. .
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Gulf

 

This thesis comprises the design, construction, and calibration
of a sixty-inch integrating sphere photoneter. Unless otherwise indi-

cated, the expression "sphere photometer" in this work shall invariably

refer to the sphere as an auxiliary unit in the photometry of light
sources.

If the sphere photometer is to constitute part of the photometric
equipment of a laboratory, it is desirable to design and dimension the
sphere in accordance with the principles of laboratory precision and
commercial practice. The features incorporated in the design of this
photometer afford the possibility of photonetering over a wide range
of luminous intensities as associated with various types of commercial
lamps and lightinr units. The sphere must provide for rapid handling
of lamps in quantity tests. As a mechanical unit, it should be suffi-
ciently flexible to permit ready replacement of parts, ease of convey-
ance, and should combine lightness with stabiliti.

It is the purpose of this work to attain a desirable balance in

the design, construction, and calibration of a sphere intended to meet

the requirements of laboratory and commercial tests.

. I I u. gun‘s-v.33}! . 1». 1' .I to . .EhaNHNflI I I-

o!‘

CU7LPBIJCXHYfIDLWD'ICCT‘

 

historical Development

 

Early determinations of total luminous flux from a light source
were made without the use of1ntegratiI devices. The point by point
method, consisting of the measurement of candle power of the source at
different angles in a vertical plane,Isas then employed. From these
candle power values the total luminous output was ob ained by sunnation
of the various zonal fluztes previouslv computed. The measurerent of
candle power at various angles in a vertical plane through the source

4.1

is still in vogue today, lar gely for the purpose of deterraininr the

.0
distribution of luminous intensity. The unsynnetrical nature of the

source makes it necessary to rotate the lanp about its vertical axis,

or to conduct measurements in a number of vertical planes throuch the

source. Very accur te results can be O“t91Pn8d by the point by point
method. Equally reliable results obtained through the use of integra-

ting devices have enpha51zed the lahorious aSpect of the point by point

method, and unquestionably “ ustifi ecl tlte use of the integrating sphere

photometer.

A nunber of photometric a: M ances were devised and used for ob-
taining the mea- Sihecical candle power of a lamp. They‘rere designed
to give t} Is I. S. C. P. in a single reading. Disadvantages inherent to
these forms of integrators and their practical linitations lead early

investigators in this field to turn their attention to the hollow sphere,

r. Ulbricht in the year 1900. At that

(-4

lThiCh was fix st investigated bg'

time Dr. Ulbricht was uninformed of an earlier publication on the dif-

fusion of light, which appeared in 1893 in the Phil. lag. and was writ-
ten by Dr. Sumpner. His photometric calculations revealed the striking
conclusion that the illumination on the inner wall of the hollow sphere
is everywhere the same, due to diffusely reflected light. Obtained un-
der the hypothesis of Lambert's cosine law of emission, this result was
the theoretical foundation for the development of the sphere photometer.
Apparently Dr. Surpner did not make Specific use of this important de-
duction, however, as applied to photometric considerations and particu-
larly to the problem of measuring the K. S. C. P. hy means of the hol-
low sphere. Contemporary investigators who did much to promote valu-
able experimental work on spheres of different sizes were Bloch, Corse-
pius, Karchant, Dyhr, and honasch. There has been very little change
in, or addition to the theory of the integrating sphere beyond that em-
bodied in the beginning treatment of the subject. much has been done,
however, to make the sphere better suited to pra tical application. In
recent years the sphere has served remarkably well in connection with
other methods of photometry which are quicker and more reliable than
the long established visual connarison process.

.‘

Descr'ntion of the Sphere Photoneter

General.

The integrating sphere is, as its name implies, an integrating
device. It integrates the illuminating effect of any source of light
mounted or suspended within its enclosing spherical wall. The latter
must be as nearly perfectly diffusing as possible. A small window of

diffusion glass replaces the equivalent surface area on the inner wall

of the sphere. Lccording to the theory of the sphere, if a source of
light be placed anywhere within the enclosure, every point on the in-
ner surface will receive both direct and reflected light. If a white,
diffusely reflecting, and opaque screen be interposed between the source
of light and the window in such a manner that the latter is shielded

from direct radiation only the illumination on the window will be due

9

to diffusely reflected light, and will be directly preportional to the

’?

mean spherical candle power of the source. since the total luminous

3
(”D

output of the source is preportional to the L . P., the brightness
of the window is a measure of the total lumens emitted by the source.
Probably the most general use of the sphere photometer is confined to
the measurement of this total luminous output, although it serves a num-
ber of other practical purposes which will be mentioned later.

The mathematical deveIOpment of the theory assumes an empty
sphere with.continuous inner surface obeying Lambert's cosine law of
emission. In order to realize a practical development, certain varia-
tions are unavoidable. They are caused by the necessary use of screens,
imperfect diffuse reflection from sphere surface, selective absorption
by paint, presence of non-luminous bodies within the sphere, imperfect
diffusion of window, position of lamps and luminaires in the Sphere,
inconstancy of wall paint, and difference in window and wall absorption
factors. These are some of the most important sources of error in the
sphere. While it is possible to minimize these errors through the se-
lection of suitable methods of measurement or the application of gen-
eral corrective measures to overcome such departures, it is neverthe-

less essential to investigate the order and magnitude of some of these

sources of error inasmuch as they may become appreciable in certain

photometric measurements. This quantitative treatment of the matter

of errors is discussed in the section on theoretical considerations.
C
screens.

The screen, unich is necessary for the proper functioning of
the sphere photoneter, reduces the illun‘nation on the window in two
ways. All direct light from the source intercepted by the screen rust
first be reflected from the latter before it can reach the diffusing
wall of the sphere. Hence this flux is diminished by an amount equal
to the screen absorption before it illuminates the sphere, from whence
it is reflected to the window. The screen acts as a secondary source
of lower intensitgu The screen also obscures a portion of the surface
of the sphere from the window; Light from this hidden area must be re-
flected to some other portion of the surface which re-reflects it to
the window. Such light flux reaching the window has suffered greater
absorption and in consequence the window illumination due to this con-
,onent is lower. Since the screen and the inner surface of the sphere
have the sane diffusing quality, that side of the screen facing the
window will reflect light from the sphere to the window and thus com-
pensate for some of the loss. By increasing the size of the suhere,

the screen error nay'be sufficiently reduced to render ibs effect nec-

[—1
Ho

gible. The ratio of screen surface to sphere surface is less. The
screen absorption is less in the sane proportion. Two other important
considerations in reducing the screen error are its dimensions and re-

lative position in the sphere. This matter is given quantitative at-

I

. c o o o 0‘ o "
tention in the discuSSion under "Theoretical ConSiuerations.

hon-luminous Bodies within the Sphere.

Included in this classification are screens and their -ittings,
lamp supports, lamp fittings, shades and reflectors. All of these will
absorb ,trt of the direct light from the source. The error involved
due to the presence of these bodies is materially reduced by giving all
non-luminous bodies except the source and accessories integral to it, a
matte white finish like that used on the inner wall of the sphere. Non-
uniform diffuse and specular reflection due to lamp shades, reflectors,
etc., constitute a departure from ideal conditions. This and other er-
rors resulting from causes heretofore outlined are minimized by follow-

titution method in photometering.

6’)

ing the sub
Sphere Paint.

The material used to render the inner surface of the sphere dif-
fusely reflecting must closely approximate theoretical requirements.

erfect diffusing quality,

\—

The latter demand non-selective absorption, p
and a unifO‘m and minimum absorbing power. Departure from these speci-
fications must be expected. Furthermore, the diffusing paint should be
permanent over a long period of time and not appreciably affected by
moisture or moderate changes in temperature. From time to time the sur-

face rust be refinished, as it becomes soiled due to collection of dust

,

nin should not be done over the soiled sur-

E“
Q

U)

and foreign matter. Refini
face. A sphere coating made up of a permanent oil base should form the

foundation for the finishing paint. The latter should be readily renov-
able when soiled, by the application of a suitable and quick-acting sol-

vent. It is obvious that such a finishing paint will expedite the re-

finishing process. It is not warranted, however, unless it possesses

d'

o a high degree the qualities prescribed by theoretical requirements.

*Vindowu

The window consists of an appropriate diffusion glass, which may

be located almost anyWhere on the inner surface of the sphere. It is
desirable to have the window flush.with the inner surface in order to
minimize the error that otherwise would exist through the discontinuity.
In practice, the offset is small. In order to facilitate measurements
with a bar photometer, the window is generally located so that the line
through its center and normal to the surface lies in the equatorial
plane. This position of the window affords greater flexibility in ob-
n

taining measurements with various types oi photometric devices. The

J.

window Opening is small compared to the inner surface of the sphere.
Glass used for this purpose must be uniformly'and highly diffusing as
well as non-selective in absorbing power. It is important that the in-
terior surface be matte, preferably of the same diffusing quality as

that of the sphere paint. The window error can.be minimized by care-

ful workmanship and selection of glass.
Kethod of Obtaining Photometric Balance.

Two general methods of obtaining a photometric balance are cus-

J." "

tomarily classified as the "Direr and Substitution" procedures. The
. - o o i .

former, sometimes called the "Direct Comparison' method, involves the

direct comparison of the test lamp with a calibrated standard lamp. The

nethod is simple, but Open to objection owing to the possibility of er-

rors which cannot be eliminated from the measured results. Although the

errors inherent to the integrating sphere become less as the diameter

of the latter is increased, the substitution method should be used to
insure maximum accuracy under the most unfavorable conditions. This
method involves the use of a third light source known as a comparison
lamp. It must be a constant source but need not be a calibrated stand-
ard. A standard lamp and a test lamp are interchanged as sources of il-
lumination within the sphere. Conditions within the sphere will then
have the same effect on the window illumination in both cases. This il-
lumination in each case is compared with the illunination produced on
the photonetric screen from the comparison lamp. The readings obtained
from the settings for photometric balance in each case are evaluated by
the application of the Law of Inverse Squares, whereby'the candle power
of the test lamp is obtained in terms of that of the standard lanp. In
some cases the scale on the photometer bar is graduated according to the
Inverse Square Law or in lumens. This is done to simplify the work.

The use of either method for the purpose of determining the H. S. C. P.
or total luminous output of the source, assumes a knowledge of the con-
stant of the Sphere as determined by calibration.

Then the candle power of the test lamp is much in excess of that
of the comparison lamp, the quantity of light transmitted from the win-
dow to the photometer head is reduced by means of an iris diaphragm.
This is, in effect, a variable aperture for control of the light flux
from the window.

Frequently the light from the test source and that from the com-
parison lamp show slight difference in color. In making a photometric
balance this color difference is a disturbing factor, often preventing

satisfactory comparison. Colored glass plates, known as color filters,

of known transmission coefficients for the ranges of spectrum over
which they are to be used, are interposed either between the window

V

—nd the photonetric head or between the latter and the conparison

$3

3

lamp. Color filters and iris dianhrarms serve to obtain a well de-

(-J

F

fined and reliable photometric balance.

IO

THEORETICAL COUSIDERATIOYS
Theory of the Sphere
Illunination Due to Diffusely Reflected Lith.

Let r represent the radius of the sphere. Assume inner sur-

face of sphere to give perfectly diffused and non-selective reflection,

and let L be a source of light of mean spherical candle power I

Let ¢ represent the total lumens flux emitted by L.

 

Then ¢= 9.". regardless f the candle power distribution of L.

It is desired to investigate the illumination at any point A on the

surface of the sphere.

11

Let B represent any other point on the surface, and consider
the differential element of area dB at B. Since ¢ is the total
flux from L, let 4.? represent the lumens flux incident on dB. The
illumination at B is 68.1% lumens per square centimeter (phots).
By hypothesis there is no specular reflection, hence let k represent
the diffuse reflection factor, where 1: is defined as the ratio of light
flux diffusely reflected from a surface to that incident on it. Then
AL - IQ represents lumens per sq. cm. reflected from dB. Since
the surface of the sphere gives a reflected flux distribution following
Lambert's Cosine Law of Emission, this quantitq,r represents the bright-

ness of the surface at B.

#:4d—L—ofl lamberts (emitted lumens per sq. cm.) and is the

same in all directions from within the sphere. Then
=- -—--k is the brightness in candles per sq. cm.

fi.d¢= 41¢, gives the reflected flux from dB, and the bright-

ness at B may also be formulated according to
fiz—L-ié’Wandles per sq. cm.
W 48
The luninous intensity of dB in direction B0 is

l . 1
50- =r‘d7§ *' ‘8: I‘d; * canciles.

Luminous intensity,r of dB in direction PA is

g4=#.d¢. i cad: candles.

The Inverse Square Lat-r gives the illuiiination at A:
E _ d¢ detect-4M;

— 8

A. ’74

lumens per sq. cm. (phots),

but datach ,

amt-hue”: _ 44H: _ dg-g
4-wh-‘Coo‘t " 4m.“ " .3 ’
wheres = 4V4} is the area of the sphere.

therefore EA =
'

EA is the illumination at A due to the flux d¢ incident on B
I

and once reflected. The expression for EA, is obviously independent
A

of 8 , and hence EA is the same for all positions of A. It follows
I

that all elenents of area on the surface of the sphere are equally il-

 

luminated by diffused}: reflected light emitted from. any; surface element

 

on the sphere and ore ip; Lantert's Cosine Law of T*l"‘10

That this is true for twice and multiply reflected light nay be
seen by considering the illumination at A due to twice reflected light.
Consider once reflected light at any point C on the surface of the
sphere. Some light flux from C will be reflected diffusely along the

path CA. From the above discussion, the illu1‘2ination at C due to

once reflected light is

54:5 —_é_d 4‘

A, 4a.”).

Brishtness of dC is 5: m3 latterts.
471%}
rig-£2

4,-2.4}.

Expressed in candles per sq. cm., 4 =

Intensity of illumination (candle power) of dC in direction CA is

_M. usOdC

41PHA.

13

Illumination at A due to twice reflected light is

g = 415' é‘ma-metc mots,

42 4,242. , [2.

Since 1 =24 (—0.3 a , therefore

E - d¢.‘a. Caste- 4-6:- dfif‘a’c - dfiiad/g nhots
42— 4173/21. 44‘cos'l- (41M? " _ 52 '

Since 9 does not appear in the final expression for EAL , the il-
lumination at A due to twice reflected light is independent of the
position of .A. éih‘ is the illumination at A due to twice reflec-
ted flux 436 from so. An extension of the above to multiply reflec-
ted light leads to the following important result:

All points on the surface of a sphere are equally illuninated by
diffusely reflected light emanating frem every infinitesimal element of

that surfac e .

 

The total illumination at A due to all light flux from L once re-

flected is readily obtained as
¢
t I S S
o
The total illumination at A due to all flux from L twice reflected

is EA =fljgg¢c=ongfd¢= f; '95

 

t 9 5’
tan—#55

14

The resultant illumination at A due to an infinitude of reflections

is %+%+%2+....+fi+..

n1
ll

—§.£(I+é+é‘+i’+ - - - 4—3;- )

i"
II

It is known that the infinite series within the parenthesis converges
for all values of k within the interval -/< k< I and defines the
functionf(‘)= ———for all values of 1: within this interval. In

"I?

practice, I: will always lie in the interval 0< *(I ;

H. ’ “ELL
6' /-é 4M‘ I-k

therefore, E = phots.
a A

Discussion of Results.

Introducing the direct illumination from source L, the result

is I Ice:

_ ¢ . é
REA—fifii— 4"} [-k pht.

The illumination at A due to direct rays from L is governed entirely

 

hy the photometric distribution of ligut from the source and its rela-
tive location within the sphere.

The significance of the expression E: ¢ * is at

M 4M at t-Ie
once apparent. The illuzitination at antipoint on the surface of tl‘e sphere

due to diff1-1se reflected light is directly proportional to the total lu-

nens enitted from the source. (Terfect Diffusion)

 

.f'_"_I_°_-_l‘;_ _
434‘ l-‘k A} 1-16

"Ie may write E
R A

15

from which it is seen that the illumination is proportional to the mean

spherical candle power of

tte source. If at the point A a small win-
dow of diffusion glass is inserted and shielded from the direct rays of
light coming from L, the illumination of the window will be directly
prOportional to the total luminous output of the source. Thus by mea-
suring the illumination at the window, either the mean spherical candle
power or the total luminous output of the source can.he readily calcula-
ted. It is liken-.r'se significant to note that RE". is tne sane regard-
less of the position of the source L within the sphere. In practice,
however, the source should not he made to approach the wall of the sphere
too closely; otherwise, the error introduced in consequence of later con-
siderations may become appreciable. A single measurement of‘eli‘ ,
carefully executed, is sufficient to give a very fair value of the I. S.
C. P. or total luminous output of the light source under consideration.
Certain refinements in construction and methods serve to minimize the
error within the limits conrensurate with the size of sphere employed.
The following consideration will serve to clarify'the simple re-

lations involved in the direct and reflected illumination. The average

illumination due to direct light from L is

I

The average total illunination is

 

 

_ _ I ‘ [0- I. I
TEN-5+5.- “/[T‘Trz+7?- A" ,..,., '

rnonyrnous with REA as employed. in the ahove.

H.
t!
3.3,
,.J
H.
O
:3“
D1
3
H-
(A
m
g A

16

Assuming an average k, for example, k = 0.80,

6R = I 0' 90 : 4—— A lumens per sq. on.

733mg

5‘ = + _1 ={—I'— llmens oer sq. cm.
TA! 4—41;

The average total illumination would be five times as great as the il-

fJo

lunination f the null if the latter Here black with a zero reflect on

factor. Again bv placinc; the source L at the center of the adhere,
1a a _ .- d ' .- ' . -..~° . ' 7d £ _. I.
the averabe irect 1ll\1.1nat1on wou- be .0" t

L is a source of uniform intensity in all directions, the illumination

and in the event

 

l

on the wall nould be the same at all points and equal to

t? :: JED lumens per sq. on.

U A‘—

Earring invisible radiation, the source supplies enerjv in the

 

form of visible radiation sufficient to balance the loss due to absorp-
tion. If a is the absorption factor for the inner sur ace of the

sphere, the total absorbed light fhxxzhs 95 , and the total reflected

 

 

 

O I.4 . I
flux 18 ’b~ . These deductions follow from elementary'considera-
ac
tions.
Light flux abs creed Light flux reflected
first absorption 4¢ First reflection (/— 4) ¢

Second " d(’ -a) ¢ Second " (I - a} ‘ ¢
Third " 4(I-aj‘¢ Third " [I 14):?

 

 

nth " 4 ’“dj "75 nth " ( I -a jn¢
cf +all-ay¢ +a[z-4j‘¢+--- 1- 1-4) ¢*"'
4% [I +(I-a)+(I—af' +- - - -+ (“‘91“)

Total absorbed flux

n H I?

ll

17

Let 3 represent the sum of the first n terms of the series in the

n
parenthesis. Then 5 = 4 _ _C_/ ‘19.)”
a ‘1 ‘L
4”” 5,, = Li/h—L— L/m M”
”*w $19004 19-“: a.

since (I—a}< | I I , Lim Milo

n-ND d ’

Therefore, [aim 5,, = —-’—
w-No 4'

Hence, total absorbed flux = 63¢ 0.1. = ¢
62

Similarly,

total reflected flux

(I-a)¢+ (I—a}‘¢+ - ~-+(I-a)“¢+--
" " " .(I-a)¢[1+(l~a)+(I—a)‘+---+(I-a)3.-]

t n u _ I “a
. ¢__a

The source supplies energy to overcmie the loss qb , which is constant

a Q -
as long

as the quality of the reflecting medium and the lurinous out-
put of the lamp remain the same.
The window in the wall of the sphere may have an area of A sq.
cm. The flux incident on the window is ¢~= ER-A .
96 := .Zifii.. 3‘ - .fflfi...___1£__. lumens
W 4M3 /- k 3 1-)?
Prightness of window as viewed from outside is t; .
5,, = £} 3‘ lamberts, in which I is the coefficient of transmission

for diffusion glass.

6..
t...

-S%}ir candles per sq. cm.

5 7(l-k)=

 

= K¢ candles per sq. cm.

4:? '4‘6- 16)

7'

h is the so-called constant of the sphere. The constant of the sphere
as determined by calibration can be formulated mathematically in a num-
ber of ways, depending upon whether the brightness or the luminous in-

tensity of the diffusion glass window is measured. It is neither neces-
sary to know or to determine the values of k and 3' , as these quan-

,

h as determined by calibration.

k1.

tities are ezhodied

._)

 

K : = {w , in which 61,, is expressed in candles per sq.
”I L .L.

4 ,

cm., Qb rrprcsents total luminous output, and I; is the K. S. C. P.

f light source.

5.73.111, Since I“: ‘6‘”. AW , K: i7“: 8 75% , in fizzITTiCh AW
‘9 0

is the area of the window in sq. n., and IL, is the normal candle

p wer of the window.

'4.

However, the constant of the sphere n:;'be calculated to conform With

the simple ratios -%1 , 4%"— , I" , I" ; whence it should be
. 75‘ I.

observed that the K's are essentially different. K may also be ex-

 

pressed as the reciprocal of these ratios. having obtained K by mea-
suring the brightness of the window as Viven by a source of known total
lumens ¢ , the luminous output of a test source May be readily ob-

tained as ¢t , in which g =K'é , where ‘6 is the brightness of

the window due to the test lamp ernressed in candles per 8 . cm.
A.’ ._ J.

Effects of Hon-Luminous Bodies within the Sphere

 

h

upon formulations Deduced under Ideal Conditions

 

 

‘

The presence of non-luminous oodies in the sphere such as the

screen, lamp fixtures, supporting devices for lighting units, etc.,
must have an effect on the uniform illumination produced on the dif-
fusing surface within, for these bodies absorb some of the direct as
well as reflected light flux. Point sources of illumination must be
excluded fran'the discussion, for all practical sources of light have

finite dimensions. There follows a discussion of the effect of non-

luminous bodies Within the sphere upon diffusely reflected light.

Hon-Luminous Eodies within the Sphere

and their Effect upon Diffusely Reflected Light.

Consider a non-luminous diffuselv reflecting body' h screened

v
I.

w

from all direct rays of light, and let the surface area of L be U.
Its reflection factor is K; . If R occupies any position in the
sphere such that it receives only reflected light, it will absorb a
small amount of light from each of the infinite reflections intercep-
ted by its outer surface. See fig. 2. Let dU represent a differen-
tial element of area on the surface U. A simple photometric calcula-
tion will disclose that any surface whose dimensions are negligible in
comparison with the distance from the source of light to the surface
I
will have an illumination E = nb , regardless of the orientation or

osition of this element of surface dU within the sphere. The quan-

"d

tity b represents the uniform brightness of the source; namely, the

20

interior surface of the sphere. It may be well to establish the rela-
tion E' = nb now, and then proceed with the discussion.

Referring to Fig. 2, consicer a sphere of inner radius r, and
whose inner surface has a uniform brightness b. The brightness of any
element of area on the inner surface of the sphere will, therefore, be

the same when viewed from every direction, and its luminous intensity

4% ‘n‘q

 

 

(N

 

 

 

Fig. 2

will vary as the cosine of the angle of emission. Kathematically,
Ia = b-dA, where Is is the candle power in any direction a from
the normal to the surface dSl, and dA is the projected area
d31°cos a. Let P be any point within the hollow sphere and d?

a differential elenent of area free to assume any fixed position at
P. Since del = In is the normal candle power of 31 in direc-
tion b0, delcos a = la is the candle power of dsl in direction

VP. But dSlcos a = an, therefore, bdA = I and

a,

illoq'lkflha ._ ‘ita; ;

ll‘ ._ -s the illumination or incident flux density at
I

P due to C181 0

Since A: ”2‘“ [175]” Od¢ = Afsin 919 d¢ , therefore

 

.d -¢ = ‘~fifI/)o’¢0$0'l€‘dd .. ‘ .. ’
A; A,’ _ fim05m0do¥¢_d£é

Hence ‘5'; = ‘ we'd“) , where —%— :1“) =51.” ed€l¢
I

is the solid angle subtended by dA. If 3' represents the total illu-
p

mination received on the right side of dP, then

'gar { . E
' I a - 8/010 2.
EP=/df = [£9110 waded? =2”; Slnom040=2flfi T
o ' °
0 . .
cr [ =..L.al"=. F4 lnCident llunens per sq. on.
P 1
T73 incident flux density on the opposite side of d? is
1' ’f
V 0 1 F
l - 6 :1
£P= fisbomadolf=—zrfi 3M0¢N040=an [JiLz
. 5 ’-
1 o
E :17; luriens per sq. on.
p
Thus the flux density is the same at every point within the
sphere, and hence the illumination or 'ncident flux density'will be
the sane at every point on the outer surface of a body K immersed in

the flux within the sphere. This result also holds for radiation of
any'wave length J1, . It is interesting to note the reciprocal case,
where the flux eritted per sq. cm. area of uniform brightness b is
E' = nb. This accounts for the existence of the conversion factor n
whereby brightness expressed in candles per sq. cm. can be converted
to lanberts (enitted lunens per sq. cm.).

how, if E represents the total uniform incident illumination

on the inner surface of the sphere, then

IO
[0

—if = t

candles per sq. cm. uniform brightness of sphere.

Therefore, nb = Ek = E' is the illumination or incident density in lu-

T7

nens per sq. cm. at every point on surface of n,

and 77“”: E‘U = ¢~ is the total flux incident on IT in lunens.
Of this, I? ' absorbs AMI-f“) = EU‘ (I ‘£n) lunens.

Total flux incident on the sphere to give it an illumination B would
be ¢ =477A‘Elunens. Of this, there is absorbed a flux equal to
47"1036 (I’fi) lunens. The total loss of flux due to absorption

within the enclosed sphere must be equal to ¢.

Hence, 4F/11F (I—£)+ EUffl-fu) =¢ . Solving for 13,

E = ¢ lul-nens per sq. cry.
470171-11?) 1- U750 ‘1‘“) ' " ‘
_é_

41M}

.. _ _ 46 __¢_
5’R e EAV 1Fh‘(I-£) +U£(I—‘,,) 4MP- ,

is the illumination. on the surface of the sphere due to dif-

rre have

The average direct illurli nat ion is AV: . Therefore,

whe r e E

.513

fuse re flected light. Removing the hody H from the sphere, the illu-

mination due to diffuse reflected light would then be

49 . 5
5?: 4me- 1—?

Thus the illumination on the wall of the sphere and therefore at the

windmr has been dininished by an amount AQdue to the presence of II.

_ ¢ . f? _ 95 2
‘7? " 4w 1—? «m? fl- 0+ 114% t.) + 4W-

AgR: 417/L'L7é_+’_ 4M‘?£§)+LHW

 

A

23

q

5
5(l—é) + Liam—>6) .

 

 

zfléiz== :g? ’:€;§ +"'_'

 

 

46‘ — -—’—- ’ ¢

’8 (1—26)5 3(/—£)+ aka—:6.)
It was assumed that b represents the uniform brightness of the sphere,
'which in practice is not true because no matte surface obeys Lamhert's
Cosine Law exactly. Nevertheless, the ratio of diffuse reflected light
to direct light in the sphere is so large as to render the error due to
assumed uniform brightness, negligible. The-wall of the sphere can be
made to meet the requirements of perfect diffusion to a degree satisfac-
tory for all laboratory and practical reasurements.

The last expression above for AER can be written

_-= 1.. /
l—(S‘ M
/+ (Hos

and shows at once the effect on the window illumination with changes in

(1) 4Q

U. Accessories within the sphere such as screens, fittings, supports,
etc., which are not a part of the lamp or lighting unit, are customarily

coated with the same diffusing paint as employed for the inrer surface

4'.

of the sphere. For these parts then, ku = k, and the above expression

simplifies to

 

lunens per sq. on.

____L _ ’
(2) AE’? (1—793 I Hug—i

It follows thee the constant of the sphere K decreases with increa-

sing values of U, since K is proportional to En. K=-é!=§fll

{\D
17>

The expression (1) for AERwould indicate that the reduction

at

in window illumination due to the presence of a non -lumir ous bod: n

$9

depends entirely upon 'he surface area and absorption factor of L,
and is independent of its position in the field of reflected light.

Verv accurate er perimente 1 work would undoubtedly disclose some varia-

TY

tion in AER with change of position of 1:. To account for this chan-

ge which, it is reasonable to believe,11:ust be well within the allow-

able limit of error, greater refinement is necessary in the analvsis.
The hj'pothesis underl"ir:g t‘e derivation of (fltie assumec the

sultant illunination 2 due to direct and reflected lig ht to he uni-

form over the inner surfs es of the sphere. Likewise, it assumed a dif-

‘

fusely reflecting bony K with no mention relative to the degree of
diffusion. All foreign bodies in the sphere except polis ded fittL mgs

glass, porcelain, metal, and sinilar sur aces strong in specular re-

flection are more or less diffusely reflecting or transmitting, but to

a varying and lesser derree t1 n the inner surface of the sphere. fur-

ther considerations will disclose the importance of rer<leri1g all bodies

within the sphere except the lamp or lighting unit including reflectors,

q

shades, and integral accessories, diff uselv reflectin , preferably using

the same diffusirr paint enployed for the inner surface of the sphere.

O
The body I in the preceding discussion nay he termed an iso-
lated body. The term "isolated" refers here to all objects within the
sphere which are wholly distinct from he source and its auxiliary equip-
4- 1?

Kent. It is important 0 investigate the effect of an isolated body 1

is again diffusely reflecting

upon AER under the assumption that

and the inner surface of the sphere is pronouncedly non-uniformly ligh 68d.

«‘0
(:1

Effect of Isolated Bodies within the Non-Uniformly

Illuminated Sphere upon Difmsely Reflected Light.

The total illumination at any point P on the inner wall of the
sphere varies for different positions of P except those screened from

direct light, and was found to be

p2. 4174}

In the following, consider the iso

E = J& mg; + __¢ j..— phots .
A 1-4?
ddi

1ff‘usel}r reflecting body N
within the sphere. When the distribution of luminous intensity from
the source is very irregular, it becomes necessary to separate the los-
ses at N due to direct and reflected light received on the sphere.

If % is the loss of flux due to absorption by N, then

¢=¢+¢'
where¢ =€R V/-*u )“ represents the flux absorbed by

N as a kresult of the uniform illumination ER, and ¢ is that absor-

. .,. I «to:
bed result1ng from the non-un110rm component —§‘p—z7£ . The sum

of the losses in the sphere must equal ¢

Therefore, 5;; fi(/~*.)u +¢’+(I-kj¢ +4M‘E AMI-é) = 55

from which 5R [fill—J wfiu )u $9”4’l(l-fij]= £¢- ‘W

*75- ¢’
:vé/x- Ma +4/T/c‘(/- fi)
Fence ¢ -.-.- é¢- ”W lumens.
R / f. {IVE/”'42
*(l‘tu/u

If ¢I is negligible compared to £¢ ,

_ w
’3? " AWN/h ’6)

16/14.) a

and ER :-

11).?“8118 .

 

If

N
(a)

The loss ¢R is a function of U, but remains practically constant for
all positions of N in the sphere. This would no longer hold when N
is sufficiently close to the wall of the sphere to cast a pronounced
shadow, whereby a portion of its surface would not be exposed to the
component of uniform illumination ER.

The absorption ¢l will vary considerably, depending upon the

 

Fig. 3

constants kn and U for the body N as well as in a large measure
upon the proximity of N to strongly illuminated parts of the sphere.
This relationship is apparent from the following differential notation.
See Fig. 3. If dEu represents the illumination at point 11 on sur-
face of N due to the uniformly bright source at P, then
dE = M. lumens per sq. cm. (phots)
u. d;
d¢’_ ”(I -k“) du lumens,

27

where dU represents a differential element of surface at U, and d¢ I
the light absorbed by' N at u as the result of the reflected compo-
nent Ia of non-uniform illumination at P.

Since ER depends upon both ¢I and ¢R , N should not be al-
lowed to approach the more intensely illuminated portions of the sphere.
As previously noted, ¢R is practically constant for all positions of
N within the sphere.

When N is located at the center of the sphere, ‘6 is constant
for all variations in candle-power distribution of the source as long
as the M. S. C. P. remains the same. The average illumination is un-
changed with Io = const., and hence thefd¢’ will give the same ab-
sorption qt: for different candle power distributions.

The decrease in Afk (window illumination) due to the loss
(¢;+ ¢R) is accounted for when calibrating the sphere. The error is
offset by Operating the standard lamp with bodies such as N in the
same relative positions which.they occupy when lighting the test source.

The effect in both cases on the window illumination will be the same.

Screen Effect and Screen Frrors

 

Effect of Screens upon Diffusely Reflected. Light.

The screen is usually a flat, opaque body interposed between
the source of light and the window in order to exclude all direct rays
from the latter. When properly dimensioned and located within the
sphere, it permits only diffused light to reach the window of which
the brightness is a measure of the total luminous output of the source.

The screen is an isolated body exposed to direct and reflected light,

{\3
('3

and in consequence lCfi'feI‘S the window illumiratim due to absorption of
both componenes of light flux. The following discussion is initially
confined to the effect of the screen upon diffusely reflected light.

Let the screen be a plane surface provided. with diffusing paint
of the same quality as that employed on the inner surface of the sphere.
If AS represents the area of one face of the screen in square centi—

g

meters, then U = 2“ Its reflection factor is k. The light absor-

.f.c.0
bed by the screen is readily calculated to be #5 , where
g=lrfiozx45 (l‘fi) lumens,

an b is the uniform brightness of the inner vmll cf the sphere in
candles per sq. cm. The brightness b is the ream-1t of the total uni-
form illuninatien on the inner surface, which is
s = 5+6 = ¢é «AL;- "5. W

75+. R D emf-(1%) 4le. 47/2 (hid

in which ER is the “all illuriration due to diffusely reflected

light, and En is the average direct illumination on the sphere.

Ll

Then
‘ = ¢ . & candles per sq. cm.
4M‘//-/U ”
= IT. ¢ .LIZA I- ;
$3 4/74‘0-10 ” :( I‘i)

- __ (/43 24/4: n
that 13,9_ 1,41 . ¢ = T .10 lamene.

{a
:3
OJ

 

 

The absorption of diffusely reflected light is a linear function of
the total lumens output of the source. With é. lunens absorbed by
the screen, the window illumination suffers a rechiction. When expres-

sed as a fraction of the original window illumination, the reduction is

J=£L1Q__
£3

where CJET, is the reduced wall illumination due to diffusely reflec-

L) -L

ted light which obtains in the presence of the screen.

Qk _( d _ é )
6‘: “MVP“ 4M‘fl-fi)+£{l-é)2.4, _ 41m}
¢éf £)
4rd} I—
¢éfls

d6: 4 IT 431/ "élé’dt/‘Wfil' __ I4:

9“ — 3/71." 7‘ kA:
{Mt/I1)

 

 

. - ¢ (~45
Likewise, [2: £2 -:£2 = 4,741 6'&)[1l7ht+ éAl—
5 ¢
2(1-é)[1 17w," *1/45]

gives the reduction in.window illumination as a fraction of the final

wall illumination, from‘which
f—A—T
4.21/1.
In the above, F is the reduced total wall illunination wiich obtains
in the presence of the screen.

Similarly,
l”: 59;» £9 - 45, + 5») ____ £2 16',
ER + 5» Era)“:
@143 .
(y ”_ 41700-04231”? 2‘ MU
- $5

4lr/o"(l ~42)

 

 

30

d": __"‘A$___
an} HUI,

where: crngives the reduction in wall illumination as a fraction of the
original total wall illumination.

The quantities J, J", and Juare essentially constants. Com-
paring d‘ and d”, it is apparent that the per cent dr0p in window il-
lumination is somewhat greater than that on the wall. The error incur-
red as the result of (f‘ is completely eliminated when calibrating the
sphere. Since its evaluation depends only upon the constants A8, k,
and the radius of the sphere, the error will be the same when calibra-
ting the sphere with a standard lamp. In other words, the reduction in
window illumination due to the presence of the screen in diffusely re-
flected light will be the same for the standard and test lamps. Thus,
when determining the luminous output of a lighting unit, all necessary
screening should be adjusted to accommodate both standard and test lamps.
With this arrangement unchanged, concurrent readings are taken, once with
the standard lamp lighted, followed by the latter extinguished and the
test lamp lighted. This procedure leaves the measurements unaffected by

the absorption of diffusely reflected light.

Direct Light Absorbed by Screen.

The screen is at all times exposed to direct light rays from the
source, and must absorb part of this incident flux before it can be dif-
fusely reflected, eventually to reach the window. It is proposed to de-
termine the resultant reduction in illumination at the windowu

Referring to Fig. 4, let L be a finite source of light, and con-

sider the screen parallel to the window. Since the size of'the screen

31

and its position relative to the source must combine to exclude all di-
rect light from the window, let a preper balance be obtained without
allowing the screen to approach either the source or the window too

closely. The line WL joining lamp and window centers makes an angle

 

 

 

 

 

 

 

 

Fig. 4

o with the diameter through W. Consider a uniform distribution of lu-
minous intensity emitted by L. It is within the limit of allowable er-
ror to assume the illumination on the screen to be uniform. This may be
seen from the following consideration.

Since the candle power of L is the same in all directions, we
may replace L by a point source of equivalent candle power, and compare
the uniform and average values of illumination on the screen for 9. nor-
mally convenient position of the source as shown in Fig. 5. From Fig. 4

it is apparent that the illumination at the center c of the screen is

h

32

g : M__¢°~d
o

xt "' 477-X‘ phOtSo

If this illumination were uniform over the area As of one side of the

screen, the direct flux absorbed by As would be

dszo.a’A¢ ¢5 =¢£°%-43

 

 

 

 

 

 

Fig. 5

where a is the absorption factor of the screen, and Eu - ED. In
practice, the window area is small compared to the area of the sphere,
ranging from 0.06 to approximtely 0.17 per cent. The angle 29, which
is largely determined by the relative positions of L and s, does not
become excessive even in cases where L may represent a fairly large
lighting unit.

Consider L vertically suspended from the top of the sphere at

a convenient distance—£1 from the center C. Fig. 5. The illumination

33

at the center of the screen due to L was found to be

E 115034 ._ IQ“! 3‘ .
u - xi... _ ‘1.

Since tn OK: 3/: , and ¢ =26° 34’
' 1

f“: -‘—L" Cd’(26'31')= 0.7/S'V7—éf- lumens per sq. cm.
The maximum illumination on the screen, which will be assumed circular

for purposes of illustration, is

5,“: 1, —'-m’(ac-o)=—1—‘- t a:’/It‘34’)

Therefore 5",“: $3,099 ‘26; , where 9 was chosen

10: Minimum illumination on the screen is

[~;~_ ___._ .4. atfxf- 19): {9f “Jfi‘o 3’9

or afi=0.f/’af'—1 ‘1. .
The average illumination on the screen will be preportional to the av-

erage value of the cosine-cube function over the interval whose limits

are a - 6 a a1 and c + 9 - a2.

 

 

The average value of }=€49’c( over the interval :11 to (:2 is
(a
1/ “33¢: doc _ {fl-Sin‘x) dosaca‘c _
d}..- d’ dt -“I
I “a. “a
an: [ac .... sin‘x carat 4/4: =-
“L-a‘l If. a;
I. 1‘ d‘
__ 5/1.!K_ sin’ar = ____’ __s’ incx(cos‘a( +1.)
I D. I
I', o!

I

34

Noting that a1 = 16° 34', and a2 . 36’ 34', also a2 - c1 = zo'= 0.349
radians, the last expression,'when evaluated, gives the average value of

the cosine-cube function as 0.7102. Hence,
_ 1,2

This also compares very favorably with the arithmetic average of Emax.
and Emin. . which is 0.6993. The close agreement is due to the rela-
tively small value of 29. However, it is obvious that Eu may replace
EAV. in this consideration. As a approaches zero, the difference be-
tween EAV. and Eu becomes extremely small, and vanishes for c a 0.
Again, a is limited to values appreciably below 45, owing to the cen-
trally located lamp structure which extends some distance below T. It
may be shown that the error involved is also negligibly small for any
position that I. may occupy in the sphere when making measurements.
Thus, the illumination on the soreen.may'be considered uniform and egual

to

 

1M0! ¢ (05% Is 3
£0 x‘ 4: xi- 1‘

The error caused by the screen absorbing direct light from the
source may be expressed as

6:; ::‘££§%2;££§éL———- where

SER represents illumination on sphere.

(screen present and absorbing diffuse light only)

ISEé represents illumination on sphere.

(screen present and absorbing difose and direct light)

35

E represents total uniform illumination on sphere.

(screen present and absorbing difmse light only)

E' represents total uniform illumination on sphere.

(screen present and absorbing diffuse arxi direct light)
ED represents average illumination on sphere due to direct light.
Since E-E-ED,and SEfi-E'-E

SR
_ £P-E
E;- E

An expression for E was obtained in previous considerations; namely,

5. = ¢ J ;_ .. ¢ +
:(I-k)[zna‘+lflg] .24 [amt +(t-4) As]

E' is obtained at once frm the following equation, which states that

D I

the sum of all the flux absorbed must be equal to the total lumens emit-

ted by the source.

4nu‘fa +EZ-ajzaz4, + ‘5‘““4-4, = g5

4vx‘

E’gfih“ f14(l")/4:J = ¢( .. Md.4’4:) . Solving for E',

 

 

4nx‘

we obtain

5’: ¢(4’7’l"‘ AA: C09 °‘)
877x14 [we +(x-a),4,] '

Since 603 d : c-‘g-n 9

2L
5’: ¢fllffi *4/43!)
/4 Ix‘d 4. [z ItA‘+//-aj/4,]

D

and, f = /_ «Nikita/4:1 ._, 44;!
‘ :Irx‘a. "’ sum

56

6‘ = ASA“. 1 I: 145'1 . All
5 7r

IX‘ 1M} 3x1

Since E' is proportional to I an irregular distribution of candle

o .
power from the source will affect E' in the ratio Tr!!- rig , where Is
is the intensity in the direction Lo toward the screezoi. The error, that
is, the reduction in window illumination, becomes
6 = Asa g . A! ,

5‘ [It‘- 5 J'x‘
and varies inversely as the square of the distance from the source to the
screen.

Occlusion of Luminous Flux Reflected

from Portion of Sphere Obscured by the Screen.

That portion of the inner surface of the sphere obscured from the
window by the screen cannot reflect the direct light received from the
source to the window without the aid of sane other portion of the spher-
ical surface. This lessens the window illumination. Fig. 6.

The flux from JV is readily obtained if the area represented by

JV can be expressed in terms of known quantities.
,4, an: (1- d-x)‘
AM” 11

AM” g—AJV. W“ '

 

I4 = I # , where A represents
JV. 3 61‘4" x); JV

the approximate area on the sphere.

Extending the analysis as above for 6 , we find

6 = M. 1’4-
w 17/5} €(1_X_d)adt

37

 

If I,r represents the intensity along Lw, then if" = {W
o

 

- A a 13/»;
éw “'wa X (I-X-d/y‘

The errors 6, and 6w are functions of x. However, if we consider

the dimensions of the screen to remain fixed, the source L may be ef-

fectively screened from W by modifying either d or x while the

 

 

 

 

Fig. 6

other quantity is held constant. Since both errors are a function of
either 1 or d, the minimum total error for variable x and constant
d is obtained by differentiating the sum 63-1-6“, with respect to x,
and allowing the resulting function to vanish.

gene = — ”:4 ref-g + gmr~%=o

3M3

W(1—x—d)= W X

 

38

x = ((—4)V£'d‘ = [—4
id:- + W /+\7-%

When 3: = const., and d is permitted to vary, we have

, —— —rz—_
new as I geese! “0

from which, 42.:1. .

Eliminating x, we have [—2.4 = 1—4 .
1+ 3 33.5;

(1—24)3 _' 33 I

from which, _ — - —— .
’ I
W

 

 

The quantity d may be obtained from the last equation for known values
of the constants involved, and when substituted in the expression solved
explicitly for x will give a value of x cmsistent with a minimum
total error 65 1- 6 . In practical work, d is frequently fixed by
the manner in which the source must be suspended or mounted, in which

case the distance from the source to the screen may be obtained directly

by evaluating _
x :13 d -
3a.. X:
I. 4‘

At this time it will be well to investigate the upper and lower limits

 

 

of 1:. These results have a practical bearing on the design of the

sphere.

39

Screen Location.

The screen must always be situated so that it excludes any direct
rays that would otherwise reach the window. Unless an adjustable screen
is provided, one or possibly two diffusing screens must fulfill this re-
quirement for the entire range of lighting units to be accommodated by
the sphere. Heretofore, the area of the screen was considered constant,
and with a definite location of lamp, the distance between source and
screen, denoted by 1, assumes a definite value consistent with the min-
immn error 65 f6". Practical luminous sources, however, vary consi-
derably in size, so tint for the customary alignment along the vertical
axis of the sphere, a large lamp will require a larger screen at the
same distance x than a smaller lamp similarly located. Again, if we
permit x to vary, a larger lamp will be effectively screened by a smal-
ler screen as x increases. Excluding from this discussion a variable
screening device created to accommodate different sized lamps at a more
or less fixed distance from the source, let us consider the effect of
variation in screen upon the x for minimum total error 65 'I- ew'é.
Practical considerations will dictate the working limits essential in
arriving at an adequate screen-to-source separation.

Referring to Fig. 7, the window Opening at W may be assumed to
approximate a circular disc of diameter dw . L represents the light
source with center at Cl on the vertical axis through C. As before,
As is the area of one side of the screen. Let IL, represent the area
of the base of the shadow on W' . Then

A“ :1!“ “LIV-PP)“. A -.4 {£—d—x-+ h)",
Av (1—4 +/»)‘ ’ ”‘ ' (14+ H“

40

Substituting this expression for A8 in (5 and w, gives rise to

the following two equations:

l _ A.“ -4-X+P)1 a I?!
(1) (3 _ (l-aH-p)‘ 74"g'fi'

.__ A.(1-d—x+b)‘_a_. . l3
(2) 6-9 "'" (1_d+’b)1 ”A; r»

 

 

 

I
V Fig. 7

The geometry of Fig. 7, triangle CQG , requires that

 

 

 

 

d ____ mafia-2x) =_¢£_._2_£c__
About Mac Asked
_ Acaszx
al- we, .
Also, l = 2rcos a [‘4 :r. A

60: ac

\b
,4

and l -- du'_

I , .
_ __ , "flC‘l‘e d m.] 2 IS the
A?-¢¥'4-/5 (iv' )7 v A

dista-ce intercepted by the boundary rays on the vertical axis W'.

 

It will be noted that this relation holds only approximately, sice for

different values of o, the tangent line

U)

and the line through C ard
center of window, will not converge to a common point. For all practi-

whether the ligh ing unit is herical in form or other-

5‘)
r1. 3

wise, the tang cnt lines to the IC'J.:-.’.]°TTIHI“. direns io. of the luminous sorroe

IJO

as viewed from the irirdow vi.-- 3 meet in a po 11‘: P 1'.th mssin
cunf‘erence of the window opening, and a line drawn from P throtgh cen—

Tm i
k. l.(

C?
d‘
3‘
('0
L.)
'3
L
y...
’D

ter of window will, in general, not pass through C1 ,
node by this line with the horizon gal GT'.’ will differ little from (1

especially if a ranges only from 0 to 3-0

It fol I owe that

 

[€_ 4'; =7
,6 1) =14!

I‘t
(‘n-I) 6.03%

 

 

5:)“-

91...

FY"
/
Substitution in Sq. (1) and (2) gives

A, ‘1.
= Ava 7’ “/1223,“ f (52" -X +‘i‘fi-UM“)
Q "/21 n1 .3!- x1.

—-’—2——x+(-—A 1
3 (coax ”-040!“ “544
It
-) co: «2°C

 

04: cc

42

Differentiating partially with respect to x , simplifying, and equating

to zero, we obtain

gL: $60512“ (ii—T“... )3_ 4£X3¢0W0< e: 0
)r . 7»

Solving for x , we have X = A’

(3) Cam 1+ L.M_y&_/_

f, a: ”at >7

 

 

 

This gives the distance x for minimum total error, and is a function
of o . The limits of x for a typical case of a source suspended ver-
tically along W' with o. = 30 , obtain as follows. Let ilr. =/ and
n = l . Then the shadow is bounded by parallel rays, and thesexpression
(3) reduces to x = 0.37488r = 0.325(l-d) . Pong—2:, and n = 9 , we
have x = 0.57735r - 0.500(l-d) . 3

Lamps and lighting units tested in spheres of commercial sizes,
40 inches in diameter or larger, (will seldom permit fit<dw . For all
practical purposes $25. ; that. is, 4‘, § 43/”. For a 60" sphere
7) :57: will rarely exceed 5. Note that dv is themaximum dimension
of an equivalent luminous scarce in the vertical plane through the lamp
center, and may be greater or less than the maximum dimension at the base
of the luminous cone intercepted by the actual light source. See Fig. 8.
Nearly all practical illuminants will disclose symmetry about a single
axis, and many types display symmetry about a vertical axis. Although
dv does not represent the maximum dimension of luminosity, it serves
very well to establish an approximte upper limit for x . Thus, to a
first approximation, 1: may be said to lie within the limits

x . 0.3(1-d) s 0.846-r

x g 0.5(1’d) = 00577.1.

43

for a. '- 309, '5”: f, , and covering values of n from less than unity

to and including 11 - 9 . If we were to use an average of these values,

then
assoc. 60:30“

This gives the distance of the screen from the vertical axis of the

sphere (o - 30°) for minimum error due to occlusion and absorption of

 

 

Fig. 8

light, and agrees very well with figures quoted in general discussions
on the sphere photometer.
Referring to a 60" sphere, it was stated that n rarely exceeds

5. This follows almost iumediately frcm Fig. 7, in which cc1 - so.tenso‘,’

cc1 - 17.32" , d, = 5d,, - 5-3.5 - 17.5"

44

This would still permit a convenient position of the source with re-
ference to V ‘without incurring any serious error due to proximity to
the wall. An average value for 1 may be obtained from the following

tabulated values:

3;.
3.2.1:. .16.

30° 5 0.5 0.68749r

. x1
0‘ 5 0.5 0.57577r - x2
30' 1 1 0.37488r - x3
0° 1 1 0.38648r - x4

The average of smallest and largest x is xAv = 0.4811r .
{,me It. 1% = 0.416 It.

Again, 0.4r comes very close in fulfilling requirements for minimum
screen error.

It is important to gain an impression of the order and magnitude
of the minimum total orrogmfiL for a given set of cmditions, and equally
essential to show that “C, exhibits a minimum. There follows the cal-
culations for minimum total screen error (fie, ) due to absorption and oc-
clusion of light for a 60" sphere under the following conditions:

n=5,c-50:r=30”,a-0.2, §=L .

$3 2-
The x for minimum.error is x 8 0.58749r .

14v (It-4' 15".)‘ .4? .1?)
.6- 4.4.4,. 8 (1-2+; a“: g{ +3; “44).,

Evaluat' we have
may, .

 

é;.== l¢26?53914k'gg
a»

4900 7r

45

For a 60" sphere, - r a 30" , dw : 3.5" ,
dv 3 n°dw = 503.5 = 17.5" .
Hence ’49=% (’7'5)‘= 240' 528 if): , from which
”onmzmgj;
Thu r - 1L- , g .
., or 5;- 1.4 ”5* “z, ,
f°r £=5§ _. ,‘f '=" 4.3 7. .

To show that x a 0.58749r represents the screen distance for minimum
error under above conditions, it is sufficient for practical purposes to
calculate the error for a slight variation in x to the right and left
of the critical point. The usual mathematical criteria may be applied to

show that X= A.

coax(/+ I... 4w9d _/_)
J; sumac n

 

3'...

represents a minimum for all practical values of n and —.

Let x increase from 0.58749r to 0.60000r. S

(memo/arm 1-? Lao-7M; 2' 0-37”
.__ $.24“? ’4 = o. 02.!!!
6,; 4s‘ooir V‘E f;

G :: gt—E-fi-ei : % 5:" 0o! Z increase in min. error.
we f '

 

Let 3: decrease 1.25%r , then X-AX: 0.579484,

._ £2866 _ . g
_ 4500” .44: -002/6? g

 

e :: 0.] 70 increase in minimum error.

46

Screen Error Influenced by Angle.

Up to this point it was merely stated that x is a function of
c . The expression for total error may be written
é- =/(X,o<)
from which 6f is a function of x and c . It is important to in-
vestigate what general effect the posit ion of the source will have upon
the screen error 6f and in particular to determine the angle a and

x for minimum total screen error.

2.5— Hush-12‘s; (__h. _LL__ 3
3X é—TI/D- 7]?- dx 4:1 (09K —X+(w—}W as“

We have

 

 

13-— —x+ I“ 2 I7
_|_€ Md Zu—lkaoL . (03¢ = 0
” cg“ —X coo‘lot

substitutions having been made fa‘ the quantities p , l-d , l , and d
in terms of n and functions of o . See page 41. The solution of this

equation for x was found to be

 

 

Xmelc‘i" Lon/flag?“ _l_
g’y €09.51“)?

In order to simplify the simultaneous solution of £520 and .16 .0

we can, without loss of generality, let r '- l . We confine the discus-

 

sion to a definite set of conditions for “V and n . The quantity r,

5
although essential to any particular solution for x , would not appear

 

in the solution of 3‘: 6* =0 . Let n = 5 , and 5’ =2 5:”. Then

XLoM(H—V: ¢%7)=l

V; and ._
x07“ +xcoao< Sad-fix '

 

47

Transposing xcosa and combining,

”Wat-E. 9912‘ = (l—xmd)3=I-3xuae( +3x’cou‘d-x’ae’ac
s w‘zu \ 1
2x3 m’x = (fr/S‘de +Irx‘cso‘a‘ —3~x3cao3o() (nav‘ac-l)

Expanding and combining in powers of x ,
X3(92 cco’at —io mm swank) +x‘(-6o Caa‘d ‘+6o max —/S‘€op‘b()
+ x (60 Mac -(.o m’x +15 coed) + (an mu +20 cao’u ~59 =o

New, differentiating 61:. partially with respect to a , we have

iét=[m —(e1-:) Mac-L :RLMot cos? -7¢1~°<c¢v6¢ av 35)

 

ad ba-I)(h.-xu-aa() £493.14

_2 ”Ii-61“!)xmo4 aim-a) xwx . ae’.‘
(m-IMIL—x covet) (w-Ij‘(/L—xme9‘- ae‘aat

M [An -x(°1‘l) coax (An-0aiuduu-th-(n-9mxlw)

 

 

+ Q's-I) mun

 

 

XL (’72-!) mac 1
_ flat m‘cx [fin-x("\")m°¢n =0
(‘52- Jl)(" L Cir-I)¢Lo<ial

Substituting lnn- 5 , r 8 1 ,
r 1|

0 t \ ‘ e 7
[5"qu“ :] (annotate d~7mxmuwg¢) _w 5(de

 

 

 

 

 

 

 

q(/ - X toad) m ’M 2(I-xw)uld

t r ‘2 ‘

+m3d._5:—9X0wal o‘md__;_ Amen—n19: f-VXW =0
xt 4406a 4m‘u ‘- 20 4mg

Multiplying both members by /‘ #04 “9,2“ (l’X 40d)1X"#= O '
X‘mx (r-yxmx)‘(6’m‘.~o< med—7443..“ duo‘s; mast)

 

.. Jae-7oz“: not 5'41“"! M“ cav’
2" x-xmx “L

+ 544;. at ease! m3:d(1-xm¢)"($-‘ 4" “9“)
3 “ac Met m’zdfi—Xcaeong-VXWXY = 0

.~

Clearing of fractional expressions,

Mime: (I‘XW)(5=7XCflxj-’{2Mdm’d - 7 dose: M‘JWZd) ..

48
4%de mad (5‘ -9x megAiwet
+ In .44»de “1339!. (I—xcesatj’CF- 9X code!)
—3M~o( MdcaazaiU—stoc) (J—qxwx)1:o

Division by (5-4xscos c) is permissible in view of the fact that
ng §fi. For if 5-4xocos sai=0 , then for c - 0', x 3%
But, physical conditions of the problem require O<X {I for a = 0 .
Therefore, 5-4xocos est 0 . Likewise for a . 45°, to satisfy the
above condition, X =§r . But, for a. = 45°, x must be at the
most equal to or less than [/2: . Hence, again (5-4xocos s) a4 O .
Thus, 2x‘ Macaw at % -jAfiv~olca‘e( can“).

{1— x wager—V x eases)
_ 4,8“? x acetaminot 4- laAiMd covet ca ’axfl—xcoexj

 

—3A~uo( coax «1.2x (l—xcnot) (S—Qxcgng =0

which simplifies to ‘2ng {’Ad“’d_ yfism‘d Mid)
I
(z—xcov d)(5‘- 9" '3’“)

 

Ange» A as: aided —A*'~ «MddaxQ—xmffi—Iuwoog =a

Therefore, sin c-cos c-U - 0
sin a. = O 3 a. a O is one solution.
cos a. = O 3 a. =I"='-;-Esolution ruled out.
Thus, 1X‘(5-9x cadet 1- ‘I-x‘m‘d)“ cos" ~79; 61m“)
- 9x3 when 246 «who: (I —xce4ec)3(.5’- szwaac) = 0

Expanding and rearranging in powers of x , we have
x"(-I'H Cognac H100 can" —7;cu‘ac 1- I2, "9'00
+-X3(‘I‘1¥Cod gut-61min! +15% cov‘et— —9/aa’at) +

49

XY-‘f‘é’ ‘09?“ 1.631446%! «30¢ en‘s! ffléw‘d)
*X(’~"m’o< -31.Yeoo“oc +I62. he’s: -z 7 e—o-e-t)

+ (~90m‘4 aaom'x ~3om‘w +5) =0

This equation together with.the one derived from the explicit solution
for x emanating from gaa 6t :0 , may be reduced to give the following
x

simultaneous set:
X722- MM -10 my“ 'I' 5‘ easier)
1- X‘ (~60 fiaa‘d +60 Lav? ~IS‘ Cov'uj
+ x (60 card. ~60 mix 1- 15‘me
+- [-2.0 €4an + no (.er -5? =0
and. x*(—3&y Wyd +s~m. data)
+ x(96 6043“ —I10 WK)
1- {-60 m‘u + ‘70) == 0
One solution of these is s = O , x =- O.57577r .
To effect the solutim of these equations for x and a. for other so-
lutions, if any, one may turn to a dialytic process of elimination.
We write these equations in the form
f(x) 2‘ aoxg+aIXt+41X+d3 =- a
and f/x) =){.,x‘+éx +41 =e .
Then, if f(x) and g(x) lave a common root, and if the first equation

be multiplied by x , and the second by x’ and x in turn, the resul-

tant of f(x) and g(x) is the determinant

50

a0 a1 a2 a3 0
0 a0 a1 a2 a3
b0 b1 b2 0 O = O
0 b0 b1 b2 0
O 0 b0 b1 b2

 

 

which is zero if the two equations f(x) and g(x) have a common so-

lution. Expanding this determinant, we get
00(0043'4576'1'4363" 2 “366‘; + 41‘, Zn’qito flit)

+ 65 (”1151‘ +4435 {“2414} £36. " 0,4;éfiL- 40414t+d,43£;é
'4' 0:535; +4;- o‘_q,a’£.' ‘1.) =0

in.which ao - 22 cos7c - 20 cos5s + 5 cossc
a1 9 ~60 cossc + 60 cos4s - 15 coszs
a2 - 60 cos5c - 60 c0330 + 15 cos a
a3 . -20 cos4a + 20 00836 - 5
b0 - -38.4 cos4s + 51.2 coszc
b1 - 96 cossa - 120 cos 5

b2 - -60 cosza + 70

Substituting the values of a's and b's and.simplifying, we Obtain
-1,007,769.6 :20 - 9,555,148.8 :19 - 9,566,899.2 :18 + 81,330,291.2 :17
+ 27,844,646.4 :16 - 227,126,476.8 :15 + 27,734,956.8 :14 +
262,624,870.4 :13 - 101,777,612.8 :12 - 108,795,494.4 :11 +

55,141,632 :10 + 220,774.4 x9 - 221,579.2 :8 + 43.2 x5 - o

in which x - cos a , where x was chosen to represent cos a to sim-
plify the expressions, and has no relation to the x employed to re-

present the distance from source to screen.

51

From the last equation it appears that x5 - cos6s is a factor which
may be discarded, since cos a# O . We have finally

(1) f(x) - 62985.6 :14 + 597l96.8 x13 + 597951.2 :12 - 5083143.2 :11

- 1740290.4 x10 + 14195404.8 x9 - l733454.8 x8 - 16414054.4 x7

+ 6361100.8 x6 + 6799718.4 x5 - 3446352 1:4 - 13798.4 x3 + 13836.2 3:2

- 2.7 - O .

The arccosines of the roots of this equation may be critical points for
the function 6f =flx’x). Any possible real roots in the closed in-
tervald = i %— are of importance; roots outside this interval are of
little or no practical significance.

According to Budan's Theorem, successive derivatives f'(x) ,

 

 

 

 

x ll 2“ /' 2"?" f‘” i’” 13k“ 1’" f"" If" f" f’" f’” f" Var-lithe»:
_/+-—--—+++++++++ 2
_ ++—++——+++—+++++ 4
ofl—o+—-—++—++——+++ 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f"(x) , f"'(x) , - - - - . f(n)(x) were obtained for f(x) and
evaluated for three significant values of the argument given in the above
tabulation.

It appears that the number of real roots between x - O and x 8 l is
either five, three, or me. Between X = g and x = 1 , there may be
either two real roots or no real root. The result is ambiguous and re-
veals nothing more than the fact tlnt there can be not more than two real
roots between 4 and 1 . It will be noted that f(O) and f(l)

have opposite signs, hence f(x) = O has at least one real root between

 

these values of the argument.

"fi
3

It is possible to determine in this problem whether there are any

C'
00

real roots of f(x) = 0 between .g and l by noting the followin
An upper limit to the number of real roots of f(x) = 0 between a and

b is obtained, if we set

 

rising, mm“ = X-A. ,
x 8‘
"+ 7f' dL-x:

and multiply f(x) = O by (Ii-y)?1 , whereupon Bescartes' rule can be ap-
plied to the resulting equation in y . For, when x = a, v = O, and
when x = b, y —)c:). Thus, the upper lirit to the number of real roots

is obtained for y ranging from zero to infinity.

‘4

1% proceed to expand f(x) in powers of (x-l) , which 13 equivalent to
synthetic division applied to f(x) . Tle origin is therety'transferred
to the point (1,0) . we obtain a second equation, nhich is f(xl + h) =

f(x) , in which 3:1 -.= 1 and h = X - X1 , The resulting e’pmtion has

the following form:

(2) 62,958.6 x14 + 1,478,617.2 x13 + 14,020,713.2 x12 + 71,590,267.0 x11
+ 215,6?8,347.0 x10 + 401,803,228.o x9 + 4ea,eze,ss4.s x3 + 308,906,029.4 x7
+ 87,810,107.8 x6 - 26,948,817.2 x5 - 38,147,888.6 x4 - 20,023,876.4 x3

- 5,600,752.6 x2 - 138,508.2 x + 197,oss.9 = o .

Subsequent substitutions are simplified by considering roots between 0.8
and 1 in the original function, which correspond to those between -O.2

and O in (2) . Again, a e O and b = 0.2 may be conveniently used in

2c=.dll’6%3:
I'tjf'

tion is:

, provided (2) is modified for x = -x . The resulting equa-

53

(3) 62,958.6 x14 - 1,478,617.2 :13 + 14,090,713.2 x12 - 71,590,267 :11
+ 215,628,347 x10 - 401,803,228 x9 + 482,626,384.8 x8 - 308,906,029.4 x7
+ 87,810,107.8 x6 + 26,948,817.2 x5 - 38,147,888.6 x4 + 20,023,878.4 x3

- 5,600,732.6 :2 + 138,508.2 x + 197,066.9 = o .
.Since X = g, substituting in (3) and multiplying by (l+y)n,

we obtain the following equation, which is significant in the uniformity

of the signs of its coefficients.

(4) + 111,182.36 y14 + 1,683,495.92 y13 + 772,347.24 y12 +
$0,598,117.82 y11 + 147,579,811.15 y10 + 312,700,908.21 y9 +
494,370,84o.91 y8 + 592,328,5oo.50 y7 + 540,317,707.2o y6 +
373,256,922.54 y5 + 192,101,766.37 y4 + 71,354,918.88 y3 +

18,069,179.91 y2 + 2,785,838.24 y + 197,066.9 = 0 .

By Descartes' rule, there are no positive real roots of (4) , conse-
quently no real roots between -O.2 and O in (2) , and hence no real
roots between 0.8 and l in the original function (1) . For an angle
(-a) , the screen is symmetrical with respect to the equatorial plane,
and the analysis holds for negative angles within the same range. Thus,
there are no real maxima or minima for (f in the intervals

0 «at g 167—; —%—§a¢<o
The solution, sin a 8 O, (p. 48) is the only critical value within the
above limits, and as yet may represent a maximum, minimum, or point of
inflection in 6t . That sin a = O renders 6t a minimum, may be
most conveniently shown by evaluating it for a somewhat greater than
and less than zero. To satisfy any doubt in the mind of the reader, this
conclusion may be confirmed by applying the customary mathematical cri-

teria to the above analysis.

Calculations for minimum total error ”.61: are given for reference.
'-

 

Since o. = 0 represents the angle for minimum error, "36¢ is

a
determined for the conditions a = O, n = 5, ——=
The value of x corresponding to c = O is x a 0.57577r .

Evaluatingflzngt , we have

. .. Avis.
ME, —l.02768 45”,,

Since Av = 240.528 sq. in. for n =- 5, therefore
g... t =o.ot74e.{,
This value of 6'6 is the 233313. value for 2.1.1. angles from -30°to +30?
Similar calculations for a = i 50,0 n = 5, and .%!.= E"- afford
6t =Oo02186§s 3
For a = i 5? £1"- : J-, and n = 5, the following values of x
5: 9..

x = 04‘7”: h.

6: =/.01331-’§5ng5°7 = 0.07747 S,

and 6t obtain:

Thus, the position for minimum errorngfit corresponds to the source lo-
cated at the center of the sphere. The largest ft will obtain stt3o°
with no intermediate real critical points. These calculations based on

the analysis cover the conditions 11 = 5, i: —L only. A like pro-
}, , 1 E

cedure may be extended to cover all practical values of n and “’ ,
I

if desired. For a given set of conditions, the per cent error will de—

1:

pend largely upon E = I— , whereas the variation in 6t is small
0
over the entire range of o. for given g .

55

Error Due to Absorption of Reflected Light from Screen by Lamp Assembly.

A reduction in window illumination is also caused by reflected
light from the screen being absorbed by the lamp assembly. The error
due to this absorption will vary with the surface exposed to reflected
light, and will depend upon the mean absorption factor for parts of the
assembly exposed to such reflected light. Although it will modify to
some extent the distance x for minimum total error €8+€W+ 6 , this
error will not permit x to fall below 0.4(L-d) . The practical
range for x will lie between 0.4(1.d) and 0.5(1.d) 3 that is,

h = 0.4r to h - 0.5r . The 60" sphere was constructed with allowance
for h - 0.416r - 12.5" . Again referring to Fig. 7, it is well to
keep in mind that within the range x I 0.4(1 --d) and x I 0.5(1-d)
' with a - 50°, 6:” will be from four to nine times as effective com-
pared to € . Consequently, whenever possible, it will be necessary
to guard against strongly illuminating any portion of the sphere such
as in the neighborhood of Q which is hidden from the window opening
by the screen.

It is not permissible to allow the screen to approach the window
too closely even though the errors Ewand 6: vary inversely with x’.’
As the screen approaches the window, the illuminated part of the wall
hidden from view by the screen increases very rapidly especially when
the screen is near the window. Thus, a large part of light from the
first reflection cannot reach the window except in the course of suc-
cessive reflections. The resultant decrease in window brightness in-

troduces an error which may not be negligible.

56

When determining the luminous output of a source, the screen
errors discussed in this work do not affect the final results in the

measure indicated. For, in calibrating the sphere for a given lamp

 

assembly, similar screen errors obtain. The actual error in any case
will be the difference of the two obtained for successive operation of
standard and test sources. Although this difference is quite close to
zero in many instances, it is nevertheless essential to know what er-
rors are involved and to what extent they may affect the final results

in questionable cases.

57

D3313? LYD CLTSTRUCTILN

 

Body of Sphere

 

The sphere, constructed in accordance with the requirements of
this thesis, is built of cast aluminum and made in sixteen sections as
per Detail No. l. The master pattern made of aluminum is fashioned af-
.ter a wood pattern constructed on the basis of the dimensions on the
above detail. The aluminum used is alloyed with 12¢ c0pper to give ri-
gidity to the construction. These castings were poured with allowance
for one-sixteenth inch finish on surfaces indicated on the blue print.
One casting of Detail Ho. 1 is converted into a door large enough to ad-
mit any commercial lighting unit consistent with the size of the sphere,
which measures sixty inches on the inside diameter. The castings for-
ming the body of the sphere were machined, filed, and when assembled,
were ground along the inner contours to insure proper alignment. Then

bolted together, they'form.the quarter-inch spherical hull.

Cover Plates

 

Upper and lower cover plates were cast of the same material as
per Detail No. 5, in order to provide for lamp assemblies normally sus-
pended and mounted vertically uprigh . The plates, cast in halves, were
bolted together on a finished surface. The cover plate surfaces exposed
to light from the sphere, conform.to the curvature of the latter. The
interior surface of castings forming the body and cover plates was given
a light sand blast to prepare them for the inside finish described in a

subsequent statement.

58

Supporting Framework

The sphere rests on a supporting framework made of standard one-
half and one inch black wrought iron pipe welded together as per Detail
Ho. 12. Flange plates welded to the risers and bent to conform to the
curvature of the sphere, are bolted to the body. The risers are provi-
ded with swivel hearinr casters for easy'movement of the photometer.
The pipe framework is fastened to the bocy in two similar constructions,
permitting the photometer to be separated into vertical hemispheres when
it is desired to move it from one room’to another. Although vertical,
the risers are amply Spaced to give stability when the photometer is di-
vided.

‘Vindow

The window Opening of three and one-half inches diameter, coun-
ter bored to receive the diffusion glass, is formed by the alignment of
two semi-circular openings in an upper and lower section respectively.
The center of the window lies in the horizontal plane through the cen-
ter of the sphere and midway between the meridian flanges. This loca-
tion of the window, although theoretically non-essential, makes it con-
venient to use the sphere in connection with almost any auxiliary photo-
metric devices. The center of the window approximates 52 inches from
the floor level, a convenient height for the eye of the observer in con-
ducting measurements. A diffusion glass cut to fit the counter bore is
held in place by a framework of steel bolted to the castings. Thin Vel-
lumoid gaskets protect the glass from slight irregularities in the bear-

inr surfaces. It is essential that the surface of the glass exposed to

‘0

59

incident light from the sphere be matte. A surface disclosing any vis-
ible specular reflection would transmit variable amounts of equal inci-
dent fluxes, depending upon the angle of incidence. Thus, light inci-
dent on the window would not be transmitted equally for all angles of
incidence between zero and ninety degrees. A matte surface exposed to
incident flux of uniform brightness will, if homogeneously translucent,
appear as a uniformly'bright disk from the outside. Such a surface dif-
fers somewhat in diffusing qualities from the sphere paint, but will

transmit light more nearly equally for different angles of incidence.

Screens and Screen Supports

 

In order that the incident flux on the window produce a surface
of uniform brightness, it is necessary to screen off all direct rays of
light from the source to the glass. The location of screens for minimum
total error was discussed at length in the theoretical treatment. A
screen rod of S/EG" cold rolled stock rests in a hearing on the under
side of the sphere, and fits into a similar device located on a vertical
line above. Screens of sheet metal are provided and held in place on
the rod by setscrews.

The screen dimensions were obtained by actual measurement and ob-
ser ation in the use of the largest hare lamp and lighting unit consis-
tent with the size of the sphere. The largest screen will effectively
obscure any direct light from a unit of 18" maximum dimension. Normally,
no light assemblies exceeding 16" maximum dirension will be under con-
sideration for test. Three screens are provided for use with.light sour-

ces. The small one with transverse memlers serves for measurerents on

6O

bare lamps. The remaining two may be used when larp assembly'tests are

to be conducted. Flexibility ohtains through rotation and axial adjust~

ment.
”sserhlies for Light Sources nrd Circuits

 

a side assembly made up almost entirely of standard equipment
provides for measurement of bare lamps with base down or up. Two stan-
dard Hogul receptacles with adapters for medium base lamps are connec-

ted to a length of curved cendtit b 'means of a suitable T unilet. The

.
‘ L

3

whole assembly is held rigidly in place by lochnuts drarn a
face plates on the sphere. The upper and lower assemblies, also con-
structed of standard equipment except for the wood bushing and steel
ring in the upper cover plate casting, make it possible to use the pho-
tometer for testing lighting units. Current leads project from the up-
per assembly and are provided with insulated clips for ready connection
to lanp terminals. Each assembly comprises a current and potential cir-
cuit brought out through standard fittings and flexible conduit to a
terrinal board rounted on the supporting franework. The potential leads
are tapped near the lamp receptacle in each case, in order to ninirize
he drOp in potential througn the power circuit. The latter is amply
dirensioned with To. 12 stranded copper wire to take care of loads as
high as 16 amperes. All connections to larp receptacles and junctions

are soldered to insure good contact.

61

Interior fir LiSh

 

When ready to assemhle, the inner surface of the sphere was

washed and cleaned with carton tetrachloride to rexove ar" rens.ining

.LL

rrease or il b hrough handlir.r and machining. Two coats of white shel-

O

lac were applied, allowed to dry, and sanded. Four coats of flat white

interior raint form t‘e hase for the finishin

material, which is a
special sphere paint used in the piflo one ric laserator" f t1 cUnited

States Tureau of S andards. Two coats of sphere paint were applied

.,4
v—J

wit: good results. hest reatlt s rav he outained tv sprayinr All
permanent parts of the sphere such as screens and conduit assenhlies
are lilew,i e finished in the manner descrihed. Determination of the

mean reflection factor k of the finished interior is a problem which

should he of interest to those conducting evnerizer s Tidh this nnoto-

 

Leter. In addition to the atrlicaticns, it :33 ee well to deterrine
the reflection factor of the snhere paint and the diff sion glam con-
start.
lecnriC“l asa
The following specifications are listed for rear" reference:

‘ ,{ I o r!"
Laterial of Eody Cast nluninun (13~ Cu)
Weight complete with ccesscries 525 pounds
Inside Lia.r eter 60 inches

wall Thicl wn ss 9/4 inch

Center of Window to Floor Level ' 52 inches

:7 0

Door Tea surerents Width, 2n inches; Len; th, 25-7/4 incl es

J

62

Laxinum Height 8 feet, 2 inches
Kaxinuy Diameter 6% "
Diameter of Diffusion Glass 4 "
Dime-ter of "'Tindow 5-1/2 "
W3 1 Paint Sonnehorn Plat White Interior Paint
Sphere Paint Special Reflecting White Paint Kanufactured by

Benjamin Loore & Company, Haw York City

Qlflk TVTKNW haw QM§QH-£INI
>\Q\k Ukkmwzgv b6 QNVQQQ >\\ MMKWEQKQtQ katlm. $<\~>§>\3 4T KWVG I35 IXKXR.

II‘
Mg)? Ll... .JAJ q
I. o- u’r. 0‘ .

' i

i ’

(I.

 

 

 

La -- 7. ’ ‘ ' .' .

SPHERE PHOTOMETER WITH DOOR OPEN
WINDOW 7'0 THE RIGHT

VIEW OF INT 5 RI OR FROM OOOR ENTRflNt'E SHOW/1V6 CONAUIT
AIJ'EMOLIEJJ SCRE£NJUPNVJ SCREé‘A’I (Viva ”IA/MW

 

 

 

O
O
O
O
C
O
O
O
O
O
o
o
O
0
o
o
a
a
O
O
i
I
o

v
I
1,.
"a.

 

x4.

As: EMB LED SP/I 6R5 WITH CL 0:5 VIA-'W 0A? “0100.? TIA/6 smelt/’95
A ND TERM/IVA L PAN! L FOR (UR/PEN? Alva AWE/V7044. 4.9m:

67

 

k?.w\<o\\§%% x-v~xv§§t )2 xx: Qhk .wzbkci mkmtkh

H.‘I."I O {*a .
II,» . .
. ., . 9.. -ewum. ‘ . .

d
‘ A

(r '- .

 

 

 

68

b— :UC'I'C: E;

rm ‘ Ira-«r
Lr'.~'ls " i

r -3
H
‘2

The method employed in measuring the luminous outru.t ofe lamp
or lighting unit will depend upon the relative size and reflection co-
efficient of tlie testu n1 it compared to these quantities when referred
to the sphere. Comnercial illuminants may'be suhdivided into two gen-

al classes in accordance with the ahove; viz., hare lamps and light-
ing units, the latter including all lanp asserflll es for reflecting, re-

fracimi . and diffusin3 reczia exemplified by the variety of seni- and

totally inclos n3 types on the market.

All present connercial bare lamps are small compared to the GO"
sphere; consequent y,, one routine type of In easurerent'will, in the ma-
jority of cases, satisfy requirements. The meaxn reflection factor of
such lamps is quite high. It was shown the b the illumination at the
window is diminished by an amount AER due to the presence of a non-

luninous diffusely reflecting body E screened from all direct li3ht,

where A ER: ¢ ‘ _ I
/-£ I
( )5 I+ (h 19) 8

Although the lamp represents the source of light, the enclosing glass

 

D

acts as a non-luminous body for diffusely reflected ligh . i we in-
terpret ku as the mean reflection factor of the glass, the analysis
may be extended to cover this ase. Th window illumination decreases

in the ratio I -F' I : I
(I-I) __\1__
(I —é.)U

 

69

and the constant of the sphere, if expressed to vary inversely as B“,

will increase in t‘e reciprocal ratio. The per crnt ircrcase in K is

iven y __ /
s b AK— (/-1()/ 5 —/ o/ooz
[(I—(JU

l

When this is less than unity, the effecu of the lanp is negligible, for

 

 

the error in K is less than one per cent. The ratio-gi-is sufficiently

U

large for a 60" sphere to render AK< I . An arrangement for photometer-

 

 

 

 

 

 

 

 

 

a——~-

 

 

 

ig. 9

ing hare lamps is shown in Fig. 9. The side conduit assembly provides
for hare lamp measurements. It is advisable to use the substitution
method whereby the calitrated lamp, which may be either a primary or
secondary standard, is mounted in the side assembly in the same position
as that demanded hy the test lamp for normal operation. A reading is ob-
tained with the comparison lamp on the photometer bench. The calihrated

lamp is then replaced by the test lamp, and a second reading is ohtained

70

for balance of test lamp against comparison lamp. It is not necessary
to know the candle power of the comparison lamp, but it is essential to
Operate this lamp at a constant voltage either equal to or somewhat less
than its rated voltage. Operating it at values in excess of its rated
voltage causes undue filanent deterioration and attendant variations in
luminous intensityu The position of the screen r mains fixed throughout
this procedure. The formulation whereby the luminous output of the test
lame obtains is as follows:
. 11,22.
96 == 9% £3’°(7‘
I
This result is readily deduced by referring to Fig. 9. Let IS
and I denote the intensities of standard and test sources respectively;
in this case, the candle powers of the window as viewed from P. Let A
and E be as shown in the figure when the standard lamp is lighted.
Then A, and B, will conveniently represent the distances involved when

,he stardard luxp is replaced by the test source. we have

-£&- :: ’4‘, and I. '—- ._112: ,
I. 5* f. 4.

 

 

 

Therefore,

 

 

«a. o o r; 0 I ' “ 0 _
In addition to following the "substitution lethoa' in order to
reduce the probable errors in sphere photometry, the procedure to be

a e ' - 1 o 0 1
described under 'Lamp assemblies" may be applied to bare lamp measure-

71

ments with even greater reduction in error and less handling of lanes.

‘4‘-

tare lamps, 1t teccmes neces-

O
:13 ell".

ci-

Vhen snaller spteres are used for

a v to have available a large supply of standardized lamps of various

sizes and types similar to those which are to be submitted to test. For
instance, if it were desired to conczuct tests on frosted laixzp in one of

the smaller saheres, standardized frosted lamps must he provided. Clear
gas- -filled 150 watt lamps would require a clear gas-filled 150 watt stan-

-:J
L

dar zed lamp. This irnracticability is reroved by conducting tests with
spheres 30 inches in diameter or greater. The error involved by using
one or probably two standa dized lamps to cover all comnercial sizes and
types, is negligible for a sixty-inch sphere. The st and.rd aid test
lamps can occupy positions in he sphere si.xl3aneously. They can be
Operated with base up or down according to design. The standard remains
in the sphere, thus requirilt no further handling. Lamps for testing are
ntroduced into the sphere in succession, and rea ings taken. Lbsorption
due to glass anl lamp bases is compensated for in this procedure. The

test lamp output is again calculated as described ahove; namely,

_ A," 3‘
¢ _¢if 41 AI.

 

When the set of lamps under test are alike, the absorption is

81.

practicall;r constant, hence A‘ls a constant, and it will not be neces-

 

ear" to check this ratio for ee ch larp. Inen the lamps tested in suc-
cession differ widely, readings for A and B are followed by those
for A and B1 for each lamp. To further nandlin; of the standard-

ized lamp is necessarv after insertion in its place in the sphere, un-

til tests are completed.

72

Lamp Lssenblies

 

Yearly all lamp assemblies absorb sufficient light to render

4K: / . Calibration and tests on lamp assemblies carnot he conduc-

o - 1 ... H
ted in the manner described under "hare Lamps without ir troducing an

appreciatle error. When dealing with a lighting unit whose I. S. C. F.
or total luminous output is desired, it is cuStomarj'to insert the unit
0 I. q

and standard lamp in the sphere m1 ultaneously. Consider, lor example,

.L
It

[—30
U1

3 suspension type which would normally be hung from the ceiling.

convenientlr located along the vertical azcis of the sp here and directl"
over the calibrated lamp rounted along the same axis through the Open-
calibrated first. Under these conditions

the trightness of the window

1

is a measure of he relative ahsorption in tne sphere when the test unit

he standard lanp circuit and closing that of the
test lamp, anothe brightness reading is obts ined for the window. The
two ree dings thus obtained, plus the known luminous output of the stan-
dard lamp, enable one to compute readily the luminous output of the test
unit. The ar*"n£enent is shorn in Fig. 10. Separate screens are pro-

vided for both test and standard lamps. The screens are located paral-

the

U!
.1

lel to the vertical axis of the sphere. This djustnent,

fl

since both screens are conveniently raised or lowered along a common

screen support. Fig. 10 also discloses a srall screen 5' placed so

‘

as to intercept the rays of light from L1 to L. This refinement

should he considered when the intensit3rof illumination of L1 in the

direction of LlL is reasonably pronounced, and when the suriace area

of L exposed to re.vs from L1 is large. Whether the auxiliary screen

73

5' shall be employed in tes tine lanp assemblies will depend upon the

(.3

distance LlL’ the intensity of L1 in the direction LlL, the surface

area of L exposed to direct light from Ll’ aid the coeffi cier t of ah-
sorption of L. areful consideration of these factors will in each ca-

se determine the advisability of using 3'. Generally, however, when the

u 0 n ’1 0 u
diameter of the sphere is 60 or greater, the use 0: 5' ll be liri ted.

 

 

 

 

 

 

\/\\L\ P 'C
- _ I’N _ ["\
_v_ V

 

H/Z/ U

 

 

n the avent .a 3' should he called into service, it will be neces-
sary to detern nine the luminous output of the aggregate; namely, Ll pro-
‘th s'. This is accomplisled ov comparing the aggregate'wit. a
well calibrated bare lamp, which is equivalent to calibrating the com-
bination Lls'. Knowing the luminous flux emitted by Lls', tests are
made in the manner described above. Lquations (l) and (2) page 44C)
serve as a check on the probable screen errors 6: and ewin an; par-

ticular lamp asserbly test.

Use of Sphere without Diffusion Glass Window

 

It is desirable to have one or more diffusing glasses available
to replace an impaired or broken glass. To meet the contingency in the
event breakage occurs during a period of continued tests, it is possible
to Operate the sphere without the diffusing glass. A slight, temporary
change in design will readily solve the problem. Remove the existing

screen rod with its screens. The resulting recesses in the wall of the

 

 

 

 

 

 

 

Fig. 11

sphere may be filled with dry, white blotting paper tightly wrapped to
fit the holes. Locate points v1 and v2 symmetrically with respect
to w1 and W2, and press rubber vacuum bushings coated with sphere
paint into place with centers at V1 and v2 as indicated in Fig. 11.
Insert screen rod into the rubber bearings. The rubber bushings must

be sufficiently rigid to hold rod and screens in normal vertical posi-
tion; hence, the rubber should be only mildly flexible. When determin-
ing the luminous output of lamp units in this manner, it is self-evident

that a screen must be employed whose dimensions will not obstruct the

bright spot on the wall of the sphere diametrically opposite the window

74

75

U)

opening. The screen should be as mall as possible in keeping with min-

is um screen absoz rption, and vet S‘a fficiently larre so that no portion of

I.

.-J
l—J
{—1

the field of View in the photometer head is n1nated by once reflec-
ted light coning from the wall opposite the'window. In other words, for

all possible positions of the photometer head over the Operating range

the field must be ill m'nated by diffusely reflected light emanatina

("

from that portion GIGZ of the sphere screened from the direct rays of

the source. The screen support has a fixed locat on relative to VV'
for minimum screen error; the adjustment is att ained by'modifyin: the
size of the screen, the range of the photometer head, or both. The area
of uniform brightness GlG2 now becomes the test source. Keasurements,
including calibration, foll ow in e.ac ctly the same manner as outlined for
the photometer equipped with diffusing g ass. It is at once apparent

1F 1r

that L cannot occupy all positions along VV' from a =-2rto c = -—z--

Thi constructional restriction is: Hinixized when photonetering bare

Yeasurement of Transnission and

 

Re ection Coe ficients for Diffusir Nedia

Diffusing media play an important role in a variety of lanp ac-
cessories us ed to overcome glare and produce the soft shadows anc gen-
erally pleasing effect characteristic of many types of direct and semi-
indirect units. The latter not only diminish the light, but scatter the
flux in such a manner as to produce much th 89$le effect as obtained from

a diffusely reflectin“ surface. The s,here photometer can he used con-

“0

:Jo

veniently to determine the coefficient of transns Hie- of diffusing media,

since the sphere can be relied upon to integrate the effect produced by

76

these substances. 'fe begin by measuring the total lumens of a source
"without the diffusing unit. Then the source is enclosed by the diffu-
sing glass, and the readings obtained for balance of'windcw and compa-
rison lamp enable one to obtain the total lumens of source with diffu—
sing bowl. The ratio of flux thus ohtained to the bare lamp flux is the
coefficient of transnission. In case the bowl does not completely sur-
round or enclose the source, the above ratio still represents the average
transmission factor, since ¢I=I°w - Lw,

In order to obtain the diffuse reflection factor, one may'utilize
the circular Opening at the tOp of the sphere to admit light from an ex-
terior source. If this flux be measured with the aid of a convenient
standard lamp, and then allowed to fall upon a plane specimen of the dif-
fusely reflecting material arranged at any desired angle within the
sphere, a second measurement will enahle one to compute the flux reflec-
ted and the coefficient of diffused reflection for the given anfile of
incidence. The reflecting medium here functions simultaneously as sour-

ce and screen.

Reflection Factor of there Paint and

 

Transmission Coefficient of Diffusion Glass Window

It was shown in the discussion of the theory of the sphere that
. *y I“! .
the constant 18 z: ————:= —————- . If is a known flux from a
¢ Aw¢
carefully calibrated lamp, and 1w is balanced against a known inten-

sitv IC of a comparison lamp, then K, the constant of the sphere, is

determined. The constant may be expressed in a somewhat different form.

77

K: K/4w= I “'1'
57%;!— ” ' KI: 33-79
" = 5;ng ‘7???“

,6 = $321—$— for 7': / (no diffusion glass)
wv

Thai.

Since

 

Thus, the reflection factor of the sphere paint may-be obtained
from measurements of s3mlere constant K' without diffusion glass and
the radii r and 10 of sphere and window respectively. The source of
known lurens ¢ must be screened so that no direct rays will fall upon
the part of the sphere wall opp031 tb e window and visible to the ob-
server stationed at the photometer head. If this precaution is not taken,
the brigh ness of that Ivortion of the sphere will be non-uniform due to
he component of direct illumination from the source which follows the

photometric distribution curve. The reflect on f9 ctor thus obtained,

3

1

however, will not be tie true coefficient for the wall pa nt, siice the
inner surface of the window will generally reflect differently than the

mt accurate for practic:1l

Ho

paint. file result for k will be su- nfc
considez ations. Since k is independent of 1?, measurement of K' may
be made with the window in pla e and 5‘ computed from known values of

the constants

 

The sphere photometer can be used with anv of the modern equip-

ment des i Hned 0 measure luninous intens itv, brightness, or illurinat ion.

78

Th e She.rp-Eillar photozeter, the Iacheth illurinoreter, and the ther
photometer are well adapted to sphere photometry. The Weston Photronio
Cell, if calibrated to read in foot-candles, ray he used to measure the
illunination produced on the sensitized disc by the window openi n.'j in
the sphere. Due to the fact that certain fares of the spectrum of the

eye differently,

illumination produced ty the window affect the cell any

the cell can be relied upon only'when used to measure light of the sane

4...]

arecter for which the cell was standardized. This liri Ho ion nay he

ch

overcore by the use of color filters, whereby a given source of mild
color tone may be made to register the illunination on the disc which

turn is proportions to the luminous output of the source.

“dv:1ntcges of the Sf: hcre lhot onet er

h.---_—-' “_

 

 

 

' §

To derive all of its nosril21e advnns1ges, certain car~ in sand-

th sphere must be closely observed. Since all parts of the spher-

ical shell are rore or less 1n tension it is recommended not to sena-

....-l-
, A

phere into upter and lower hemispheres, in order to preserve

«:3
Ci-
(D
CE
b
m

Anent at the window. When necessary to separate the sphere into

‘ c

henispheres preps atorv to man1ng a change in location, the contour a-

long the plane of separation should be refinished writh Sphere faint ul-

ter asserhly. It is advisahle to check the constant of the there tefore

and after moving, using the sane standa d toth tires. The sphere paint

coating will teoone soiled and discolored with age and should he renewed.

If soiled, the finish should he cleaned with ce.rhon tetrachlor1(e and

given 0 light coat of sphere paint. If clean but discolored, 1t 18 suf-

(s

ficient to annlv one coo t of sphere paint. The upper and lower conduit

79

m

assexolies may be refinis ed outside the Sphere. ihe side asscrbly can

be removed and

sition

painted, tut a simpler procedure is to refinish it in po-

care to protect the adjacent surinces Tron stray paint.

vantages in the use of the sphere rhotometer are:

simplicity in construction.

Limited adjustment of parts.

gbsence of flicker due to rotation of lamps.

Ll tion of am

fJo
‘1

Ho
:3

p
c I'
i—Jo
O
:3
O
“J
C)”
"S
O
F3
'p'
C”?

(I)
{L
C
CD
(.1.
O
*1
O
"U
(n
0

Use not confined to dark room.
Greater accuracy ban other types of integrating

rhotoneters.

8O

CALIBRATION

As previously described, the constant of the sphere will depend
upon the nature of the interior finish, and is affected by the presence

of light absorbing surfaces.

It was shown that the constant may be expressed in various forms.

It is convenient, when using the bar photometer, to standardize the

 

 

 

 

 

 

 

\ \
-;£;-
“—1F_‘
a}
IQ

 

 

 

 

. Sid.

Fig. 12

sphere in terms of candles per lumen; that is, candle power of window

per lumen output of source.

The 60" sphere was standardized using a two meter bar photometer.
A fixed point near the left end of the latter was set at a distance of

60 centimeters from the surface of the window. See Fig. 12.

81

Notes and Data

 

Standard Lamp. Std.
Tungsten Filament, B. S. No. 3264, standardized base up by the
United States Bureau of Standards.
Volts 105.0
Amperes 4.227

Lumens 8040

Comparison Lamp. C.
vacuum.Tungsten Standard Lamp, B. S. No. 4772, E.T.L. 5452,
standardized by the United States Bureau of Standards tip up

and stationary.

Vblts 109.0
Amperes 0.350
Candles 33.8

The above figure, 33.8, represents the candle power in the direction
normal to the screen in the Lummer and Brodhun photometer head.

The sphere was standardized with upper conduit assembly removed,
top closed, lower conduit assembly in place, and wall finished with one
coat of sphere paint. The diffusion glass was used as furnished by

Leeds and Northrup Company.

82

Photometer Bench Readings.

 

.4... .4... Std. _c__

82.7 cm. 82.8 cm. E I 105 Volts E .- 109 Volts
84.1 " 81.8 “ I = 4.24 Amps. I - 0.358 Amp.
81.7 " 81.5 "
81.6 " 82.6 “
82.3 " 81.0 "
82.4 “ 81.0 “
82.6 " 82.6 "
82.5 "

The mean value for A from the table is A = 82.21 cm.

 

Calculations
_..r_.,_ .. __A‘
R _ (ace-A)‘
__._ I _/4_‘__
c:(accr-¢l)‘

’ A: It - '4‘
¢ ¢ (aw-A)‘

 

 

a
’2 33" (’2'1’) =1. 0- 00099 candles per lumen.
80 Y0 (no-02.2!)
- I” 7'22 0 [/6' candles
= —: _ = 0 per sqe cm.
5” A... 62.07

bW = 0.36442 lamberts = 364.42 millilamberts

_ é. _ 3090 _
5+1I“— _——’—r—_631.e+ c.p.

83

The discrepancy in the current readings is due in part to the current

taken by the voltmeters, i , as well as to slight variations

”‘5;
in effecting the scale readings.

The constant of the sphere for the conditions above described
is K' = 0.00089 candles per lumen.

Calibration curves for the sphere may be obtained with various
sizes and types of bare lamps. As pointed out in a previous discussion,
however, the variation in K' will be negligible when conducting tests
on such lamps in the larger spheres. It is advisable to check K' when

measuring the luminous output of lighting units having an appreciable

absorption.

BIBLIOGRAPHY

 

Transactions of Illuminating Engineering Society.

Vol. III, No. 7, October 1908, p. 502.

Text in Illumination, by Kunerth.

Illuminatin Engineering, by F. E. Cady and H. B. Dates, 1925.

Light Photometry and Illuminating Engineering, by W. E. Barrows, 1925.

Illuminating Engineering Practice.
Lectures on Illuminating Engineering delivered at the University
of Pennsylvania in 1917 under Joint Auspices of the University

and the Illuminating Engineering Society.

The Integrating Photometric Sphere, by E. B. Rosa and A. H. Taylor.
Transactions of Illuminating Engineering Society,

Vol. XI, 1916, p. 455.

Sphere Photometer, by R. Ulbricht, 1920.

Lehrbuch der Photometrie, by Uppenborn-Nonasch, 1912.

Advanced Calculus, by woods.

Theory of Equations, by Dickson.

Handbook for Electrical Engineers, by Pender.

 

214,;

 

 

 

 

 

 

”RED WOOD- WELL 55/750pr 4 4 ,1ng W009 :1!sz 55,4750pr

/ REQUIRED / / REQUIRED

/"
9346 0.5.5. rRR- £532 DRILL

2 HOLES - U___J_'_£ 52" g"
SETJCREWJ

 

 

 

 

 

 

 

 

 

 

 

 

 

ROI/”050 7'0
1" / 7' (9.5 TIA/6'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

U. Q. 5. 6.4.

55557 JTEEL ”-5.5. CF20

SHEET JTEEL

 

 

/
./

"a - 5,? "£1.47 HERD

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

52 2 ,1-
4‘» ~   ’ —
6’ i ,9 gg.‘ _ , 34-? D__R____//.L
DRILL
c) e _
-/ BETH/L N0. /4 _ Harm)“ DETfl/l. N0. /6 - / REQD.
MATE/{NHL '- C.R. 5.

 

 

 

31“; A32!- MCH. 57:
4 R600.

 

   
  

3,, 32 at
law Lag
/ REQD.

 

 

 

 

 

 

 

BETH/L N0. /4 - / R5012

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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- - \ I r I _$pg u 1; TA' — .
.— =2 /s u .5 5 TRR 54352216222. ‘_ 3;- _- - 2-,: X -p M, p
Z HOL £5 , , ..__ i i" j ‘ ' ‘
[—6 '5 33-2 DR/L L

 

 

 

 

DE 774/1. N0. /7 - I REoD.
JCflLE.‘ ’42-1”

 

 

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52- DRILL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 HOLES
DETR/z. No.7.
DErn/z. N0. 6
——-+—+;-.:_ DE TAM. N0. /5 BETH/[.5 " SRHERE‘ PHO TOME TE)?
3, I, J DErR/L xva/s W-4REQQ MCH 5T~IREQD ' ,
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