THE MAGNETIC SUSCEPTIBILITY OF OXYGEN AND NITRIC OXIDE
AT LOW FIELD STRENGTHS

By
Albert

Burris

A THESIS
Presented to the Graduate School of Michigan State College
of Agriculture and Applied Science in Partial
Fulfillment of Requirements

for the Degree

of Doctor of Philosophy

Physics

Department

East Lansing, Michigan
1943

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2

-

TABLE OF CONTENTS
Page
I. INTRODUCTION

4

A.

Magnetic materials.

Susceptibility.

B.-

Calculations from theory.
1. Oxygen.
2. Nitric oxide.

C.

Measurement of magnetic susceptibility.

D.

Other measurements on oxygen andnitric oxide,
1. Oxygen.
2, Nitric oxide.

II. THE RANXINE BALANCE
III. APPARATUS

4
7
7
9
10
14
14
16
17
22

A.

The
1.
2.
3.
4.
5.
6.
7.

magnetic balance.
Construction.
The magnet.
The test cell.
Cell filling arrangement.
Control circuit.
Temperature effects andcontrol.
Sensitivity and stability.

B.

Production of quartz fibers.

IV. EXPERIMENTAL PROCEDURE

22
22
24
25
27
27
29
35
37
44

A.

Liquids.

44

B.

Gases.

45

C.

preparation of gases.
1. Oxygen.
2. Nitric oxide.

45
45
47

D.

Analysis of nitric oxide.

48

V. EXPERIMENTAL RESULTS

51

A.

Benzene.

51

B.

Oxygen.

52

-

3

-

EXPERIMENTAL RESULTS (continued)
1.
2.
3.
C.

Undried tank oxygen.
Dried tank oxygen.
Electrolytic oxygen.

Nitric oxide.

CALCULATIONS.

52
53
54
56
57

A.

Oxygen.

57

B.

Nitric oxide.

58

DISCUSSION

59

A.

Preliminary results.

59

B.

Electrolytic oxygen.

61

C.

Nitric oxide.

61

CONCLUSIONS

63

LITERATURE CITED IN THIS THESIS

65

ACKNOWLEDGMENTS

68

-

4

-

HJTHQDUCTION
A*

Magnetic Materials*

Susceptibility*

With respect to their magnetic properties material substances
may be classified as ferromagnetic, paramagnetic, and diamagnetic*

When

placed in a magnetic field, ferro- and paramagnetic materials acquire a
net magnetic moment in the direction of the applied field#

Diamagnetic

materials acquire a magnetic moment opposite to the applied field*
The magnetic moment per unit -volume per unit applied field
strength, usually denoted by fc , is defined as the volume susceptibility
of the material#

The corresponding quantity,

called the specific or mass susceptibility*

X , per unit mass is
Another quantity, X * .

the

molar susceptibility, is defined as the magnetic moment per mol per unit
field strength*

These quantities vary widely for the different types of

magnetic materials and are negative for diamagnetic materials and positive
for para- and ferromagnetics#
Bismuth, which is one of the most strongly diamagnetic materials,
acquires a moment very small in comparison to that exhibited by many para­
magnetic materials*

In turn, most paramagnetic materials exhibit moments

very small in comparison to those acquired by ferromagnetic materials,
such as iron cobalt and nickel#

For purposes of comparison the following

table of approximate values is given*

-

Table !•

5

-

Approximate value of the susceptibility for various types of
magnetic materials#
Material

Type

Susceptibility

Water

diamagnetic

7.200 x 10“7

Oxygen

paramagnetic

1.06

Nickel

fe rromagnet ic

3.0

Iron

fe rromagnet ic

2.5

x 10"4

x 10 2

According to the molecular theory of magnetism, each molecule
or atom is assumed to be a magnetic dipole#

In the case of diamagnetic

materials the dipoles are created by the applied magnetic field#

In

paramagnetic materials, on the other hand, the atoms or molecules are
supposed to be permanent dipoles -which are oriented at random in the un­
magnetized state and thus produce no external magnetic effects#

'When

a magnetic field is impressed the magnetic moment vector of the atom or
molecule is caused to precess about the field direction, giving rise to
a net moment in the direction of the applied field#
Diamagnetism may be accounted for on the basis of Amperian
currents within the atom#

An electron revolving about its nucleus is

equivalent to a circular current; the strength of wh.ich, depends upon the
angular velocity of the electron.

Such a circular current gives rise to

a magnetic moment, wnose value depends upon the angular velocity of the
electron#

In the absence of an impressed field a diamagnetic atom exhib­

its no net magnetic moment due to orbital or spin moment of its electrons#
The absence of a permanent moment is associated with uhe fact that the

-

6

-

number of electrons in the molecule, in a great majority of cases, is
even and the electron spins are balanced in pairs • The orbital moments
either compensate each other or do not change their orientation in an
applied field owing to strong electrostatic forces within the molecule.
However, if an external field is applied there will be in general a com­
ponent normal to the plane of a particular electron orbit#

When a field

is applied normal to the plane of an electron orbit and in the direction
of the angular velocity vector, the angular velocity of the electron is
decreased without changing the size of the orbit#
crease in the moment in the direction of the field*

This results in a de­
A field applied

opposite to the direction of the angular velocity vector increases the
angular velocity, thereby increasing the moment opposite to the field
direction#

For a group of Amperian currents oriented at random the effect

is a net magnetic moment opposite to the field direction#

Such a result

is also predicted by Lenzfs law, for the induced moment would necessarily
be opposite to the inducing field if no permanent dipoles were present#
All materials, therefore, tend to be diamagnetic, but this tendency is
completely masked in certain materials (para- and ferromagnetic) by the
much larger effect due to permanent dipoles#
Since diamagnetism is a fundamental property of the atom, the
effect does not vary appreciably with temperature#

No variation in the

diamagnetic susceptibility with field strength is expected for saturation
is not approached with fields obtained in the laboratory#

Likewise, para­

magnetic materials are not saturated with fields obtained in the laboratory,
but the susceptibility does vary with temperature#

This is due to the

_

7

-

thermal agitation -which reduces the effective component of the permanent
magnetic moment in the direction of the applied field*

On the other hand,

the ferromagnetic susceptibility varies widely with both temperature and
field strength*

For this reason the theoretical treatment of such materials

is more difficult than for para- and diamagnetic substances*
This thes-is deals with the experimental determination of the
susceptibility of oxygen and nitric oxide at low field strengths.

These

are the only two common gases which have a permanent magnetic moment*
They are both therefore paramagnetic and the theoretical value of the
susceptibility has been calculated in each case*
B*

Calculations From Theory*
1.

Oxygen •
In 1905 Langevin (1) derived, on the basis of classical

electrodynamics, the formula

* ="[< + # r ]
In this equation fc

for the susceptibility of a paramagnetic material*

is the volume susceptibility, N the number of atoms or molecules per unit
volume,

the magnetic moment of the atom or molecule, k Boltzmann fs

constant, and T the absolute temperature* oC

is a constant independent

of the absolute temperature and represents the induced diamagnetic moment*
c<

is usually negative and small in comparison to

generally neglected in paramagnetic calculations*

3KT

* It is

Van Vleck (2) has shown

that the above equation can be derived quite generally on the basis of the
new quantum mechanics*

He has considered the special cases of oxygen and

-

8

-

nitric oxide (3) from the quantum mechanical standpoint*

For oxygen, the

formula obtained is

K — N£4*S(S+l)t

J 3 KT1

(la)

When applied to molecules, the quantities in the above equation have the
following significance•

is the volume susceptibility of the gas, N

the number of molecules per unit volume, s the total spin moment,

<rK

the resolved electronic angular momentum along the nuclear axis, and ^
the magnetic moment of one Bohr magneton*

The measured value of the

susceptibility indicates that the ground state for the oxygen molecule
is a

state, for which s a 1 and

— 0*

been confirmed by analysis of the oxygen bands*

This ground staue has
If these values of s and

(J^ are substituted in the above formula, the equation may be written

S L/3 *

3 KT

m

where
number*

is the molar susceptibility of the gas and L is Avagadro's
The product X T

\

XT

is therefore given by
T

—
—

% LPh
3K

(lb)

is easily calculated from fundamental constants and is

therefore convenient for comparison of experiment with theory*

Equation

(lb) is a mathematical statement of Curie*s law, than is, that the molar
susceptibility of a paramagnetic material is inversely proportional to
the absolute temperature*

-

9

-

Using recent values of the physical constants (4) in the calculations, Equation (la) gives 0*142 x 10” for the volume susceptibility
of oxygen at 20°C and 760 mm pressure*
x*j

is 1*000*

From Equation (lb), the value of

It should be pointed out that this result is somewhat

larger than the value 0*993, as given by Van Vleck (5)*

The difference

results from slightly different values of the physical constants in the
calculations•
2*

Nitric Oxide*
Nitric oxide requires special consideration since the separation

of the energy levels in the ground state of the molecule is comparable to
the equipartition allowance kT*

It is known from band spectra data that

the multiplet width is about 120*9 cm”'*', which results in an energy
separation of about 0*6 kT*

In the case of oxygen the multiplet width is

less than 1 cm”"*# The corresponding energy separation is therefore small
in comparison to kT and can be neglected in the derivation of the suscepti­
bility formula*
An inclusion of these so-called umedium frequency terms” results
in the formula

K. - - ^ © 1

3KT

■where

4

i - o* + x e -x
x + xe~*

,^

6

and
for the volume susceptibility,

KT
a of nitric oxide.

(

2)

-

In these equations AT?

10

-

is the separation, in wave numbers, of the two

component normal states of the molecule and h is Planck's constant.

The

other symbols have the same meaning as in the previous equations.
A calculation of

, using Equations (2), gives 0.0597 x 10"

for the volume susceptibility of nitric oxide at 20°C and 760 mm pressure.
This value rather than 0.0600 x 10“ , as given by Van Vleck (3), results
from the use of more recent values of the physical constants in the cal­
culations •
The value of the apparent Bohr magneton number,

©
/j- , as

calculated from Equations (2), with AT? —1 120*9 cm“^, is 1.836 at 20°G •
This quantity changes somewhat with temperature and is a measure of the
deviation of the susceptibility of nitric oxide from Curie's law*
0.

Measurement of Magnetic Susceptibility.
The most common procedure in determining the susceptibility of

para- and diamagnetic materials is by means of the non-uniform field
method. With proper modification of the apparatus either absolute or
relative measurements may be made on solids, liquids or gases.

In

principle the method depends upon the fact that when a specimen is placed
in a non-uniform magnetic field a force acts on it which is proportional
to the difference between the susceptibility of the specimen and that of
the surrounding medium.

If the specimen is paramagnetic It tends to

move into the more intense field and In the opposite direction if dia­
magnetic.

Actual measurements involve the -use of some type of balance to

determine the force acting on the specimen, or at least a quantity pro­
portional to the force.

11

-

-

For measurements on liquids a simple form of tne apparatus is
a IJ-tube partially filled with the liquid to be tested and so placed that
one meniscus is between the pole pieces of a powerful electromagnet*
If V

When the field H is turned on the level of the meniscus is altered*
is the small change of volume of liquid in the field,

, and fC^ , the

susceptibility of the liquid and air respectively, then uhe change in
magnetic energy is

The change in gravitational potential energy is

f

xdx =

O
where yO

is the density of the liquid (air neglected), A the cross-

sectional area of the tube, and h the change in height of the meniscus*
Equating the two gives

v _ u

*£
from which

—

*«. —

3l ?PV\

--

/C may be calculated if
JL

is known*

This type of balance, known as the manometric balance, has been
greatly improved by Wills and Hector (6) for measurements on gases*

In

this method the gas is balanced magnetically against a solution of known
susceptibility*

Instead of observing the motion of the meniscus directly,

the motion of gum-mastic particles in a constricted portion of uhe tube
was observed with a microscope*

This indicator is very sensitive and an

accurate balance can be obtained*
Wills and Boeker (?) have further modified this form of balance

-

12

-

in their work on the variation of the susceptibility of water with temper­
ature*

In this experiment the water in one a m of the balance was heated

to various temperatures and balanced magnetically against the water in
the other arm, which was kept at the reference temperature• From the
measurements, the ratio of the susceptibility at temperature t to that at
the reference temperature could be calculated.
In the method devised by Curie (8) for determining the suscepti­
bility of solids, a small sample of material of volume V and susceptibility
is attached to the arm of a balance and suspended in a non-uniform
magnetic field H in air*

The force, which is measured with the balance,

may be derived from the change in magnetic energy*

This force, say in the

x-direction, is given by

Knowing

, the field H and its gradient, the susceptibility of the

solid can be calculated*
Son£ (9) has used the principle of the Curie balance to
determine the susceptibility of several gases, including nitric oxide,
relative to water*

In this case the solid was replaced by a rather long

capsule into which the gases could be introduced*

From a measurement of

the force exerted on the capsule when evacuated, when filled with the gas,
and when filled with air the susceptibility of the gas relative to air
could be deduced*

Knowing the susceptibility of air with respect to water

the results could be referred to water as a standard.

Since the magnetic

effect of gasses is small, the measurements were made with the gas under

-

13

-

several atmospheres pressure*
Another metnod for gases for which high sensitivity is claimed
is the Faraday test body method*

A light test body is suspended, by

means of a fine torsion fiber, in a gas in a suitable container placed in
a non-uniform magnetic field*

Under these conditions a torque acts on

the test body which is proportional to the difference between the
susceptibility of the test body and that of the surrounding medium*

If

- Tq is the difference between the torque on the test body when
surrounded by the gas under test and when in an evacuated space, and
- T0 the corresponding quantity for the standard gas, it is easily
shown that
A*

—

X

- T„

Ts - To
where fCX and JC are the susceptibilities of the gas under test and the
standard gas respectively* The calculation for
carried out by
replacing the torques in the above equation by the corresponding angular
twists of the fiber necessary to restore the test body to its initial
position*

For high sensitivity the test body should be made as nearly

magnetically neutral as possible-*
Havens (10) has used this method to determine the magnetic
susceptibility of nitrogen dioxide relative to oxygen*

The test body

consisted of two small evacuated glass bulbs attached together, with a
compensating cross-piece of quartz*

By the use of fine quartz fibers for

the suspension a sensitivity of 3 x 10*"-^ was reported for volume
susceptibility measurements*

-

14

-

In general, relative measurements of this sort are more easily
carried out and are more accurate than absolute measurements since a
knowledge of the field or its gradient is not necessary.
In all of the methods described above the sample is either
suspended, or placed in some manner in a strong, fixed magnetic field.
This appears necessary because the magnetic effect of para- and diamagnetic
materials is extremely small.

However, in 1933 Kankine (11) described a

novel form of balance designed for measurements at low field strengths.
He later constructed such a balance, but it failed to function with the
requisite sensitivity, largely because of ferromagnetic impurities in
some of the materials used in the construction (12).

The principle of

this balance is fundamentally different from the others in than the sample
is fixed while the magnetic field is supplied by a small suspended bar
magnet.

This type of balance, as improved by Iskenderian (13), is used

in the present experiment and will be subsequently described in detail.
For a more detailed discussion of the various other methods for
measuring magnetic susceptibility see E. C. Stoner, Magnetism and Matter,
Cnapter III.
D.

(Methuen & Co. Ltd., London.

1934)

Other Measurements on Oxygen and Nitric Oxide.
1.

Oxygen.
The susceptibility of oxygen has been the subject of a good

many investigations • The gas was particularly well suited to early and
less refined methods, for it is strongly paramagnetic and may be prepared
in a pure state with little difficulty.

The variation of the susceptibility

-

15

-

with temperature follows Curie's law quite closely over a very wide
temperature range#

The theoretical value of the product X * T is accur­

ately known and so furnishes an excellent means of checking various exper­
imental methods•
The experimental values of ~Xm T

from several independent in­

vestigations at high field strengths are in essential agreement with the
theoretical value*

Some of the results obtained are as follows?

(14)

0.983 (Curie), 0.970 (Onnes and Oosterhuis), 0*975 (Son6), 1*001 (Bauer
and Piccard), 1*021 (Wills and Hector), 0.979 (Lehrer), 1.002 (Woltjer,
Coppoolse, and Wiersma).
Iskenderian (15) has used the Rankine balance to make measure­
ments on oxygen at a field strength of about 40 oersteds.

Previous

measurements on the gas had usually been made at field strengths of the
order of several thousand oersteds.
X,t

He obtained the value 0.979 for

, whicn is definitely lower than the theoretical value.

The low

value is apparently due to the faot that the gas used was tank oxygen
which, as he points out, probably contained some diamagnetic impurities.
From his results it appears that there is no appreciable change in the
susceptibility over uhe range of field strengths of from several thousand
to some 40 oersteds.
On the other hand, Hector and Peck (16) have used an improved
form of the Hughes induction balance to make measurements on oxygen and
several liquids an field strengths of from 5 to 35 oersteds*

They have

reported finding oxygen approximately 7 per cent more paramagnetic and
water about 6 per cent more diamagnetic in these fields than in strong

-

fields*

16

-

Following a suggestion by G* Temple (17), Meeks and Jamison (18)

used a modified form of the Eankine balance which makes possible absolute
as well as relative measurements if the distribution of magnetism in the
suspended magnet is known*

Relative measurements were made on carbon

tetrachloride, benzene, and toluene using very pure samples*

Measurements

on each of these three liquids gave values (assuming -0*7200 x 10”

for

water) which were in excellent agreement with those reported by others
using strong fields, indicating that a discrepancy of 6 per cent did not
exist between the susceptibility of water in high and low fields*

This

makes the reported variation for oxygen appear very questionable*
Jamison (19) later reported that preliminary absolute measurements on water
yielded a value a few per cent below that obtained at high fields, but
staced that refinements in experimental technique and computations might
well bring the two values into agreement*
2*

Nitric Oxide.
Relatively few measurements of the susceptibility of nitric oxide

have been carried out*

The gas is rather strongly paramagnetic, its

susceptibility being a little less than half that of oxygen*

However, it

is somewhat difficult to prepare in a pure state and is not easily handled
since it combines readily with oxygen to form the dioxide*

The few re­

liable values of the susceptibility available have been obtained from
measurements on the more or less impure gas with corrections applied for
the susceptibility of the impurities.

No previous measurements on this

gas at low fields have been reported*

Values of the mass susceptibility

of nitric oxide, from measurements at high field strengths, have been re-

-

ported as follows:

17

-

46*68 x 10"® (Weiss and Piccard (20)), 48*7 x 10"®

(Bauer, Weiss and Piccard (21)), 48*80 x 10"® (Sone (22))*
ponding values of the volume susceptibility, K

The corres­

, at 20°C and 760 mm

pressure are 0*0583 x 10“^, 0.0609 x 10™^, and 0.0610 x 10”® respectively,
or approximately within 2 per cent of the theoretical value*
II*

The Bankine Balance

If a bar magnet is placed parallel to the surface of a
magnetizable material a force is exerted on the magnet due to a distor­
tion of its field by the material.

This force is an attraction if the

material is paramagnetic, and a repulsion if diamagnetic*

The force is

proportional to the susceptibility of the sample and is given approximately
by the equation (23)

P =

TT'T'”* &

r

where m is the pole strength of the magnet, JC

the volume suscepti­

bility of the sample, and x the distance from the magnet to the surface
of the material*

To make use of this effect in the determination of

susceptibility, an apparatus such as that pictured schematically in Fig* 1
is used ♦
In this arrangement the magnet M is suspended close to the
cell

C,into which liquids or gases may be placed*

made

bymeans of a fine quartz fiber F attached to a short and very light

beam

B* The magnet is counter balanced by the weight W.

turn supported by another quartz fiber attached

go

The suspension is

The beam Is in

a torsion head above.

18

The deflection of the suspended system

F

is measured by means of the mirror 0#

W

Current in the control wire N is used

*— I —

O

to return the magnet to its original

--F

position against the force exerted by
the sample.

B

- O

This type of suspension
-c

is designed to reduce the control on
the system from extraneous magnetic
Fig. 1

fields, "which may in some cases
entirely mask the effect sought.

Unless the magnet has a horizontal

magnetic moment, a uniform magnetic field does not exert any directive
torque on the beam.

However, it is found in practice that the poles of

the suspended magnet do not in general lie on a vertical line even when
the axis of the magnet is vertical.

This introduces a horizontal moment

and therefore a directive torque on the beam in a uniform magnetic field.
In general the axis of the magnet will not be exactly vertical because of
a slight tilt due to the earth*s field.

This effect also contributes to

a horizontal moment»
By making the torsion constant of the lower fiber small in
comparison to that of the upper fiber, the torque on the beam due to
extraneous fields can be considerably reduced.

Rankine (24) has shown

that the effective torsional coefficient of such a system is given by

where 7" as

"kke torque on the beam (due to the force

-

19

-

between the specimen and magnet) to the resulting angular displacement,

/ and '7' ' the torsion coefficients of the upper and lower fibers
respectively,

horizontal moment of the magnet, and H che ex­

traneous uniform magnetic field*

a and may be neglected*
and if

In practice iffr H is small compared to

The expression then reduces to T 5* r + T

T'// is made small in comparison to

T*^ »

effective torsional

coefficient is nearly that of the upper fiber*
Iskenderian (13) has further reduced the effect of the ex­
traneous fields by suspending the magnet as follows j A Duralumin hook
is attached to the magnet so that the
tended axis of the magnet*

point of the

hook lies on the ex­

The point of this hook

is tungsten tippedand

rests in a jewel set in a Duralumin ring attached to the upper fiber*
It was found early that all ferromagnetic materials must be
avoided in the construction and in the immediate neighborhood of the
balance*

Sucn materials distort the otherwise practically uniform earth*s

field and exert a torque on

the beam, which may be

exerted by the sample*

effect of such materials is to impair the

The

sensitivity of the instrument*

greater than that

That the balance be constructed of materials

free from ferromagnetic impurities seems to be one of the most important
specifications in the design of a successful instrument*
The factors which determine the sensitivity of the balance can
be deduced from Fig* 2, which shows the arrangement viewed from above*
In this figure the beam is supported at 0*

b is the arm of the balance

which carries the magnet represented by m, at a distance x from the face

-

2 0

-

C£LL

of the cell.
The equilibrium condition for
the beam is

T0 + T +

r ( 0 + e o) = o
A. A

O
Fib. 2

where TQ is the torque due to extraneous fields and to the magnetiza­
tion of the cell by the magnet, T the torque due to the current in the
control wire, and d o an unknown angular displacement of the beam.
If To and T are held constant, then

A©

■*------ ■ I ^bsiwae - x c o s e
1T/m
abSiNeL

■jjr r n a-b/C-2T~j

The precision in a measurement of /£ will be greatest when the above
expression is a ninimum.
the optimum value of Q

In the balance designed by Iskenderian (25)
was found to be about 29°, but due to accidental

disturbances, an effort to obtain greater sensitivity than that for which
0 =5 90° was not justified.

When

0

— 90°, we have

A/C

AB
For the balances yet constructed the last term in the parenthesis is
small compared to the first and may be neglected, giving

A/4 =

£J>K.A9

(3)

X

For the balance used by Iskenderian (13) and also for that

-

21

-

-10
used in the present work, the sensitivity is of the order' of 10
for
—6
susceptibilities of the order of 10

The relative susceptibility,

, of a liquid or gas may be

determined from the following considerations:
With the cell evacuated, the equilibrium equation for the
beam is

T0 + c ic + re„ = o
where i

(4)

is the control current necessary to keep the magnet in its

fiducial position near the cell, and c is a constant whose value de­
pends upon the magnetic moment of the magnet and the distance from the
magnet to the control wire.

The other symbols have the same meaning as

in previous equations.
When the cell is filled with the standard liquid, the equili­
brium equation is

i; + c'(cs + c Ls + re0= 0
where i

(5)

is the control current which returns the magnet to its original

position, and C'AL is the torque exerted by the standard liquid of susceptibility AT J c' is a constant depending upon the pole strength of
€
the magnet and its position with respect to the cell.
When the cell is filled with a liquid or gas of susceptibility
X

, the equilibrium equation becomes

T0+ c ‘/cx + c L x + re0 = o

(6)

where i

is the current which again returns the magnet to its predeter-

mined position with respect to the cell*
From equations (4) and (5), considering the magnitudes of the
currents without regard to sign, we have

C\

= c (is— c j

(?)

From equations (4) and (6) we obtain

(8 )
Combining equations (7) and (8) we have for the susceptibility
, of the test specimen
X

K

(9 )

-

X

III.
A.

Apparatus.

The magnetic balance.
1.

Construction.
The general form of the Rankine balance used in this experiment

to determine the susceptibility of oxygen and nitric oxide, is simi­
lar to that used by Iskenderian (13) in his work on the susceptibili­
ty of HjpO, D£0 and HDO.

However, the construction differs in some

respects and will be described in detail.
The moving system is suspended from a torsion head A, as indicat­
ed in Fig. 3.

To avoid any

ferromagnetic materials in the construc­

tion this torsion head was fashioned from OFHC copper.

By means of

-

23

-

- G
— L

Fig. 3.

The Magnetic Balance

-

24

-

this head the whole moving system may he raised or lowered to adjust
the magnet above the base plate, and also a twist may be applied to
the upper fiber if desired.
The torsion head is supported by the tripod B which is made en­
tirely of pyrex glass.

The over all height is approximately 55 cm,

and the diameter of the circle containing the base about 15 cm.

The

support was made by sealing three 11 mm pyrex tubes radially into a
short length of 45 mm tubing then bending these over to form a tri­
pod.

To secure the tripod the ends of the legs were waxed into

shallow holes in the base plate C,
The base plate is also of OFHC copper and is about 8 in. square
and 3/8 in. thick.

It is secured to a heavy hardwood board somewhat

larger than the plate by means of four short OFHC copper legs.
board is fitted with three large OFHC copper leveling screws.

The
In

use the instrument was placed on a concrete pier.
The balance beam D is made of a narrow strip of Duralumin. It
is 6 cm long and the point of attachment of the upper fiber is about
2 cm from the end which carries the magnet.

The counter weight W

is a small strip of copper bent to ride on the beam.

The mirror M

is a small plane electrometer mirror fastened to the beam with
shellac•
2.

The magnet.
The magnet U is of an alloy called Nipermag and was obtained

from Cinaudagraph Corporation.

It is in the form of a right circular

cylinder 24 mm long and 2 mm in diameter.

Its weight is 0.5 gm and

-

25

-

its pole strength about 10 emu.

The magnet is attached to the lower

fiber by the arrangement shown at E.

The pointed end of the hook

attached to the magnet rests in an indentation in a small glass bead
set in the upper hook.
wire.

These hooks were made from No. 30 Duralumin

The arrangement allows the magnet to take up its preferred

orientation about its vertical axis with respect to extraneous magne­
tic fields, thereby reducing the torque exerted on the suspension
fiber.

It is doubtful if such an arrangement is of any great value

in the present case since the torsion coefficient of the lower fiber
is quite small in comparison to that of the upper fiber.

However,

this manner of suspension does greatly facilitate setting up the
suspension or replacing quartz fibers#
The lengths of the upper and lower quartz fibers are about 24 cm
and 17 cm respectively, and their torsion constants of the order 10-4
—6
and 10
dyne-cm per radian. The production and measurement of
quartz fibers will be described later in this section.

The torsion

constants of the fibers used in obtaining the data presented in this
thesis were not actually measured but were estimated from, actual
measurements on fibers drawn under similar conditions.
The total weight of the suspended system is slightly over 1 gm.
The deflection of the beam was measured by means of a telescope and
scale arrangement.

The mirror-to-scale distance in the present set­

up i s slightly more than two meters#
3.

The test cell.
The construction of a suitable test cell offered some difficulty

-

26

-

as did the electrostatic shielding of the cell from the magnet.

The

test cell finally adopted was made by sawing off two 50 ml pyrex
beakers a short distance from the bottom.

These halves of the cell

were finely ground and partially polished then fused together.

While

sealing these two parts together, entrance and exit tubes of small
tubing were also sealed in.

The cell so formed is approximately a

cylinder about 4 cm in diameter and 1.5 cm long.

It was supported

in the proper position with respect to the magnet by sealing the
connecting tubes through holes drilled in the base plate.

The en­

trance and exit tubes were not in direct contact with the base
plate but were ring sealed into short lengths of larger tubing which
were set into counter sunk holes underneath the base plate and held
rigidly by

sealing with hard wax.

supporting

is shown at F in Fig. 1.

The

test cell and method of

For purposes of clarity of the

diagram, the exit tube is shown leaving through the base plate to
the right, actually the exit is made directly behind the test cell.
It was found that in cleaning or in admitting air to the cell
electrostatic charges were sometimes built up which completely
vitiated the effect of the sample.

To remedy this, a thin copper

box was made to just fit over the test cell and the portion of the
exit tube which extended above the base

plate.

apparently

was not of OFHC copper,

complete, but the box, which

attracted and held the magnet to it.

The shielding was

To neutralize this effect a

thin piece of cover glass was attached to the side of the box facing

-

the magnet.

27

-

This arrangement proved to he quite satisfactory and

apparently did not appreciably decrease the sensitivity of the
balance.
4.

Cell filling arrangement.
The arrangement for filling the test cell is shown schematically

in Fig. 4.

From the bulb B the cell and connecting tubes may be

evacuated, as well as the gas train when first put into use.

The

bulb B serves mainly to facilitate cleaning the test cell, for
cleaning solution or other liquids may be introduced into C and drawn
through the cell into B, from which they are easily removed.

The

connection to the gas train is a small copper tube which is soldered
into a brass plate D*

Both the plate and the top of the tube C were

ground and sealed with stopcock grease.

The tube is sufficiently

flexible that it may simply be lifted up slightly and turned to one
side when liquids are to be introduced into the test cell.

Liquids

were introduced into C by means of a pipette calibrated to deliver a
volume sufficient to fill the test cell and exit tube to some point
A.

The volume of liquid required was about 26 ml.

Liquids were also

drawn out of the cell by means of the pipette, the entrance tube be­
ing slightly inclined to facilitate removal.
5.

The control circuit.
At first the control circuit consisted of a single wire, mounted

directly beneath the copper base plate, in series with one cell of a
6 volt storage battery, variable resistance, and a 10 ohm standard
resistance.

The current was measured by means of a L and N Type K

-

28

-

-P
d
(l)
S
0
to
d
d
Sw
u
<
h.0
d

<D

o

h£)

*H

K-JI

I

-

29

-

potentiometer by measuring the potential difference across the
standard resistance.

Later the mounting of the control wire was

improved to insure its remaining in the same position, and a second
wire mounted parallel to thefirst and just below it.
were mounted in the plane ofthe beam

Both wires

in its zero position. The

current in the second wire was used to bring the beam to its zero
position making it possible to begin each determination with the same
zero current in the upper wire.

This was done since it was thought

that perhaps more consistentreadingsmight be obtained if the mag­
net were subjected to approximately the same field gradients at the
beginning of each run.

The results did not indicate that there was

any particular advantage in using this second wire.

So far as control

over the motion of the beam was concerned, a single wire was found
quite sufficient and adjustments were more easily made than when two
wires were used.
The control circuit and the method of mounting the wire is shown
in Fig. 5.

All variable resistances for controlling the current, as

well as the potentiometer, were placed in an adjoining room so that
it was only necessary to enter the constant temperature room to change
sample s.
6.

Temperature effects and control.
One of the most serious problems in connection with the opera­

tion of the balance was that of disturbing temperature effects.

It

was noted early in the work that light falling on the fiber caused

30

-

-

BASE PLATE
Co n t r o l

RESISTANCE'

w ir e

BOX

E.V STORAGE CELL

5 O H M VA R I A B L E RESISTANCE

S T A ND AR D

RE SI ST A NC E

A A / W W W V i

To

Potentiometer

BRASS PLUO

(0.) CONTROL CIRCUIT

W IR E

PYREX T U B E

Cb)CONTROL W IRE
MOUNTING

Fig. 5.

Contro1 Wire Mounting.

-

31

-

an immediate deflection of the beam.

To guard against this, the

upper fibe'r was surrounded with a heavy walled copper tube G (Fig. 3).
A polished copper cylinder H, with only a small hole for viewing the
mirror, was made to fit just inside the pyrex cylinder L which housed
the balance.

The whole was then surrounded with a Celotex box coated

with aluminum paint.
To operate at the desired temperature and in order to control the
temperature of the room it was necessary to provide both a heating and
cooling arrangement.

The cooling was accomplished by placing a large

fan behind an auto radiator through which tap water could be circulat­
ed.

To furnish the heating a 550 watt heater element was unwound and

stretched in the form of a grid directly in front of the radiator.
Water was allowed to flow continuously through the radiator while the
temperature control was effected with the heater.

The current in the

heater was controlled by means of a sensitive thermostat in connection
with a vacuum tube arrangement.

The thermostat was mounted on the

Celotex box surrounding the balance.

The current through it was only

one or two microamperes which did not affect the balance, and also
made for better operation of the thermostat.

The vacuum tube circuit

and control relays were located in an adjoining room well away from
the instrument.

All of the relays were alternating current operated

except for the one in the plate circuit.
In spite of the precautions mentioned to protect the instrument
against temperature fluctuations, it did not operate satisfactorily al­
though some preliminary data were taken with benzene as the test

-

liquid*
tried.

32

-

Th© expedient of thoroughly insulating the balance was first
The base was packed with rock wool and a double walled Celo­

tex box prepared which was also packed with rock wool and placed
over the instrument.

This increased insulation did not much improve

the performance of the balance and in addition greatly increased the
time necessary for it to come to equilibrium when for any reason the
temperature of the room had to be changed.
At this point a series of experiments were performed in an at­
tempt to locate the basic cause of these disturbing temperature ef­
fects.

With the base alone insulated, the temperature of the room

was allowed to increase slowly while the deflection readings were
taken every few minutes for about an hour.

The temperature increase

was only about 1.3° C, but the deflections were surprisingly large.
To illustrate the magnitude of the effect the results of this test
are shown in Fig. 6.

Graph I shows the effect of increasing the

temperature and Graph II the effect of decreasing the temperature.
When the insulation was removed from the base similar results were
obtained but with deflections in the opposite sense.

With the copper

cylinder removed the deflection took place more rapidly and reversed
its direction after several minutes.
Although it was not possible to isolate specific factors which
contributed to the temperature effect, the results of the tests prov­
ed of value in other respects.

In all cases the extreme temperature

sensitivity of the instrument was apparent, which explained why it
failed to function satisfactorily

even when reasonable precautions

-

33

-

50

BASE INSULATED
A T = 1.3° C.

cr
10

30

o

40

So
TIM E

CO

-10
- Zo

-30

-

BASE I N S U L A T E D
A T = - l. 2°C.

4-0

Fi ~. 6.

£o

\N M l N U T E S

-

were taken.

34

-

However, the most significant observation made during

the series of tests was the fact that if sufficient time (a matter
of hours) were allowed, the beam returned in each case to approximate­
ly its original position even at the higher or lower temperature.
This was taken as an indication that practically all of the
trouble was due to temperature gradients set up over the instrument.
With the thought in mind to eliminate as far as possible tempera­
ture gradients, all of the old insulation was removed.

A wood form

about four inches high was built around the base of the instrument
and also around the cell-connecting tubes and filling arrangement,
leaving sufficient space for free circulation of air.
this form was lined with Celotex.

The inside of

A single walled Celotex box which

rested on the form was placed over the balance and a similar box over
the cell filling arrangement.

To provide for circulation of air a

small rubber fan was placed in each box.

The fans were mounted on a

common shaft which extended through bearings in the wooden form.
The fans were driven rather slowly from outside by means of a small
motor belted to the shaft.

A baffle was arranged in the large box

to provide for vertical circulation of air about the instrument.

An

auxiliary fan was used in the room to insure a better mixing of the
air.

This improved the temperature control considerably.
With the arrangement just described the performance of the balance

proved satisfactory and consistent readings were obtained for the
first time.

-

7.

35

-

Sensitivity and stability*
Fig. 7 shows the relation between deflection in terms of scale

divisions and control current in the neighborhood of zero on the
scale, with water in the test cell*

The data were obtained by chang­

ing the control resistance in steps of 1 ohm.

From this graph, the

current change which produces a deflection of one scale division is
-6
,
about 6 x 10
amp. Deflections could be estimated to 1/10 of a
-7
scale division, corresponding to a current change of about 6 x 10
amp.

The value is somewhat smaller with the test cell empty or when

filled with oxygen or nitric oxide, but still of the same order of
magnitude•
A typical value of i

is 0.0030960 amp.

Thus the uncertainty in

reading the deflection is about 6 in the last place.

This relatively

more important in the case of nitric oxide where the current difference
contains only three significant figures instead of four as in the case
of water and oxygen.

However, the uncertainty introduced in reading

the current and deflection is far less than that due to extraneous
effects which could not be controlled.

Since the balance was used as

a null instrument, with settings made on a particular zero mark on the
scale, it is probable that the error introduced in the process of
determining the fiducial current is less than that mentioned above.

-

36

-

D E F L E C T IO N - CONTROL

Il
i
o
c
U)

377

379

380

current

381

387.

C U R R E N T IN AMPERES X 10-*

Fig • 7

-

B.

37

-

Production of Quartz Fibers.
Some preliminary work was done on the production and measurement of

quartz fibers used in connection with the magnetic balance. Fig. 8a is
a photograph of the apparatus used in drawing the fibers.

The method is

a variation of the elastic catapult method used by Holbourn (26).

Instead

of using a long length of elastic to supply the drawing force, a window
shade spring was employed as shown in Fig. 8b.

By means of the wheel and

axle arrangement the motion of the spring was amplified so as to swiftly
separate the two pieces of quartz.

The guide for the upper quartz holder

was mounted on a rack and could be easily adjusted for height by the hand
wheel shown at the right of Fig. 8a.

The guide is fitted with a catch

which is released by an electromagnet when a foot switch is closed.

With

the hand wheel adjustment and magnetic release the proper moment for re­
leasing the upper quartz is more easily controlled than in the apparatus
described by Holbourn.
To catch the fiber, two short lengths of heavy wire were inserted
perpendicular to the back board and close to the line of flight of the
upper quartz.

These were placed about 50 cm apart and were covered with

a sticky compound made by melting together rosin and castor oil as recommend­
ed by Holbourn.

A sheet of air from a wing top was blown under each wire,

so that as the fiber is drawn it is blown against the wires and held.
To fasten the upper quartz in the holder the sides of the holder were
filed through so as to expose the rod.

This section was first wrapped with

a narrow strip of cellulose tape then tightly with fine thread.
method of securing the upper quartz in the holder is shown in

The

-

Fig. 8a.

38

-

Quartz Fiber Apparatus.

-

Fig. 8b.

39

-

Quartz Fiber Apparatus.

-

Fig. 9a.

40

-

Fig. 9b shows the method of holding the lower quartz;

the end

of the rod was swelled in an oxygen flame then inserted from the bottom
of the holder.

Quarter inch quartz rods were used.

To draw a fiber, a needle a fraction of a millimeter or so Is first
drawn on the upper quartz.

A strong oxygen flame is then directed over

the rounded top of the lower quartz until it is red hot.

The upper

quartz is quickly lowered by means of the hand wheel and the needle stuck
to the lower quartz, then immediately released by pressing the foot switch.
In drawing a small fiber it is necessary to use a small needle which
is sometimes melted away before it can be stuck to the lower quartz.

In

such case it was found helpful to direct a sheet of air from a wing top
just over the too of the lower quartz to confine the flame to a thin sheet.
This attachment is shown in Fig. 8a.
It was found that the diameter of the fiber is controlled largely by
the size of the needle from which it is drawn, although for fine needles
the tension in the spring must be increased somewhat.
This apparatus proved to be quite satisfactory and easy to use.

It is

compact and can be moved and used wherever gas, air, and oxygen are avail­
able.

Fibers may be quickly made as needed making it unnecessary to store

them.

With the present apparatus the length of the fiber which can be

drawn is limited to about 50 cm, but by increasing the height of the instru­
ment longer fibers could certainly be drawn.
Several common methods for measuring the diameter of fibers were tried.
In general, the results on the same fiber by various methods were not in
particularly good agreement.

The elastic straining method described by

-

41

-

-VACUUM TUBING

RELEASE

“THREAD
GUIDE
DL/RAL H O L D E R
Q U A R T Z ROD

Fig. 9a.

Upper Quartz Holder.

-

42

-

o

cc
M

Quartz

Holder.

oc

Lower

I

co
Co
or
CO

OO
o

o
o

43

Rolt (27) proved to be the simplest and was the one generally used.

In

this method the fiber is held in a horizontal position and small weights
hung at its center.

The corresponding depressions from the horizontal

position are measured with a cathetometer. From these data and knowing
Young’s modulus for quartz and the length of the fiber the diameter can
be calculated.

The smallest fiber measured in this work was about

in diameter.

-

IV.
A.

44

-

Experimental Procedure.

Liquids.
In preparation for taking a reading the pyrex cylinder surrounding

the instrument was first evacuated using a fore pump.

The vacuum in the

cylinder was maintained by continuous pumping in order to avoid any dis­
turbances which might have resulted from small pressure changes.
test cell was then evacuated using a separate pump.

The

After allowing suffi­

cient time, usually an hour or more, for the instrument to settle down,
the current i was noted which brought the magnet to its predetermined
position with respect to the test cell.

When benzene was used as the

test liquid it was introduced before the water sample since it could be
removed with less disturbance to the instrument than could water.

To

introduce the benzene, air was first admitted to the test cell, then the
proper volume of liquid was drawn up into the pipette which was then in­
serted into the filling tube C (Pig. 4).

It was then carefully released

in order to avoid air bubbles and allowed to fill the cell.

The current

ig was then noted which brought the magnet back to its original position.
After removing the benzene the test cell was dried and the procedure re­
peated for water.
Even the removal of benzene from the test cell so disturbed the bal­
ance that two hours or more were usually required for it to again reach
equilibrium.

For this reason a new zero current reading was usually

taken before introducing the water sample.

In view of the time required

for a complete set of readings, the procedure finally adopted was to take
the benzene reading one night and a reading on water the next.

It was

-

45

-

found necessary to take readings at night since accidental disturbances
could
B.

not be avoided during the day.

Gases.
The procedure for gases was considerably simpler and all of the data

for a complete calculation could be obtained in one evening.

The pressure

of the gas in the collection bulb was first built up to about 15 cm of
mercury, which was sufficient to fill the cell to a pressure somewhat
above atmospheric.

After noting the current reading with the cell evacuat­

ed the gas was introduced and the pressure subsequently reduced to atmos­
pheric.

After obtaining the current reading for the gas the cap of the

cell-filling arrangement was removed, a little air drawn through the cell,
and the water sample introduced.
The time required for a complete run on oxygen or nitric oxide was
about two hours, but a much longer time was necessary for the balance to
come to equilibrium after removing the water and pumping the test cell
in preparation for the next run.
C.

Preparation of Gases.
1.

Oxygen.
Fib. 10 shows the plan of the apparatus used in preparing the

oxygen.

The gas was generated in an ordinary demonstration electro­

lysis apparatus using about a 10 per cent sulfuric acid solution.
The tank shown at the left of the figure is a gallon can connected
to a manometer and also to the bulb of the electrolysis apparatus.
Tank oxygen was allowed to flow through this part of the system to
flush out the air from above the solution in the bulb and from the

Apparatus for Preparing Oxygen.

46

Fig. 10.

-

-

tank.

47

-

The pressure was "then built up sufficiently ho give the neces-

sary pressure in the collection bulb*

Besides furnishing the neces-

sary pressure, tank oxygen was used above the electrolyte to avoid
dissolved air.
The generated gas was first bubbled through a tall column of
distilled water to remove sulfuric acid vapor, then passed over hot
copper oxide in an electrically heated furnace to remove any hydro­
gen which might have washed over into the oxygen side of the system.
The gas was then passed through tubes containing calcium chloride
and phosphorus pentoxide respectively, into the collection bulb.
2.

Nitric oxide.
Several methods which reportedly gave pure or very nearly pure

nitric oxide were investigated.

Since the volume of gas required

was rather small, the method of Emich (28) seemed most promising.
In this method the gas is formed by the reduction of nitrous acid
by mercury in a sulfuric acid solution.

The solution recommended by

him is one of pure sulfuric acid containing 2 per cent of sodium
nitrite.

When mercury is added the reaction takes place at the mer­

cury surface.

The evolved gas is freed of N^ 0^ by passing over

potassium hydroxide.

In experimenting with this method it was found

that apparently a better gas could be obtained using a less concen­
trated surfurlc acid solution.

It was also observed that when the

gas was bubbled through and collected over mercury the purity was
much improved.
to NO

A reaction with the mercury was noted and attributed

in the evolved gas.

The dilute solution, aside from requiring

-

48

-

much less sulfuric acid, was more easily handled.

The reaction takes

place without shaking since the heavy precipitate does not form on
the mercury surface as it does when the concentrated solution is used.
The mixture finally adopted was a 20 per cent sulfuric acid solu­
tion containing 2 per cent of sodium nitrite with enough mercury to
provide the necessary surface for a reasonable rate of evolution of
gas.

Fig. 11 shows the plan of the apparatus used.

The acid solu­

tion containing the sodium nitrite is placed in flask B, leaving only
a little space above the liquid.

The mercury is placed in flask A.

To generate the gas some of the mercury is allowed to flow through
the stop cock into the lower flask.
through which the gas must pass.

C is a double mercury bubbler

The mercury serves to remove the

nitrogen dioxide and probably some of the higher oxides which may be
present;

it also aids in preventing too violent a reaction by main­

taining a few centimeters pressure on the solution in the lower flask.
D is a drying tube containing phosphorus pentoxide.

At E the gas may

be led outside for test or through the drying tube into the collection
bulb G.
D.

Analysis of Nitric Oxide.
Many solutions are known to absorb nitric oxide and are used in the

analysis of the gas.

In some cases the gas is merely absorbed and can be

driven out by heating as is the case with ferrous sulphate.

In others a

chemical reaction takes place as when the gas is absorbed in KMnO^.

Solu­

tions which react chemically with the gas are to be preferred since in
the case of true absorption an equilibrium may be set up with some of the

Apparatus for Preparing Nitric Oxide.

49

Fig. 11.

-

-

50

-

gas unabsorbed.
Two solutions which react chemically with the gas were used in the
present analysis.

The first was a saturated solution of sodium sulphite

made slightly alkaline with potassium hydroxide, and the second a solu­
tion of potassium dichromate to which was added one-fifth its volume of
concentrated sulfuric acid.

The analysis was carried out by collecting

the gas over water in 11 mm glass tubes about 50 cm long, then placing
them with the open end under the absorbing solution.

As the gas is ab­

sorbed the solution rises in the tube and the remaining volume of unab­
sorbed gas gives a measure of the purity*

It has been found that nitric

oxide is slowly decomposed by contact with water.

For this reason a

special absorption tube was constructed for collecting the gas over mer­
cury.

The tube was similar to the others but had a three-way stopcock

at the upper end.

To collect the gas, the lower end was placed in a

dish of mercury and the tube pumped until filled with mercury to the stop­
cock.

The gas was then admitted above the mercury, with which it was in

contact for only a few seconds.

The results obtained with the two solu­

tions and with the different absorbing tubes were in excellent agreement.
The average purity of the gas used in the measurements, as indicated
by this method of analysis, was 99 per cent nitric oxide with very little
variation.
A single attempt at titration of the potassium dichromate solution,
which had absorbed nitric oxide, gave a somewhat divergent result.

How­

ever, the accuracy of the one determination was not considered sufficient
to form any good basis of comparison with the other values.

Time did not

- 51 permit any further work with this method of analysis#
V.
A#

Experimental Results.

Benzene.
Benzene was used in the preliminary work merely to test the perform­

ance of the balance and the results are not to be considered as giving
an accurate value for the susceptibility of that liquid.

These measure­

ments were made under rather poor conditions before a suitable tempera­
ture control had been installed.
The measurements in Table 2 were made on thiophene free benzene at
a temperature of about 25° C.

In the calculations the mass susceptibi—6
o
lity of water was assumed to be -0.7200 x 10
at 20 C, which gave
—6
-0.7179 x 10
for the volume susceptibility at the temperature of mea­
surement.

Table 2.

The density of benzene at 25° C. was taken to be 0.8734 giry'ml.
Preliminary Measurements on Benzene.

fo7 A i B*f07 A £w**°7

i07

Trial

to X /07

1

22963

31966

33312

9003

10349

7150

2

14567

21830

23178

7263

8611

6933

3a

13510

20728

3b

13700

8380

7080

4

13761

7616

7035

7218
22080

20301

" X * /06

21317

Mean value (mass susceptibility)

6540

7049

In the above table i0 , i,,
and iw denote the control currents, in
d
amperes, with the cell evacuated, with benzene in the cell, and with water
in the cell, respectively.

-

52

-

Z^tfgand a\Lw denote the quantities

— CQ

and Cw ~~ C0 • ~)C. rePr0~

sents the mass susceptibility of benzene at the temperature of measure­
ment.

Although the -variation is rather large, the mean -value is in good

agreement with the value

(0.7036 zfc

0.0012) x lo”

as obtained

by Meeks and Jamison (18) using a similar balance.
B.

Oxygen.
1.

Undried tank oxygen.
The following set of measurements was made using tank oxygen.

The gas was taken directly from the tank without being dried.
Table 3.
Trial

Measurements on Undried Tank Oxygen.

lo * 10*

U . x !°7

^

* 10 7

1

28502

26754

1748

2

28499

26747

1752

3

28526

26766

1760

4

28549

26755

1794

Mean Values
In the above table
,

in the test cell.

Ai^xfO7 X i T

1764

9589

0.968

Lo„ refers to the control current with oxygen
!
denotes the quantity V ~

*

L0 • X « T is the pro­

duct of the molar susceptibility by the absolute temperature;

for

pure oxygen the theoretical value is 1.000.
The above data were taken with the balance in essentially its final
form.

The temperature control had been improved so that the temperature

of the room could be kept constant to within 0.1° C.

Fans had been in-

-

53

-

stalled in the housing to prevent temperature gradients from being
set up over the balance.

Instead of taking a reading on water follow* 9589 x 10—7 was used.
ing one on oxygen, the average value of A
This value was the mean of six separate measurements on water taken
over as many days.
per cent.

The average deviation from the mean was only 0.04

In view of the constancy of these readings it did not ap­

pear necessary to repeat readings on water with each test on oxygen.
The temperature of measurement was 21.8° C.

at which temperature the
—6
volume susceptibility of water is -0.7184 x 10 . The density of
oxygen was calculated for the temperature and pressure of measurement
from the value of 1.4290 gjn/l at 0° C. and 760 mm pressure.
2.

Dried tank oxygen.
For the next set of measurements, oxygen was taken from the same

tank and run through a drying tube before being admitted to the test
cell.

Table 4 shows the results of four determinations on the dried

gas.
Table 4.
Trial

Measurements on Dried Tank Oxygen.

Lo * H > 7

Lo^tO7

1

28563

26761

1802

2

28517

26733

1784

3

28552

26740

1812

4

28595

26803

1792

Mean Values

Ai0a* io7

1798

A L w x lo7

9589

ICm T

0.987

-

54

-

A comparison of the above data with that of Table 3 would indicate
that water vapor may be the chief diamagnetic impurity in the tank
oxygen used.

However, some measurements were made later on the

dried gas from another tank and a value considerably lower than the
one above obtained, indicating a variation in purity from one tank
of the gas to another.
3.

Electrolytic oxygen.
Table 5 shows the results of the final measurements on oxygen.

The gas used was electrolytic oxygen, purified and carefully dried
by passing over calcium chloride and phosphorus pentoxide.

The condi­

tions of measurement were kept as nearly constant as possible through­
out the series of runs.

Except in one or two cases a reading was taken

on water immediately following the one on oxygen.
o
measurement was 21 C.

The temperature of

-

Table 5.
Trial

55

-

Measurements on Electrolytic Oxygen.

(20° C.)

ALox* / 07 A U x 107 Kox * to* ~Xox* IOb O U T

1

1893

9959

0.1407

105.7

0.992

2

1907

9830

0.1429

107.3

1.007

3

1909

9830

0.1437

107.9

1.012

4

1857

9821

0.1395

104.8

0.983

5

1878

9866

0.1407

105.9

0.994

6

1890

9867

0.1420

106.6

1.000

7

1887

9867

0.1418

106.5

0.999

8

1876

9897

0.1409

105.6

0.993

9*

1857

9892

0.1389

104.3

0.979

10*

1860

9943

0.1382

103.8

0.974

11*

1840

9826

0.1384

104.0

0.976

12

1893

9779

0.1430

107.4

1.008

13

1863

9829

0.1397

104.9

0.984

Mean Values

0.1415

106.3

0.997

Av. Deviation From Mean

0.0012

0.9

0.008.

Probable Error in Mean

0.0003

0.2

0.002

* Deleted from the final calculations.
In the above table ICo^ and
mass susceptibilities respectively.

denote ’the r0lative volume and
The values of /£0 and"}^
ft

have

been reduced to 20° C. and 760 mm pressure.
Those trials marked with an asterik have been deleted in calculat­
ing the mean values and probable error.

There was reason to believe

-

56

-

■that "the gas had become contaminated when these measurements were made.
Before making the next run (No. 12), the entire system was pumped out
and refilled with oxygen.
C.

Nitric Oxide.

Table 6.

Measurements on Nitric Oxide.

Trial

io '

A

10 7

"X-x

10 ^

£ W X I0b

756

9796

46 .5

0.0581

2*

699

9740

43.2

0.0540

3

789

9740

CO
sP

0.0606

4

757

9534

47.4

0.0592

5

742

9538

46.4

0.0580

6

763

9580

47.6

0.0594

7

,748

9551

47.0

0.0587

47.2

0.0590

0.6

0.0007

Average Deviation From Mean

.

Mean Values

LO

1

* Deleted from the final calculations.
The results shown in Table 6 are those obtained for nitric oxide, us­
ing a gas which was shown by analysis to be 99 per cent pure.

AL wo in the above table denotes the value of Cp/o “
mass susceptibility, and

Ko

»"Xno

the volume susceptibility of nitric oxide.

These values have been corrected for 1 per cent nitrogen and reduced to
20° C.

The density of nitric oxide at the temperature and pressure of

measurement was calculated from the value 1.3402 gm/l ai> 0
mm pressure.

C. and 760

The density of nitrogen at 0° C . and 760 mm pressure was

-

57

-

taken to be 1.2505 gm/l, and the mass susceptibility at 20

C. to be

-0.27 x 10 6.
Trial No. 2 is definitely out of line with the other values and has
been deleted in determining the mean and average deviation from the
me an.
VI.
A.

Calculations.

Oxygen.
In every case, whether the test specimen is a liquid or a gas, the

first step in the calculations is to find the volume susceptibility rela­
tive to water at the temperature of measurement.

This is carried out

using Equation (9), in which

now becomes the volume susceptibility of
S
water and must be calculated from the known mass susceptibility.

/Ctv is determined as follows:

The mass susceptibility
of water at
17
o
-6
20 C. is assumed to be -0.7200 x 10 . The volume susceptibility is
given by

, where /*

ture of measurement.

is the density of water at the tempera­

>

Having thus found the volume susceptibility,

of the test specimen, the mass susceptibility is given by
where

,
/°

is the density of the test specimen at the temperature and

pressure of measurement.
In the case of oxygen the mass susceptibility at 20° C. was calculat­
ed from the value of 21° C. assuming that ~)C is inversely proportional to
the absolute temperature.
the value of

K

, at 20° C., was then determined from

at 20° C., using

, where

of the gas at 20°C. and 760 mm pressure.

t u t

is now the density
is the product of the

mass susceptibility, the molecular weight, and the absolute temperature.
g

It will be noted that-0.7200 x 10™

is taken for the mass suscepti-

-

58

-

bility of water at temperatures other than 20° C. for which it is given.
In case of the measurements on benzene this value is taken at 25° C., and
also at 21

C. at which temperature the final measurements on oxygen and

nitric oxide were made.

Experiments indicate that there is very little

if any variation of this quantity with temperature, and that the varia­
tion observed depends upon the previous treatment of the water, that is,
whether or not it has been standing in contact with air or some other gas.
Wills and Boeker (7) have made measurements on water over the tempera­
ture range from 20° C. to about 70° C.

^hey found that boiled water
o
indicated less diamagnetism at temperatures higher than 23.5 C. and more

diamagnetism above that temperature when the water had stood in contact
with helium gas for several days before measurement.

The variation,

which is less than 1 per cent in either case, is erratic and difficult to
account for.

This paper also gives a good summary of the previous work

on the variation of the susceptibility of water with temperature.
B.

Nitric Oxide.
The method of calculating the observed susceptibility of nitric oxide

is the same as that used for oxygen.

However, this gas requires special

consideration in that a correction must be made for the impurity in the
gas.

The calculation is as follows:

Assuming that the constituent sus­

ceptibilities are additive and that the impurity is entirely nitrogen,
we have

%06s. Owno

nm

~

wo Pft\no +

7-^ rm

-

59

-

Putting the mass of each gas in terms of volume and density, we obtain

x-=
_

Assuming Sone’s value (29) of -0.27 x 10

0

for the mass susceptibi-

lity of nitrogen, the correction to the observed value amounts to about
1 per cent in this particular case.
It may be mentioned that the temperature variation is here assumed
to be the same as that for oxygen.

However, theory predicts that the

susceptibility of nitric oxide, unlike that of oxygen, should not strict­
ly follow Curie’s law.

The deviation is very small and certainly would

not be detected over the temperature range involved here.
It was also assumed that the residual gas was entirely nitrogen.
This seems a rather bold assumption, but is supported by the work of
Moser (30), Weiss and Piccard (20), and Sone (22).

Unless oxygen or water

vapor, for example, are present in appreciable quantities in the residual
gas, the correction due to the actual susceptibility of the

impurity is

of little consequence in a gas which is 99 per cent nitric oxide.
VII.
A.

Discussion.

Preliminary Results.
The performance of the Rankine balance in this experiment has been

found thoroughly satisfactory, with the precision in a single determina­
tion limited largely by accidental disturbances which could not be com­
pletely controlled.

The average deviation from the mean of a number of

determinations on oxygen is practically the same as that reported by

-

60

-

Iskenderian (15).
0

Equation (3) with b =: 2 cm, x = 0.5 cm, and

0.1400 x 10

shows

that the theoretical sensitivity of the present balance for measurements
on oxygen is about 2 x 10

This sensitivity is not attained in a

single determination, but the probable error in the mean of measurements
-10

on oxygen is but 3 x 10

• The data shows that the effect of these

accidental disturbances is entirely a random one, with the maximum devia­
tion of any one measurement from the mean of about 2 per cent and the
average deviation 1 per cent.

It is felt that considerable significance

may therefore be attached to the mean values given here.

These values are,

in the author’s opinion, about as precise as can be obtained with the
balance in its present form and used under usual laboratory conditions.
From the preliminary measurements on tank oxygen, four determinations
on the gas taken directly from the tank gave 0.968 for "XaiT* J when the
gas was carefully dried the same number of determinations gave the value
of 0.987.

However, some later measurements on the dried gas from another

tank gave a considerably lower value.

It is thus apparent that the some­

what low value obtained by Iskenderian (15) is accounted for on the basis
of impurities in the gas;

also that a variation in the purity of the gas

from tank to tank may be expected.

It is evident that one of the impuri­

ties is water vapor which is strongly diamagnetic and would, therefore,
be particularly effective in lowering the observed value.

However, other

likely impurities in the gas have susceptibilities small in comparison to
that of oxygen.

These impurities, even though their magnetic effects are

small, displace oxygen in the test cell and also contribute to a lower

-

61

-

observed value.
B.

Electrolytic Oxygen.
Measurements on electrolytic oxygen in the present research give a

mean value of 0.997 for ^^7", which is in excellent agreement with the
theoretical value of 1.000.

The agreement with the results obtained by

other methods using high field strengths is also good.

The average of

the results of seven other investigations (14), using a different method,
is 0.990, with a maximum deviation from the mean of about 3 per cent.
G.

Nitric Oxide.
In view of the results on oxygen it is difficult to reconcile, on

thebasis of experimental error, the

3 per cent difference between the

value obtained here and that obtained by Son6 (22) for nitric oxide.

The

highest single value obtained in the present work is a little more than
0.5 per cent below that reported by Son£.
An important factor which enters into measurements on nitric oxide
is the question of the purity of the gas.

Most measurements have been

made on the more or less impure gas and the observed value of the suscepti­
bility corrected for the impurities.

In the present analysis of the gas

the two different absorbing solutions used gave results in agreement to
0.2 per cent.

Sinceit is generally agreed that absorption methods are

reliable, especially when used on a gas of rather high purity, it is pro­
bable that the 99 per cent purity stated Is very close to the correct
value.

It therefore seems improbable that a more accurate analysis of

the gas would change the value of the susceptibility by more than a frac­
tion of 1 per cent.

-

62

-

The gas used by Sone was about 95 per cent nitric oxide bv volume.
In his paper he states;

,T*..... thus the correction for the suscep-

"bibility due to nitrogen was about 3 per cent.” According to the
authorTs calculations the correction would be nearer 5 than 3 per cent*
However, this would result in an even greater discrepancy between the
two values.
It will also be noted that the volume susceptibility obtained here
is about 1.2 per cent below the theoretical value.

Van Vleck (3) points

out in his paper that x in Equation (2) should be about 5 per cent larg­
er, due to the fact that the constant B, in the term value, is different
in the two component normal states of the molecule.

He states that by a

crude estimate this would affect the susceptibility by about 1 per cent.
It is apparent from his final equation that an increase in x lowers the
susceptibility.

Hence, it is entirely possible that his value 0.0597 x 10—6

may be as much as 1 per cent too high.

This would bring the value

0.0590 x 10 6 into excellent agreement with the theoretical value, while
-6

it would appear that 0.0610 x 10

obtained by Sone Is too high.

At the beginning of the present work it was thought that the balance
might be adapted to making measurements over a temperature range.

It

appears that this would be almost impossible with the present arrangement
for the balance itself was found very sensitive to temperature changes.
It would be necessary to thermally insulate the test cell from the magnet
which would introduce many difficulties since the magnet must be kept
quite close to the test cell.

Nitric oxide would be particularly inter­

esting in this respect for the theoretical deviation from Curie's law

-

63

-

could "be tested at low field strengths.

Van Vleck (3) has calculated

the value of the apparent Bohr magneton number for various temperatures
ranging from 0° K to an infinite temperature.

The value varies from 0

at absolute zero to 2.000 at an infinite temperature.

Assuming that the

same precision could be attained for nitric oxide as in the present work,
measurements over a temperature range of 100° C. or so, about room
temperature, would be sufficient to at least show the deviation.

Measure­

ments over a much larger temperature range would be desirable.
A number of investigations (31) of the relative susceptibility at
different temperatures have been made by other methods.

The temperature

range extended from 113° K, which is below the boiling point of nitric
oxide, to about 300° K.

The experimental values agree with those calcu­

lated over the entire range investigated to within 1 per cent.
The value of the apparent Bohr magneton number (—G in Equations (2))
r*
-6
o
as calculated from the value 0.0590 x 10
obtained here is 1.82 at 293 K.
The value obtained by Van Vleck (3) at the same temperature is 1.836.

The

value from Sone's data is 1.85.
VIII.
1.

Conclusions.

The results demonstrate that the performance of the balance is

satisfactory under usual laboratory conditions if measurements are made
at night when conditions are best.

The precision in a single determina-

■fcion is limited by accidental disturbances which at present cannot be
controlled.
2.

Results show that the high theoretical sensitivity of this type

-

64

-

of instrument is not attained, but the probable error in the mean of a
large number of determinations does approach the theoretical sensitivity.
The values, particularly those for oxygen, are therefore about as pre­
cise as can be obtained with the balance in its present form.
3.

The instrument is very sensitive to temperature gradients,

but

with proper precautions their effects can be controlled.
4.

The value of

X.T

, reported by Iskenderian for oxygen, is too

low because of Impurities in the gas.

The value for electrolytic oxygen

is in excellent agreement with the theoretical value and with the average
of the results of several other investigators using intense fields.

It

is apparent that the susceptibility of water shows no appreciable change
in passing from high to low field strengths.
5.

The susceptibility of nitric oxide is in essential agreement

with the theoretical value, but definitely lower than that obtained by
Son£.

The discrepancy does not seem to be accounted for on the basis of

experimental error.

Whether or not it Is due to an actual change in sus­

ceptibility with field strength is questionable.

-

IX.
1.
2

.

65

-

LITERATURE CITED III THIS THESIS

Langevin, P., Magnetisme et theorie des electrons,
Ann. de Chim. et de Phys. (8) 5, 70 (1905).
Van Vleck, J. H., On Dielectric Constants and Magnetic Suscepti­
bilities in the New Quantum Mechanics
(Part I) Phys. Rev. 29, 727 (1927).

3.

Van Vleck, J. H., On Dielectric Constants and Magnetic Suscepti­
bilities in the New Quantum Mechanics
(Part III) Phys. Rev. 31, 587 (1928).

4.

Birge, Raymond T., New Table of Values of the General Physical
Constants. Reviews of Modern Physics 13, 233 (1941).

5.

Van Vleck, J. II., The Theory of Electric and Magnetic Suscepti­
bilities, p. 266. (Oxford Univ. Press, New York 1932).

6.

Wills, A* P. and Hector, L. G., The Magnetic Susceptibility of
Oxygen, Hydrogen, and Helium, Phys. Rev. 23, 209 (1924).

7.

Wills, A. P. and Boeker, G. F., Diamagnetism of Water at Different
Temperatures, Phys. Rev. 42, 687 (1932).

8 . Curie, P., Proprietes magn§tiques des corps k diverses temperatures,

Ann. de Chim. et Phys. 5, 289

(1895).

See also: Stoner, E. C., Magnetism and Matter, p. 72.
(Methuen & Co. Ltd., London 1934).
9.

10

.

11

.

1 2 .

Son£, T., On the Magnetic Susceptibilities of Hydrogen and Some
Other Gases, Science Reports 8, 162 (1919);
Phil. Mag. 39, 305 (1920).
On the Magnetic Susceptibility of Six Nitrogen Oxides, Science
Reports 11, 139 (1922).
Havens, G. G., The Magnetic Susceptibility of Nitrogen Dioxide,
Phys. Rev. 41, 337 (1932).
Rankine, A. 0., The Measurement of Magnetic Field Distortion,
Proc. Phys. Soc. 46, 1 (1934).
Rankine, A. 0., A Simple Method of Demonstrating the Paramagnetism
and Diamagnetism of Substances in Magnetic Fields of Low Inten­
sity, Proc. Phys. Soc. 46, 391 (1934).

-

66

-

13.

Iskenderian, Haig P., The Rankine Magnetic Balance and the
Susceptibility of HgO, HDO, and DgO. Phys. Rev. 51, 1092 (1937).

14.

Stoner, E. C., Magnetism and Matter, p. 342, (Methuen & Co. Ltd.,
London 1934).

15.

Iskenderian, Haig P., Paramagnetic Measurements at Low Fields With
the Rankine Balance, Phys. Rev. 52, 1244 (1937).

16.

Hector, L. G. and Peck, M. F., Magnetic Susceptibilities in Weak
Fields, Phys. Rev. 55, 672(A) (1939).

17.

Temple, G*, The Mechanical Force on Bodies of Small Susceptibility
Due to Induced Magnetization, Proc. Phys. Soc. 48, 393 (1936).

18.

Meeks, W. W. and Jamison, N. C., Magnetic Susceptibilities in
Weak Fields, Phys. Rev. 57, 71(A) (1940).

19.

Jamison, N. C., Absolute Measurement of Magnetic Susceptibility of
Water in Weak Fields, phys. Rev. 57, 1089 (1940).

20

.

Weiss, P. and Piccard, A., Sur l'aimantion de 1'oxyde azotique et
la magneton. C. R. 157, 916 (1913).

21

.

Bauer, E., Weiss, P. and Piccard, A., Sur les coefficients
d’aimantion de l’oxygene, de lfoxyde azotique et la theorie du
magn§tom. C. R. 167, 484 (1918).

22 . Sone, T.,

On the Magnetic Susceptibility of Six Nitrogen Oxides,
Science Reports 11, 139 (1922).

23.

Mason, M. and Weaver, W., The Electromagnetic
(Univ. of Chicago Press. 1929).

Field, p. 149.

24.

Rankine, A. 0., Reference 11, p. 11.

25.

Iskenderian, Haig P., Reference 15, p. 1245.

26.

Holbourn, A. H. S., The Production of Very Fine Quartz Fibers,
Jour. Sci. Instr. 16, 331 (1939).

27.

Rolt, F. H., Gauges and Fine Measurements, Vol. II, p. 260.
(Macmillan, 1929).

28.

Emich. F., Zur Darstellung des Stickoxydes.
13, 73 (1892).

29.

Sone, T., On the Magnetic Susceptibilities of Hydrogen and Some
Other Gases, Science Reports 8, 162 (1919); Phil. Mag. 39,
305 (1920).

Monatsh. f.

Chemie

-

67

-

30.

Moser, L. , Die Darstellung und Bestimmung von Stickoxyd und sein
Verhalten zu Wasser, Zeits. f. Anal. Chemie 50, 401 (1911).

31.

Stoner, E. C.,

Reference 14, p. -345.

-

6 8

-

X . AC KNCWLEDGMENTS.
The writer wishes to express his thanks to Dr. C. D. Hause for his
valuable assistance, guidance, and helpful suggestions during the en­
tire course of the work, and to Prof. E. Leininger of the Department of
Chemistry for his useful advice concerning the preparation of nitric
oxide.