CONDENSATION OF VAPOR AS INDUCED
BY NUCLEI AND IONS

FOURTH REPORT

BY CARL BARUS
Hazard Professor of Physics, Brown University

WASHINGTON, D. C.:

Published by the Carnegie Institution of Washington

1910

CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 96 (PART 2)

(UfefURYlSo

A / ^7

/ X - • • / X//

PREFACE.

In Chapter I of the present publication the investigations on the
residual nuclei of pure water (compare Carnegie Institution of Washing-
ton Publication No. 96, Chapter V, 1908) have been resumed with regard
to the size and persistence of such nuclei. These are obtained by the
precipitation of water on the nuclei of pure water vapor, in a dust-free
fog chamber, by sudden cooling. The fog particles so produced evaporate
to water nuclei on compression, the number of the latter as compared
with the former being greater as the evaporation of fog particles is more
rapid and as their size is larger. In the extreme case nearly 50 per cent
of the fog particles were represented by these residual water nuclei. It
is a curious observation that whereas the relatively enormous fog particles
of pure water evaporate at once beyond the range of visibility, such
evaporation stops in cases of certain of the invisible water particles (0.5 to
50 per cent of the total number of fog particles) as the evaporation is more
rapid in the manner specified. The remaining fog particles evaporate
completely. It was impossible to detect any electrical effect due to rapid
evaporation. The cause of these phenomena is difficult to ascertain, but
it may be suspected that it is associated with the composite nature of the
molecule of liquid water.

The first part of Chapter II contains further studies of the optics of
coronas. It was shown that the interference phenomenon superimposed
upon the diffraction phenomenon in the case of coronas may be treated in
a way similar to the lamellar grating, consisting of a uniform succession of
alternate strips of thin and thicker transparent glass. Given types of
coronas are reproduced in successively increasing size, when the respective
fog-particle diameters are in the ratio of . . . . 5, 4, 3, 2, i, o. The
ratio of fog-particle diameters d and interference plate thickness D for the
same color minimum in the interferences and a film of water is d/D = n
(n — i ) , where n is the index of refraction of water. The experimental
value of d/D agrees well with this. It must therefore be possible to com-
pute the nucleation corresponding to a given corona purely from optical
considerations of diffraction and interference, as indicated. To further
verify the theory suggested, special study was made of the axial or inter-
ference colors of coronas by the aid of large drum-shaped chambers 2
meters long.

The coronas obtained with electric light are almost too complicated
for practice, for which reason a part of the mantle of a Welsbach burner

in

IV PREFACE.

has usually been used as a source of light. Much better results are
obtained, however, by the use of the virtually monochromatic mercury
lamp as a source. This is sufficiently intense and admits a more definite
optical interpretation. Experiments are therefore given in the second
part of Chapter II, with a view to standardizing these simplified coronas
by the method of successive exhaustions and phosphorus nuclei.

The third part of the chapter gives an account of further progress made
in increasing the efficiency of the fog chamber by reducing its size com-
patibly with the use of a new type of goniometer.

In an endeavor to standardize the coronas in terms of the nucleation
involved, by the aid of separate small sealed aluminum tubes containing
radium, used singly or in groups, very little progress was made, because
the coronal diameter varies as the sixth root of the intensity of ionization.
The experiments of Chapter III, however, lead to certain remarkable
results on the distribution of ionization with reference to the position
within the fog chamber of the sealed aluminum tubelets (beta and gamma
rays being in question, largely the latter).

If the parts of the fog chamber consist of different materials or not,
the maximum ionization due to primary and secondary radiation rarely
coincides with the position of the radium. In a horizontal cylindrical
fog chamber, closed at one end and open for exhaustion at the other,
the maximum ionization is found to move from the closed end to the
exhaustion end as the radium moves from the closed end to the middle
of the chamber. As the radium moves further the maximum remains
near the exhaustion end, but the ionization diminishes in marked degree
throughout the whole chamber. The ratios of ionization are frequently
greater than 2 to i. To obtain maxima of ionization near the middle
of the chamber the sealed radium tube must be near the closed end.
In other adjustments even minimum ionization was produceable in
the middle, as compared with the ends. It appears from the results that
it is possible to appreciably displace the ions during the period of ex-
haustion, the rate of reproduction being insufficiently rapid as compared
with the displacement.

In a final investigation, Chapter IV, the endeavor is made to stand-
ardize the coronas in relation to the number of fog particles represented
under given circumstances of exhaustion by aid of Thomson's electron
and correlative constants. After a number of trials the first successful
method consisted in making a closed aluminum tube, containing an even
distribution of radium, the core of a cylindrical condenser, leaded to an
inch or more in thickness without. This core was suspended axially from
fine wire leading to Dolezalek's electrometer for the measurement of the
small voltages and currents involved. The core in question was then
removed from the electrical condenser and put into the axis of a dust-

PREFACE. V

free fog chamber, where the nucleation (ionization) was found from the
constants of the coronas obtained upon exhaustion, or vice versa.

Using the method which depends essentially on the known velocity of
the ions in the unit electric field and my earlier values of the constants
of coronas, a few rough tests of the charge of the electron gave consistent
values. There was, however, an inherent difficulty of great importance,
the nature of which has already been referred to — the ionization differs in
different parts of the fog chamber and the extreme ratios may exceed 2
to i. It does not follow, therefore, that the mean ionization observed
in the fog chamber is the same as that obtaining within the heavy leaded
electrical condenser. To secure this identity the fog chamber itself must
be the condenser.

The method was, therefore, varied by using the cylindrical fog chamber
(glass wet within, put to earth) with its axial core of charged aluminum
tube both as an electrical condenser for the measurement of current and
as a fog chamber for the measurement of ionization. The end of the
aluminum tube within the fog chamber is hermetically sealed ; the other
is open without for the introduction of the sealed tubelets containing
radium. By properly adjusting these along the axis an approximately
uniform ionization within the fog chamber is obtainable. The trials made
seemed promising enough to make it worth while to repeat the determi-
nation of e by Thomson's method, using, however, the mercury lamp as
a source of light and a purely optical method for the measurement of the
nucleation as suggested above. Results will be given in a later report.

The correlative method of determining e in terms of the decay con-
stant of the ionization has also been tried. If Ar be the number of ions
in the fog chamber due to the radium in the aluminum tube when the
latter is not charged and n the number when it is charged the constant e
ma be written

where C is the capacity and v the volume of the cylindrical condenser
fog chamber and V the (constant) fall of potential of the core per second,
due to the current passing through the ionized air within the chamber.
In this case very large potentials (250 volts) may be used, and a graduated
Exner electroscope suffices for the measurement of V.

The experiments by the decay method in the second part of Chapter
IV, made for the present merely to test the standardization of the fog
chamber, as detailed in the earlier publications of the Carnegie Insti-
tution of Washington, nevertheless lead to very acceptable values of
e, even at the enormous ionizations (exceeding 500,000 nuclei per
cubic centimeter) employed.

The values for e in Chapter IV were too high, even with the admission
that negative ions only are caught in the fog chamber employed. The

VI PREFACE.

method is, therefore, repeated in Chapter V with greater detail. Con-
denser and fog chamber are now identical, and the data obtained are of
reasonable value.

In Chapter VI, finally, the effect of incidental voltaic contacts occur-
ring in Chapter V is critically studied, with a view to using a condenser
whose parts are of different metals separated by an ionized medium for
the measurement of voltaic potentials.

My thanks are due to Miss Laura C. Brant for efficient assistance
throughout the course of this work.

CARL BARUS.
BROWN UNIVERSITY,

Providence, R. I., August i, 1909.

CONTENTS.

CHAPTER I. — Nuclei of Pure Water.

Page.

1 . Introductory i

2. Rapid evaporation of fog particles. Phosphorus nuclei. Table i ; fig. i i

3. Spontaneous evaporation of fog particles. Phosphorus nuclei. Table 2 3

4. Slow spontaneous evaporation of fog particles. Vapor nuclei. Table 3 4

5. Rapid evaporation of fog particles. Vapor nuclei. Table 4 7

6. Evaporation retarded as the diameter of fog particles decreases 8

7. Time losses. Table 5 8

8. Effect of changes of the drop of pressure 10

9. Exceptionally rapid evaporation 1 1

10. Conclusion 1 1

11. The same, continued 12

1 2. The same, continued 13

13. The same, continued 13

14. Statistical hypothesis 14

CHAPTER II. — Standardization and Efficiency of the Fog Chamber.
AXIAL COLORS AND INTERFERENCES.

15. Introductory 15

1 6. Causes of axial colors. Table 6 15

17. The lamellar grating 16

1 8. Disk colors of coronas 16

19. Experiments with long tubes. Table 7 ; fig. 2 17

20. Short tubes. Table 8 19

CORONAS WITH MERCURY LIGHT.

2 1 . Preliminary survey • 20

22. Apparatus 21

23. Equations 21

24. Data with white light. Table 9; fig. 3 22

25. Data with green mercury light. Tables 10 and 1 1 ; figs. 4 to 9 24

26. Inferences. Interference and diffraction. Table 12 31

EFFICIENCY OF LARGE AND SMALL FOG CHAMBERS ATTACHED TO THE

SAME VACUUM CHAMBER.

27. Fog chambers 33

28. Data. Table 1 3 ; fig. 10 34

29. Data for apertures. Table 14; fig. 1 1 37

30. Results 39

3 1 . Conclusion 39

CHAPTER III. — Regions of Maximum lonization and Miscellaneous

Experiments.

REGIONS OF MAXIMUM IONIZATION DUE TO GAMMA RADIATION.

32. Introductory 41

33. Short fog chamber 41

34. Behavior after removal of radium 42

35. Long fog chamber 43

36. Data. Table 1 5 ; figs. 1 2 to 1 5 43

37. Inferences 47

VII

1 1

VIII CONTENTS.

MISCELLANEOUS EXPERIMENTS. Page.

38. Experiments to detect the region of positive ions. Table 16; fig. 16 48

39. Radium within the fog chamber. Sealed tubes. Table 17 50

40. Distance effect. Table 1 8 51

41. Attempt to calibrate the fog chamber with five separate sealed tubelets of

radium. Tables 18 and 19 51

CHAPTER IV. — The Standardization of the Fog Chamber by A id o] Thomson's

Electron .

THE CONSTANT e, EXPRESSED IN TERMS OF VELOCITIES OF THE IONS.

42. Advantages 54

43. Plate. Fig. 17 54

44. Cylinder. Fig. 18 55

45. The same. Preliminary data. Table 20 56

46. The same. Wires surrounded by earthed pipes 57

47 . Conclusion 58

THOMSON'S CONSTANT e, EXPRESSED IN TERMS OF THE DECAY CONSTANT

OF IONS WITHIN THE FOG CHAMBER.

48. Introductory 59

49. Electrical condenser fog chamber 59

50. Auxiliary condenser 60

5 1 . Methods 6 1

52. Data disregarding external gamma rays. Table 21 61

53. Further data. Table 22 63

CHAPTER V. — The Electron Method o) Standardizing the Coronas of Cloudy
Condensation in Terms of the Velocities of the Ions.

54. Introductory 65

55. Apparatus. Fig. 19 65

56. Auxiliary electrical condensers 66

57. Methods pursued 67

58. Data. High ionization currents. Table 23 69

59. The same. Coronas 70

60. The same. Summary. Figs. 20 and 21 71

61. Data. Moderate ionization. Electrical currents 72

62. The same. Coronas 72

63. The same. Summary. Figs. 22 and 23 72

64. Data. Small ionizations. Electric currents 74

65. The same. Coronas 74

66. The same. Summary. Figs. 24 and 25 74

67. Conclusion 75

CHAPTER VI. — Electrometric Measurement of Voltaic Potential Difference
between the Conductors of the Condenser Separated by an Ionized
Medium.

68. Introductory. Fig. 26 76

69. Theory 78

70. Data. Origin of the electrometer current. Fig. 27 80

71. Aluminum core charged with radium tubelets. Table 24; fig. 28 82

72. Results. Ionization and voltaic contact potential difference 82

73. Voltaic contacts: aluminum-zinc, aluminum-copper, aluminum-aluminum.

Table 25 ; fig. 29 82

74. Further experiments and conclusion 83

CHAPTER I.
NUCLEI OF PURE WATER.

1. Introductory. — In case of a fog chamber but 4 cm. high and
broad and lined with wet cloth, I was surprised to find that if each of a
succession of fogs precipitated on phosphorus nuclei is allowed to (appar-
ently) subside, i. e., to be completely dissipated without influx of air
before the next exhaustion is made, it nevertheless takes about 10 or 12
exhaustions before all the nuclei are precipitated. It follows, therefore,
that for very small fog particles the dissipation by evaporation in origin-
ally* saturated air is enormously more important than the dissipation
by subsidence. The fog particles do not, however, vanish completely,
but the evaporation terminates in persistent solutional water nuclei,
large enough to keep the air bluish or hazy.

If the same experiment is made with rigorously dust-free air and vapor
nuclei, the fog particles vanish almost completely in a single slow evapor-
ation, so that but one additional exhaustion is needed to quite clear the
fog chamber. Very few water nuclei (several per cent) are left behind in
this case. The number increases when the evaporation is more and more
accelerated by the rapid influx of dust-free air.

It is this feature of the experiment, the tendency of the water nuclei left
after precipitation of dust-free wet air on the vapor nuclei of its own
medium to persist in proportion as the evaporation is faster (more or less
compression or rise of temperature) , that is the chief burden of the present
paper. The fact that water nuclei may persist, while the enormously
larger fog particles from which they have been obtained all but evaporate,
is the interesting part of this result. Some restraining tendency! must
therefore be evoked by which the accelerating effect of convexity is much
more than canceled, for the nuclei here in question are produced in
rigorously dust-free air by the precipitation of water vapor on water
vapor. A solutional effect is therefore absent.

To investigate the question it is expedient to begin with a medium of
phosphorus or solutional nuclei, to subject the fogs thereupon to more or
less rapid evaporation, and thereafter to compare these results with the
corresponding case for vapor nuclei.

2. Rapid evaporation of fog particles. Phosphorus nuclei. — In the

following experiments I have endeavored to trace these results quantita-

*Probably the rise of temperature is sufficiently rapid to render saturated air from
which a fog has been precipitated temporarily unsaturated.

tThe earlier work has been quoted in Part I of Publication No. 96, Carnegie Institution
of Washington.

I

2 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

lively. For this purpose fog particles precipitated on phosphorus nuclei
were successively evaporated as rapidly as possible by compression
(influx of air), so as to make the loss by subsidence negligible except at
the end of the series, when so few nuclei are present that the precipitate
is rain-like. In such a case the only loss of nuclei is due to the exhaustion,
as the normal time loss* is relatively small. In table i, taken from an
earlier report, f I have given a typical case, the exhaustion ratio being
y = o."jS, nearly. As dust-free air is introduced after each exhaustion the
successive nucleations are clearly in geometric progression. As long as
the nucleation is less than 100,000, subsidence may be disregarded, as the

'0 £ 4- 6 8 10 /£ 14- 1Q IS 20

FIG. i. — Chart showing the survival ratio, n'/n, in successive exhaustions, for
phosphorus nuclei (A, 2, 3,) and water nuclei (4, 5, 6, 7). Scale of latter magni-
fied ten times.

curves A in fig. i show. The table also contains the angular diameters
(f> = 5 / 30 of the coronas and the nucleations n computed therefrom . Finally
the ratios n'/n of the successive nucleations n and n' are given in each
case. These should be equal to the exhaustion ratio if no other loss of
nuclei occurs. In fact, if we take the data above w= 100,000 the mean
ratio of the ten cases is nf/n = o.j6, agreeing practically with y = o.jS.

If we plot the successive ratios n'/n in terms of n, the results show a
jagged curve oscillating about n' /n = o.'j&, but descending rapidly below
n = io5 as the result of subsidence. (Compare curve A , fig. i .) The irreg-
ularity of the curve is inevitable, as it corresponds to a ratio between two
large coronas whose outlines are no longer sharp ; but there is compen-
sation in the successive values, as the curve, taken as a whole, indicates.

*Compare chapter n.

jCarnegie Institution of Washington Publication No. 96, chap, in, table 17, 1908.

NUCLEI OF PURE WATER.

TABLE i. — Quick evaporation. (Reproduced from Carnegie Institution of Washington
Publication No. 92, chap, in, table 17, 1908.) y = o-

SERIES A.

Corona.

s.

nXio-3.

Ratio n'/n.

Corona.

s.

nXio~3.

Ratio n'/n.

w r

1500

0.67

g

7-8

IOO

0.69

w v

....

IOOO

•71

0

7-5

89

•74

sb

715

•9i

6.8

66.5

•65

bp

650

.89

5-9

63.0

•57

g

• > • •

580

•79

4-9

24.6

.66

gy

13

460

.70

4-2

16.3

•53

w o

11.7

320

.78

3-4

8-7

•35

w r

10.5

250

.60

2-4

3-o

.40

w p

9.0

152

.67

1.8

I . 2

....

3. Spontaneous evaporation of fog particles. Phosphorus nuclei. — With
the above data one may now compare the corresponding cases for very
slow evaporation, in which the fog has disappeared spontaneously in the
lapse of time, apparently by subsidence, but in greater measure by
evaporation. Part i of table 2 shows the results obtained in a very long
(2 meters) brass tube, lined with wet cloth but 4 cm. high and broad.
Twrelve exhaustions are needed for removing the nucleation, in spite of
the spontaneous disappearance of each individual fog. The disappointing
feature about these experiments with 2 -inch tubes is the total absence of
disk or axial color throughout. They were made in the hope that such
colors would appear.

In parts 2 and 3 of the table these observations are continued, but now,
with a glass fog chamber, where the line of vision passes through but 8 cm.
of fog as compared with 200 cm. above. The exhaustion ratio is ^ = 0.78,
as in table i . Besides the disk color of coronas, the successive nucleations
n and the nucleation ratios n'/n are given. These ratios are also con-
structed in fig. i in terms of n, in the curves 2 and 3 of the chart. Not-
withstanding the complete apparent subsidence, nine exhaustions are
needed to clean the fog chamber of these solutional nuclei ; but the effect
of subsidence is here unmistakable at least below n= io6 nuclei per cubic
centimeter. From a smooth curve, embodying series 2 and 3, the sub-
sidence effect, together with other permanent loss, may be stated as
follows (y — o.'jS). The approximate diameter is d.

Evapora-

ioRd

i o~3n

Exhaustion
loss.

n'/n.

.Subsidence
loss.

tion to
water

nuclei.

cm.

164

1500

O. 22

o. 76

0.02

0.98

189

IOOO

. 22

.68

. 10

.90

203

800

. 22

.63

• 15

• 85

225

600

. 22

.56

. 22

.78

255

400

. 22

.48

•30

.70

320

200

.22

• 30

.48

•52

CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

From these data it appears that above w= 200,000 nuclei dissipation
is due more and more largely to evaporation; below n= 2 X io5 more and
more largely to subsidence. Above w=io5 or d = 0.003 cm-. moreover,
the tube in part i remains permanently hazy and the fogs (if seen through
some thickness) quite black.

TABLE 2. — Persistence of solutional water nuclei. Shows number of exhaustions to

clean with complete (apparent) subsidence.

Exhaus-
tion No.

Corona.

wXio-3

Ratio.

Exhaus-
tion No.

Corona.

« X io-3

Ratio.

Part i. — Phosphorus emanation. Long brass tube; length 200 cm.; diameter 5

cm.; cloth lined. Barometer 77.1.5 at 20°. <?/>3= 17 cm., about. Each fog appar-

ently falls out. Time consumed, about 30 minutes.

i

black

7

corona

2

black

8

corona

3

black

....

....

9

corona

....

....

4

translucent

. . • .

10

faint cor.

....

....

5

fawn

....

1 1

very faint

....

6

fog

12

very faint

Part 2, series 2. — Glass fog chamber (observations transverse); length 45 cm.;

diameter 12 cm.; height of cloth 8 cm. Each fog allowed to fall out or dissipate.

Two sources. Barometer 77.75 at 20°. Sf>3=i~; e?/>3//> = 0.205. Time consumed,

27 minutes. Fogs dissipate into blue haze.

i

Fog r'

7

*=9; g

150

0.31

2

Fog r'

1700

0.82

8

j = 5; cor.

46

.04

3

Fog c'

1400

•72

9

5=15; cor.

2

4

Fog v

IOOO

.60

JO

....

....

5

g

600

.67

1 1

....

6

5=12; o

400

•37

12

....

....

Part 3, series 3. — Repeated. Same glass fog chamber. Same time, about. No. 4

still evaporates to blue haze.

i

Fog

6

•y=io5; c

250

0.50

2

^=163; r

1700

0.83

7

5=70; cor.

125

.06

3

*=i47; c

1400

• 57

8

^ = 27; cor.

7

•03

4

-f=i43: gb

800

•63

9

j=io; cor.

2

5

^=130; gy

500

•50

4. Slow spontaneous evaporation of fog particles. Vapor nuclei. — We

may now contrast with the preceding the evaporation of fog particles
precipitated on the vapor nuclei of dust-free air. Table 3 contains the
results arranged on a plan similar to the above. A slight difference of pro-
cedure is necessary, because the vapor nuclei are not caught in sufficient
quantity except at very high exhaustion. Moreover, these exhaustions
have no effect in removing vapor nuclei, as these are instantly reproduced
by the kinetic mechanism. The water nuclei, however, should be pre-
cipitated at an exhaustion less than the fog limit of dust-free air. Beyond
this the exact value of the exhaustion ratio ^ = 0.71 to o. 7 7 is of no import-
ance, because the ratio of successive nucleations, n'/n is usually less than

NUCLEI OF PURE WATER.

i per cent, showing that almost all nuclei have vanished in the first
evaporation of the corresponding fog particles. The curves Nos. 4 and 5,
fig. i , give these results on a scale ten times larger than the preceding, to
bring out the small values n' /n, which would vanish on the scale adopted
for the solutional nuclei. For reasons which do not clearly appear, the
data in series 4 are larger than corresponding results in series 5, possibly

TABLE 3. — Persistence of water nuclei when fogs are precipitated on vapor nuclei.
Glass fog chamber. <J/>3= 32 for vapor nuclei; <J/>S= 22 or 23 for water nuclei. Lower
dp = 22 or 23 is above fog limit, but vapor nuclei are inactive.

sp,

Corona.

wXio-3

Ratio.

8p,

Corona.

n X io~3

Ratio.

Part i, series 4. — Barometer 77.75 at 20°.

32

22

Jj = io8; o
J2 = 30

720
12.4

0.017

42

23

^1=150; g
•T2 =25

2170
6-9

0.003

36

^=120; y

*2=3I

1080

13-3

O.OI2

Part 2, series 5. — Repeated in glass fog chamber. Barometer 75.77 at 22°.

39

i?

•*i=*3o; g

S2~ 2O

13/0
3-o

O.002

27
17

*i=45

S,= 12

47

• 5

O.OOI

36
i-

j,= i2o; g

.y2=24

*iogo

5- i

.005

28
17

-5-1 = 84; p
S2= 12

320

•5

.002

32
i?

•5-1=122; g
s.2= 19

fio30

2.6

.002

28
17

-^1 = 85; p
•^2=25

326
5-5

.007

29
17

sl = 1 1 1 ; r o

•^2=25

780

5-5

.007

*Long waiting (3Om)for«2- tNo waiting ( ira) for st.

because the exhaustion in the former case was above the fog limit of dust-
free air and would therefore catch the smaller order of water nuclei than
occur in series 5. These water nuclei, in fact, are reduced appreciably in
number in the lapse of time, as will be seen by comparing the two experi-
ments for w = 320,000 nuclei in series 5. The following exhibit may be
regarded as a smoothed curve for about the same period of dissipation.
The curves rise for smaller nucleation; the exhaustion loss is 0.23.

Number

io6d

IO~*tt

n'/n

Complete
evaporation.

completely
evaporating

Subsidence
loss above.

per cm3.

cm.

1 60

1500

0.003

0-75

1050

O.O2

190

IOOO

.006

.66

660

. 10

200

800

.007

.61

490

•15

220

600

.008

•54

320

. 22

250

400

.009

.46

185

•30

320

200

.010

.28

56

.48

CONDENSATION OF VAPOR AS INDUCED. BY NUCLEI AND IONS.

This accentuates the effect of subsidence, which with the exhaustion
evaporation must account for the total number of nuclei removed. At
first sight it would appear that the number of residual nuclei is inde-
pendent of the number of vapor nuclei present, as if some other nuclei
which may accompany the vapor nuclei were responsible for residual
water nuclei.

TABLE 4. — Case of rapid evaporation by compression (influx of dust-free air).

dp

Corona.

s

Corona
dissipated by —

ap/p

nXio~3

Ratio.

Part i, series 6. — Barometer 76.86 at 23.5°. Time between exhaustions, 5 min-
utes, usually. Curve No. 6, fig. i.

35-7
18.5

28.7
18.5

28.7
18.5

28.7
18.5

30-5
18.5

30.5
18.5

32.2
18.5
32.2
18.5

*Time

r o
corona

w b p
corona

w b p
corona

y

corona

P
corona

P
corona

r
corona

r
corona

interval t

ii. 8
6.0

9.0

2.8

8-5

5-3

8.0
4-5

1 1 .0
5-6

10. O

3-5
10.5
5-5
10.7

5-2

etween ot

> Compression . . . .

{ 0.465
I -240

•373
I -240

/ • 373
.240

/ • 373
I -240

/ -397
I -240

/ -397
.240

.420
I -240

.420
. 240

;. y=o.75

600
49
220
5
190
33
1 60

21

355
39

*27O
*IO

*320

*37

34°
3i

| 0.082
| -023

} .,„

.130

. I IO

} -037

} .,,5

.091

> Slow evaporation.
\ Compression

} . Do..

J
} . ..Do..

J
\ Evaporation*

> Compression* .

iservations 3 minute:

Part 2, series 7. — Green coronas. No subsidence. Barometer 76.70 at 22°. Time
between exhaustions, 3 to 5 minutes. Temperature 25°. Curve No. 7, fig. i.

dp

Corona.

5

Fog
dissipated by

ap/p

nX io-3

Ratio.

36
18

36
18

36
18

36
18

36
18

g
br b p

g
gbp

g
gbp

g
corona

g
corona

16.0
5-6

16.0
5-6

16.0
5-6

16.5
1.8

16.0
4-5

1 Compression or
J influx . ...

[ 0.4-0
.240

/ -470
l -240

r .470
1 -240

f -470
1 -240

• 470
. 240

IOOO

39

IOOO

39

IOOO

39

IOOO

I

IOOO
21

J 0.039
•039
} -039
.001
.021

..Do..

J
J ....Do

Slow evaporation;
no influx

NUCLEI OF PURE WATER.

7

5. Rapid evaporation of fog particles. Vapor nuclei. — Finally, the
fog particle precipitated on vapor nuclei may be rapidly evaporated by
compression (influx of air). In order that all results may be comparable,
it is necessary to allow the same time interval between the first ex-
haustion (capture of vapor nuclei) and the second (capture of residual
water nuclei). Since filtered air enters in the same way here as in the
foregoing section 4, its effect (if any) is eliminated from the results. Sub-
sidence, however, is essentially reduced by the present method, since the
time for subsidence is but one-third to one-fifth as large as in section 4.
The results are given in table 4 on the same plan as in table 3. In part i
two control experiments with gradual exhaustions are introduced to
indicate the difference. The nucleations are as a rule low. In part 2 they
are high and there is one control experiment. The curve is shown in Nos.
6 and 7 in fig. i.

The data taken from smoothed curves will therefore be about as
follows, d being the approximate diameter of fog particles, subsidence
being ignored and the exhaustion loss 0.25.

Number of

Number of

I08d

io~3n

n'/n

Complete
evaporation.

nuclei
evaporating

residual
nuclei

(nXio~3).

(wXio-3).

cm.

16

1500

....

....

....

19

IOOO

0.039

0.71

710

39

20

800

.060

.69

550

48

22

600

.082

.67

400

49

25

400

.105

-65

260

42

32

200

.126

.62

125

25

The apparently greater persistence of water nuclei on rapid evapor-
ation is thus sustained. Subsidence is in excess in section 4; and though
of the same order as the number of persistent nuclei, it always refers to
the total charge of nuclei. As the number to be accounted for in the
present instance can not well be estimated, it is safe to conclude that
about 95 per cent of the fog particles precipitated on vapor nuclei evapo-
rate without residue, when about io6fog particles are suspended in each
cubic centimeter ; and that this percentage decreases with the number of
fog particles or vapor nuclei caught, or as their size increases. Conversely
the number of residual water nuclei persistent within 5 minutes increases
as the number of fog particles decreases (i. e., as their size increases) from
a persistence of about 0.054 at n=io* to over 0.17 at n = 2Xio5. One
would thus be tempted to conclude that larger fog particles take a longer
time to evaporate completely ; but that the case is far more subtle will
appear in the next paragraph.

8 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

6. Evaporation retarded as the diameter of fog particles decreases.—

A suggestive inference may be drawn from the results obtained. The
visible part of the fog vanishes within less than a minute after the com-
pression, or the (necessarily slow) influx of dust-free air begins. Here,
then, by far the greater bulk of the particle vanishes. In the ensuing 5
minutes or more, optically quite inappreciable water nuclei are still
present, to the extent of 5 to 20 per cent of the original charge of vapor
nuclei. In other words, whereas the tendency to evaporate increases
rapidly with the diameter of the fog particle, there must be, in case of the
fog particles in question, some counteracting tendency in action, by
which this evaporation is retarded much in excess of the accelerating
effect of convexity. All this occurs in rigorously dust-free air, in which
water vapor and the ions (less than 1,000 per cubic centimeter, whereas
there are from 25,000 to 50,000 water nuclei) inseparable from air and
due to natural causes, are alone present. It therefore becomes interesting
to endeavor to ascertain the reason of this complete inversion of the
behavior usually characteristic of these exceptionally small droplets.

7. Time losses. — The effect of lapse of time between the exhaustions
has already been shown to be of minor importance within intervals like
those of the above observations. It is important, however, to add
quantitative work, and table 5 supplies relevant data, dp being the drop
of pressure on exhaustion, n the nucleation, n' jn the ratio of successive
nucleations. Table 5 shows that the nucleation is spontaneously reduced
by diffusion to about one-half, in the interval between the second and
tenth minutes, and so far as may be observed the decrease is fairly
uniform. One may therefore estimate a time loss of about 6 per cent
per minute. Consequently the coronas obtained in the second and
third minutes (or even later) are liable to show no discernible difference
comparable with the other possible complications involved. Thus, for
instance, the loss of water nuclei proper can not begin before all the fog
particles have evaporated, a process which must consume a minute at
least if an influx of strictly dust-free air is to be assured.

Table 5 also gives evidence to the effect that no nuclei come through
the filter. If the partial vacuum is gradually raised to dp = 36 cm. without
sudden exhaustion, i. e., without initial coronas, and filtered air is then
passed in the identical way through the filter into the fog chamber, no
water nuclei whatever are detected by the sudden exhaustion at dp = 1 8
cm. This is conclusive proof that the evaporation of fog particles is the
sole cause of nucleation.

Again, table 5 shows that by keeping the influx cock open, nearly 9
per cent of the fog particles may be represented by water nuclei even
when n—io6. It is not safe to admit a more rapid influx at the filter,
but the sudden introduction of previously filtered air suggests itself as a
means to the same end, and will be tried in turn.

NUCLEI OF PURE WATER.

TABLE 5. — Water nuclei from evaporation of fog particles precipitated on Vapor nuclei
in dust-free air. Effect of lapse of time and of drop of pressure.

Time

elapsed
between
exhaus-
tions

8p

Corona.

s

Fog
dissipated
by-

dp/p

«Xio~3

Ratio

n'/n

(minutes).

Part i. — Effect of lapse of time between exhaustions. Barometer 75.26 at 26°.
<J/>=36 and dp = 18 or dp/p = o.4J5 and o. 245.

2m 1

....

g
rg

72

....

IOOO

86

} 0.86

3m {

* ...

g
rg

12

....

IOOO

86

| .86

5m {

I0m |

g
g

70
56"

Slightly
• open influx
cock.

....

IOOO

79

IOOO

40

} -»

J .40

2m |

g
rg

72

....

IOOO

86

| .86

5m {

....

g
rg

66

....

IOOO

65

} •«

I0m

g

55

....

....

IOOO

37

} -

2m |

....

none
none

o

....

{ ::::

o

0

}::::

Part 2. — Effect of different drops of pressure dp. Barometer 75.26 at 26°.

2m
2m |

36.0
19.9

36.0

21.6

g
g

72
72

Slightly
• open influx
cock.

0.475
.265

•475
. 290

IOOO

90

IOOO

98

....

2m |

36.0
27.0

g

60

•475
.360

IOOO

66

Part 3. — Very rapid evaporation (0.25 minute). Barometer 76.22 at 24°.

i-5m {
i-5m {

36.0

20.0
36.0

20. o

g
gbp

g
v b p

80
80

Rapid
influx from
tank of
dust-free

....

IOOO

123

IOOO

145

J 0.123
• H5

i-5m {

36.0

20. O

g
!gbp

So

air.

....

IOOO

123

} .„,

IO CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

TABLE 5. — Water nuclei from evaporation of fog particles precipitated on vapor nuclei

in dust-free air — Continued.

Time

elapsed
between
exhaus-
tions

dp

Corona.

•

Fog
dissipated
by—

sp/p

«X,o-.

Ratio

ri/n

(minutes) .

Part 4. — Larger particles. Rapid evaporation (less than 0.25 minute). Baro-
meter 76.69 at 23°.

i-5m {

29.8
17-3

yo
r b p

8.0

1

1

0.388
.225

540
108

> 0. 20

i-5m {

29.8
17-3

yo
r b p

7-7

• 388
.225

540

97

} ''8

1-5- {

28.0
17-3

c

yb

9-0
8.0

Influx of
filtered

•365

.225

290
108

} .38

*.g* {

28.0
17-3

r
g !bp

9-5

7 • 7

air from
reservoir.

•365
.225

260
97

} •»

i.5m {

26. 2
17-3

corona

5-7

4-2

•342
.225

54
16

} .30

m (

27.0

corona

7.6

•352

130

1

1

17-3

....

5-4

•

.225

33

1

*A11 conditions identical to the above, except that there is no primary exhaustion or fog precipitation
on vapor nuclei. The absence of all condensation at 18 shows that no nuclei come through the filter.

8. Effect of changes of the drop of pressure up. — The second part of
table 5 contains results in which residual water nuclei are captured at
drops of pressure from up=i& to 27 cm. At first the coronas do not
change ; eventually they decrease in a way to be referred to the increased
amount of water precipitated. Vapor nuclei are inefficient in the presence
of water nuclei.

f The constancy of coronas after all nuclei have been caught through a
considerable range of values of dp, occurs here as elsewhere and has not
yet been fully explained. As the nucleation n varies with the precipi-
tation (m grams per cu. cm.),wThile n increases with dp, the computed
values of n must also do so, thus conflicting with the observed fixed
coronal aperture. It is difficult to conjecture where the excess of water
precipitated goes to, even if we recall the slow change of 5 implied in
dcC'i/m or s^/ni = const. In some way, probably coincident with the rise
of temperature after adiabatic cooling, the excess of precipitation is again
removed before coronas can be observed. The efficiency of the fog
chamber virtually breaks down, as no more water is deposited when dp
increases.

It follows in general that neither by the time loss nor by the effect of a
varying drop of pressure is the tendency of rapid evaporation to produce
persistent water nuclei materially influenced. It must, therefore, be an
occurrence of its own kind.

NUCLEI OF PURE WATER.

II

9. Exceptionally rapid evaporation. — -In the third and fourth parts
of table 5 the influx of dust-free air was increased in a marked degree,
by withdrawing the influx of dust-free air from a large independent
reservoir. In this way the time of evaporation was reduced to about 1 5
seconds. Nevertheless it required about 1.5 minutes to reduce the pres-
sure from dp = 36 cm., to dp = 20 cm., so that some water nuclei vanished
by decay. The yield of water nuclei has been materially increased. Thus
even when n=io6 or d = o. 00019 cm., rapid evaporation will convert at
least 1 8 per cent of the fog particles of pure water into persistent water
nuclei. The case is most pronounced for n = 300,000 to 400,000 nuclei
per cubic centimeter, or d = 0.0002 7 cm., when 48 per cent of the nuclei
(about one-half), persist. Beyond this, n = io5, the persistence decreases,
a result doubtless referable to the increasing importance of subsidence.
Within reasonable limits persistence increases as the original number
of nuclei decreases, which result is identical with the character of the
earlier series.

Naturally all these data are lower limits. In appropriate apparatus
the time of evaporation, the interval of observation, etc., might be made
much shorter; but this would not change the general trend of the data.
Again, many particles must be washed out by contact with the sides of
the vessel or by coalescence, during the turbulent motion which accom-
panies the influx of air. The following is a digest of the data found:

Ratio

Corrected

rfXio9

nXio~3

Exhaus-
tion loss.

Subsid-
ence loss.

Evapora-
tion loss.

Residual
water
nuclei.

residual
water
nuclei to
total water

number of
residual
water
nuclei

nuclei.

(rcXio-3).

cm.

190

1000

0.23

o

0.64

0.13

0.17

170

240

500

•23

0

•58

.19

•25

125

270

350

•23

o

.40

•37

.48

168

410

IOO

•23

o

•49

.28

.36

36

10. Conclusion. — For very small fog particles suspended in dust-free
air saturated with water vapor and left without interference, the dis-
sipation by evaporation is enormously more important than that by
subsidence. In the above plug-cock fog chambers the transition occurs
when the number of nuclei per cubic centimeter, n = 200,000, or the
diameter of fog particles, d = 0.0003 cm-> when about half evaporate and
half subside.

Fog particles precipitated on solutional nuclei (phosphorus) , evaporate
to persistent water nuclei without other loss than is attributable to sub-
sidence and in a small degree to time losses (diffusion) . There is no loss
by complete evaporation.

12 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

Fog particles precipitated on the nuclei of water vapor in dust-free air,
in contrast with the preceding case, evaporate under the same circum-
stances almost without residue, the yield of water nuclei (after allowing
for subsidence and in the absence of all interference) being but 0.004
when d = 0.00016 cm., increasing to 0.0036 when d = 0.0003 2 cm- These
fog particles evaporate into the wet air from which they were precipi-
tated, and the experiment may be repeated indefinitely. Relatively more
water nuclei persist as the fog particles evaporated are larger.

1 1 . The same, continued. — The persistence of water nuclei obtained
in the last case from the nuclei of water vapor is much increased by
accelerating the evaporation of the fog as soon as formed. Such forced
evaporation is produced by the rise of temperature due to the com-
pression accompanying the influx of dust-free air after the exhaustion
which precipitated the fog. This result can not be associated with losses
due to subsidence.

When the rate of evaporation is increased by compression, moreover,
the number of water nuclei (derived from the reasonably rapid evapor-
ation of fog particles precipitated on vapor nuclei and persisting within
5 minutes after the evaporation) may be as large as 5 per cent to over 20
per cent, depending upon the size (d=i9Xio~5 to d = 32Xio~5 cm.,
respectively) of the fog particles evaporated. Again, relatively more
water nuclei persist when the fog particles evaporated are larger within
limits given. By keeping the influx cock for dust-free air slightly open
on sudden exhaustion, 10 per cent of the fog particles evaporated may be
represented by persistent water nuclei, even when d — 1 9 X io~5 cm. or n =
io6. If it were safe* to make use of more rapid evaporations, this limit
could unquestionably be much increased. Thus on the rapid evaporation
of fog particles by the influx of filtered air from a large independent reser-
voir into the fog chamber, about 18 per cent of the fog particles were
converted into residual water nuclei when n— io6 and actually 48 per cent
when w=io5. All such values or lower limits, because the loss of fog
particles at the walls of the vessel and by coalescence is not included,
but tests under most rapid evaporation possible showed that a limit had
been practically reached.

The loss of nuclei by decay (diffusion) in the lapse of time (say 6 per
cent per minute within the given interval of observation) and the effect of
changes in the drop of pressure on sudden exhaustions have no causal
bearing on the production of water nuclei by rapid evaporation. They
merely modify the number. Similarly the effect of subsidence is second-
ary. Hence the cause of the production of persistent water nuclei in
rigorously dust-free air must be associated with the speed of evaporation
or with the motion of the fog particles during evaporation. It is a curious

*Naturally the efficiency of the filter must be tested before each experiment.

NUCLEI OF PURE WATER. 13

fact that whereas the relatively enormous fog particle evaporates at once
beyond the range of visibility, this process stops in case of certain of the
invisible particles making about 0.5 to 50 per cent of the total number
as the evaporation is more rapid in the manner specified. The remaining
fog particles evaporate completely.

12. The same, continued. — J. J. Thomson, Langevin and Bloch, and
others* have referred the persistence of pure water nuclei of about io~8
cm. in diameter, to the minimum of surface tension discovered by Reinold
and Riickerf for thicknesses of films of about the same value. Since all
fog particles are so much larger than this order of values, it is difficult to
see why, under quiet evaporation without any interference, they do not
all terminate in water nuclei, allowance being made for subsidence. Yet
under these circumstances the yield of water nuclei is least, being usually
within i per cent. Whatever losses may be due to coalescence should
be increased when the rate of evaporation is increased, because there is
more motion of the air relatively to the fog particles. Again, precisely
the reverse occurs, inasmuch as an increased rate of evaporation enor-
mously increases the yield of water nuclei.

Moreover, the residual water nuclei may, on rapid evaporation, exceed
the order of io~6 cm. in diameter two or three times; or on slow evapor-
ation they may fall below 5Xio~7 cm. and yet persist for half an hour
or more. Under any circumstances they are graded. They appear to
diminish in size with extreme slowness in the lapse of time, so that an
appropriate interval of waiting will yield any size.

13. The same, continued. — Since the fog particles are absolutely pure
water (water condensed on water vapor), it is tempting to suggest electri-
cal charge as the cause of the observed persistence, such charge being
acquired either by friction during the motion of particles undergoing
rapid evaporation (influx of air) or by the mere act of evaporation. The
latter, like the minimum of surface tension, would require the same
persistence of all fog particles under conditions of quiet evaporation. As
has frequently been shown, this is not the case. A frictional mechanism,
suggested in view of the occurrence of convection during the period of
evaporation and influx of air, if in action, would account for the discrimi-
nation between fog particles as to survival. Thus drops of larger size are
stirred about for a longer time before complete evaporation, and they are
therefore more favorably circumstanced to persist, as they have been
found to do ; water nuclei should not be of the same size and they are not ;
etc. But all my experiments have failed to detect the amount of charge
commensurate with the persistence of nuclei.

*J. J. Thomson: Conduction of Electricity through Gases, p. 152, 1903; C. T. R.
Wilson, Trans. St. Louis Electrical Congress, vol. i, pp. 364-378, 1904.
jReinold and Riicker: Proc. Roy. Soc., vol. 40, p. 441, 1886.

14 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

If the radius of residual water nuclei be taken as io~6 cm., the charge
needed would be roughly e = 6.3 X io~8 electro-static units per particle and
its potential would be about 18 volts. If about 200,000 of these droplets
or residual water nuclei are present per cubic centimeter (as were found
above), the charge would be about 4 coulombs for a cube each side of
which is 100 meters. If all the particles of the cubic centimeter were
brought to coalescence the size of the drop would be 58 X io~6 cm. at its
potential of about 63,000 volts. Finally, the electric contents of my fog
chamber should be about 30 electro-static units of quantity, and ought
thus, in spite of the moisture present, to be easily determinable. The
experiments showed only about o.^oX io~6 electro-static units per cubic
centimeter, less than the contents (o.88X io~6) in the room air without,
at the time; thai is, the average charge per nucleus was about 5X io~12
electro-static units, or less than i electron. Hence the electrical hypoth-
esis must be abandoned. It would in any case be improbable for the
charge to show so small a coefficient of decay as do the water nuclei.

14. Statistical hypothesis. — Under the circumstances it seems per-
missible to suggest an hypothesis of a statistical character; namely, that
the molecule of liquid water is composite, consisting of virtually more
volatile and less volatile constituents. Such a view is quite compatible
with the composite molecule observed in water vapor, where millions of
nuclei may be captured long before the molecule proper is reached, the
evidences of which are now beyond question. In case of fog particles,
when the evaporation is reduced to extreme slowness, we may conceive
that all groups of molecules evaporate together at about the same rate,
and that therefore the residue, i. e., the persistent water nuclei, are present
in least amount. On the other hand, when the evaporation is forced, or
accelerated by the heat due to compression, the more volatile constituents
of the fog particles evaporate faster than the less volatile, and there is a
correspondingly greater residue of persistent water nuclei, because of this
concentration of the less volatile molecular aggregates of water in each
fog particle. It follows also that relatively more persistent nuclei are
obtained by the evaporation of large fog particles than by the evaporation
of small particles, because a greater relative number of these droplets
would contain a sufficient number of the less volatile groups to persist;
i. e., the opportunities for concentrating the less volatile aggregates are
enhanced. Finally, it should never be possible to replace all fog particles
by the water nuclei derived from them. All of these deductions are in
keeping with the experimental evidence, as pointed out.

CHAPTER II.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.
AXIAL COLORS AND INTERFERENCES.

15. Introductory. — The axial colors of the steam jet and of coronas
overlie the source of light when looked at through a long column of wet
air in which uniform cloud particles are suspended. It makes no differ-
ence whether the source is a point simply or a disk (say) 4 inches in
diameter; it appears uniformly colored, as if seen through colored glass,
so long as the cloud lasts. The order of colors, beginning with particles
of extreme smallness, is the same as that of Newton's interferences seen
by transmitted light. In case of the steam jet, however, on passing the
transition from crimson to violet in the first order, the field becomes
opaque, while the steady flow of the jet usually breaks down and becomes
turbulent. In the case of coronas I have thus far failed to reach this
transition, the medium showing mere fogs of uncertain character.

To produce the actual colors vividly, and especially the tints of the
second and third orders for relatively large particles, the columns of fog
must be long and very uniform. The steam jet soon fails in this respect,
but a wide drum i to 2 meters long used as a fog chamber shows saturated
colors surrounded by coronas. In the case of hydrocarbon vapors the
columns may be shorter, because the particles throughout are larger for
like numbers per cubic centimeter than is the case with water vapor.

16. Causes of axial color. — In my earlier work* I was inclined to
regard these colors as interferences superimposed on the coronas, regard-
ing the small field of refraction possible with small particles as in keeping
with the long columns needed for observation. The explanation at best
is purely tentative. Later in my work, when the size of particles was esti-
mated from data given by successive exhaustions,! it appeared that the
sizes of the fog particles were of an order about ten times larger than would
be needed to produce interferences of the same kind. The interference
hypothesis was therefore abandoned. In my more recent results the
diameter of fog particles d and the ratio in question are somewhat reduced
but remain of the same order. Thus if n be the number of fog particles
per cubic centimeter, D the thickness of an air plate giving like inter-
ference colors, the results given in table 6 may be selected at random.
They show that the strong axial blues of the first order must belong to
particles even larger than o.oooi cm. in diameter, and that all particles
are more than six times larger than would be demanded for interferences.

*Phil. Mag. (5), xxxv, p. 315, 1893; BuU- U. S. Weather Bureau No. 12, 1895.
fPhil. Mag. (6), iv, p. 26, 1902; Smiths. Contrib. No. 1373, 1903; No. 1651, 1905.

15

16 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AHD IONS.

TABLE 6. — Data for axial colors. ra = 3.6X io~8 grams; v • — = i.9oXio~2.

DXio6

Corona.

Axial.

J

dXio5

c/Xio5

«X io~3

e/Xio5
computed.

Ratio

d/D.

H

V

36

i?

....

b

....

....

....

O7

gv

46

* 1

J

tf\j

29

bg

y

14-5

22

47

650

22

7-7

i •?

ci

oo

O A

....

7fi

^ ^

Ou

OvJ

41

gy

p

13.0

25

55

460

25

6.1

42

y

V

12 .O

27

60

360

26

6.4

45

b

I I .O

29

65

280

29

6-5

55

p

g

IO.O

32

67

213

32

5-8

57

y

9.0

36

70

152

36

6-3

69

gy

V

8.0

40

79

1 08

40

5-8

17. The lamellar grating. — Recently I have considered the case of
coronas in relation to the lamellar grating, in which diffractions are
obtained from a uniform succession of alternately different thicknesses
of clear glass. Experiments with such gratings were originally made
by Qiiincke and there is a full theoretical treatment by Verdet. The
behavior of this grating differs from that of the usual kind in the occur-
rence of an additional factor

cos*(7cd(n — i) + Tea sin o) jX

where n is the index of refraction, d the difference in thickness between
thin strips of width a and thick strips of width b, a the angle of dif-
I r^.ction. Hence since for axial color, 0 = 0, minima occur at (» — i)J =
+ i) .XI 2, whereas for Newton's interferences, the mimima occur for
a thickness D in the case of transmitted light where 2 ;j.D= (2111+ i) .XI 2;
whence

d/D = -^-

n — i

In case of water ;/ = 0.133, or d/D = 8.o. This result applied to a grating
of transparent strips is so near the above datum d/D>6 for a medium
of transparent particles (for which there is no theory), that it seems
reasonable to conclude that the actual colors are referable to the same
type of phenomenon in both cases. The need of observations through
long columns in case of fog particles suspended in air is additionally con-
firmative, since the contribution of color due to one particle must be
exceedingly small.

18. Disk colors of coronas. — One might be tempted to explain the
disk colors in the same way, for in case of deviation d from the axial ray

D I d= (n— i)/2W + a sin 0/2 dn

But here there are several insuperable difficulties which refer the disk
color to a different origin. In the first place, they are much more intense

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER. 17

than the axial colors and are seen distinctly through very small thick-
nesses of fog; disk colors are apparently abruptly complementary to the
axial colors and there is certainly no continuous transition; finally, there
is no incident light of the requisite obliquity.

The appearance is, therefore, as if, corresponding to the interferences
by transmission, there were complementary interference by reflection
toward the source of light. This phenomenon could then be reversed in
direction at any fog particle in its path, and thus turned again toward
the observer. But apart from the complementary nature of disk and
axial color, no other evidence bears on this explanation. Moreover, any
such theory must account for the intensity of disk colors in general, and
in particular for the vividness of the greens.

19. Experiments with long tubes. — In a long chamber and intense
illumination the axial colors may be extended over a considerable area
and intensified by strong illumination. It did not seem improbable that
they might then be serviceable for spectroscopic investigation, in which
case the mean wave-length of the interference bands would serve for
their identification. Thus they might afford a means of further investi-
gating the fog phenomenon at a degree of fineness beyond which the
coronas cease to be available. Unexpected difficulties were, however,
encountered, as will presently appear, and the endeavor to remove them
has not been successful.

JB

-tt r" -ir-

vs 5 em. <\ :

d : il ^ ^> : ^

— Roocm-

FIG. 2. — Section of brass tube for observing
axial color.

Experiments of this kind were begun by using long brass tubes (fig. 2)
with plate glass ends, carefully put together. Sometimes wet cloth linings
were introduced; but they had no other effect than to dispel the hori-
zontal columnar vortices seen on each side of the axis after exhaustion.
With a naked tube the fog observed rises on the outside and falls in the
center of the field, so that the axes of the two vortical columns are eccen-
trically placed parallel to the axis of the tube. Phosphorus nuclei, ions,
and vapor nuclei were tried, and incidentally some fog and rain limits
determined.

The following summary of results with vapor nuclei or with ions (dp
being the drop in pressure) , shows that in no case was there any color
obtainable. In these narrow tubes the only manifestation is a more or
less densely black fog.

l8 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

TABLE 7. — Observations for axial color. Dust-free air, vapor nuclei, and ions. Long

brass tube, 5 cm. diameter, 200 cm. long.

SP

Precipitate.

Up

Precipitate.

dp

Precipitate.

Part i. — Barometer 77.28
at 18°.

Part 3. — Barometer 77.34
at 18°.

Part 7. — Barometer 77.65
at 20°

21 .O
22 .6
24.6
26.3
28.0

Fog
Fog
Fog
Fog
Fog

*IQ.8

19.4
20.4
20.9

21 .O

Just seen
None
None
Just dim.
Faint fog

*i8.o
18.0
19.4
20. 3
21.3
22.4

Darkness
Darkness !
Darkness !
Darkness !
Rain
Corona

Part 2. — Barometer 77.37
at 19°.

lall round hole;
:eing ; barom-

.rart 4- sr
sharper s<
eter 77.34

Part 8. — Barometer 77.65
at 20°.

15-4
16. 2
17.6
*i9.4
21.3
20.4
23.0

24-5
26.4
28.0
29.9
31 .6

33-i
35-0

None
None
None
None
Light fog
None
Fog
Fogt
Fogf
Fogf
Fogf
Fogt
Fogt
Fogt

*2I . I
2O.4

Rain

Rain, faint

21.4
20. 6
19.4

18.5

Corona
Corona

(?)
Darkness

Part 5. — Radium on tube,
outside; barometer 77.34.

Part 9. — Radium on tube.

*2O-4

19.4

19-3
20.3

21.1

Fog dense
Rain !
Rain !
Dense
Fog

iS.o
18.9

19-5
20.4

24-3
25.0

(?)
Rain ?

Corona !
Corona !
Dense
Dense

Part 6.— Cloth hung in
brass tubes; barometer
76.24 at 21°.

Part i o — Dust-free air
again. J

17.6

19. 2
21 .O
23
24
26
28
3«

None
Fog?
Fog ?
Fog !
Fog !
Fog !
Fog !
Fog! J

24-5
26.4
28.0
No colo

Corona
Corona
Corona
r appears.

*Fog limits. fDense but no color. JDense fog but no color.

The same is true of phosphorus nuclei put into the identical (now cloth-
lined) apparatus. Thus in case of long brass tubes 200 cm. in length and
5 cm. in diameter with the barometer at 77.15 cm. at 20°, thirteen succes-
sive exhaustions of air charged with phosphorus nuclei showed no color
effects, but merely fogs gradually decreasing in density. The drop of
pressure lay between 10 and 16 cm.

Again, four exhaustions with fresh charges of phosphorus nuclei be-
haved similarly. The nucleated air was usually fawn-colored by trans-
mitted light and bluish by reflected light. Finally, when many successive
charges of phosphorus nuclei were introduced, densely black fogs appeared
without color, gradually lifting.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

The endeavor to clean the fog chamber by successive exhaustion and
apparently complete subsidence failed utterly. Fog particles evaporate
before subsidence to persistent water nuclei, so that for small particles
(above the middle green corona), subsidence is negligible as compared
with evaporation, even in a long brass channel lined with a square tube
of wet cloth 4 cm. high and 4 cm. wide.

20. Short tubes. — Believing that any irregularity in the size of the
fog particles might be particularly harmful in the case of tubes 2 meters
long, short tubes of the same diameter were next tried in the endeavor
to obtain axial color effects with vapor nuclei. The results are given in
table 8.

TABLE 8. — Observations for axial color. Dust-free air. Vapor nuclei. Short brass
tube, 5 cm. diameter, 75 cm. long. Tube not cloth-lined. Part 15. — Barometer 77.00
at 21°.

dp

Precipitate.

dp

Precipitate.

sp

Precipitate.

*i8-5

Rain

*2o.g

Corona

3,5-7

Dense

*i8.o

Rain

21.6

Corona

40.6

Dense

*i?-5

None

23-4

Corona

43-i

Dense

*i7.o

None

25-3

Corona

46.6

Dense

*i8.o

None

taS.7

Dense

*i9.g

None

32

Dense

*The difference of fog limit or rain limit for descending and ascending Sp is noteworthy.
tNo colors seen. Subsidence with a horizontal plane on top.

The attempt again failed. No colors were observed, merely an evenly
subsiding, gradually (increasing dp] more intensely black fog.

These results are disappointing. To obtain axial colors (coronas are
not observable longitudinally in tubes) ; it therefore seems essential that
drums of considerable equatorial diameter be used. In other words, the
vessel must not only be long but voluminous to obviate the radiation
effect from the walls after exhaustion, as much as possible. In fact, the
external layers of foggy air seem effectually to screen the interior from
the radiation.

Incidentally a number of fog limits and rain limits were obtained,
which, however, present nothing new, except that on diminishing pressure
differences dp, the rain limit falls at a lower dp than on ascending differ-
ences. The appearance is as if the fine droplets generated nuclei. But
more probably very fine nuclei escape capture in the presence of coarse.

Summarizing the above results, we may therefore conclude that the fog
particles producing the axial colors of coronas are of such a size as to
recall the interference phenomena of the lamellar grating, with which
their constants agree.

The disk colors of coronas can not be similarly explained.

The observation of axial color fails unless long, capacious fog chambers
are used. Tubes show opaque fields only.

20 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

CORONAS WITH MERCURY LIGHT.

21. Preliminary survey. — The inferences of the preceding papers*
gave the promise that on judiciously using monochromatic light as the
source of illumination the optical nature of the coronas might be fully
brought out. Such light must be strictly homogeneous and at the same
time very intense. Hence the usual methods of obtaining it are unsatis-
factory. The strong green line of a mercury lamp, however, fulfills the
requirements admirably, and this was therefore used. The results show
that the green disk and the first green ring alternately vanish as the result
of the interference phenomenon superimposed on the diffraction phe-
nomenon. If, therefore, the nucleation of a highly charged medium is sys-
tematically reduced, a series of angular diameters may be obtained, both
for the green disk and the inner or outer edge of the first green ring.
From the loci of these values the position of the first diffraction mini-
mum for green light may be inferred, and the size of droplets computed
from the usual equation for small opaque particles.

If the reduction of the nucleation is accomplished by successive partial
exhaustions, all of them identical, while filtered air is allowed to enter
the receiver systematically between the exhaustions, the nucleations of
any two consecutive exhaustions should show a constant ratio. Allow-
ance must, however, be made for the subsidence during the later fogs and
for time losses, if any. This is the method used hitherto in my work and
the results seem to have been trustworthy.

In the case of mercury light, however, it is now possible to compare
the latter with the former (diffraction) method of obtaining the diameter
of particles, with a view to throwing definite light on the optical phenome-
non. Subsidence methods are out of the question for large coronas, as
these are invariably fleeting in character and pass at once into smaller
coarse coronas.

The results of the two methods may be regarded as coincident as long
as not more than 300,000 nuclei per cubic centimeter, or diameters of
particles not smaller than 0.0003 cm- are m question. For larger numbers
and smaller diameters the divergence rapidly increases. Indeed, for
particles larger than the size given, the optically measured loss per
exhaustion exceeds the exhaustion ratio, a result which is satisfactorily
explained by the contemporaneous subsidence of these relatively large
particles. For particles smaller than the limit in question, however, the
loss computed by the optic method is larger than the exhaustion loss, as
if fresh nuclei were produced or rather made available at each exhaustion.
It is this result which the present paper purposes to bring out in detail
and to consider in its bearings on the optical phenomenon.

*Amer. Journ. Sci., xxv, 1908, p. 224; xxvi, 1908, p. 87; xxvi, 1908, p. 324.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER. 21

22. Apparatus. — The fog chamber was of the usual pattern, cylin-
drical in form, with its axis horizontal. The clear walls, being of blown
glass, showed some refraction disturbances, not, however, of a serious
character. The fog chamber was connected with a large vacuum chamber
by a short, wide passageway, though width is of little consequence here.
The cylinder was lined with wet cloth, closely adhering, except at the
narrow horizontal windows for observation.

For exhaustion the stopcock was suddenly opened at the beginning
of the first second, closed after 5 seconds, and the corona quickly measured.
Filtered air was then at once introduced and the next exhaustion made
at the beginning of the sixtieth second. This rhythm is essential. The
isothermal value of a drop of pressure [8p2] was carefully predetermined.
It fixes the ratio y of the geometric progression of nucleations, since

where p is the barometric pressure and n the vapor pressure at the given
temperature. If the cock were left open for a longer time than 5 seconds
[dp2] would increase to the limit dp3.

The goniometer was of the usual type, the eye being at the center
or apex, while two needles on radii 30 cm. long registered the angular
diameter of the coronal disks or annuli. Formerly the whole instrument
was placed 011 the near side of a fog chamber, the eye being about 30 cm.
from the nearest wall. It conduces to much greater sharpness of vision,
however, and admits of a measurement of larger coronas, caet. par., if
the eye is placed all but in contact with the nearer wall and the needles
(or in this case preferably the inner edges of round rods) beyond the
further wall. In such a case the refraction errors are also diminished.
In addition to these advantages I may mention the decidedly increased
(about 25 per cent) value of the aperture obtained. These excessive
apertures show, however, that the ordinary diffraction equation for
coronas is not fully applicable; for aperture varies with the position of
the eye along the line of sight. It is often surprising how large a corona
can be measured by the second method, in a small fog chamber scarcely
6 inches long. The distance between lamp and chamber is kept about
D= 250 cm.

23. Equations. — The equations needed in the present work are derived
in my last report* and need merely be summarized here. If y is the
exhaustion ratio, the nucleation ng of the 2th exhaustion in terms of the
original nucleation nQ will be

where 5 is a subsidence constant and 5 the chord of angular diameter of
the coronal disk on a radius of 30 cm.

*Carnegie Institution of Washington Publication No. 96, 1908, chapters I, in (equat.
i to 12).

22 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

To find S, two consecutive values of 5 suffice, or

approximately. The diameter of particles d is, in terms of n

d9 — 6m Inn

If X= 54. 6 X io~6 cm. is the wave-length of green mercury light and 0
the angular radius of the first green minimum of the coronas, sin 0<=o.6i
\l(d' /2). Since sin d = s/2R, R being the radius of the goniometer of
which 5 is the chord, d' the diameter of fog particle (the primes referring
to optic measurements),

d' = 0.004/5

for mercury light. Hence optically the nucleation is

io~Gnf = 2 9. 8ms3

where m grams of water are precipitated per cubic centimeter on ex-
haustion, and found in the exhausted fog chamber.

24. Data with white light. — The results in the following tables are
reported in accordance with the same plan throughout. The fog chamber
is initially at atmospheric pressure p, the vacuum chamber exhausted to
p — dpf. When the exhaustion cock is closed 5 seconds after exhaustion,
the pressure in the fog chamber, after the original temperature is rees-
tablished, will be p — [dp2\. The common isothermal pressure in vacuum
and fog chambers when communicating after the exhaustion is eventually
p — §p3. If Ti is the vapor pressure at the given (isothermal) temperature,
the exhaustion ratio is

The amount of water precipitated per cubic centimeter is m at the
temperature and pressure given.

TABLE 9. -Standardization of the fog chamber. Welsbach burner and phosphorus.
Cock open 5 sec. Observation interval 60 sec. Bar. 75.9 cm. at 22°. Temp. 26°.
[o>,] = i6.5 cm.; «5/>3= 17.4 cm.; dp'=i8.6 cm.; y= (l>-it-[dp2])/(p-it) =0.775;
df>3'/p = o.22g; iofim = 3.77 grams at 20°; 4.22 grams at 26°; 11 = 2.5 cm. Gonio-
meter in front. Distances of eye and lamp 30 cm. and 250 cm., on opposite sides
of fog chamber. Radius of s, R = 3O cm.

z

Corona.

5

z

Corona.

s

z

Corona.

^

I

Fog

25

9

g

H

17

Cor.

6.8

2

Fog

22

10

gy

13-5

18

Cor.

5-8

3

Fog

18

1 1

y

12.5

19

Cor.

5-i

4

r'

i?

12

o

«. S

20

Cor.

4.0

5

r

16

*I3

r

10.5

21

Cor.

3-o

6

V

15

H

P

9-5

22

Cor.

2.O

7

g'

15

g'

7-5

23

Cor.

I -O

8

g

H

16

g'

7-0

*Two identical series beyond this.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER. 23

To facilitate comparison with the later work, where mercury light is
used, a series of coronas in geometric sequence is given in table 9, in which
the Welsbach mantle still furnishes the light. Here 5 denotes the chord
of the angular diameter of the coronal disk on a radius of R = 30 cm. , when

?0 18 16

FIG. 3. — Charts for white light (Welsbach burner), -?/3°> °f the reddish edge of
the disk of coronas, in terms of a number, z, of the successive identical partial
exhaustions in the series.

FIG. 4. — Charts for green mercury light, showing the coronal apertures, 5/30,
of the edges of the greenish disks of coronas, in terms of the series number
2 of the partial exhaustions. Series I for 2-minute intervals between
exhaustions, series II for i -minute intervals.

24 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

eye and lamp are at distances 30 and 250 cm. on opposite sides of the fog
chamber. The colors of the edge of the disk are denoted by r red,
v violet, g green, etc. The number of identical exhaustions made is equal
to z = 23. Beyond 2=13 the series was obtained twice with identical data.

No attempt at computing nucleations from these data need be made,
as they are practically identical with the earlier series given in the pre-
ceding report. In fact, in fig. 3 the 5 values or apertures have been con-
structed in the curve a in terms of the number of the exhaustion z in the
geometric series. At b corresponding data (Carnegie Institution of Wash-
ington Publication No. 96, table 35, series i) are taken from the report
in question and represented in the same manner.

The feature of these results which I wish to accentuate is this, that
after the tenth exhaustion, i. e., for small and moderately large coronas,
the s-data lie nearly on a straight line. In curve a this is the case almost
throughout, or at least until the coronas become so large as to be vague
and filmy, while the ends of the fog chamber interfere with the measure-
ments. The slopes of these lines are:

In case a, ds/dz = 0.95

In case b, ds/dz =0.95

or about the same in both cases.

25. Data with green mercury light, 10^ = 54.6 cm.— Table 10 and figs.
4, 5, contain corresponding results obtained with a mercury arc lamp as
the source of light. Different annuli are measured and the chords 5, on
a radius of 30 cm. are distinguished by accents as follows :
5' is the chord of the green disk,

s" is the chord of the inner edge of the first green ring,
s'" is the chord of the outer edge of the first green ring.
The edges are fairly sharp. Hence

may be taken as the chord of the first green minimum. Optically the
diameter of the particle is then d' = 0.004/5.

The water precipitated per cubic centimeter, in, differs with the drop
of pressure dp3/ p and the temperature. Putting n' as the optical
value of the number of nuclei per cubic centimeter in the successive
seven parts of the tables the data are :

IO6OT

n'

Table 10:
Parts I and II

Grams.

A.. I

122 S3

Parts III and IV. ..
Table 1 1 :
Parts V to VIII

4.12
4.. O2

123 s3

I 2O S3

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

TABLE 10. — Standardization of fog chamber. Coronal disks. Mercury lamp. Phos-
phorus nuclei. Cock open 5 sec. Temperature 24°. [<?/>' 2] = 17.0 cm.; dp3= 17.6 cm. ;
(?/>'= 18.9 cm.; y=(p — n — [dp2])/(p — x) =°-770', ^/>3/^>=o-23I ; 7^ = 2.2 cm. m =
4.iXio-6g.

Inter-

Ob-

Inter-

Ob-

No.

Corona.

polated

served

5

No.

Corona.

polated

served

s

sf

s'

s*

sf

Part I. — Interval between observations

Part III. — Goniometer beyond fog

2 min. Barometer 76.17 cm. at 26°.

chamber, eye at wall. Barometer

Eye and lamp distances 30 cm. and

75.82 cm. at 25°. y =0.769; 3p3/p

250 cm. Goniometer in front.

= 0.233; w=4-iXio-8g.

i

2

Vague
Vague

13.0

12. 0

12 ?

ii ?

ii. 5
10.6

o

i

2

3

g
g
g

23.0

21.8

20. 7

23

22
21

25
24

22.6

*•

s

II .O

10. 8

9 • 8

O

4
5
6

7
8

O

1

10. 0
9-0

8.0
7.0
6.0

9-9
9.0
8.0
7-o
S .4

.7-

8-9

8.1

7-2

6-4

S . S

4
5
6

7
8

Vague
Vague
Vague
Vague
g

19-5
18.4
17.2
16.1
14.9

2O
19

16

15

21.4
2O. I
18.9
17.7
16-5

9

IO

....

5-o
4.0

»J T^

3-4

2.2

vJ \J

4-7
3-8

9

10

g
g

13-8

12.6

13-5
13.0

15.2
I4.O

o

ii

g'

ii-5

ii. 7

12.8

12

Vague

10.3

10.5

ii. 6

Part II. — The same. Interval between

13

Vague

9.2

9-4

10.3

observations i min. More rapid niter.

14

g

8.0

8.4

9- 1

j r

Vague

6-9

7- 3

7-9

16

g

' y

5-7

1 \j

6-3

/ 7

6-7

i

Vague g

16.4

I6.5

14.2

17

4-6

5- 2

5-4

2

Vague v

15-6

15?

13-5

18

3-5

4.0

4.2

3

Vague v

14.8

14 ?

12.8

19

2-3

2-3

4

Vague v

14.0

14 ?

12 . I

5
6

Vague v
Vague v

13.2
12.4

13-9
12-5

ii. 5
10.8

Part IV. — The same, repeated.

7

|'

ii. 6

ii. 6

IO. I

^

I

8
9

IO

ii

12
13
14
15

16

17
18

I'
g

Dull
Dull
g

i.

10.8

IO.O
9-2

8.4
7-6
6.8
6.0

5-2

4-4
3-6

2.8

II . 2

10.8
9-5
8-9
7-9
7-0

6.2

5-5
4-7
4.0

2.8

9-5

8.8
8.1

7-5
6.8
6.1

5-5
4.8

3-5

2.8

i

2

3
4
5
6

7
8

9

IO

ii

g

g
Vague

Vague
Vague
Vague
g
g
g
Vague
Vague

21.7

20.6

19-5

18.3

17.2

16.1
14.9
13-8
12.7

ii. 5

10.4

24
19

16

15
14-5
13-3

12
IO

23.6
22.4

21.2
20.0

18.8
17-6
16.4
15-2
14.0

12.8

ii. 6

12

g

9-3

9-O

10.4

19

2 .O

2 .O

2 . I

O

;?

13

g

8. i

8.0

9-2

g'

7.0

7-0

8.0

15

g

5-9

6.0

6.8

16

g

4.8

5-0

5-6

17

3-6

4.0

4.4

18

....

2-5

2-5

3-2

In parts I to IV of table 10 the angular diameter 5' of the green disks
only was measured. The diameter s of the corresponding first minima
may, however, be obtained by using the method of reduction found in
parts V and VI, where 5 = 0.44 + 0.85 s'.

In parts V and VI the data for s' and 5", the angular diameter of the
inner edge of the first ring are both observed, while in parts VII and VIII
data for s' and s'" ', the outer diameter of the first ring, appear.

26 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

Turning specifically to parts I and II, in which the goniometer is in
front of the fog chamber, it will be noticed that in series I a two-minute
interval between exhaustions has been (exceptionally) introduced. The
result is not good ; for, as fig. 4 shows, there is a sudden break of the curve
after the seventh exhaustion, probably due to time losses in the extra
minutes. The reason, however, is by no means obvious. In series II,
for i -minute intervals, there is no break and the locus passing through
the points for green disks (the others, not marked g, are to be disregarded)
is persistently straight throughout. The curves show for series I, ds/dz =
i. oo, green points only, and for series II, ds/dz = 0.80, suggesting a time
loss in the first case. Compared with table 9, the values of ds/dz should
be in the ratio of red and green minima, or

dSfjdz : dsg/dz = o.g$ : 0.80 correspond to ^1^ = 63. 0/54. 6
The last ratio, 1.15, is somewhat short of the former, 1.19.
In series III and IV the pins of the goniometer are behind the fog
chamber, the eye being at the front wall. In series III the relation

5' = 2. 30+1. 15(19-2)
is remarkably well sustained throughout, and in series IV

S'=2. 50+1. 13(18-2)

gives a good account of the green coronas, if the dull cases are ignored.
The most interesting results are given in parts V and VI of table 1 1
and fig. 6, and the computations have been fully carried out. In these
cases the chords on a radius of 30 cm. of the edge of the green disk s',
and the inner edge of the first green ring s", were successively observed.
Fig. 6 contains both pairs of curves and their linear character is again
astonishing. We may write

PartV: s' •-= 2.0+ 1.10(19 — 2) $" = 3. 4+ 1.21(19— 2)

5 = 0.59+1.065'== —0.56 + 0. 965"

Part VI: 5'= 2.0+ 1.13(18-2) $" = 3.3+1.30(18-2)

5 = 0.50+1.075'= -0.44 + 0.935"

where the minimum is located midway between 5' and 5", both of which
are fairly well demarcated.

From both series the mean value

5 = 0.55+1.06 5'= —0.50 + 0.93 5"

may be derived for the general reductions in this and other cases where
5' is observed.

With the given value for 5, the optical data for the diameters of the
particles, d' — 0.004/5, and for the nucleation, w'= 120 53 were computed.

The subsidence constant

was obtained from the observations between 2=13 and 2=19 and a mean
datum, 5=i2, accepted as most satisfactory. It is, then, possible to
compute n0, the original nucleation, as

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

27

from each of the groups of values specified. The mean results are: in
part V, n0 — 4,540,000; in part VI, = 3, 430,000.

Knowing Wy.the series of data for nucleation given under n\ io~3, table
ii follow. From these the diameter io4d= iggn~113 of fog particles and
the apertures 5 = 0.004/6? are finally computed. In other words, n and d
are the data obtained in view of the occurrence of geometric series of
nucleations with allowance for subsidence.

$0,60

W.SO

10,40

0,30

0

FIGS. 5, 6, 7. — Charts for mercury light, including measurements of the aperture of
the disks s', of the aperture of the inner edge s", and of the aperture of the outer
edge s'", of the first green ring, in terms of the number z of the partial exhaustion.
Vivid greens marked g, greenish g'; dull not marked. Apertures 5/30 often displaced
vertically for clearness.

28 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

TABLE 1 1 . — Standardization of fog chamber.
open 5 sec. ; 60 sec. between observations.
23°. Distance to lamp 250 cm.

cm.; ^3=17.6 cm.;

Mercury lamp. Phosphorus nuclei. Cock
Barometer 76.4 cm. at 25°. Temperature
Goniometer behind. 7r = 2.icm. 5= 12. [df>2] = ij.o

cm.; ^=0.771; <?/>3//>= 0.231 ; w = 4.oXio-6g.

Part V. — Coronal green disks and inner green edge of first rings.

No. z

Obs.
5'

Interp.

s'

Obs.
s"

Interp.
s"

s

io4Xd'

io-3X"'

io-3Xw

I04d =

i ggn~1/3

^^
o. 2 $/n
com-
puted

from n.

i

gi 23

21.8

25.2

23.6

i-7

1580

4540

i . 20

33

2

gl 21

20.7

....

24.0

22.4

1.8

1350

3420

•32

30

3

19.6

g25

22.8

21.3

1.9

1160

2580

•45

28

4

....

18.5

g 22

21-5

20. i

2.0

974

1940

.60

25

5

....

17-4

g 20

20.3

18.9

2. I

810

1450

.76

22.8

6

....

16.3

g' 19

I9.I

17.8

2-25

677

1080

•93

20.8

7

g'i5

15.2

....

17-9

16.6

2-4

549

800

2.14

18.8

8

g H

14.1

....

I6.7

15-5

2.6

447

589

2-37

16.9

9

g 13

13.0

....

»5-5

14-3

2.8

350

432

2.62

15-3

10

gy

11.9

g 15-5

14-3

i3-i

3-05

270

3i3

2-93

13-7

ii

10.8

g 13

I3-I

12. O

3-3

208

225

3-27

12.2

12

g'

9-7

g' 12

ii. g

10.8

3-7

151

159

3-67

10-9

13

gS-5

8.6

....

10.7

9-7

4-i

no

I IO

4. 16

9.6

H

y'

7-5

g9-5

9-4

8-5

4-7

73-7

73.8

4-74

8.4

15

6.0

6.4

g'

8.2

7-3

5-5

46.7

47-4

5-50

7-3

16

y'

5-3

g6.8

7.0

6.2

6.4

28.6

28.3

6-52

6.1

17

gy4-5

4-2

....

5-8

5-0

8.0

15.0

14.9

8.10

5-o

18

y 3-0

3-i

....

4.6

3-9

10.3

7-1

....

....

....

19

2.O

2.O

....

3-4

2-7

14.8

2-4

....

....

....

Part VI. — The same, repeated.

No. 2

Obs.
sf

Obs.
s"

s

io<X<f

io-sX«'

io~3X»

I04d =

i99«1/3

.y=o.2«1/3
computed.

I

g' 27

23-3

i-7

1520

3430

•32

30.2

2

g 22

....

22. I

1.8

1300

2580

.46

27.4

3

....

g24

2O.9

i. g

IIOO

1940

.60

25.0

4

....

g22

19.7

2.0

918

1460

.76

22. 7

5

g'-.

g' 20

I8.5

2. 2

760

1090

•94

20.6

6

g' 15-5

....

17-3

2-3

622

811

2.14

18.7

7

gi4-5

....

16.0

2-5

492

600

2-37

16.9

8

13

....

14.8

2.7

389

441

2.62

15-2

9

gy !

g' 15-5

13-6

2-9

301

321

2.92

13-7

10

....

gi3-5

12.3

3-3

226

232

3-25

12.3

ii

g'

g 12

II . 2

3-6

168

164

3-66

10.9

12

g8.2

....

9-9

4.0

118

"5

4.12

9-7

13

y

g 10

8-7

4.6

79

77-7

4.68

8-5

H

g'

8-5

7-5

5-4

50

50-4

5-42

7-4

15

7-2

6-3

6.4

30

30-5

6.56

6-3

16

y'4-9

g'

5-i

7-9

16

16.5

7-84

5-1

17

3-o

3-8

10.5

6.8

6-9

10.5

4.0

18

2.O

....

2-7

14.8

2-4

i .0

....

....

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER. 2Q

TABLE n. — Standardization of fog chamber — Continued.

Part VII. — The same. Coronal green disks and outer green edge of first ring.

No. 2

Obs.
5'

Interp.
s'

Obs.
s'"

Interp.
*"'

s

dr = 0.004/5

io~3Xn'

I

18.6

g33

35-6

20.3

1.97

1000

2

17-5

g29

33-5

19.1

2.09

836

3

....

16.3

? 28

3i-3

17.9

2.23

688

4

g'i6

15-2

....

29. 2

16.7

2.40

559

5

g 14

14.1

....

27.1

15-5

2.58

446

6

g 13-5

12.9

....

24.9

14-3

2.80

350

7

g' 1 1 . i

n. 8

....

22.8

i3-i

3-05

270

8

....

10.7

g 21

20-7

11.9

3-36

202

9

g'

9-5

?I9

I8.5

10.7

3-74

H7

10

g8.5

8-4

....

16.4

9-5

4.21

103

1 1

gg7-6

7-3

....

14-3

8-3

4.82

68.6

12

g'

6.2

12-5

12.2

7-i

5-63

43-0

13

g5-5

5-0

....

IO.O

5-9

6.78

24.6

14

g'

3-9

g8.o

7-9

4-7

8.51

12.5

15

2.8

6.0

5.8

3-5

11.4

5-i

16

....

1.6

4-5

3-6

2-3

17-4

i-5

17

•5

3-o

i-5

i . i

36-4

. 2

Part VIII. — The same repeated.

i

g22 S

IQ. 2

35-8

21 .O

i .90

I I IO

2

• o

x

18. I

g35

\j *J

33-9

19.8

2. O2

930

3

*

I7.I

g32

32.0

I8.7

2.13

785

4

16.0

29

30.0

I7.6

2.27

654

5

g''i5

14.9

28.1

16.4

2-43

529

6

g'3-8

13-8

....

26. 2

15.3

2.61

43°

7

g 12.5

12.8

24. 2

I4.I

2.84

336

8

gy

ii. 7

g22

22.3

13.0

3.08

264

9

10.6

g 21

2O-4

II.9

3-35

202

10

9.6

18.4

10.7

3-74

H7

1 1

g'

8.5

g' ie'.s

16.5

9.6

4-i7

I O6

12

g7-5

7-4

....

14.6

8.4

4.76

71.2

13

/

g

6.4

g 12. I

12.7

7-3

5-48

46.7

14

gy

5-3

g 10

10.7

6.2

6-45

28.6

15

4-2

g8.7

8.8

5-o

8.00

15 -0

16

3-i

6.8

6.9

3-9

10.3

7-i

i?

....

2. I

5-0

4-9

2.7

14.8

2.4

18

I .O

3-5

3-0

1.6

23-5

•5

All the results shown in table 1 1 have been constructed graphically in
figs. 8 and 9 for parts V and VI of the tables, respectively. The observed
and computed apertures 5 are first given ; then the observed or optically
computed d' ', and the computed d from sequences appear, and finally the
observed or optic nf and the computed nucleation n from sequences.
The corresponding data coincide very closely after nine or eleven ex-
haustions, i. e., for moderately small and small coronas; but in the case
of large coronas and nucleations there is marked systematic divergence.
A discussion of these results will be given presently.

30 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

60

FIGS. 8, 9. — Nucleations «, «', coronal apertures s/$o, and diameters d, d' , of fog parti-
cles observed and computed for the successive partial exhaustion, number z.

Finally, parts VII and VIII of table n contain measurements of the
chord of the angular diameter (radius of 30 cm.) of the outer edge of the
green disk s' and the outer edge of the first ring s'" . The minimum may
be deduced from s', since 5 = 0.54+ 1.065' has been accepted. From s the
optic value of diameter of fog particle d' and the nucleation n' has been
computed. The apertures are very fully given in fig. 7, in relation to the

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER. 31

number z of the exhaustion. The curves are again linear in character,
but in case of the outer edge s'" ', the insufficient size of my fog chambers
and the greater vagueness of definition interferes with close measurement.
The results are —

Part VIII: s' = i. 00 + 1.07 (18-2) 5"' = 3.oo + 1.93 (i8-z)

5 = 1.61 + I-I4 (18—2)

Part VII: $' = 0.50+1.13(17-2) s'" = 1.50+ 2.13 (17 -z)

5 = 1.08 + 1.20 (17 — z]

As a rule s'" is less than twice 5'. The data for sf and 5 are obtained
alternately, as the table shows, the green color passing from the disk of
the first ring and returning again in succession.

/

26. Inferences. Interference and diffraction. — The tables and charts
show, in the first place, that the disk and first ring of the coronas
are alternately vivid green, other colors being dull because the remaining
lines of the mercury spectrum are faint. At intervals neither disk nor
ring are quite green. Hence there is a periodic term impressed on the
diffractions, which may be identified as an interference similar to the
case of the lamellar grating referred to in another paper.*

When monochromatic light is used it is necessary, therefore, to observe
both the edge of the disk and the inner edge of the first ring, for neither
appear vividly at the same time. The chord 5 on a radius of 30 cm., for
the minimum in terms of the corresponding chords, s' and s", of the first
and second edges specified, may then be written

5 = 0.55+1065' 5=-o. 50+935'

Probably the ratio s/s' and s js" should be constant and the absolute
term in these equations is an error of observation; but as it is small
little depends upon it, millimeters only being significant.

If we summarize all the observations for dsjdt, the agreement as a
whole is in keeping with the nature of the observations and reasonably
satisfactory. Thus in

Series I, II, ds'/dz = o.<)o s = 0.44+ 0.855' (goniometer in front)
HI, 1.15

IV, 1.13

V, 1. 10

VI, 1.13

VII, 1.13

VIII, 1.07

5 = 0.55 + i -065' (goniometer behind)
mean dsf jdz =1.12

*Amer. Jour. Sci., xxv, p. 224, 1908.

32 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

The astonishing feature of these data is the occurrence of linear loci
for 5 and z nearly throughout the extent of the curves. It is as difficult
to even conjecture a reason for this as it is easy to find reasons against
it. The presumptive equation for 5 is

and for nz if r. denotes the product

"z = »u

Hence _^

s = 0.004 O" 0/6w)1/3(/ 77)1/3

If we disregard the subsidence correction / / for large coronas

ds/dz OC//3

in which there is no suggestion of a sustained constancy of the coefficient
ds/dz such as the experiments show.

To come to some conclusion as to the cause of the discrepancy between
the optic value of the nucleation n' and the presumable value n (geo-
metric progression), we may, as in table 12, compare the successive value
n'z+i/n'z = sz+i3/sz3 m their relation 10^ = 0.771, the exhaustion applied.
The table shows that for very large coronas n'z+l/n'g>y, whereas for
VITV small coronas n' z+l jn'z<y. For the intermediate coronas (g3),
i. e., from the seventh to the tenth exhaustion among twenty, the ratio
is nearly equal to y. Ratios smaller than y may be reasonably inter-
preted as due to subsidence and the subsidence constant S is actually of
the order of values to be computed from the viscosity of the medium
and the size of the vessels and fog particles. Within this range (coronas
smaller than ga) the optic and the presumptive nucleation may in fact
be brought into agreement.

In case of the large coronas, however, subsidence is virtually absent
and the occurrence of n'z+l/n'z>y calls for some apparent production of
nuclei at each exhaustion, which is naturally altogether improbable. In
table 12 I have therefore additionally inserted n' and n — n' , the latter
showing the number of nuclei not registered by condensation.

For, no matter whether condensation on a given group of nuclei occurs
or not, no matter how many nuclei have failed of catching a charge of
water, the removal of nuclei by partial exhaustion must take place in the
same way. Such removal is independent of condensation and would
occur in a dry atmosphere under similar treatment. Consequently y can
not be too large. It may be too small not only from subsidence, but from
time losses (decay) or as the result of the purification of air due to turbu-
lent motion across a solid or liquid surface. Consequently n may be
regarded as an inferior limit of the nucleation with a probably close

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

33

approximation to the true value. A comparison of n and n — nr would in
such a case show the percentage of nuclei of irregular size which have
failed of capture, the number being n — n'.

At the same time it must always be recalled that no adequate theory
of coronas exists and that therefore the meaning of n' is obscure. We
must in any case place a part, if not all, the discrepancy between n and
n' within the province of such a theory. The need of it is particularly
manifest for the large coronas, in which there is accentuated superposition
of interference and diffraction. Small coronas may be tested by coinci-
dent results obtained from subsidence, and the agreement is then well
within the errors of observation.

TABLE 1 2. — Comparison of nucleations.

Part V. Part VI.

2

'Sff

w*

io-V

i o~*n' i o~* (n — n')

I

0.90

0.86

1580

2960 i i . 1 1 o . 86

1520

I9IO

2

.89

.86

1350 2070 i i . 10 .84 1300

1280

3

.92

-^

1 1 60 1420 ~< .09 .84 looo

940

4

•93

.83 974 966 4 .08 .83 918

542

5

.92

'-

Sio 640 .06 .82 , 760

330

6

•95

.81

6/7 403 6 .03 .79

622

189

7

•95

.81 549 251 | 7 .03 - 492

108

8

.98

•79 447

142 - .01 .77

389

52

9

i .00

•77

350

82 9 .97 [ -75

301

20

10

I .00

•77

270

43 10 .96 -74

226

6

ii

.06

•73

208

17 n .91 ; .70

: • •

-4

12

.06

.72

151

8 12 .87 ! .67

118

-3

13

•14

.67 i no

O 13 .83 ! .64

79

— i

14

. 22

•63 74

o 14 -77 -59

50

0

15

.26

.61 47

o 15 , .68 .53

30

o

16

.46

•53 • 29

-i 16 .56 .43

16

0

17

•63 -48 15

o 17 -45 -34

7

0

18

2.32 -33 7

18

2

— I

1Q

2 .A

In the first eight exhaustions there is an In both cases V and VI there is accession

apparent production of nuclei. of nuclei at first and withdrawal finally.

EFFICIENCY OF LARGE AND SMALL FOG CHAMBERS, ATTACHED TO

THE SAME VACUUM CHAMBER.

27. Fog chambers. — The large apparatus used in the experiments*
for the displacements of ions showed relatively low degree of conden-
sational efficiency. It was therefore thought worth while to compare
fog chambers both larger and smaller than the normal size (Xo. i) with
regard to their powers in catching nuclei. In addition to the large re-
ceiver (Xo. 2) specified, an exceptionally small fog chamber (Xo. 3^
was specially constructed. Experiments were made with each in turn,
both for the case of the vapor nuclei of dust-free air and of ions.

*See chapter III, fig. 12.

34 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

The dimensions of the three fog chambers were:

Number.

Apparatus.

Length.

Diameter.

i

Old cylindrical ....

cm.

4.5

cm.

12

2

Large conical

I IO

14 to 22

3

Small cylindrical ....

16

II

The axes were in all cases horizontal and care was taken to insure the
occurrence of saturated air.

It is interesting to note that immediately after the small fog chamber
was put together, there was an internal source of high nucleation active
throughout 10 or 20 exhaustions, a result frequently obtained in other
similar cases. It is none the less difficult to detect the reason for its
occurrence. It vanishes completely in the course of time. It is probably
identical with the emanation obtained by Russel* from metals and resins;
at all events its eventual evanescence renders it harmless.

28. Data. — The preliminary data are given in table 13, where in the
case of small apparatus the color of the corona was chiefly used to deter-
mine the nucleation. The ordinary form of goniometer would have been
useless, as most of the larger coronas transcend the limits of the appar-
atus. The barometer is as usual denoted by p and the sudden drop of
pressure after the return of isothermal conditions with both chambers in
communication, by dp; n is the estimated nucleation per cubic centi-
meter.

These results are given with sufficient detail graphically in fig. i , and
are compared with the curves holding for the normal apparatus, No. i,
taken from a preceding report for identical exhaustions. In case of the
large vessel, No. 2, it was impracticable to carry the exhaustions very
high because of the danger of breaking the vessel.

The results show that fog and rain limits are not materially changed,
no matter whether large or small apparatus is used. But few experi-
ments were made.

The efficiencies of the apparatus, however, differ in marked degree.
In case of the large apparatus, No. 2, less than 150,000 vapor nuclei
respond, even at the highest exhaustions. The number of nuclei caught
increases pretty uniformly with dp/p, even beyond the limits tested,
but the efficiency is enormously lower than obtained for No. i , where
1,500,000 to 2,000,000 is the maximum number caught. The small
apparatus, No. 3, is even in excess of this value, inasmuch as over
3,000,000 nuclei per cubic centimeter are precipitated, while for equal

*Russel: Proc. Roy. Soc. London, LXI, 424, 1897; LXIII, 102, 1898.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

35

values of dp/p, it is nearly twice as efficient as No. i. What is particu-
larly interesting is the definite occurrence of coronas of the first order, viz:
the crimson c1; and the red rt, above the green g2. The observer is left
in doubt as to this, unless correlative measurements of aperture are made,
which in case of table 13 was not feasible for so small apparatus. Such
results are given, however, in table 14.

TABLE 13. — Comparison of large and small fog chambers. Dust-free air. Fog chamber
No. 2, length 1 10 cm., diameter 14 to 22 cm. ; fog chamber No. 3, length 16 cm., diam-
eter 1 1 cm.

dp/p

s

IO~3»

dp/P

s

io~3re

Fog chamber No. 2.* Barometer
76.35 at 25°.

Fog chamber No. 3. Barometer
76.69 at 27°.

o. 202

0.334

4

19

.248

r

r

•348

g' 5-2

40

.287

2.6

4-5

.360

g 7-2

157

. 296

2-7

5-i

•370

9-7

440

•340

4.0

19. 2

-385

g 10.2

910

.360

4.6

30.2

•396

b 10.5

1070

•405

6.2

80.6

•364

c 9.0

310

.440

gbp 7.0

120.0

Fog chamber No. 3, with wet

Fog chamber No. 3-f Barometer

cloth lining.

76.43 at 25°.

0-335

1.9

2

0.241

o

....

.362

7.0

144

.262

I

0. 2

.385

10.8

9IO

.288

I

.2

.410

12.0

22OO

•313

2

•3

•433

r

2900

.338

4

19

.600

r

3470

.360

c

1 06

.388

g

912

.410
.420
.460
.481
.501
.528

vp
c
r
o-r
o-r
o-r

1560

2 2OO
3OOO
3000
3130
3220

*Not quite free from leak.
fFreshly put together, shows an
internal source of nucleation
throughout 10 or 20 succes-
sive exhaustions.

All fog chambers which have aged are free from internal sources of
nuclei, whereas when freshly installed they may generate them through-
out many successive exhaustions. Even after this, production of nuclei
is still appreciable if long intervals of time elapse between the exhaustions.
An endeavor was made to detect the nature of this phenomenon, but a
satisfactory answer has not yet been reached beyond the surmise given
above. The production is observed both in large and in small chambers
and the nuclei are dust-like in size.

36 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

•38. -34 -36 -38 -40 -4£ -H -46 -^ -50

FIG. 10. — Condensational efficiency of large (i), intermediate (2), and small (3) fog
chambers, as appearing in the number n of vapor nuclei of dust-free wet air caught on
exhausting as far as Sp/p.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

37

29. Data for apertures. — To identify the coronas in case of the small
vessel, No. 3, as to the order to which they belong, a special goniometer
was constructed. In using this the eye is placed at the nearer wall of the
fog chamber, while the two round vertical rods for defining the angular
aperture are placed beyond the further wall, on a radius of 30 cm., the
eye being the center. The inner edges of the rods determine the aperture
by aid of a sliding scale passing across them. In this way very large
coronas may be measured in relatively small apparatus. The angular

-The same as fig. 10, obtained by goniometer measurement, including Wil-
son's colors and the effect of weak radium.

38 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

diameters are increased (caet. par.) and vision is at an advantage as to
clearness. Test experiments made with definite coronas showed that the
aperture 5 of the old goniometer was about equal to 0.9 5 of the new, and
with this number the reductions needed were made with the results given
in table 14. The apparatus showed the same corona for the same dp/p
on a number of successive days, so that fixed conditions had been reached.

TABLE 14. — Efficiency of the small fog chamber, No. 3, with special goniometer.
Length 16 cm., diameter u cm., 2-inch exhaustion pipe. Dust-free air and ionized
air. Radium I .... V, axially placed.

Dust-free air.

Ionized air.

sp/p

,$•

io~3n

sp/p

s

IO~3W

I. Barometer 76.54 at 25°.

III. Barometer 76.54 at 25°.

0.249

o

0

o. 242

o

0

.261

.8

.06

.249

.6

.06

•273

I .0

•23

•251

i . i

• 27

.285

i . i

•30

•255

i-5

• 50

.300

1.4

•50

.268

6-5

48

•314

2.O

i-5

.282

12.5

360

•327

2-5

3-3

.288

!3-5

436

•340

2.8

4-5

.318

M

537

II. Barometer 76.85 at 23°.

IV. Barometer 76.85 at 23°.

0.340

3-o

5-6

0.277

9-7

159

•350

r 6.5

57-4

.308

gy 14-0

584

.361

c 10.8

278

•378

fro 13.0

507

.366

*c 11.4

335

•472

fr 12.0

454

•372

ot y 16.0

599

•540

fc 11.5

416

.382

t>t g 17-0

1070

•394
.408

•433
•453
.500

•573

V

V

r 18.5

r

O 21
0

1530
1870
2250
2790
3390
4320

V. Radium II at 75 cm.,
observed at 50 cm. from ex-
haustion end in large fog
chamber, No. 2, length no
cm.; diameter 14 to 22 cm.
Barometer 76.85 at 26°.

0.194

.217

....

....

.238

i

0.2

.260

3-5

10.6

.281

gbp 7.2

97-2

.326

br 7.8

133

.427

7-7

1 60

VI. Barometer 76.35 at 25°.

•3i9

P8.5

169

•367

P8.5

187

•434

P8.4

208

*Note different apertures for the same color.
tCoronas.decreasmg with increasing precipitation.

STANDARDIZATION AND EFFICIENCY OF THE FOG CHAMBER.

39

30. Results. — The results are constructed in fig. 1 1 in comparison with
typical results for apparatus No. i. The same high efficiency already
recognized in case of this apparatus in table 13 is again exhibited, the
nucleation caught actually reaching over 4,000,000 per cubic centimeter
or invading the region of orange coronas, ot, of the first order. It is now
probable that with green monochromatic light the green corona, gt, of
the first order may actually be detected. With white light, however, the
initial effect is a mere fog.

A number of trials with radium (I to V, within the chamber) exhibited
the same terminal coronas as in the fog chamber No. i . Ions are caught
with the same facility in both chambers and about at the same dpi p.
In other words, whereas vapor nuclei are caught in greater number by
the more efficient small fog chamber, this is not the case with ions, as
comparisons of the earlier records for No. i show, nor with the positions
of the fog limit and rain limit. Moreover, in series 5 and 6, obtained with
the excessively large apparatus, the ions are appreciably displaced after
condensation has begun, showing that the supersaturation is excessive.

In series IV there is a pronounced decrease of the nucleation with
increasing dp I p. From the maximum n = 584,000 at dp/p = o.^i, the
nucleation drops uniformly to ^=416,000 at dp/p = o.$4. Inasmuch as
the correction for increased precipitation has been applied (smaller
coronas at high pressure-differences, because more water is precipitated),
this result is to be associated with the greater removal of nuclei at high
exhaustion. The coronas show the number of nuclei in the exhausted
fog chamber.

The smaller nucleations in series V and VI are referable in part to
the weaker radium used and in part to the exceptionally large vessel
employed.

31. Conclusion. — The final question of interest is a revised comparison
of these results with C. T. R. Wilson's disk colors, if his two extreme
greens are interpreted as g2 and gj instead of g3 and g2, as preferred in the
preceding report.* In such a case the nucleations may be estimated as
follows:

dp/p

Color.

«Xio~3

dXio"

cm.

0.360

Fog limit

o

....

.384

g

800

230

.418

g

7,000

1 20

*Am. Jour. Sci., xxiv, 1907, p. 309; Carnegie Institution of Washington Publication
No. 96, 1908, sec. 35.

40 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

As far as 11=1,500,000 nuclei per cubic centimeter, this curve would
still lie below the curve for the small apparatus. It then crosses and
passes beyond it to a limit of over 7,000,000 nuclei, instead of 4,000,000
nuclei per cubic centimeter, estimated for the small fog chamber, No. 3.
It is difficult, of course, without an actual measurement of aperture, to
come to a conclusion as to the order of mere colors, but the possibility
of reaching 10,000,000 nuclei per cubic centimeter does not now seem out
of the question. The probability that the initial white fogs seen with
ordinary light may be resolved with sufficient clearness for measurement
when monochromatic light is used, has already been suggested. One may
notice, however, in conclusion, that even in case of the extreme green, the
diameter of particle would still be over twice the wave-length of light.

CHAPTER III.

REGIONS OF MAXIMUM IONIZATION, AND MISCELLANEOUS EXPERIMENTS.
REGIONS OF MAXIMUM IONIZATION DUE TO GAMMA RADIATION.

32. Introductory. — I have recently* standardized the fog chamber
by the aid of Thomson's electron. The method (as will be shown in the
following chapters) is not only expeditious, but leads by inversion, when
my old values of the nucleations of the coronas are inserted, to values of
e which agree with Thomson's and other estimates. This affords an
incidental check on the broader bearings of the work. Before describing
these experiments it will be expedient to refer to a number of incidental
results bearing on the work, among which the displacement of ioniza-
tion on rapid exhaustion is most important. This has been studied both
in long and in short fog chambers.

33. Short fog chamber (see fig. 18, below).— The experiments them-
selves run smoothly and take but a few minutes each; but there is an
inherent difficulty involved in the interpretation of the distributions of
ionization observed in the fog chamber. The radium (10 mg., ioo,oooX ,
contained in a small, thin, sealed glass tube), is introduced into the inside
of a cylindrical fog chamber, 45 cm. long, by aid of an aluminum tube
(walls i mm. thick and about 0.25 inch in diameter), thrust axially from
one end to the other of the horizontal chamber. The inner end of the
aluminum tube is thoroughly sealed ; the other end lies quite outside the
fog chamber, is open, and serves for the introduction of the radium tube.
In this way the latter may be moved axially from the glass end of the
fog chamber on the right of the observer to the metal cap which closes
the fog chamber on the left.

When the radium is placed successively at distances of about 1 1 cm.
apart, within the available 45 cm. of the length of the fog chamber,
the maximum nucleation (ionization) coincides with the position of
the radium when both are near the glass end of the chamber (12 cm. in
diameter). The nucleation then falls off rapidly and at first uniformly
from the glass end to the metal end, where the coronas are strikingly
smaller and the nucleation less than one-half of that observed at the glass
end. Considered alone this would appear like the natural effect of an
increasing distance from the source, except that the coronas near the
distant end approach a constant diameter.

*Am. Jour. Sci., xxvi, pp. 87-90, 1908.

41

42 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

When the radium is moved about 12 cm. (one-quarter of the length of
the fog chamber) from the glass end toward the metal end, the maximum
nucleation, moving at a greater rate toward the brass end, has already
outstripped the position of the radium and now lies near the middle of
the chamber. The coronas and the corresponding nucleations, therefore,
fall off rapidly toward both ends. In other words, the maximum nucle-
ation is seen where there is no radium.

On moving the radium to the middle of the chamber, the position
of the maximum nucleation coincides with the brass end, over 20 cm.
beyond the radium. The coronas now fall off from left to right, to a
uniform size near the glass end of the chamber, the ratio of the extreme
nucleations being at least 200,000 to 100,000 per cubic centimeter in the
cases examined. Finally, when the radium is placed in the brass cap of
the chamber, the maximum still lies there and the nucleation falls off
toward the glass end, but all nucleations are reduced throughout about
one-half.

It is clear that the two ends of the chamber behave differently, but
no simple hypothesis of the known properties of the rays, at least, will
account for the occurrence and location of regions of maximum nuclea-
tion, nor for the high nucleation ratios specified. Moreover, plates of
lead placed outside over the glass end of the chamber to modify the
secondary radiation are quite without effect. Covering the aluminum
tube with a thick lead pipe the phenomenon is slightly reduced in magni-
tude, but not in character. It follows that the gamma rays are chiefly
concerned.

34. Behavior after removal of radium. — A final element of interest
is the behavior of the axial aluminum tube after the radium (in small
sealed glass or aluminum tubes) has been removed. The internally-
sealed aluminum tube is distinctly radioactive for several hours, even
though gamma rays alone have passed through it. The activity vanishes
gradually, and more quickly if the ions are continually precipitated by
exhaustion. The behavior of this residual nucleation is very peculiar;
if the aluminum tube is pushed into the fog chamber, axially, from the
glass end as far as the middle, the part of the chamber around the tube
shows strong coronas on exhaustion, while the other half (toward the
brass cap) is blank. Something, consisting of very slow-moving particles,
gradually diffuses radially out of the aluminum tube. Of course it is
difficult to deny with assurance that merest traces of emanation decaying
within the aluminum tube may not possibly account for the activity;
but what is remarkable in any case is the existence side by side of a region
with nucleation and a region without it, in the absence of anything like
a partition. The fog chamber itself must at all times be scrupulously free

REGIONS OF MAXIMUM IONIZATION.

43

from infection such as an emanation would produce, and anything of
this kind is at once detected.

35. Long fog chamber.— After obtaining these results, the work was
resumed with the aid of a larger fog chamber, F F, fig. 12, conical in
shape, no cm. long, 22 cm. in diameter at the broad end, tapering down
to 14 cm. at the small end, E, whence the exhaustion took place. It was
so mounted as to place the axis slightly inclined above the horizontal,
in order that an even depth of water, w, from end to end, might be stored.
In the first experiments the large end was of glass, in the later of metal,
but this difference is without appreciable effect upon the present results.
In each case a hole H, 2 or 3 cm. in diameter, was available near the
center of the large end for the introduction of an axial aluminum tube
AR (walls o.i i cm. thick), running from end to end of the chamber and
closed at R within it. In the inside of this tube the sealed radium tube-
lets could be moved from place to place, in a way similar to the method
followed in the preceding experiments. No wet-cloth lining was intro-
duced, because the experiments had to be performed so slowly that
saturation in case of a clean fog chamber, to which water adheres in an
even film, was assured. The best method of cleaning is vigorous rubbing
with a soft rubber probang, as for instance, a thick piece of rubber tubing
at the end of a metal rod. Every part of the glass must be scoured.

FIG. 12. — Section of long fog chamber with hollow aluminum core.

The chamber was too large to admit of the capture of as many ions for
like conditions of exhaustion as was the case with the preceding smaller
apparatus, but this difficiency is of no importance here. Filtered air is
admitted through 7.

36. Data. — Table 15 gives an example of typical results as obtained
both with the glass and the metal capped fog chamber, the opposite
(exhaustion) end being always of brass. In the first two parts of the
table the chamber was not quite tight, but the leak was sufficiently insig-
nificant to virtually filter the inflowing air, as was proved by the direct
experiments and by the third part of the table, where the adjustment
remained quite free from leak throughout. In the fourth part some
miscellaneous experiments are added. Naturally the greatest care was
taken to remove water nuclei.

tv

<! ^

Sf/

•»

44 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

TABLE 15. — Distribution of ionization. Fog chamber no cm. long, 12 to 20 cm. in
diameter. Sp/p = 25/76 = 0.33. Distance D from brass or exhaust end turned
toward glass or closed end. Radium at d.

£> = 8o cm.

D = t-,o cm.

D = 2O cm.

d

5

io~3n

s

io~3n

s

io~3n

I.

TOO

g b p 8.0

140

7.2

1 08

6-3

74

80

gbp 7-9

138

7-9

138

7.0

99

50

6.1

66

7-2

108

7.0

99

20

4-9

33

5-4

44

5-i

37

35

5-3

4i

5-6

50

6.1

66

65

7-5

119

7-5

119

6.8

90

no

7-5

119

6.6

82

5-i

37

II. Both ends of fog chamber of metal waxed.

IOO

8.0

140

7-i

104

5-2

39

80

gbp 7.8

134

P8-5

!74

6.0

62

50

5-8

55

7-2

109

gbp7-5

119

20

4-7

29

4-9

33

5-4

44

So

7-7

130

8.0

140

7-0

94

III. The same; fog chamber quite free from leak.

80

7-5

119

p 8.2

161

6-5

87

80

gbp 7-5

119

P8.4

175

6.2

70

50

5-5

47

6.0

62

7-5

119

20

5-9

58

5-6

50

5-9

58

IV. Miscellaneous experiments.

*8o

5-0

35

4-7

29

4.1

20

fSo

8.0

140

9.0

200

7-8

135

J8o

8.2

155

9-0

200

7-5

119

* Core charged to 250 volts.

t Core uncharged.

t Influx at large end.

The results are also shown in the charts figs. 13, 14 and 15, the two
latter being the more typical. The abscissas indicate the position of the
axial radium tubelets measured in centimeters from the exhaustion end
of the fog chamber, the ordinates the observed nucleation. The three
curves correspond to three goniometers, placed at 20, 50, and 80 cm. from
the exhaustion end, respectively. The results are seen to be of the same
nature as those discussed above.

Fig. 14 shows particularly that the maximum always lies on the
exhaust side of the position of the radium. Moreover, the ionization
when the radium is near the exhaustion end is always small and nearly
uniform throughout. The maxima are largest when seen in the middle
(D— 50 cm.) and smallest when seen at the exhaustion end (D = 20 cm.).

REGIONS OF MAXIMUM IONIZATION.

45

cm.

20

0

10

2.0

30 40

-loo cm.

FIG. 13. — lonization at different points along the axis of the fog chamber for
different positions of the sealed radium tubelets within the aluminum core.
Position of lines of sight shown on the curves.

20

0

1Q

w

30

40

loocrii.

FIG. 14. — lonization at different points along the axis of the fog chamber for
different positions of the sealed radium tubelets within the aluminum core.
Position of lines of sight shown on the curves.

46 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

In the third part of the table the occurrence of the maximum at 50 cm.,
for radium placed at 80 cm. from the exhaustion end, is again brought
out. Furthermore, the destructive effects of electric charge on the insu-
lated aluminum core extending from end to end of the fog chamber are
clearly manifest, the number of ions being everywhere relatively very
small. Specially favorable conditions obtaining in some of these experi-
ments are accompanied by comparatively large ionizations with the
uncharged core. This part of the table also contains an observation
proving that if filtered air enters at either end of the fog chamber, the
result is the same. Identical displacements were observed. In other
words, there is no deficiency of saturation involved in the occurrence in
the results in question, nor any difference between the freshly filtered
air and the stagnant residue in the fog chamber, nor any effect attribut-
able to parts of different material.

ZOO

0

30 40 50 60 70 80 90C02.

FIG. 15. — lonization at different points along the axis of the
fog chamber for different positions of the sealed radium
tubelets within the aluminum core. Position of lines of
sight shown on the curves.

REGIONS OF MAXIMUM IONIZATION. 47

37. Inferences. — At first sight one would conclude that in a region of
maximum ionization there must either be a larger rate of production or
a smaller coefficient of decay. The latter might be expected if in the
given region the ions had largely the same sign. The frequent occurrence
of the ionization ratio 2 to i in the earlier work lent some plausibility
to this view, but the later experiments with a much longer fog chamber,
and where much greater ratios occur in the ionizations of different parts of
the chamber, quite disprove this surmise. The correlative view that the
maximum might be referred to the superposition of primary and second-
ary radiations from different parts of the fog chamber is negatived by
changing the character of these parts from glass to metal, or the reverse.
Hence the maximum of ionization obtained must be associated with the
exhaustion itself for in each case the displacement of the maximum
is from the radium, wherever placed, to the exhaustion end of the fog
chamber. And, in fact, since the exhaustion amounts to a volume ratio,
vl/v, if vapor pressures be neglected, and

v1_P'(1~clk)pclk+[v/V]p

where pf — 46 cm. at the vacuum chamber, p=j6 cm. at the fog chamber,
Pa= 51 cm., the final common isothermal pressure when both chambers
are in communication, and where the volume ratio of the chambers [v/F]
= 0.3 nearly, the exhaustion is about VIJV=I.T)T>. Hence the bodily
displacement of air at the exhaust end would be 36 cm., and at the middle
1 8 cm. if the fog chamber were cylindrical. The conical form with the
small end at the exhaust pipe would considerably enhance this bodily
transfer of air from the closed to the exhaustion end of the chamber.
Thus we infer, if the radium is at the closed end, that is, at the extreme
distance from the exhaustion end, the maximum should lie there also,
since there is no appreciable displacement of air. In proportion as the
radium lies nearer the exhaustion end of the fog chamber, the displace-
ment of maxima of ionization will be greater, compatibly with the greater
bodily displacement of air, until in the case of the conical chamber, no
cm. long, like the above, the displacement may exceed 40 cm. Further-
more, at the exhaustion end there will never be a proportionately large
maximum, because the ionization has been removed into the vacuum
chamber, and the whole series of coronas is of exceptionally small size
throughout, due to increasing distance from the radium. In fact, it can
hardly be said that any specific evidence of the occurrence of an appre-
ciable secondary radiation has been adduced by the experiments.

In this way the above phenomena are at least qualitatively accounted
for, as it must be acknowledged the displacement is often larger than the
data here estimated, the reason for which is not sharply determinable

48 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

and may be due to turbulent motion immediately after the exhaustion.
At higher exhaustions the distribution is often more uniform and other
exceptional conditions supervene. For instance, with radium at d = 8o
cm. from the exhaustion end and dp/p = 0.43, nX io~3= 120, 150, 140 at
D= 20, 50, 80 cm., respectively; with a tube containing six radium tube-
lets evenly distributed and extending from ^ = 65 to no cm., the corre-
sponding data at dp/p = o.^^, were «Xio~3=i55, 185, 240. In no case
was more than a single maximum encountered.

Finally, the assumption has been made tacitly that the ions may be
removed faster during the exhaustion and displacement than they can
be reproduced by the presence of the radium, and that they may be
caught before they appreciably decay. To take the example of the above
cases: if the nucleation is equal to N = 500,000 per cubic centimeter, the
production would be a = b N2 = io~6X 25 X io10= 25 X io4 or 2 50,000 nuclei
per second per cubic centimeter, nearly. If the interval of displacement
is between o.oi second and o.i second, 2,500 to 25,000 nuclei should be
produced to replace the 250,000 removed, which would at once imply a
striking difference in the size of the coronas near the radium, such as has
actually been observed.

In conclusion, therefore, the feature of great interest in these experi-
ments is the definite proof contained that the ions may be displaced
during the exhaustion at a rate much faster than they can be reproduced
and that the maximum of ionization is therefore rarely found where it
was generated.

MISCELLANEOUS EXPERIMENTS.

38. Experiments to detect the region of positive ions. — In table 16
a series of detailed experiments is recorded to determine the character of
the relation between the drop of pressure and the number of ions captured
in the fog chamber of the usual shape (No. i, section 27). It was partic-
ularly desirable to locate the rather sudden flexure of the curve of dis-
tribution between its oblique and its horizontal branches and to see if
any evidence could be found of a second region of flexure corresponding
to the positive ions, by aid of a fog chamber like the one in question.
The method of two independent sources was employed, the coronas being
put in contact, 5 denoting the chord on radius of ^ = 250 cm., or if 26
is the angular diameter of the coronas, 5=2 R tan 6. It was not thought
necessary to reduce 5 to the number of nuclei per cubic centimeter, as the
former is in some respects a more convenient datum. There are two
independent series (see fig. 16), in the first of which the sealed radium
tubelet is on the outside of the chamber, in the other on the inside in the
axial aluminum tube. In both cases the flexure of the curve lies at about
= o.2%$, notwithstanding the decidedly greater nucleation in series 2.

MISCELLANEOUS EXPERIMENTS.

49

The region of positive ions should begin at about dp/p = o.^i cm., but
neither curve shows the slightest suggestion of any increase in nucleation,
though the drop in pressure has been intensified to an extreme case. Fog
chambers of the above type thus refuse to admit the separate occurrence
of positive ions. To this extent, therefore, the statement that negative
ions only are captured would be justified.

f40r

.PC .5>Q .2fl .3/ .20 .00 OA o/r

r»,O fwy c?V/ c2l .JUj cJt/ Or i)J

FIG. 16. — Absence of evidence for the region of positive ions beyond dp/p = o.j>it
in case of a plug-cock fog chamber. Aperture _S in terms of the exhaustion ratio
8p/p.

TABLE 1 6. — Endeavor to find the region of positive ions in radium curve.

dp

8p/p

S

Corona.

dp

8p/p

S

Corona.

I. Barometer 75.9 cm.; temperature
26.0°. Radium I to V on top. D = ycm.

II. Radium I, inside of fog chamber.
D = o. Barometer 76.3 cm.; temper-
ature 24°.

26.6

0.350

78

gy

19-5

0.254

10

24.8

• 327

80

gy

20. 6

.268

67

o

23-5

.310

82

gy

21 .O

• 274

82

g

23.0

.302

79

gy

22.3

.292

102

0

21 .9

.287

79

gy

22.8

.298

105

o

21-5

.282

76

o

24.8

•324

110

o

2O.4

.267

5i

o

19. 2

.252

13

....

20.6

. 270

50

o

21.2

.278

68

r

21-5

.282

69

r

22.3

.292

78

gy

21.7

.285

76

o

5O CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

39. Radium within the fog chamber. Sealed tubes. — An early series
of experiments on the observed distribution of ionization within the
chamber due to the presence of radium in different parts is given under
special treatment in table 17. Coronas from two sources of light were put
in contact, giving S. The radium was placed alternatively 12 cm. from
the two ends of the fog chamber, 45 cm. apart. The lines of sight, I near
the brass and II near the glass end, were 20 cm. apart in the middle of
the available length.

TABLE 17. — Radium within chamber. Tubes I-V.
25.7°; airS=i.o; §p3=2i,.o.

Barometer 75.9;
=0.303.

temperature

S

Corona.

wXio-3

aXio~3 =
bn2 (i + b/cn)

I.

Radium*

near brass-cap end. Observation lines 20 cm

apart.

Observed nea

Observed at <
Observed at |

r middle .

r 84

82

83
92
71

w p
w p
w p
w r o
g

268

243
258
334
159

79
68
76
124
3i

"*ap end

jlass end .

II. Radium near glass end.

Observed nea
Observed at <
Observed at ,

r middle

1 06

no

91

w y
w y
w r

517
580

334

286
356
124

^ap end

jlass end .

III. Fog limits.

^3=18.4
^3=17.7

0.9
.0

I .0

.0

8p/p = o. 2424 <5/>0//> = o. 240
.2332 .231

!>,/•!>= i. 215
i .205

* Fog chamber cleaned with 3 exhaustions.

There was no vertical distribution of the ionizations, but the horizontal
distribution was as usual very evident. Assuming that the number of
ions produced per second, a, is given by a = 6w2-f-cw where 6= io~6 is the
decay constant and c = 0.036 an absorption constant. The values of a
are thus as follows:

io-3w

io~8a

Radium at I (within fog chamber) :
Observed at I

-3-14

124

Observed at II

I S9

^i

Radium at II (within) :
Observed at I

1.1.4

124

Observed at II

SSO

320

Radium on top (outside)

I7S

^7

MISCELLANEOUS EXPERIMENTS.

A few rain limits were incidentally tested, as the opportunities were
exceptionally good. These data are given in part III of the table. They
have the usual values in my work, dp/p = o.2^ orvl/v=i.2i, and lie below
Wilson's values.

40. Distance effect. — A few experiments wyere incidentally made to
determine the effects of the distance D of the radium from the fog chamber
in terms of the numbers of ions produced per second, a, where a = bri2 + cn,
as above explained. The method of two sources (chord 5) with the
coronas in contact was used. Table 18 shows the chief results.

TABLE 18. — Distance effect. Radium I to V. Barometer 76.4; temperature 21.6°.
D from axis of fog chamber. Air, 5=1.0. 8p3=22.8; dp/p3 = o.2g8; 6=io~9;
0 = 0.0356.

D

5

io~3X«

io-"X
n-D* (i + c/bn)

D

S

io-3Xw

io-"X
n2£>2 (i+c/bn)

*;.o

4

i74

1784

IOO

30

13

4630

73

167

1656

3°

13

4630

73

167

1656

200

22

4.6

7200

20

59

92

4720

22

4.6

7200

61

104

5800

7

72

165

1612

50

45

4i

7800

44

38

6975

*Radium tube lies on the glass vessel, 7 cm. from the axis.

Inferring that w2D2(i + c/6w) should be constant, the following com-
parison results:

D = 7 20 50 loo 200 cm.

10 — l2w2Z?2 (i + c./bn) =* 1.7 5.2 7.4 4.6 7.2

At D — 7 cm. the radium is too close for any law. The agreement there-
after is an attempt at constancy in so far as the small coronas beyond
D < TOO cm. admit.

41. Attempt to calibrate the fog chamber with 5 separate sealed tubelets
(I, II, III, IV, V) of radium. — These results are given in table 19. The
tubes were placed in a gutter on the outside of the chamber at a dis-
tance D, or in a sealed aluminum tube within the chamber. The
table gives the aperture 5 (two sources of light), the nucleation n com-
puted therefrom and the number of ions a generated per second, where
a = bnt-\-cn as in the preceding instance.

52 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 19. — Calibration with radium I to V.

Radium.

5

Corona.

nXio-3

io~3a

Computed

aXio-3

Part I. Barometer 75.9; temperature 25.7°; air, S=i.o; dp = 2T>.o; 5^/^ = 0.303.

Radium I on top, each in its niche. D= 7 cm.

200000X0 oio g II

6s

122

19. 2

20 ooo X V

56

78

8.8

10 ooo X I

61

IO2

14.0

(Mean) I + II + V

74

w r

176

37- 2

42 .0

10 ooo X HI

S3

71

7-5

10 ooo X IV

ss

74

8.1

I + . . . +V

74

g

176

37-2

57-6

Part II. Repeated. D = ~] cm. Barometer 75.3; temperature 26.4°; dp = 23.0;

8p/p = 0.306.

II+V+I

68

gg

149

27-5

72

g

169

34-6

....

72

gy

169

34-6

....

Part III. Larger distance. D = 22 cm. from axis. dp/p = o.T,o6.

II

49

55

5.00

V

4i

32

2. 16

....

I

47

....

50

4.27

....

III

37

....

25

i-52

....

IV

35

....

21

1.19

....

1+ . . . +V

60

....

103

14.2

14.1

1+ . . . +V

60

....

103

14-3

....

Part IV. Higher dp. D = -j cm. Air, 5 = 4.6. Barometer 75.9; temperature

26.6°; <J/>3=26.6; <J/>/p = o.35o.

II

61

"3

16.8

V

56

....

8?

10.7

....

I

63

....

125

20.0

....

III

54

....

78

8.9

....

IV

54

....

78

8-9

....

I ... V

79

gy

238

65.1

65-3

Part V. Barometer 76.3; temperature 24°; dp3=2^.o; dp/p = o.j>oi.

II

"5

o

400

»74

V

99

r o

260

77

....

I

105

o

300

IOO

....

III

93

r

2IO

52

....

IV

95

r

225

59

....

I ... V

130

y

570

344

461

MISCELLANEOUS EXPERIMENTS. 53

The results in parts I and II are not satisfactory. Thus the separate
determination of a for each tube added together are much larger than the
corresponding datum for the tubes abreast:

I, II, V:

Separately 0 = 42,000 ions per second.

Together 37,ooo

I, II, III, IV, V:

Separately 57, 600

Together 37,000

With the tubes together, a certain number of ions apparently failed of
capture, but this is not the case, as is shown in table 1 6, where all ions are
caught for dp/p = o.2%, much below the present datum.

The third part of the table, however, shows accordant results, giving
14,000 ions per second separately and 14,300 when the tubes are acting
together, but the ionization is lower (D = 22 cm.).

In part IV the drop in pressure is larger. The agreement is satis-
factory, 0 = 65,000 ions per second when the tubes act together and
0 = 65,000 when their separate effects are added, but in other similar
cases the results were not so good. Thus in the last series V, the separate
and joint effects are 460,000 and 340,000; here, however, the high nucle-
ation is due to the presence of radium within the chamber in sealed
aluminum tubelets, and the diffuse coronas are hard to measure.

The method of graduation depending on the use of sealed batches of
radium, together and separately, has not, therefore, given trustworthy
results. The chief reason for this is that the rate of production a is as the
sixth power of the aperture 5

/R

a/a' = S*/S

If the tubelets were equally strong their sum would be ^$a = i.3\/a,
which is about the relation of aperture for contiguous crimson and green-
yellow coronas. Hence small subjective differences play a large part in
such experiments.

CHAPTER IV.

THE STANDARDIZATION OF THE FOG CHAMBER BY THE AID OF

THOMSON'S ELECTRON.

THE CONSTANT e, EXPRESSED IN TERMS OF VELOCITIES OF THE IONS.

42. Advantages.— Of all the methods which I have tried to evaluate
the coronas in terms of the number of nuclei which they represent under
given conditions of exhaustion, the above method is the most expeditious
and promising. A single experiment need take but a few minutes. Inci-
dentally the observer learns whether negative and positive ions have
been captured, for on using the table of coronas which I developed here-
tofore, the value of e may be computed and the result must coincide with
Thomson's datum.

a

a

FIG. 17. — Fog chamber with plate electrical condenser.

43. Plate. — These experiments were of a tentative character and the
condenser used was a plate of brass P, of area .4 = 5X15 scl- cm- sus'
pended at a distance of i cm. above the water W, and parallel to it. It
was supposed under these circumstances the discharge current in the
presence of radium in sealed aluminum tubes placed at R in fig. 17
would be largely confined to the narrow space between plate P and
water W, which was earthed, but this proved not at all to be the case,
as will be seen presently. In the absence of radium, the leakage was
throughout negligible, the conductor a being sheathed by the hard rubber
tube b, kept dry except during use. The fall of potential was measured
by a graduated galvanoscope, whose capacity was in parallel with P.
The number of ions n was found from the aperture of the coronas on
condensation. We may therefore write for the charge per ion, if i is the
distance of P above the water-surface W, and V the potential difference
in volts

Cl V

300 A Un V

54

STANDARDIZATION OF FOG CHAMBER.

55

where C is the total capacity and U the appropriate velocity of the ions
in the field of i volt per centimeter, each ion carrying the charge e, in
electrostatic units, positive or negative, depending on the charge on
the plate.

While the apparatus as a whole apparently functioned very well, it
was found that the removal of the plate made no difference whatever.
Thus if D is the distance of the radium from the fog chamber:

Condenser plate P in place.

Condenser plate P removed.

D

Leak.

v/v

D

Leak.

V/V

cm.

Volt /cm.

cm.

Volt/cm.

40

O.OOOI2

0.00286

40

o . 00028

0.00242

287

30

277

289

29

260*

15

. OOO4O

475

15

. . .

635

21

547

. . .

808

'4

544

. . .

720

435

0

.OTOISf

o

.OOO2I

635

. . .

.00975

....

703

. . .

995

....

685

. . .

*With two lead plates each i mm. thick covering the radium, V/V-= .00298.
fWith two lead plates each i mm. thick covering the radium, V/V= .00800.

The results (due to incidental reasons) are thus even larger in the absence
of the plate P than when it is present, although the conduction-leaks
are throughout negligible. It is therefore impossible to interpret the
results obtained or to compute the e from them. When D was 15 cm.,
or larger, the effect of one or more thin lead plates over the radium was
no apparent deduction. In the adjustment given, therefore, the whole
region of the radium conducts and the fog chamber is merely effective
as a part of the region.

44. Cylinder. — If the sealed radium tubelets rr are inserted by aid of
a wider aluminum tube AR (closed at one end) into the axis of the cylin-
drical fog chamber FF, the closed end A projecting within as in fig. 18,
the difficulties referred to are in a measure obviated. Nevertheless, in
the present experiment it was thought preferable to use the fog chamber
for measuring the number of ions only, while an independent condenser
was installed for electrical measurements.

The cylindrical electrical condenser is employed as follows: A closed
aluminum tube 0.62 cm. in diameter, 18 cm. long, containing weak
radium in sealed tubelets equally distributed along its inside, is made
the core of the condenser, the outer surface being 2.1 cm. in diameter
and leaded to an inch or more in thickness beyond. The aluminum core
in question is suspended axially from a fine wire leading to a sensitive

56 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

electrometer. The voltages here to be measured must of course be small,
and hence all connecting wires are to be inclosed in earthed metal pipes.
The core in question is then removed from the electrical condenser and
put into the axis of a dust-free fog chamber (fig. 18), where the nucleation
(ionization) is found on condensation from the constants of the coronas,
or vice versa. Here there are some outstanding difficulties, for the
coronas are not the same throughout the length of the fog chamber, as
discussed in Chapter III. Even immediately around the radium core a
single corona may be green on one side and red on the other. In a fog
chamber 45 cm. long, the coronas may vary from the glass end to the
metal end of the chamber in a way to correspond to from 100,000 to
200,000 nuclei, respectively, while the radium core is fixed in the middle.
Inferring secondary radiation, one might naturally expect to obtain still
larger coronas near the metal end if the radiimi core, thoroughly sealed,
is placed there instead of in the middle of the chamber. But this is not
the case, the coronas being markedly smaller than before, decreasing
uniformly in size toward the glass end. As the sealed aluminum tube
is within the chamber, this behavior is clearly of great importance.

Jl L

1

FlG. 1 8. — Fog chamber used as a cylindrical electrical condenser. AR, aluminum core.

These difficulties are inherent in the phenomenon and merely exhibited
by the fog chamber. The latter has the great advantage that enormous
nucleations, like millions per cubic centimeter, are not excluded. Under
these circumstances the coronas alone are available for finding the
nucleation, inasmuch as all the fog particles evaporate before subsidence.
Finally, the occurrence of maxima of nucleation may in a large measure
be obviated by distributing the radium along the axial tube.

45. The same. Preliminary data. — To test the efficiency of the fog
chamber it is sufficient to make a preliminary measurement of Thom-
son's e. Let the radii of the electrical condenser be Rt and R2, its length

STANDARDIZATION OF FOG CHAMBER.

57

7; let C (electrostatic units) be the capacity of the electric system, con-
denser, and electrometer, together with such auxiliary capacity as may
be inserted to get a leakage of proper value. Let U be the efficient*
velocity of the ions, positive or negative as the case may be, in a field of
i volt per centimeter, V the voltage and V the change of voltage per
second. Finally, let N be the nucleation caught when the identical
condenser core is placed in the fog chamber. Then for the cylindrical
condenser (if natural logarithms be taken),

ClnRJR2 V
'' 6oo7tlUN V

If V is small enough to keep V/V constant, the curves show this at
once. Rough tests, using the old data of my fog chamber, led to values
about as shown in table 20, where the irregularities are in the electro-
meter, due it was supposed to the connecting wires, which were not at
the time surrounded by earthed pipes. It has been assumed that relative
ions only are caught in the fog chamber and that a negative current only
is observed. The e so found is too large.

TABLE 20. — Preliminary values of e. Wires not surrounded by pipes.

_ClnRl/R, V/V
6oonlU N

C=i3o; [7=1.87 cm. /sec. (neg. ions); F<o.5 volt; field 0.7 volt/cm.; N— 210,000
per cm3 (neg. ions); 2/^ = 2.1 cm.; 2R2 = o.62 cm.; /=i8.2 cm.

V/V

<?Xio10

V/V

eXiow

V/V

eXio10

0.049

0.054

0.056

56

62

....

68

65

56

....

67

....

71

50

65

....

67

.060

7-3

0.56

6.9

.065

8.0

*o.o5

6.4

*Same with N = 185,000 per cm3 (neg. ions).

46. The same. Wires surrounded by earthed pipes. — In order to
make use of the high sensitiveness of the Dolezalek electrometer, the
wires were now surrounded, so far as possible, with pipes of galvanized
iron, 2 inches in diameter, put to earth. Under these circumstances there
was less irregularity, though the current still continued to be far from
proportional to the voltage, even for low values of the latter. It will
not, therefore, be worth while to give a detailed account of V/V, and the
mean value for a field of i volt per centimeter was taken, as found from

*If one shell of the condenser is put to earth, positive or negative currents only are
measured and not the whole current.

58 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

five independent series of measurements of the fall of the potential of
the core per second. The following is the summary, referring to the
negative current, where C is 136 cm., £7=1.87 cm. /sec., P=i8.8 cm.,
= 2.i cm., 2^2 = 0.62 cm.

(Negative

V

Field.

V/V

ions)

eXio16

N

Volt

Volt/cm.

Els. units.

0.7

i

0.04

1 50,000

6.6

•9

I . 2

.14

570,000

5-9

When the condenser was disconnected there was no leakage, showing
the piping to be nearly free from such currents as might result from
irregular penetration of the gamma rays. The approach of the final
values of e to those currently in use is no closer than before. It has again
been assumed that negative ions only have been caught in the fog cham-
ber, and that a negative current alone is in question when the core (con-
nected with the electrometer) is charged positively and the shell of the
condenser is put to earth.

47. Conclusion. — The values of e obtained under widely varied con-
ditions in the present rough experiments, are of the same order and to
this extent show that the present method is not unworthy of develop-
ment, with a view to the further measurements of this important con-
stant. For this purpose I have been at work on a redetermination of the
nucleation values of the coronas (see Chapter II), using as a source of
light the virtually monochromatic mercury lamp. This is sufficiently
intense and the coronas admit of a more definite optical interpretation.

All of the e values are too high, however, when it is assumed that a
negative current only is in question and that negative ions only are
caught. The reason for this high value of e is probably referable to the
aluminum-brass condenser, which contains an electromotive force not
allowed for nor eliminated by commutation. Such a case would modify
the ratio V/V in the above results by changing the zero-point of the
electrometer. The experiments were abandoned at this point owing to
the dampness of the summer season. They will be resumed in Chapter V.

STANDARDIZATION OF FOG CHAMBER. 59

THOMSON'S CONSTANT e, EXPRESSED IN TERMS OF THE DECAY CON-
STANT OF IONS, WITHIN THE FOG CHAMBER.

48. Introductory. — In the last paper* an account is given of certain
tentative experiments to determine Thomson's electron, by aid of the
fog chamber and a separate well-leaded cylindrical electrical condenser.
The results obtained were in keeping with the accepted values. It was
presumed that the constants of coronas are determinable from purely
optical considerations of diffraction and interference, and that the
accuracy of the method may be enhanced by using the mercury lamp as a
source of light for the coronas. There was, however, one grave misgiving,
inasmuch as the distribution of ionization within the fog chamber varies
in marked degree from place to place for any given position of a sealed
radium tube, and that the mean value assumed was in a measure gratui-
tous. The results seen in the fog chamber are a complication of the effects
of primary and secondary radiations, together with a very marked ex-
haustion displacement of the ions. The maximum ionization (Chapter
III) does not coincide, as a rule, with the position of the radium, and there
is no reason why the ionization in the fog chamber should be quite
identical with the ionization produced by the same radium tube in the
electrical condenser, unless both are one and the same apparatus. This is
the case in the experiments of the present paper. The results also show-
that the same method may be applied under the circumstances of the
last paper, where e was obtained in terms of the velocities of the ions.

49. The electrical condenser fog chamber. — It is therefore necessary
to make a fog chamber itself the electrical condenser, and this is easily
done, if the chamber is cylindrical, by installing a tubular core of alumi-
num closed in the inside of the chamber and running axially from end
to end, as in fig. 18. This core is charged to a definite potential and made
the inner surface of the condenser, while the scrupulously clean inner
wall of the glass chamber (to which water adheres evenly) is the outer
surface and put to earth. Finally, the radium, contained in small sealed
tubelets of aluminum, is placed within the length of the axial aluminum
tube or core in such a way as to make the ionization within the fog
chamber uniform — a condition vouched for in case of the occurrence of
uniform coronas on exhaustion, from end to end of the chamber.

There are thus three currents to be determined:

(i) The conduction current due to inevitable leakage between the
condenser surfaces. This is made a minimum and nearly negligible in
value by keeping the aluminum core out of the condenser when not in
use and by sheathing it with an annular air-space beyond the condenser.
It is found experimentally by direct measurement in the absence of
radium.

*C. Barus: Am. Journ. Sci., xxvr, pp. 87-90, 1908.

60 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

(2) The current due to the ionization of the room air near the fog
chamber and on the outside of it, due to gamma rays. This is made a
minimum by allowing the thin wire communicating with the electro-
meter to run axially away from the fog chamber, for the gamma rays,
in spite of their penetrating powers, are quickly reduced by distance.
The current is found in the presence of radium within the axial tube by
leaving all adjustments identically in place, but breaking the metallic
connection between the aluminum core and the electroscope, etc., by a
hard rubber insulator. If an auxiliary condenser is used, the measure-
ment (i) must be made without it, as otherwise its leak would be counted
twice. Fortunately the conduction current is quite negligible.

(3) The current due to ionization within the fog chamber. This is
found by deducting from the total current found on connecting the
charged aluminum core and the electrometer the two preceding currents.

50. Auxiliary condenser. — To vary the experiments to the extent
that different speeds of leakage may be obtained, as well as to find the
capacities of the electrometer and fog chamber, an auxiliary condenser
must be inserted as a part of the electroscope. This condenser consisted
in the present experiments of two plates of brass, having an area of 315
sq. cm., and usually kept at a distance of 0.32 cm. apart by outrigged
feet of hard rubber, which stood on a plate of glass. By putting small
glass plates under these feet the capacity could be varied at pleasure.
The usual equation was corrected by aid of the factor

i + ( d + din 1 6 v7 J^ (d + d) /d2 + din (d + <5) / #) / v7!^

where a is the area, d the distance apart, and d the thickness of the plate
of the auxiliary condenser. Naturally a guard ring condenser would
have been preferable for standardization, but none was at hand.

To determine the very small capacity C of the electroscope-fog-cham-
ber, two successive full charges from the lighting circuit, at a potential V =
250 volts, were in turn imparted from C to the auxiliary condenser of
capacity C'. If V" be the potential observed after these two charges and
S=V"j (V-V"), C = C/5/(i + \/i"+5). It is curious that this method
of successive charges leads to involved cubic, quartic, quintic equations,
etc., which follow no simple rule. The ratios R of the potentials, after
four and after two charges R = V " /V is, however, still available

for if r = C'/C,thenr=(R-i)i + \/i + (2-R)/(R-i /(2-R). Apart

from these complications, the large deflections obtainable after many
successive charges would, in the absence of conduction leakage in the
condensers, make this method very satisfactory.

In the definite measurements, however, almost the whole capacity
may be placed in the auxiliary condenser, so that the capacities of the

STANDARDIZATION OF FOG CHAMBER. 6l

electrometer and fog chamber are of small importance. Ratios of
C' 10 = 86/17, 30/17, 20/17, and others, were tried.

51. Method. — In the preceding paper the value of e found was ulti-
mately dependent upon the velocity of the ions in the unit electric field.
In the present experiments a value will be found, based on the decay
constant 6= i.i X io~°, of the ions. This method has the advantage that
large-core potentials are admissable in the electrical condenser, so that
an ordinary graduated Exner electroscope suffices for the measurement
of current. The small capacities of the instrument make it necessary to
insert an auxiliary condenser, as otherwise the discharges are too rapid
for trustworthiness.

If a is the number of ions produced per second per cubic centimeter
by the radium within the condenser core, n the number of nuclei per
cubic centimeter in general, and N the number of nuclei (ions) found
when the core is free from charge, dn/dt = a — £w2==o, if n = N. Again, if n
is the number of nuclei found when the core is charged and i the cor-
rected current observed, e Thomson's constant, and v the effective volume
of the fog-chamber condenser,

(i)

Hence if the capacity of the system is C and V, the corrected fall of
potential per second

(2)

Usually V is measured in volts, so that 1^/300 replaces V in the equation.
It is obvious that V must be large enough to keep the current V constant
and the observations always show this at once.

If equation (i) is multiplied by £ throughout it will express the case
for the negative ions alone and the negative current alone. Hence
equation (2) is at once applicable here.

52. Data disregarding external gamma rays. — By the aluminum-foil
electroscope it was made convenient to use the high potentials of the
electric-lighting circuit (about 250 volts) for charging.

The number of nuclei (ions) found in the presence of the radium tube-
lets and in the exhausted fog chamber free from charge at its central core
was ./V = 474, ooo. The number of nuclei found in the exhausted fog
chamber when the core was charged 250 volts was »'==82,5oo. Hence
about 391,000 vanished in the presence of the electrical current, the
original apertures of the coronas being reduced from about 22° to 13°.
The drop of pressure, dp/ '£ = 0.30 nearly, was taken high enough to catch
all the available ions, but not so high as to catch the vapor nuclei of dust-
free wet air.

62 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

The amount of exhaustion was equivalent to the volume ratio v1/v =
1.29. Thus the number of ions in the fog chamber at atmospheric pres-
sure was N = 611,000 per cubic centimeter for the uncharged core.

TABLE 21. — Fall of potential and currents. V' conduction leakage ; V" due to presence
of radium. Wires not piped. Four-second intervals between observations.

V

V'

V"

V"

V"

V"

V = 3.0 volt/sec.; C=iO3.

F = 5-8 volt/sec.; C = 4J.

250

247
237
226
216
205
195

1.6

2.6
2.6
2.6
2.6

250
230
206

183
1 60
140

122

5-5
5-9
5-7
5-4

249
229
205
1 80
155
135
no
90

5-5
6.1

6.2

5-6
5-6

5-6

5-6

5-8

V

r f\ A \rc\\i I

sec.; C = 47.

F=i2.i volt/sec.; C=iy.

250
236

221
207

195
182

168

3-6

3-4

3-2
3-2

250
216

175
133
99

9-4
10.4

9-5

249
209

153
103

12. O
13.2
IO-4

12. O
13.0
IO.9

I2.3

12.7

9-8

3-4

249
207

153
103

249
205

151
103

12.1

The value of 6=i.iXio6 is taken from Professor Rutherford's book.
The source of light for the coronas is part of a Welsbach mantle, as usual,
and the old constants of coronas were used, since it is a part of the purpose
of this paper to test those constants. The volume of the fog chamber was
estimated at 51,000 c. cm. In the first experiments the effect of the
gamma rays penetrating into the air on the outside of the fog chamber
was neglected and the data, summarized from table 21, on using different
condensers, were as follows, all data being given in electrostatic units.
C denotes the capacity of the system, V the drop of potential per second,
7 the corrected current passing through the condenser-fog-chamber.

C

I'Xio3

j'Xio2

eXio10

103

10

103

5- i

47

21

IOI

5-0

47

19

92

4-5

17

40

70

3-4

STANDARDIZATION OF FOG CHAMBER.

The last observation being made without an auxiliary condenser. The
current i was quite constant throughout the voltage interval (near 250
volts) of observation. Hence the effect of gamma-ray penetration has
seriously increased the leakage, and e therefore appears too large, except
in the last observation, where i is probably no longer measureable.

53. Further data. — In the following experiments the effect of the
external gamma rays was eliminated as specified in section 49. The con-
duction current was usually quite negligible. The nucleations observed
in the exhausted fog chamber were n = 82,000 and N' = 506,000, when
the core was charged and uncharged, respectively. The exhaustion was
again equivalent to a volume increase of v1/v=i.2g. Hence in the fog
chamber full of air the respective nucleations are ./V = 653,000 and n =
106,000, whence Ar2 — n2 = 4i$X io9. The drop of pressure dp/p = o.$o
was about the same as before.

TABLE 22. — Fall of potential and currents. V in the presence of radium; V" due to
f rays; V leakage due to conduction; 4-sec. intervals. Wires in earthed pipes.

V

V'

V

V"

V'"

V'"

V

Vf

V"

V"

V'"

^ = 2.24 volt/sec. ; C=IOT).

F= 5.88 volt/sec.; C = 37.

245
232
218
203
189
174

*57
141

3-4
3-6
3-6
3-6
3-9

3-7

244

236
232
228

221
217
209

i-5
.0

•4

•4
• 5
•5

247
243
240

237
235
232
230

0.9

.8
.6
.6
.6
•9

240
204
i75
139

8.1
8.1
8.1

241
231

221
21 I
205

195
I87

2.5
2.5

2.O

2 .O
2. 2
2. I

. i
.6
• 7
•4
.6

• 5

8.1

•38

2 . 22

.48

V

/olt/sec

7-

V = 5. 1 5 volt/sec.; C = 4y.

— IO.O 1

, C — I

248
1 80

121
70

248
I87
130

74

15.9
13.8
14.8

H-7
14.1

245
226
209
191

i/5

4-5
4-4
4-3
3-9

O. 21
•17
-19

245
217

189
161
134

7.0
7.0
6.9

244
232
225
217
2O9
203

195
I9O

i -9

2.O

1.8
1.8
1.6

....

•4
. i

.8
•3

. 2
.0

-19

6.97

4-4

1.82

14.4

I-I3

The electrical measurements, if all data are given in electrostatic units,
may be summarized from the data in table 22, as follows:

C

FXio3

iXio2

eXio10

103

7-5

77

3-3

47

17.2

Si

3-5

37

19.6

72

3-1

17

33

58

2-5

64 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

Thus, with a correction for the external gamma radiation, the data for
e show reasonable values, in spite of the simplicity of the experiment.
It follows, therefore, even in the case of such large numbers of ions as
occur in these experiments (over 500,000), that the constants of coronas
used heretofore are substantially correct. In case of the last value
<?Xio10=2.5, for the small capacities of 17 cm., the aluminum leaves
on the electroscope converge too rapidly for measurement, so that the
air resistance may have produced an appreciable discrepancy. Hence
both i and e are too small. No refinement has been attempted in these
experiments, their chief purpose being to test the standardization of the
fog chamber in terms of coronas and the degree to which positive and
negative ions may be caught even at very high nucleation. One may note
in conclusion that the currents 2=77 electrostatic units or 2.6Xio10
amperes are already quite within the reach of the sensitive galvanometer.

CHAPTER V.

THE ELECTRON METHOD OF STANDARDIZING THE CORONAS OF CLOUDY
CONDENSATION, IN TERMS OF THE VELOCITIES OF THE IONS.

54. Introductory. — In the following experiments I have returned to
the measurements* of TV in terms of e and the velocities of the ions,
Chapter IV, modifying the method by using the cylindrical fog chamber
both as an electrical condenser for the measurement of current, as well
as for the specification of the number of ions in action by aid of the
coronas of cloudy condensation. It is to be assumed that negative ions
only are caught in the fog chamber.

55. Apparatus (fig. 19.) — This consists of a cylinder of glass CF,
about 45 cm. long, 13.4 cm. internal diameter, closed at one end F, and
provided with a brass cap C with exhaust E and influx attachments /,
in the usual way. There is a layer of water w at the bottom. The glass
must be scrupulously clean within, and this is best secured by scouring
with a probang of soft rubber under water, until the water adheres as an
even film on shaking. The fog chamber is put to earth.

A

FIG. 19. — Electrical condenser and fog chamber combined, showing the dis-
positio"h of the auxiliary condensers C' and C", the Clarke cell 5, and the
electrometer K, diagrammatically. Earthed wires are shown at e.

The end F is perforated at h to receive the aluminum tube tt', closed
at t' and open at t, 40 cm. long and 0.64 cm. external diameter. Sealed
tubelets of radium rr may be placed at intervals within this tube to ionize
the surrounding wet air. The walls being about o.i cm. thick, ft and y

*Amer. Journ. Sci., xxvi, 1908, p. 87; idem., p. 324.

66 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

rays are wholly in question. Neither emanation nor a rays escaped the
double thickness of aluminum. The tube it' is grasped at t by a sheath of
hard rubber with an annular air-space and fixed in place by a rubber
cork. If care be taken to keep the tube in dry air except when in use,
there is no conduction leakage of consequence.

The end /, moreover, is placed in connection with a Dolezalek electro-
meter, by aid of a thin wire running axially within an earthed tin drain
pipe and away from the fog chamber, to escape the action of y rays as
much as possible. In fact, their combined effect does not exceed 2 per
cent and is determined in special measurements.

The keys to the electrometer were all placed on pillars of hard rubber
and actuated by long wooden rods from a distance. So far as possible
the electrical wires of the room were surrounded by earthed pipes, but
it was not practicable to carry this out completely, so that a method of
correction appears in the tables below. Even when the electric-lighting
circuit was completely cut out the electrostatic drift in question, supposed
to be due to this cause, remained. It was afterwards found that the
source of drift was due to an imperfection in the electrometer, but that
it could be eliminated by commutation, as was done.

The measurements were standardized and the electric system charged
by a Carhart-Clarke cell. The radium tubelets used were as follows:
I, 100 nig., strength 1 0,000 X ; II, iomg., strength 200,000 X ; HI, 100
mg., strength 10,000 X ; IV, 100 mg., strength 7,000X1 V, 100 mg.,
strength 2o,oooX-

56. Auxiliary electrical condensers. — To give the fall of potential
a suitably small value relatively to the period of the damped drop of the
needle a number of auxiliary condensers (fig. 19), are needed. It suffices,
however, to measure three capacities, viz: (i) that of the cored fog
chamber alone, c; (2) that of a relatively large auxiliary condenser,
including the electrometer, the piped wires, and the fog chamber, C" -\-c\
(3) that of a standard condenser C' for reference.

In the present paper C' was computed by the equation

A /
= - - , i

(d+dln

- , -

47ra\ \/7cA a* d /

where A is the area, d the distance apart, and d' the thickness of the brass
plates. Since A is equal 315 sq. cm., ^ = 0.082 cm., d' = 0.67 cm.,

C' = o-6(;i + o.o84) = o cm.

This value will suffice for the present purposes, though it needs further
correction by comparison with a standard condenser not now at hand.

ELECTRON METHOD OF STANDARDIZING CORONAS. 67

A special key was provided whereby C' could be switched into the
electrometer system or out of it and put to earth. Hence in a series of
successive discharges

(C" + c)V= (C" + C' + c) V (C" + c)V'= (C" + C' + c) V" , etc. ,

so that for n discharges, if the residual potential is Vn

from which the total capacity C = C" -f C' + c is determinable in terms
of C' . The results were

Positive charge C"+ C'+ c= 1445 1443 1422

Negative charge C"+ C'+ c= 1482 1480

Mean C= 1459

the experiments alternating from positive to negative charge, because
of the marked drift by the electrometer system when isolated from the
cell, as already specified. To measure the small capacities c of the fog
chamber, the same method with ten discharges suffices, if C" is excluded
and C' retained. Thus the data were successively found,

+ Charge c=n.S I2-4 12.2 12.9

— Charge c=io.8 10.4 n.i 11.5

Mean c=n.3 11.4 n.6 11.2

eliminating the drift in the final mean £=11.4.

Since the capacity c in terms of the effective internal radius R3 and
external radius Rr and lengths / of the cylindrical condenser may be
written

i i R^ i_

7 RZ 2X2. T,XC

the constant c furnishes a mean value for the factor on the left. The
ratio of 4.6^ to the measured value of (log R/Rz)/l was 0.568, a reduction
factor used throughout the tables below.

57. Method pursued. — If C is equal to C"+C' + c we may write the
equation for the negative ionization N (positive charge)

_ C\nR1/Rz d(\nV) d(\nV)

i V — ~ ; ~ — K

600 TT Ive dt dt

where Rlf R2, and / are the effective radii and length of the condenser,
io10<?=3.4, z;=i.5i cm. /sec., and li^i.^j cm. /sec., the velocity of the
negative and positive ions in the unit field, volt/cm., and in case of moist
air. The factor (lnRl/R^)/l is replaced by C/2, as specified in section 56,

68 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

which must here be regarded as an adequate correction for the ends and
the imperfect cylindricity of the condenser fog chamber. Similarly the
equation for the positive ionization is (negative charge)

C\nRjR2 d(lnV') ,d(lnV')
AT =- - - =K

600 nine dt dt

and the total ionization is therefore N+N'.

The experiments below will show that even if the fog chamber is put to
earth there is a drift towards negative potential sufficiently steady as
to be eliminated in the mean results.

The drift is due to a high permanent voltage which has its seat in the
electrometer and is not due to the lighting circuit of the building, for,
even when this circuit is cut out, the effect remains with undiminished
intensity. It will appear in Chapter VI that in the absence of radium and
of initial charge in the condenser the equation Ia=CV a, where Va for
any given ionization is a constant quantity, of the same sign as the
voltage of the needle, applies very closely within the limits of measureable
Va values. Hence in the presence of radium in the core of the cylindrical
fog chamber and a positive charge

/a+6oo TT IVNev/lnRJR^C V
Thus in this case

VN = *d(V-Va)/dt -V'N' = K'd(-V'-
and for the same V = V , to a first degree of approximation,

numerically, as before. If the equation for N is integrated, and N /K = K,
since Ia = CVa, Va being intrinsically negative for a negative needle,

V = £~Kt(V0 - VJK] + VaK V = e-K''(V'0+ VJK'} - VJK'

where V0 and V0 are the initial positive and negative potentials. Both
of these are of the form

where k is a constant, considered in the next chapter. If & = o,asin the

V
present case, and V= V , the correction would be •—?(*' — «), which shows

that large values of V only are admissible.

ELECTRON METHOD OF STANDARDIZING CORONAS.

69

58. Data. High ionization. Currents. — The following tables con-
tain the mean potentials V, the positive and negative logarithmic cur-
rents d(\og V)/dt (apart from the constant), the apparent nucleation N
positive and N' negative, computed from these data and the additional
information at the head of the tables. In most of the cases the corre-
sponding logarithmic currents due to rays outside the fog chamber was
carefully measured in the same units by placing a short hard rubber rod
between the end t of the aluminum tube (fig. 19) and the wire leading to
the electrometer. This cuts out the fog chamber, but leaves the whole
remaining circuit undisturbed.

Similarly the leak value of d (log V) jdt in the absence of radium and due
to mere conduction of moist parts is always quite negligible. Thus in the
first part of table 23, for relative logarithmic currents in the order of
0.035, ^e y ray effect is o.ooio, the conduction leakage smaller than
o.ooo i. The other extreme, i. e., the value of d(log V)/dt for the freely
falling needle is about o.i in the same units. Hence it follows that in the
first part of table 23 the needle falls faster than would be quite trust-
worthy, therefore the auxiliary capacity selected is too small.

Moreover, the negative current only is here measured, as the indis-
pensable need of measuring both currents was not then apparent. Hence
in the second part of table 23 the measurement of both currents is under-
taken. At the same time the capacity of the condenser has been increased
to give the needle the necessary slow descent. The time interval between
observations for V is 4 seconds in both parts.

TABLE 23. — Number of ions per cm3. Cylindrical condenser fog chamber. Capacity
of system: small auxiliary condenser, 330 cm. ; electrometer and wire, 69 cm. ; fog
chamber, 11.4 cm.; total, 410 cm. Fog chamber: glass 2R} = 13. 4 cm.; aluminum
core, 2.^2 = 0.635 cm.; / = 3g.5cm. Velocity of ions: u= 1.37 cm./sec.; v= 1.51 cm. /sec.
in field of volt/sec; e = 3.4Xio~10. Current due to f-rays without: d (log V)/dt =
o.ooi; current due to conduction leakage d (log V)/dt = 0.000081. Accelerated free
fall of needle, d (log V)/dt = o.o6 to 0.16 for corresponding deflections. Time interval
4 sec. Radium I + II + III + IV + IV' + V. K = 76Xio6. Cm. of scale equivalent to
0.0585 volt.

V

d (log V)/dt
Xio4

JVXio-3
corrected.

V

d (log V)/dt
Xio<

NXio-3
corrected.

I Charge + .

I Charge H — Continued.

i-32

H5

621

0-37

5i8

2230

I . IO

262

1130

•19

1360

5870

•83

355

1530

.06

1118

4850

•58

445

1910

70 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

TABLE 23 — Continued.

The same, with larger auxiliary condensers: Capacity of fog chamber, 11.4 cm.;
C", 1049 cm. ; C', 330 cm.; wires and electrometer, 69 cm. ; total, 1459 cm. Current
due to gamma-rays without d (log V)/dt = o. 00021 (pos. ch.) to 0.00022 (neg. ch.).
Time interval 4 sec. Radium I-V. Charges positive and negative. Positive
charge K = 28gXio6; cm. of scale equivalent to 0.0608 volt. Negative charge
/t' = 3i9Xio6; cm. of scale equivalent to 0.0613 volt.

V

d (log V)/dt
Xio<

WXio-3
corrected.

V

d (log V)/dt
Xio4

N X io-3
corrected.

II. Charge-.

III. Charge + .

i-43

4

74

•42

9

138

1.42

19

323

•39

33

503

i-39

3i

525

•34

54

827

i-35

37

625

.26

68

1040

1.30

4i

694

.18

86

i3H

•25

37

625

. JO

72

IIO2

. 21

35

599

•03

7i

IO92

•17

39

678

•97

75

1150

•13

35

594

• 9i

66

IOI2

.09

36

610

•85

78

I 192

.06

34

583

•79

84

1288

•03

32

54i

•73

72

I 102

.OO

30

509

.68

88

1346

•97

3i

525

•63

84

1293

•94

28

472

•58

9i

1399

•92

32

54i

•53

87

1330

.89

33

567

•49

94

1447

.87

27

456

....

....

.84

3i

530

.82

32

54i

....

....

.80

21

355

•37

107

1643

.78

34

578

•34

98

1505

.76

26

440

•30

131

2OI4

•74

27

456

•27

122

1876

.72

18

302

•24

137

2104

•71

28

472

•19

158

2427

.69

26

440

.18

145

2230

59. The same. Coronas. — Table 23 contains the data for the maxima
obtainable with the radium tubelets I, II, III, IV, V, at my disposal.
The corresponding corona was a large orange-yellow type, corresponding
in my former reductions to 506,000 nuclei in the exhausted fog chamber.
I have supposed this to be equivalent to 653,000 when the fog chamber
is at atmospheric pressure, seeing that the coronas are actually displaced
during exhaustion; i. e., at the maximum ionization does not coincide in
the position with the largest corona on exhaustion,* but is displaced in
the direction of the exhaust currents. This would seem to mean that
exhaustion is more rapid than the reproduction of ions to restock the
region of dilatation. In general this inherent discrepancy of a marked

*See Chapter III; also Science, xxvui, p. 26, 1908.

ELECTRON METHOD OF STANDARDIZING CORONAS. 71

distribution of ionization increasing from end to end of the fog chamber
is still outstanding. It is partially allowed for, since the observations
are made near the middle of the chamber, where the average conditions
supervene.

8

FIGS. 20, 22, 24. — Deflection at the electrometer in successive observations
4 seconds apart, for successive negative and positive charges in the orders
of the numbers on the curves.

60. The same. Summary. — The data of table 23 are given in figs. 20
and 21 ; fig. 20 merely shows the fall of potential in scale readings in
the successive observations 4 seconds apart, for positive and negative
charges. Fig. 21 gives the corresponding positive and negative apparent

72 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

ionizations. If the two curves between 0.8 and 1.2 volts be considered,
the mean ionization of each is

»

Apparent positive ions, negative charge N= 540,000

Apparent negative ions, positive charge N' — 1,164,000

Total true ionization N + N' = 1,704,000

Total nuclei caught 650,000

It will be seen that N + N' is the true total ionization positive and nega-
tive, if io10£ = 3.4. Only 65/170, or about 38 per cent, of this is actually
caught in the given fog chamber on exhaustion, provided the old coronal
values are correct.

If, however, it is assumed that negative ions only are caught during
exhaustion in the fog chamber in question, then the value of the electron
would be

io10<? = 3.4X2.62X- = 4.4 electrostatic units.

2

61. Data. Moderate ionization. Electrical currents. — These results
were obtained by placing but one radium tubelet, No. IV, in the alumi-
num tube it' of the condenser fog chamber (fig. 19). The data were
assembled in the same way as the above, N = Kd(\og V")/dt, as usual, but
they are here withdrawn, as they are sufficiently reproduced in the curves
(figs. 22 and 23). In the first and second parts of the table positive charges
only are treated and the results show the apparent negative ionization.
In the third part of table 23, however, both currents are observed in
succession and the true total ionization is TV+TV' as before. Moreover,
in parts i and 2 the capacity of the condensers is widely varied, 410 to
1459 cm., without showing serious divergence; though to bring this effect
out fully both positive and negative currents should have been averaged.

62. The same. Coronas. — At a fall of pressure of 2 1 cm. or dp/p — o. 2 7 ,
the nucleation was stationary and equal to N == 1 13,000 in the exhausted
fog chamber. At atmospheric pressure, therefore, 113,000X1.37 = 154,000
nuclei should have been present. The effect of a charge on the core of
the condenser did not appreciably diminish the nucleation or at least the
estimate could not be pushed below about 140,000.

63. The same. Summary. — For the case of the third and fourth parts
of table in question the successive observations at intervals of 30 seconds
apart are shown in fig. 22, the slopes only being of interest. The appar-
ent values of TV are given (fig. 23). Though the positive and negative
currents are both taken in one section only, parts 3 and 4, all the four
series show about the same drift, even though taken many days apart.
The condenser effect (excessive rapidity of needle) may be considered
eliminated for capacities greater than 500 cm.

ELECTRON METHOD OF STANDARDIZING CORONAS.
\

73

0 -2. -4 -6 -8 1-0 -f-& i'4-

FIGS. 21, 23, 25. — Apparent ionization, N per cu. cm.,
corresponding to the different voltages, V .

74 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

By averaging the ionizations between F = o.6 and ^=1.24 in both
parts 3 and 4 of the experiments made, the data found are as follows :

Apparent negative ions N = 278,000

Apparent positive ions N' = 107,000

True total ions N + N' = 385,000

Total nuclei , 180,000

Hence about 47 per cent of all the ions were caught on exhaustion if the
values of u, v, e, N, inserted, are correct. Supposing that negative ions
only are caught in the above fog chamber the value of the electron would
be

io1V = 3.4X2.i4X- = 3-6 els. units.

2

64. Data. Small ionizations. Electric currents. — In the next series
the aluminum it' , fig. 19, was surrounded by a lead tube with walls o.i 1 7
cm. thick, leaving the y rays only effective and these much reduced in
intensity. The data are given in figs. 24 and 25.

65. The same. Coronas. — The coronas found at a drop of pressure
similar to the above, op/p = o.^oo, corresponded in my reductions to
46,200 nuclei in the exhausted fog chamber. Hence at atmospheric
pressure there should have been 64,000. The effect of charging the core
was not clear; the reduction could be estimated at 51 ,000 at the uttermost.

66. The same. Summary. — The drop of potential in scale parts in
successive intervals 30 cm. apart is given in fig. 24, showing how much
more slowly the negative charges are lost than the positive charges. The
apparent values of ./V are given in fig. 25, to which remarks similar to
those already made are applicable. There is the usual drift and the usual
temporary fluctuation.

If the mean data be taken between V = i.i and 1.4 volts the results are

Apparent positive ions N'= 37,000

Apparent negative ions N = 98,000

True total ionization N + N'=> 135,000

Total nuclei caught 60,000

It follows, then, that about 44 per cent of the total ionization computed
from io10£ = 3.4, u and v, is caught on condensation.

If we suppose the negative ions only are caught in the above fog cham-
ber, the electron value is

*?Xio10=3.4X2.3X- = 3-9 els. units.

ELECTRON METHOD OF STANDARDIZING CORONAS. 75

67. Conclusion. — Supposing the electron value to be io10e = 3.4 electro-
static units as before, the normal velocities of the ions in wet air to be
M = i.37, ^=1.51 cm. /sec. in the volt/cm, field, the coronal value of the
ions caught in the above fog chamber is in the several cases

Total ions, 1,700,000 Total nuclei, 38 per cent.

385,000 47 per cent.

135,000 44 per cent.

When N is 1,700,000 the coronas are too diffuse for sharp specification.
If it is assumed that negative ions only are caught, and if the nucleations
corresponding to the coronas seen in the given fog chamber be taken as
developed in my earlier work, then for N+N' = 1,700,000, 385,000, and
135,000, the electron values are io1V = 4-4, 3.6, and 3.9 electrostatic units.

With regard to the two parts of this paper that need revision the first,
the comparison of the computed condenser capacity C' with a standard,
is a minor matter, but the other, i. e., the marked distribution of ioni-
zation along the axis of the fog chamber, will need further inquiry. In
the direction of the exhaustion the amount of ionization may vary in the
ratio of more than i to 2, in a fog chamber of about 0.5 meter of length,
and this under conditions where there should apparently be no variations
and irrespective of the production of radiation from within or from out-
side of the fog chamber. The final question relating to the drift, and the
asymmetry of the curves will be considered in all its bearings in the next
chapter.

CHAPTER VI.

THE ELECTROMETRIC MEASUREMENT OF THE VOLTAIC POTENTIAL DIFFER.

ENCE BETWEEN THE TWO CONDUCTORS OF A CONDENSER,

SEPARATED BY AN IONIZED MEDIUM.

68. Introductory. — The difficulties encountered in the preceding paper
(Chapter V, section 57), were made the subject of direct investigation
by replacing the fog chamber with a metallic cylindrical condenser, the
core of which was an aluminum tube 50 cm. long and 0.63 cm. in diameter,
the shell a brass tube 50 cm. long and 2.1 cm. in diameter, coaxial with
the former. Sealed radium tubelets could be placed within the aluminum
tube or withdrawn from it. Moreover, either the outer coat or the core
of the condenser could be joined in turn with the Dolezalek electrometer,
the other being put to earth. The conducting system now appears as
shown in fig. 26, C being the outer coat or brass shell, A the aluminum
core, and r the radium tubes in the cylindrical core. Conductors are
earthed at e. BB show the metallic connections with the auxiliary con-
densers C' C" , E is one of the insulated quadrants of the electrometer
with the highly charged needle N, E being virtually also a condenser.

A Clark standard cell 5 may be inserted for standardization, but it is
otherwise withdrawn.

£

J

e/

V \

\*_b

1 I

C'

£

FIG. 26. — Disposition of cylindrical condenser C, auxiliary condensers
C' C", key to earth K, electrometer E, standard cell S. All earthed at e
Diagram.

Direct experiment showed the self-charging tendencies to come appar-
ently from the highly charged needle N, or at least to arise in the electro-
meter E. Positive ions are lodged into the conductor EBB A for a positive
needle, negative ions for a negative needle. In addition to this, how-
ever, there is a voltaic difference, aluminum-brass, at AC when radium is
in place and the medium therefore highly ionized. The latter potentials
are usually negligible. These are the chief electromotive forces, the first

76

VOLTAIC POTENTIAL DIFFERENCE BETWEEN CONDUCTORS.

77

very high (150 volts) and in a weakly ionized medium, the other low
(0.2 volt), but in an intensely ionized medium, but they may eventually
produce equal currents. Effectively this is the case. Other voltages such
as the room potential may be operative, but their effect proved to be
secondary. If the capacities C'C", are successively removed, the electro-
meter current increases proportionately, showing its origin to be directed
from the needle or the electrometer case toward the insulated or non-
earthed pair of quadrants.
60

FIG. 27. — Increment of potential (cm. of scale), in the lapse of
time (seconds), when the auxiliary condensers are successively
removed.

FIG. 28. — Variation of potential V (cm. of scale), in the lapse of
time (seconds) , when the aluminum core or the brass shell of
the electrical condenser are alternately put to earth. Subscript
zeros indicate the earthed metal.

If the electrometer metals are reversed (see fig. 26), the voltaic couple
is reversed. This makes it possible to obtain both the voltaic contact
potential and the ionization in the cylindrical condenser C, from a pair
of commutated measurements. If the sign of the charge of the electro-
meter needle is reversed, the deflection of the needle is not reversed, but

78 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

continues to grow indefinitely in the lapse of time in an invariable
direction. Hence there must be a source of current in the electrometer,
as intimated.

69. Theory. — Let Vn be the potential of the needle, Vc the voltaic
potential difference of the two metals of the condenser, the shell being
put to earth, V the potential of the insulated conductor BB, measured
by the electrometer. Let n be the apparent ionization in the electro-
meter, N the (radium) ionization in the condenser (length /, radii R^R^} .
Let C be the total capacity of the systems CBBE. Then

where A is a constant, u and v the normal velocities of the positive and
negative ions, e the charge of the electron. The needle is supposed to be
positively charged. This may be written

V=Va-K(V-Vc)
where for N = o, K = o, or

i. e., the current in the electrometer, observed in the absence of radium,
from needle to quadrants. This is directly measurable with accuracy. It
is nearly proportional to Vn since V is much within i per cent of V n.
The integral of this equation is, t being the time,

V=(VJK)(i-KVc/Va)(i-e~Kt)

the sign of V is negative if Va<KVc> which is the case below. If there
is an initial potential VQ imparted by the standard cell, which is then
removed,

V=V0e-Kt+(VJK)(i-KVc/Va)(i-e-Kt)

If, now, the needle is left positively charged, but the condenser metals
exchanged (commutated), so that the aluminum core is earthed and the
shell now put in contact with the electrometer (see figure) , the equation
becomes

Here K refers to the negative current or normal velocity of negative ions
v. Similarly let Kr refer to the normal velocity of positive ions u. Also
let « = N/K and Kf = N/K'. Then if k = Vcl«v'a, and kf = Vc/f'Va

~Kt ' ~Kt

= Va(i -kN)e~Kt V' = Va(i+kN}e

VOLTAIC POTENTIAL DIFFERENCE BETWEEN CONDUCTORS.

79

If the potential V = V w at / = t»,

two equations from which both N and Vc may be found, if the limiting
potentials V^.V'^ and the electrometer current l^are severally observed.
If VM is not obtainable, it may be computed from observations at t and
tl = 2t as

Vao = (2V- V,) I V2 and V „ = (2 V - V\) / V*

Here, however, there is a difficulty, as the curves begin with a double
inflection not yet explained. The times tl = 2t must therefore be esti-
mated from the observations beyond the double inflections, or the rear-
ward prolongation of the curve for those observations, to meet the time
axis. The initial tangents may be found in the same way, but this is not
necessary, since their values are, respectively,

while

and Va(i + kN)
~Kt

V=Va(i-kN)

i-e

K

,etc.

A few other relations are often useful, as, for instance,

V

vr = v °° v = v d -V iv

0 aV -V c °°^ a' c

' 00 V C

all of which, however, have limited application because of the initial
double inflection of the curves.

To solve the transcendental equations the times of two observations
may be chosen, so that if V and /, V and t' correspond, /' = 2t. Thus,

Kt

e~Kt=

V'~V

-
V

from which N = «K follows. Similarly,

I 2V -V

V

V

00

V2

If t' = 2t and t/l = 2tl, the initial double inflection may in a measure be
ignored in

,-«,-„>_ .V_-VL I,

V,-V\ V

8o CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

70. Data. Origin of the electrometer current. — The seat of the chief
electromotive force or charging current in the electrometer follows
from the following data, summarized in fig. 27, in which the capacities
C, C', C", fig. 26, are successively removed. The currents increase in the
same ratio as the reduction of capacities, E being that of the electro-
meter. The data are, potentials in scale parts (where i cm. is equivalent
to 0.0595 volt), Va being the fall per second:

Capacities.

Va in cm.

Va in volts
per sec.

C + C' + C" + E

o. 14

0.0083

C' + C" + E

•15

.0089

C' + E

•58

•0345

E

4-3

.256

The change of voltage throughout the main contours of the curves
is almost a linear variation with the lapse of time, except that at the
beginning the motion is accelerated from rest as usual; for instance:

Time o

Va o

•3

12 16 20 24 28 32 60 sec.

3-7 6.1 8.7 ii. o 13.4 15.5 3i.ocm.

It is the linear character of these curves that greatly simplifies the
following measurements.

TABLE 24. — Measurement of ionization N, and voltaic contact difference Vc. Time
intervals 4 sec. Aluminum-brass condenser. / = so cm., a/?, = 2.01 cm., 2^2 = 0.634
cm. Scale part cm. =0.0588 volt. Radium I, II, III, IV, V in aluminum tube.
N= i, 750,000; Fc = 6.37 cm. or 0.375 volt.

Deflection.

(i) Aluminum to
electrometer, brass
to earth.

(2) Aluminum to
earth, brass to
electrometer.

(3) Aluminum to
earth, brass to
electrometer.

(4) Aluminum to
electrometer, brass
to earth.

o.o

+ 0.0

o.o

— o.o

— . i

•3

• 3

— . i

- -4

I .2

i-4

- -4

- -9

2-5

2.7

- -9

-1.4

4.0

4-i

-i-4

-1.9

5-o

5-3

-1.9

— 2.2

5-9

6-3

-2.3

-2-5

6.6

6.9

-2.6

-2.7

7-1

7-4

-2.8

-2.9

7-5

7.8

-2.9

-3-o

7.8

8.0

-3-0

-3-i

8.1

8.2

-3-i

-3-2

8-3

8.4

-3-2

-3-2

8-5

8-5

-3-3

-3-3

8-7

8.6

-3-3

-3-3

8.8

8-7

*-3-5

*-3-4

8-9

*g. 2

*-3.6

9.0

*9-4

*9.o

*9. 2

* After additional 60 sec.

VOLTAIC POTENTIAL DIFFERENCE BETWEEN CONDUCTORS.

8l

TABLE 25. — Voltaic contacts, Al-Zn, Al-Cu, A1-A1. Four-sec, intervals (usually) between
observations for V. Scale part cm. =0.092 volt. 1^0 = 0.0454 cm. Positive needle.
Radium I to V. # = 36.1 Xio + 8.

V

' for Al-Z:

i.

V

' for Al-Ci

i.

V

r for Al-A

1.

Zn to
earth.

Al to
earth.

Zn to
earth.

Cu to
earth.

Alto
earth.

Cu to
earth.

Shell to
earth.

Core to
earth.

Shell to
earth.

— o.o

0.0

— o.o

o.o

o.o

o.o

+ O.O

+ 0.0

+ 0.0

— .0

.0

— .0

. i

. i

. i

.0

.0

.0

— . 2

•4

. I

- -5

•7

- -5

.0

. i

.0

•3

.8

• 3

-1.2

1.6

-i-3

.0

•3

. i

- -5

i-3

- -3

— 2.0

2.6

-1.9

. i

.6

. 2

- -7

i-7

- -5

-2.7

3-5

-2.6

. 2

.8

•3

- -9

2.O

- .6

-3-2

4-2

-3-i

•3

•9

•4

- .0

2. 2

• 7

-3-7

4-7

-3-5

• 3

. i

•4

- .0

2-4

• 7

-4.0

5-i

-3-8

•4

. 2

•5

- . i

2-5

- .8

-4-2

5-4

-4.1

•4

•3

•5

- . i

2.7

- .8

-4.4

5-7

-4-3

• 5

• 5

• 5

— . i

2.8

- -9

-4.6

5-9

-4.4

• 5

.6

.6

— . 2

2.8

- -9

-4-7

6.1

-4-5

.6

i-7

.6

— 1.2

2.8

- -9

-4.8

6-3

-4-7

.6

1.8

.6

— 1.2

2.9

- -9

-4-9

6-5

-4.8

.6

i-9

.6

-i-3

2.9

- -9

-5-0

6.6

-4.8

*.6

i-9

.6

* — 1-3

*3-°

— i .0

*5-3

*6.9

*— 5-2

i-9

*.8

*i.i

*5-3

*6.9

*-5-2

*2. I

.8

* After further 60 sec.

FIG. 29. — Variation of potential (cm. of scale) in the lapse of seconds for
aluminum-copper, aluminum-zinc, and aluminum-aluminum condensers.
Subscript zeros show the earthed metal.

82 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

71. Aluminum core charged with radium tubelets I=V. Data. — The

air in the condenser C is now highly ionized and its voltage becomes
appreciable. The data obtained are given in table 24 and fig. 28. The
needle is positively charged thus (virtually) impelling positive ions to-
ward the quadrants of the condenser. In the four series of data observed
the aluminum core of the condenser is twice joined to the electrometer,
the brass shell being put to earth (series i and 4) and twice commutated
(aluminum to earth series 2 and 3). The results are identical, except that
in series 3 the insulation was perhaps better. The accelerated march of
the needle from rest is obvious in both curves and is thus independent of
the sign of the limiting voltage V '^. It may be mere inertia, but it is of
less consequence here because the initial data are not needed in the
computation of table 25.

72. Results. lonization N. Voltaic contact potential difference Vc.-
The equations

may now be used to compute N and Vc. The constants are numerically
(all in scale parts, i cm. equivalent to 0.0595 volt)

* = 36.iXio6 1^ =-3-45 ^=0.142 K' = 39.7Xio6 V"«, = + 9-3

Hence

JV= 1,750,000 ions, either positive or negative.
1/^=6.37 cm., or 0.38 volt.

73. Voltaic contacts: aluminum=zinc, aluminum=copper, aluminum-
aluminum.— The results obtained for aluminum-brass made it desirable
to investigate similar cases for other metals and zinc; copper and alumi-
num suggested themselves. These were used in form of thin sheets of
the metal, bent into cylindrical shells about as large as the above brass
shell. No special care was here taken to secure accurate diameters,
nor to prepare the metal surfaces. The aluminum core with the radium
tubelets (I to V) within, was the same as heretofore. The data are shown
in table 25 and in fig. 29. All potentials are given in scale parts where
i cm. is equivalent to 0.092 volt. The charging current for the electro-
meter, found in the absence of radium before and after these experiments,
was Va = 0.0454 cm.

Since we may write algebraically

and

VOLTAIC POTENTIAL DIFFERENCE BETWEEN CONDUCTORS.

remembering that V^is negative, while Vfx is positive, the following data
appear:

Couple.

N

Vc

V'oo

V*

Al-Cu

S.oso.ooo

Volt.
o. S5§

cm.

— ">• 25

cm.
+ 6 .00

Al-Zn

1,700,000

• IQI

— I . 17

T, .OO

A1-A1

i . 1 4.0,000

.o6s

+ O.7^

2.15

The large nucleation obtained here for copper remains unexplained.
It was somewhat reduced in other similar experiments, but remained
high. Since V'^-}- Vx = 1-65, slight differences in contact would produce
a serious effect. From these data it follows, finally, that the voltaic
contact zinc-copper is 0.367 volt. After cleansing with acids data like
Al-Cu = o-58 volt, Al-Zn = o.o6 volt, or Zn-Cu = o-52 volt were obtained,
which varied again after other treatment.

74. Further experiments. Conclusion. — In addition to the above
experiments, a great variety were made, as, for instance, with weaker
radium (single tubelets) in the core of the condenser ; with radium inside
and outside of the condenser; with the metal surfaces cleansed with acids,
or polished, or aged, etc. A few data may be referred to here.

The highest nucleation for an aluminum core charged with radium
tubelets occurs in case of a copper envelope for the condenser. Some-
what smaller values occur for zinc and brass, and the smallest for alumi-
num shells. The agreement is usually unsatisfactory. The voltaic con-
tacts are such as to place zinc-copper at 0.4 to 0.6 volt. The data for
groups of radium tubes are larger than the values computed from indi-
vidual tubes, N=\/N12 + N22+ . . . ., probably from the effect of
secondary radiation and non-uniform ionization. We may also ascribe
the high ionization in a copper shell as compared with a low ionization
in an aluminum shell to the same cause. If the radium is placed without
the condenser the voltaic contacts do not appreciably differ from the
values found when the radium tubelets lie in the core. One may note
that even in the aluminum-aluminum condenser the voltaic contact is
not zero but about 0.05 volt. In other instances non-commutated electro-
motive forces often appear. The contact Al-Zn is peculiarly variable even
as to sign.

As a whole these experiments lead to no general conclusion of relevancy
here and they have therefore been withheld from detailed consideration.

Finally, to detect the source of the electromotive force in the electro-
meter, this was replaced by another instrument, No. 2, of the same kind,

84 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.

as soon as it could be obtained. The absence of electric current V"a = o
in the new instrument and its presence in the old electrometer made it
necessary to overhaul the latter. It was eventually found that the brass
case had been insufficiently earthed,* so that a current from the Zamboni
cell, breaking through the hard rubber insulation at the top of the quartz-
fiber suspension kept the case charged to a high-constant potential.
This charge thereupon gradually leaked into the insulated quadrant
through the amber insulators, producing the current Va corresponding
to the sign of the electrode of the Zamboni pile and of the electrometer
needle. On providing the case of the old electrometer with a well-earthed
clamp, the current Va vanished. The new electrometer did not show this
defect even when the case was not specially earthed, whereas any insu-
lation of the old electrometer immediately restored Va.

Fortunately, however, Va is so remarkably constant that it can
actually be used in the measurements with advantage, as was done in the
present chapter, or eliminated by commutation, as was done in Chapter V.

*Probably owing to a thin film of varnish which had escaped detection. The room
was so dry that no discharge occurred through the feet of the instrument.

CONDENSATION OF VAPOR AS INDUCED
BY NUCLEI AND IONS

FOURTH REPORT

BY CARL BARUS
Hazard Professor of Physics, Brown University

WASHINGTON, D. C.:

Published by the Carnegie Institution of Washington

1910

MBL/WHOI LIBRARY

UH IfllE 4