CONDENSATION OF VAPOR AS INDUCED
BY NUCLEI AND IONS
THIRD REPORT
BY CARL BARUS
Hazard Professor of Physics, Brown University
WASHINGTON, D. C.:
Published by the Carnegie Institution of Washington
1908
CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 96
PREFACE.
In the following report I have given an account of experiments made
with a plug-cock fog chamber during the last year and a half.
The first chapter summarizes the equations frequently needed and
adds other important suggestions relating to the efficiency of the ap-
paratus used for condensation of water vapor suspended in air.
I have adduced, in Chapter II, the results of a long series of experi-
ments begun May 9, 1905, to determine whether the colloidal or vapor
nucleations of dust-free air show any interpretable variations in the
initial regions (ions), which would correspond to variations of a natural
radiation entering the chamber from without. The fog-chamber method
seems to be too complicated to give trustworthy indications of such
changes of ionization as have been since discovered with the aid of the
electrical method by Wood and Campbell. An interesting result, how-
ever, came out of the experiments in question, as a whole, showing that
the vapor nucleation is variable with temperature in the region exam-
ined to the extent of about 2 per cent per degree.
The fog chamber used in the present research having undergone
varied modifications since the coronas were last standardized (1904),
it seemed necessary to repeat the work for the present report. This
was particularly necessary because the subsequent investigations were
to depend essentially on the values of the nucleation observed. These
comparisons are shown in Chapters III and IV. In the former the
diffractions are obtained from a single source of light and the angular
diameter of the coronas is measured by a goniometer; in the latter the
fiducial annuli of two coronas due to identical sources of light are put
in contact and the distance apart of the lamps is measured under known
conditions. This contact method has many advantages and above all
admits of the use of both eyes. In both cases, moreover, the nucleation
of dust-free air, in the presence as well as in the absence of penetrating
artificial radiation, is redetermined. All results agree among them-
selves and with the older work, as closely as may be expected in work of
the present kind, below the middle green-blue-purple corona (usually
corresponding to io5 nuclei); but above this there is much divergence,
which will probably not be overcome until some means for keeping the
air rigorously homogeneous in nucleation throughout a given series of
experiments has been devised.
Chapter V contains some remarkable results on the properties of
nuclei obtained from the evaporation of fog particles. It will be seen
in
IV PREFACE.
that such residual water nuclei behave very differently, according as
the precipitation takes place on solutional nuclei like those of phos-
phorus, or upon the vapor nuclei of dust-free wet air, or upon the ions;
80 per cent of the nuclei may vanish in the first evaporation in the
latter case, fewer in the second case, and none in the first.
In Chapter VI the endeavor is made to standardize the coronas by
aid of the decay constants of the ions as found by the electrical method.
The curious result follows that in order to make these data agree with
those of Chapters III and IV it is necessary to assume an absorption
of nuclei varying as the first power of their number as well as a decay
by their mutual coalescence. If a be the number of nuclei (ions) gen-
erated per second by the radiation, b the number decaying per second,
and c the number absorbed per second, the equation dn/dt — a + bn^ + cn
is suggested.
My thanks are due to Miss L. B. Joslin, who not only assisted me in
many of the experiments requiring two observers, but lent me efficient
aid in preparing the manuscripts and drawings for the press.
CARL BARUS.
BROWN UNIVERSITY, July, 1907.
CONTENTS.
CHAPTER I. — Efficiency of the Plug-cock Fog Chamber.
Page
1 . Introduction i
2. The variables. Table i i
3. Approximate computations of p^ and p2. Table 2; fig. i 3
4. Definite computations of p1 and p2. Table 3 6
5. Computation of vjv. Table 3 ; fig. 2 7
6. Approximate computation of rt 8
7. Approximate computation of p2 9
8. Rate of reheating of the fog chamber. Table 4; fig. 3 10
9. Definite computation of TI( plt r2, p2, etc. Table 5 n
10. Conclusion 13
CHAPTER II. — Changes of Vapor Nucleation 0} Dust-free Wet Air in Lapse
of Time, together with Effects of the Limits of Pressure between which
a given Drop Takes Place, on the Efficiency of the Fog Chamber.
11. Introduction. Table 6; fig. 4 14
1 2. Data. Tables 7 and 8 ; figs. 5 and 6 17
13. Explanation. Table 9 21
14. The effect of vapor pressure. Table 9; fig. 7 22
15. New data for vapor nucleation in lapse of time. Tables 10 and 1 1 ; figs. 8, a, b . . 24
16. Effect of barometer 33
17. Effect of temperature 33
1 8. Effect of ionization. Table 12; fig. 9 33
19. Mean results. Tables 13 and 14, fig. 10 36
20. Nucleations depending upon dp/ 'p. Table 15 37
21. Possible suggestions as to the temperature effect 39
22. Another suggestion 41
23. Conclusion 41
CHAPTER III. — The Nucleation Constants of Coronas.
RESULTS WITH A SINGLE SOURCE OF LIGHT.
24. Introduction 43
25. Apparatus and methods. Fig. 1 1 43
26. Equations and corrections. Tables 16 and 17; figs. 12 and 13 45
27. Data for moderate exhaustions 49
28. Remarks on the tables and charts 49
29. Data for low exhaustions. Table 18; figs. 14 and 15 51
30. Data for high exhaustions. Table 19; fig. 16 54
31. Standardization with ions 56
32. Further data. Table 20; figs. 17 and 18 56
33. The violet and green coronas. Tables 21 and 22; fig. 19 59
34. Insertion of new values for m. Table 23 61
35. Wilson's data and conclusions. Table 24 62
36. Longer intervals between observations. Conclusion 63
DISTRIBUTIONS OP VAPOR NUCLEI AND OF IONS IN DUST- FREE WET AIR. CON-
DENSATION AND FOG LIMITS.
37. Introductory 65
38. Notation 65
39. Data. Tables 25, 26, 27, 28, and 29 65
v
VI CONTENTS.
Page
40. Graphs. Dust-free air. Figs. 20, 21, and 22 68
41. Weak radiation 70
42. Moderate radiation 70
43. Strong radiation 70
44. Other nucleations 70
45. Temperature effects. Table 30 71
46. New investigations. Tables 31, 32, and 33; fig. 23 72
47. Conclusion 75
CHAPTER IV. — The Nucleation Constants 0} Coronas. — Continued.
ON A METHOD FOR THE OBSERVATION OF CORONAS.
48. Character of the method. Fig. 24 76
49. Apparatus 77
50. Errors. Table 34; fig. 25 77
51. Data. Table 35 78
52. Remarks on the tables and conclusion. Table 36; fig. 26 81
DISTRIBUTIONS OF VAPOR NUCLEI AND IONS IN DUST-FREE WET AIR.
53. Behavior of different samples of radium. New fog chamber 84
54. Data. Table 37; fig. 27 84
55. Distributions of vapor nuclei and ions. Tables 38 and 39; figs. 28 and 29.. . 87
56. Remarks on the table 88
57. Condensation limits and fog limits. Conclusion 90
CHAPTER V. — Residual Water Nuclei.
PROMISCUOUS EXPERIMENTS.
58. Historical 92
59. Purpose, plan, and method 93
60. Residual water nuclei after natural evaporation of fog particles. Table 40. . 94
61. Rapid evaporation of fog particles. Table 41 ; fig. 30 95
62. Continued. Tables 42 and 43 ; fig. 31 98
63. Persistence of water nuclei. Table 44; fig. 32, a, b 103
64. Summary 104
THE PERSISTENCE OF WATER NUCLEI IN SUCCESSIVE EXHAUSTIONS.
65. Standardization with ions. Table 45 ; fig. 33 105
66. Further data. Tables 46 and 47 ; fig. 34, a, b, c 106
67. Data for vapor nuclei in
68. Remarks on tables. Table 48; figs. 35, 36, a, b, c, d, e, f, and 37, a, b, c, d . , in
69. Loss of nuclei actually due to evaporation. Table 49; figs. 38 and 39 117
70. Conclusion 120
CHAPTER VI. — The Decay of Ionized Nuclei in the Lapse o] Time.
7 1 . Introduction 121
72. Data. Table 50; fig. 40 121
73. Exhaustions below condensation limit of dust-free air. Table 51 ; fig. 41 .... 124
74. Data for weak ionization. Table 52 125
75. Further experiments. Table 53; figs. 42, 43, and 44 128
76. Case of absorption and decay of ions 128
77. Absorption of phosphorus nuclei. Table 54 130
78. Data. Table 55; figs. 45 to 49. . 134
79. Remarks on tables. Tables 56 and 57 135
80. Conclusion 138
CHAPTER I.
EFFICIENCY OF THE PLUG-COCK FOG CHAMBER.
1. Introduction.— In the last few years I have had occasion to use the
fog chamber extensively for the estimation of the number of colloidal*
nuclei and of ions in dust-free air under a great variety of conditions.
These data were computed from the angular diameter of the coronas
of cloudy condensation; and it is therefore necessary to reduce all
manipulations to the greatest simplicity and to precipitate the fog in a
capacious vessel, at least 18 inches long and 6 inches in diameter. To
obtain sufficiently rapid exhaustions it is thus advisable to employ a
large vacuum chamber, and the one used was about 5 feet high and i
foot in diameter. The two vessels were connected by 18 inches of brass
piping, the bore of which in successive experiments was increased as far
as 4 inches; but 2 -inch piping, provided with a 2. 5 -inch plug stopcock,
sufficed to produce all the measurable coronas as far as the large green-
blue-purple type, the largest of the useful coronas producible in a fog
chamber by any means whatever. Moreover, it is merely necessary to
open the stopcock as rapidly as possible by hand, using easily devised
annular oil troughs at top and bottom of the plug, both to eliminate
all possible ingress of room air and to reduce friction. Fog chambers
larger than the one measured were often used, and it is curious to note
that the efficiency of such chambers breaks down abruptly, while up
to this point different apparatus behaves nearly alike. The vacuum
chamber is put in connection with an air-pump, the fog chamber with a
well-packed filter by the aid of stopcocks. Water nuclei are precipitated
between exhaustions from the partially exhausted fog chamber.
2. The variables. — After reading the initial pressures of the fog and
vacuum chambers, it is expedient to open the stopcock quickly and
thereafter to close it at once before proceeding to the measurement
of the coronas. Eventually, i. e., when the temperature is the same in
both the fog and vacuum chambers, they must again be put in com-
munication and the pressures noted, if the details of the experiment
are to be computed.
*See Smithsonian Contributions No. 1309, 1901; No. 1373, 1903; No. 1651, 1906;
Carnegie Institution of Washington Publications No. 40, 1906; No. 62, 1907. In place
of the term "colloidal nuclei," the term "vapor nuclei" will be used in preference in the
text below. These vapor nuclei of dust-free wet air are probably aggregates (physical
or chemical) of water molecules.
I
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The series of variables given in table i, where p denotes pressure,
p density, r absolute temperature, TI vapor pressure, is to be considered.
The ratio of volumes of the fog and vacuum chambers was about
v/V = 0.064.
TABLE i.— Notation. Drop of pressure op = p — p3, observed; 8p = p — pv computed.
State
No.
Fog chamber.
Vacuum chamber.
Remarks.
i
P
P
1
7T
P'
P'
T
B
Initial states; cham-
bers separated.
2
P,
Pi
~1
*J
P',
P\
1*1
T'.
Adiabatic states,
after exhaustion;
chambers commu-
nicating.
3
Pi
Pi
T!
*I
P*t
P\
r',
^
The same, after con-
densation of water
in fog chamber.
4
P2
P2
T
n
P',
P',
T
S
Chambers separated
before condensa-
tion ensued ; orig-
inal temperature
regained.
5
P2
Pz
T
7T
PT,
P7?
I
!T
Chambers separated
after condensa-
tion ; original tem-
perature regained.
6
P3
PS
7°
71
Pa
P3
T
n
Chambers communi-
cating after ex-
haustion; original
temperature re-
stored.
At the beginning (case i), the fog chamber is at atmospheric pressure
p (nearly), the vacuum chamber at the low pressure p', and both at
the absolute temperature T. On suddenly opening the stopcock the
adiabatic pressures, etc., given under No. 2 appear, supposing that no
condensation has yet taken place in the fog chamber. If the stopcock
could now be suddenly closed and the whole apparatus allowed to
regain the original temperature T, the conditions under No. 4 would
obtain. This is virtually the case in Wilson's* piston apparatus,
and consequently these variables are comparable with his results
(cf. sections 3 and 4). In my apparatus, however, condensation takes
place within the fog chamber before the stopcock can be closed, and
thus an additional quantity of air is discharged from the fog chamber
into the vacuum chamber. After condensation and before the stopcock
is closed the conditions under No. 3 apply; when the stopcock has been
closed and the apparatus allowed to regain the room temperature T,
the conditions are shown in No. 5, and may be observed with crude
*C. T. R. Wilson: Phil. Trans., London, vol. 1992, 1889, pp. 405 et seq.
EFFICIENCY OF PLUG-COCK FOG CHAMBER. 3
approximation in the isolated chamber. Finally, when the chambers
are put in communication, the variables (No. 6) are the same in both.
This account of the phenomena may seem prolix, but it is essential
to a just appreciation of the efficiency of the plug-cock fog chamber.
Quantities in table i referring to a given chamber may be connected at
a given time by Boyle's law, as for instance, (p — n)=Rpr. This gives
eleven equations, some of which may be simplified. Corresponding
quantities in groups i and 2, as, for instance, r/rl, may be connected
by the law for adiabatic expansion, giving two equations. In addition
to this, an equation stating that a given mass of air is distributed in fog
and vacuum chambers (volumes v and V, respectively) is available; or
All the quantities TT are supposed to be given by the corresponding r,
though at high exhaustions the lower limit of known data, n = f(r), is
often exceeded, at least in case of vapors other than water vapor.
3. Approximate computation of pt and p2. — It will first be necessary
to compute p2, the pressure which would be found in the fog chamber
when it has again reached room temperature r, if there were no further
transfer of air from fog chamber to vacuum chamber, due to the con-
densation of water vapor in the former after adiabatic cooling.
For the purpose of obtaining more nearly symmetric equations it
seemed to be expedient to write
-•/* and r/r'
at the outset, in correspondence with Boyle's law, and thereafter to
correct for the temporary introduction of TT into the adiabatic equation.
Believing that the completed equations would be much more com-
plicated by contrast than they actually are, I made many of the com-
putations, where a mere guidance as to the conditions involved is aimed
at, with these symmetrical equations. The constants for use will be
computed by the more rigorous forms of sections 4, 5, 8, and 9. Mean-
while the comparison of both groups of equations will make it easier to
pass from the equations with p — re, wherever they were used in my
work, to the correct forms of the next paragraph. It is for this reason
that the equations now to be given were retained.
The pressure p2 is given by the gages of the piston apparatus, since
there is but a single chamber, and in this respect the plug-cock appara-
tus differs from it because the corresponding gage-reading is essentially
even less than p2. (Sections 5 and 9.)
The solution when the air in both chambers is continually saturated
leads to transcendental equations for the adiabatic pressures pl=p'l,
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
which can therefore only be obtained approximately. If the vapor
pressures T:I and n\ correspond to pt and p\, the results would be
_ =
,,
_ - \C/K-_
7- \
where approximate values must be entered for
inator on the right side of the equation.
Similarly
TT^, />t, in the denom-
Making use of the values found incidentally elsewhere, the data of
table 2 were computed on a single approximation. They are repro-
duced in the graph (fig. i).
TABLE 2. — Successive values of pressure and temperature in the plug-cock fog cham-
ber. Volume ratio of fog and vacuum chambers, v/V = 0.064; p = j6; t=2O°C.\
11=1.7 cm.; / refers to degrees C., r to absolute temperature, dp denotes the
drop in pressure. r/rl=(p/plY~e/k and T/T/I)«=(/»/£/I)I-«/* assumed.
Observed.1
Computed.2
P'-
PB-
fc.
/>V
P»
P\.
^2.
Pf
P*-
43-5
5i.5
59-5
45-5
52.5
59-7
47-9
54-3
?62.2
45-6
46. i
52.5
59-3
46. i
52.5
59-3
54-7
59-6
64.6
44-9
52.0
59-4
49-9
55-5
61.5
7T,.
*v
fi-
'i-
ti-
*v
^3 =
/>-/>3-
tya=
P-P,-
8PJ8P*
0.0
. 2
• 5
2. 2
1-9
i-7
0.7
•9
i . i
o
-17.8
• 8.3
+ .8
0
+ 5.2
9-4
12.7
o
+ 24. 1
21.3
19.8
o.o
16.3
23-5
o.o
11.4
16.4
[lo.7o
J 0.69
30.5
21.3
J
1 These observations merely illustrate the equations. No attempt made at accuracy. See chart.
2 The values of P)/Pi = o.gi, 0.93, 0.95, respectively.
The corrections, (p2 — p3) varying with (p — p3), lie on a curve which
passes through zero, but with a larger slope than for dry air. In fact,
they are much in excess of these cases* and throw the whole phenom-
enon into a lower region of pressures.
*Am. Journ. Science, xxu, p. 342, 1906.
EFFICIENCY OF PLUG-COCK FOG CHAMBER.
FIG. i. — Pressures in plug-cock fog and vacuum chambers, for different initial pressures
of latter, the former being initially at atmospheric pressure. (See table i.) The
notched curve shows the march of successive pressures for p' = ^§ cm. and £ = 67
cm. in a single exhaustion. The upper curves show corresponding temperatures in
the fog and vacuum chambers under like conditions. The adiabatic temperature
ratio T/T, is here an approximation.
A few incidental results deserve brief mention. The first of these is
the nearly constant difference of about 8p2 = 2 cm. between the observed
value p2 (nominal) and p3. Since for dry air or not
is constant for a given exhaustion, op'2 = —v/V • dp2. Hence if
dp2 = 2 cm., since v/V = 0.064, —dp' 2 = 0.064X2 =0.13 cm., nearly.
This case is illustrated graphically for £' = 45 cm. in the notched curves
of the figure in a way easily understood. It seems probable that whereas
the smaller fog chamber has lost too much air to even approach the
isothermal pressures p2, the large vacuum chamber is only a millimeter
short of them when the cock is again closed. The constancy of the
observed difference p2 — p3 seemed at first to be referable to the system-
6 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
atic method of investigation, though the effect of the precipitated
moisture (which has not yet been considered) will largely account for it.
(See section 9.)
Anomalous relations in the data for the fog chamber, as in the case
of p' = S9-S cm-> are direct errors of observation. On the other hand,
however, since within the ranges of observation p = a, p2 = a2 + b2p',
p3 = a3 + b3p' very nearly.it follows that (p—p^Kp—pz) mav approxi-
mately be written A + Bp', where a, b, A, B, etc., are constant. Fre-
quently B is negligible, so that (p2 — P^Kp—ps) is constant, in which
case the graphs for p2 — p3 varying with p — p3 pass through the origin.
4. Definite computation of px and p2. — If the adiabatic equations be
written without approximation
TX P
the equations for pl and p2 become
*t~ fi*i-clk) I V
V1
and
PI—XI (Pa-*)
from which pv may be found after putting an approximate form for p^
(p3 nearly) into the vapor-pressure term of the second member. A
single approximation usually suffices.
From these equations
__
. i-c/k 2 -- f d_
V\ V i
follow at once. Subsidiary equations
and
P»—P' dp'—t
v/V = -
remain as before in section 3. To compute v/V in this way high ex-
haustion is essential, otherwise p' and p3 differ but slightly. Between
the present group of equations, which are nearly rigorous, and the
preceding group the corrections to be added to the former may be
estimated.
EFFICIENCY OF PLUG-COCK FOG CHAMBER.
5. Computation of \Jv. — Since (vl/v)k/c = p/pl, the volume expan-
sion is a cumbersome datum to compute rigorously, and it appears as
v
71 i \ V / 7T,
L_ I _i_ /T 1
*i-c/k V \\ 2 = 57-8; />2 =
'From the chart />'1 = 5O.2; p'3=$o.o.
cm.
EFFICIENCY OF PLUG-COCK FOG CHAMBER.
II
FIG. 3. — Observed value of apparent isothermal pressure p2, after lapse of different
seconds of time after exhaustion; also corresponding drop of pressure df>2 from
atmospheric pressure.
9. Definite computation of rlt p,, r2, p2, etc. — In view of the
equation
*i w
the density of saturated vapor at the temperature T becomes
;i
= d-
— r,)
where ti is the density of saturated water vapor at T; p, c, L, the density
of air, its specific heat at constant volume, and its latent heat. The
other quantities have the same meaning as before. Hence the quantity
12 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
of water precipitated per cubic centimeter of the exhausted fog cham-
ber is
c -
=
fl-Tl)
If the coefficient of d in the above equations be written x,
— pcx Pcx_
L, L TI
where a and b are constant, so that T is the temperature at which the
line d, T, crosses the vapor-pressure curve d=f (rj, which for water
vapor is known as far as — 50° C. In place of absolute temperatures r,
degrees centigrade /x and tt may be used. Table 5 contains a series of
useful data for m, dp (if £ = 76), dp/p, vjv, tlt and tr
TABLE 5. — Water precipitated at different exhaustions and temperatures.
^ = 76 cm.; dp3=p-p3cm.
v±
V
dp
P
dp.
At 10° C.
At 20° C.
At 30° C.
mXio6.
*i-
«i.
mXio6.
'••
*!•
wXio6.
*i-
*i-
I. II
1.24
i-43
1.56
2.15
0.132
.263
•395
.466
.660
10
20
30
40
50
1.88
3-4i
4.48
....
i-4
- 14.0
-28.4
T 4-6
1.8
- 10. 0
2. 26
4.18
5.65
6.61
7-58
+ 8.3
- 4.8
-19.7
-37-i
-58.3
+ 15-9
+ 10-9
+ 4-6
• 3-3
- 9-5
2.61
4.91
6-75
+ 17.8
+ 4-3
- ii . i
26.6
22 . 7
I7.8
Incidental data, 3p = p — pl.
1.18
1.29
1.42
0.214
•309
.401
16.3
23-5
30.5
3-57
4-75
5-58
- 19.0
- 9.6
— . 2
+ 12.7
+ 9.0
+ 4-9
1
To compute p2 and p'2 the equations are
and p'a-TT--
P i
i-c/fc
where pl/ pv depending upon Boyle's law, will have the same value as
before (section 7) and in the approximate form becomes
Since
Pi— *
pi— 7i
Pi
with a similar equation for p'lf the pressures p^ and p\ may be computed,
since the values of the second member of the equation are now known.
EFFICIENCY OF PLUG-COCK FOG CHAMBER. 13
10. Conclusion. — If the fog chamber is combined with a large
vacuum chamber, through a sufficiently wide passageway containing an
ordinary plug gas-cock to be opened and closed rapidly by the hand, all
the measurable coronas of cloudy condensation, due to the presence of
colloidal or vapor nuclei in wet, strictly dust-free air, may be evoked.
While such an apparatus admits of capacious fog chambers and ex-
tremely simple manipulation, it has not been shown to be inferior in
efficiency to any other apparatus whatever.
The conditions of exhaustion must, however, be computed from the
initial pressures of the fog and vacuum chambers when separated and
their final pressure (after exhaustion) when in communication, in all
cases at the same temperature and the volume ratio of the chambers.
The chief pressures and temperatures are shown in fig. 2 for different
initial pressures of the vacuum chamber, the fog chamber being at
atmospheric pressure.
CHAPTER II.
THE CHANGE OF THE VAPOR NUCLEATION OF DUST-FREE WET AIR IN
THE LAPSE OF TIME, TOGETHER WITH THE EFFECT OF THE LIMITS
OF PRESSURE BETWEEN WHICH A GIVEN DROP TAKES PLACE ON
THE EFFICIENCY OF THE FOG CHAMBER.
11. Introduction. — Recently* I published certain results which showed
(apparently) that the colloidal nucleation of dust-free air varies peri-
odically in the lapse of time in a way closely following the fluctuations
of the barometer. This nucleation (particularly when the larger groups
of nuclei lying near the region of ions are taken into consideration) is a
maximum when the barometer is a minimum. The development of
the investigation was peculiar. At the outset the data appeared like
an immediate confirmation of Wood and Campbell's! discovery, which
had then just been announced. Maxima of colloidal nucleation appeared
where Wood and Campbell had found minima of ionization, and vice versa.
By supposing that the ions, which are virtually larger than the colloidal
nuclei, capture most of the precipitated water, the two sets of results
would be mutually corroborative.
Later this cosmical feature of the phenomenon became of secondary
importance as compared with an apparent direct effect of fluctuations
of the barometer. Nucleation of dust-free air increased when the barom-
eter decreased, and maxima of nucleation were apt to coincide with
minima of the barometer. Such a result, whether direct or indirect
(removal of radioactive matter from porous earth accompanied by
falling barometer), would have been of considerable importance, and
great care had to be taken in the endeavor to verify it. Unfortunately
the correction to be applied for barometer fluctuation, in its effect upon
the aperture of the coronas, was in the same sense and very difficult to
estimate; and in fact upon using two fog chambers side by side (one
with 2-inch, the other with 4-inch exhaust pipes), adjusted for different
sizes of coronas and accentuating the barometric correction, the vari-
ations in one vessel might be made to show a tendency to follow the
barometer, whereas the other departed from it. Table 6 and fig. 4 give
an example of such a case, where 8p is the observed fall of pressure
(P — PS)* P the pressure of the fog chamber before, p3 the pressure after
*Carnegie Institution of Washington Publication No. 62, chap, vi, 1907. Cf. Science,
xxm, p. 952, 1906; xxiv, p. 1 80, 1906.
fWood and Campbell: Nature, LXXIII, p. 583, 1906.
CHANGE OF VAPOR NUCLEATION IN LAPSE OF TIME.
exhaustion with fog and vacuum chamber in communication, all at the
same temperature; s is the angular diameter of the corona on a radius
of 30 cm., when the source of light and the eye are at 30 cm. and at
250 cm. on opposite sides of the fog chamber. Finally, n shows the
number of nuclei per cubic centimeter.
TABLE 6. — Time variation of the larger colloidal nucleation of dust-free air. Conical
filter, dp readjusted. App. I, 4-inch pipes; app. II, 2-inch pipes.
Apparatus I.
Apparatus II.
Date, etc.
»Pi-
Si-
P-
?'
•* i-
n X io~3.
dp,.
S2.
s2.
«2Xio-3.
July 12, 8h50m
27.1
3-9
76.2
3-9
19
25-5
2-9
3-3
10
3 45
27. 2
5-i
76. 2
4-9
37
25-5
2.6
3-0
7
5 35
27.1
5-2
76.1
5-i
4i
25-7
3.2
3-0
7
July 13, 10 40
27-3
5-2
76.1
4.8
35
25-4
3-i
3-7
16
3 oo
27.1
5-2
76.1
5-i
4i
25-4
2-5
3-3
10
5 30
27.2
5-0
76.O
4-7
33
25.6
2-5
2-4
3-7
July 14, 8 41
27. 2
5-6
76.O
5-3
46
25-4
2.6
2.0
2. I
3 20
27.2
5-0
75-9
4.6
30
25.6
2-4
2-3
3-0
6 oo
27.4
5-7
75-8
5-o
39
25-7
3-o
2.6
5-2
July 15, 8 oo
27-3
5-2
75-9
4-7
33
25.6
3-1
3-o
7-4
3 30
27.2
5-6
75-9
5-2
43
25.2
2.6
3-5
12.7
5 25
27 . 2
S . 2
7S . 9
4.8
7=;
July 1 6, 9 oo
/
27-3
«j
5-5
t \j 7
75-7
*T
4-9
O <->
37
25-5
2-9
2-9
Y.7
2 30
27-3
5-4
75-7
4.8
35
25-6
3-i
2-9
6-7
6 oo
27.5
6-3
75-6
5-4
49
25-4
2.8
3-o
7-4
July 17, 9 oo
27-3
5-7
75-5
5-0
39
25-7
3-5
2.8
6.2
4 oo
27-3
6-7
75-3
5-8
58
25.6
3-2
2.6
5-2
July 1 8, 951
27 . 2
5-5
75-8
5-0
39
25.2
2-5
3-4
ii -5
3 55
27-3
5-4
75-8
4.8
35
25-7
2.9
2-4
3-7
9 15
27.4
5-i
76-3
4.6
30
25.6
2.6
2-4
3-7
2 30
27-3
5-2
76.2
4.8
35
25.6
2.8
2-7
5-9
6 10
27-4
6.1
76.2
5-6
54
25.6
2.O
1.9
2.O
While the data for apparatus I still recall the barometer graph, this
is not the case for apparatus II, and neither of the graphs I or II are
as strikingly suggestive of the variations of atmospheric pressure as
was the case in the earlier report. The discrepancy in the new results
may be an overcompensation, although all the details of the experi-
ments themselves were gradually more and more fully perfected; or
the rise in the region of ions may just balance the decrease of the num-
ber of efficient colloidal nuclei due to the increase of the former. In
fact the region where ions predominate may rise while the regions where
the vapor nuclei are more important may correspondingly decrease,
producing a diminished slope of the initial part of the graph such as is
often actually observed. It is necessary, therefore, to inquire somewhat
more carefully into the errors involved, to investigate some datum or
invariant which if kept constant will mean a corona of fixed aperture
in the given apparatus, unless there is actual radiation in varying
amount entering from without.
i6
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
I purpose, therefore, in the present paper, to study the same phenom-
enon for an artificial barometer; in other words, to accentuate the
present discrepancies, let the pressure drop from a given upper limit to
varying lower limits, as well as from varying upper limits to a given
lower limit. The results so obtained are enormously different for the
same drop of pressure. Much of this would be anticipated; but the
question nevertheless arises whether the colloidal nucleation of the gas
is actually dependent in so marked a degree on its initial pressure, or
whether this dependence can be explained away.
74
76
78
10
FIG. 4. — Apparent nucleation of dust-free air in lapse of time. Apparatus I with
4-inch exhaust pipes; apparatus II with 2-inch exhaust pipes; otherwise identical.
A new and more pervious filter was installed on July n. The upper curve shows
corresponding barometric pressure within the fog chamber.
Later in the course of the work I made additional comparisons with
the contemporaneous ionization of the air determined by Miss L. B.
Joslin and with the temperature of the fog chamber as distinguished
from the temperature of the air. These results as a whole finally showed
that a direct dependence of the vapor nucleation of the dust-free air
DATA OF VARYING PRESSURE. 17
in the fog chamber on the barometer, on the ionization of the air, on
any form of external radiation, or on the temperature of the atmosphere,
can not be detected. All the variations may be referred to the temper-
ature of the fog chamber itself, as if it generates increasing numbers of
colloidal nuclei as its temperature increases. Since the colloidal nuclei
in dust-free moist air are to be associated (from my point of view)*
with the saturated vapor, and are only secondarily dependent upon the
air itself, the result so obtained is curious, as one would expect a decrease
of the colloidal nucleation with rise of temperature. Correction for the
increased water precipitated at higher temperatures merely accentuates
the difference. If rt is the low (absolute) temperature obtained by
sudden expansion adiabatically from r the ratio TX/T should be wholly
dependent upon the corresponding pressures; and yet, for the same
ratio, more nuclei are obtained as r is larger. This difference of be-
havior is maintained for larger and smaller ratios of r1/r, in like degree.
12. Data. — The results are given in tables 7 and 8, and refer to a
fog and vacuum chamber, the volume ratio of which is about v/V = o . 06,
combined with sufficiently wide piping (2 -inch bore) and an interposed
(2. 5-inch) stopcock. The former communicates with the filter, the
latter with 'the air-pump. At the same temperature the fog and vacuum
chambers are initially (before exhaustion) at pressures p and p' ' , finally
at pressure £3, when in isothermal communication after exhaustion;
p2 and p'2, respectively, would be the pressures at the given temperature
if the chambers could be isolated immediately after exhaustion and
before the precipitation of fog. P denotes the barometric pressure, and
pm the initial gage-reading within the fog chamber before exhaustion,
so that the drop of pressure is (apart from the moisture content, which
will be treated in turn below) dp = P—pm—p3, and the drop of pressure
takes place from p = P — pm adiabatically to pt, isothermally to pz if the
fog chamber were isolated as specified, or isothermally to p3 when fog
and vacuum chambers are left in communication.
For a given value of P the same drop of pressure dp may thus be
obtained in two ways — either by giving a suitable value to pm, i. e., by
starting with a partially exhausted fog chamber and a vacuum chamber
at fixed exhaustion pf , which implies a nearly fixed p3; or by keeping
pm constant (small, nearly zero), thus starting with the fog chamber
about at atmospheric pressure, and determining p' of the vacuum
chamber and therefore pa.
Briefly, then, the condensational effects of a given difference dp when
lying between different pressures p and pa, are to be tested, and this is
best accomplished by constructing separate complete graphs for the
aperture 5/30 of the coronas, first by keeping p' and p3 nearly constant
*Am. Journ. Sci., xxn, p. 136, 1906.
l8 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
and varying pm (lower pressure limit, p, variable) and second by keeping
p fixed and varying pr and p3 (upper pressure limit variable). Tables
7 and 8 show these data, the latter for a wider range of coronas than the
FIG. 5. — Nucleation of dust-free air for different drops of pressure Sp = p — p.2; [dp]'
denoting that the upper limit, [/>], that the lower limit of the drop of pressure dp
I is varied. Also corresponding nucleation referred to the exhaustion Sp/p. Four
I series. Small ranges of nucleation as compared with fig. 6.
former, while n denotes the number of nuclei per cubic centimeter.
From 5 the number of nuclei, n, per cubic centimeter is computed.
The results, moreover, are graphically given in figs. 5 and 6, the abscis-
sas being the drop dp=p—p2, the ordinates nX io~3. It will be seen at
once that the two curves ([dp\ denoting that the lower limit of pressure,
DATA OF VARYING PRESSURE.
[dp]' that the upper limit of pressure is varied) are strikingly distinct in
both figures and that the variation of the lower pressure limit [dp^
corresponds, as it should, to a highly increased efficiency of the fog
chamber. The coronal fog limits are far apart, being respectively below
[c^li = J 7 • 4 and [dp]' = 19. 4 cm. in fig. 6, where all data (table 8) were
obtained in one series of experiments.
TABLE 7. — Effect of varying p in dp = p-p3=P-pm-p3. Chamber II. Bar. = /> =
P-pm. v/V = 0.064; P~p2 = o.775 dp; ^=2.3; t= 25° C.; 7r-7r, = i .8.
P.
£m-
P-/V
#.
5.
Cor.
«Xio-3.
dp/p.
P.
I
75. 7
'0.2
27. 3
27 . i
6.9
g'B P
2ios
°-359
75-5
. I
I .O
2 O
• 5
•5
-2
•4
26.5
2S ^
6.9
7.0
c . i
g'BP
g'BP
2io6
104
T.Q
.362
•355
• ^44
75-6
71-7
73-7
2.O
•5 o
.6
6
25.6
24. 6
6.4
4. S
w y
72
27
•348
• 379
73-7
72. 7
-i n
7
24 7
4 2
21
• 14O
72. 7
40
8
2"? 8
2 ^
4. T.
. ^2
71 • 7
. w
4. O
7
•^o • u
27 7
2 . 4
1- S
• "HI
71 . 7
6 o
6
^i 6
I c
I .4
.in
69. 7
II
75. 7
3O.I
27.6
27. s
9-5
w r
190
• 364
75-6
40
7
21 7
2 4
T..Q
• ni
71 .7
• w
1 .0
6 o
.6
8
26.6
21 8
7-i
1.8
g'BP
116
1.6
.356
• 113
74-7
69.7
r ....
7 c r
I .0
O 2
.6
24.. 0
26.6
24. 7
7-5
1 . 7
g'BP
116
1.8
.356
.328
74-7
75-3
t — 2 1 4° C
2S 6
2 ^ d.
i. 6
i s
• 337
*O • u
26 4
26 2
c 6
S'?
• 348
7T — 7Tj= 1.4.
II'
476.2
. 2
2S -9
25. 7
3-2
cor
9-5
•338
76.0
<=23°C.
7T = 2.1.
7T — 7T, = 1.6.
5I
7 S S
2
26.9
27.4
28.7
29.4
30-5
33-5
24.9
26.7
27. 2
28.5
29.2
30-3
33-2
24. 7
6.4
6.8
IO. 2
12
13?
13?
I .7
w p
gBP
w r
yr
gBP
Do
76
1 20
2IO
3IO
380
4IO
1.8
•351
•359
•375
•384
•399
•437
.328
75-3
/ —0.3° P
2c 6
2 ? A
i 6
i s
•337
» zo *-•
•*o • u
ofi /i
^ J • T-
26 2
s 6
S3
•348
7T — ;!,= 1.6.
"Water nuclei not precipitated. 4 From Carnegie Institution of Washington
2 Too small. Initial values. Publication No. 62, chapter n, table 26.
3 Water nuclei precipitated. Coronas usually blurred. 5 Ibid., chapter vi, table x.
In fig. 5 the results of series I' and II' are taken from data for the
same apparatus in an earlier report to the Carnegie Institution of Wash-
ington.* Consequently some reconsideration is needed. In the lapse
of time the efficiency of the fog chamber has for some reason increased,
for the new results (fig. 6 and dotted line in fig. 5) are distinctly higher
in nucleation than those quoted from the report.
*Carnegie Institution of Washington Publication No. 62, chapters n and vi, 1907.
20
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
Compared with the graph n and [dp]', table 7, where the upper limit
only is varied, the graph n and [dp^ lies in the main above it, in the
smaller exhaustions, and it should be remembered that the range of
variation is here smaller. But it does not lie as much above n and
[dp]' throughout as would be expected, seeing that only the upper points
FIG. 6. — Nucleation of dust-free air for different drops of pressure 8p = p — p2', [dp]'
denoting that the upper limits, [], that the lower limit of the drop of pressure
dp is varied. Also corresponding curve referred to the exhaustion dp/p. Three
series. Larger ranges of nucleation than in fig. 5.
should coincide, intimating that there is some variation as compared
with fig. 6 not accounted for. This becomes specially evident when
the two graphs for [dp] in figs. 5 and 6 are compared, as shown in the
former.
DATA OF VARYING PRESSURE.
TABLE 8. — Data1 corresponding to table 7 for larger ranges of dp.
21
P.
0».
P-P*
0>=
P-P*
S.
Cor.
ttXiQ-3.
P.
III
7c g
O . I
27 6
27 ?
O T
w r
T "7O
*7 C *7
/ o • °
•*/ • V
•*/ • 3
V • l
1 /V
75 • 7
n =2.5
28.5
28.4
H-5
2w r o
244
n — TCI = 2 . o
29.1
29.O
it. 8
2w r o
332
29.9
29.8
g
375
26.8
26.7
8.0
139
25-4
25-3
4-3
24
26.6
26.5
7.3
"5
....
IV
7S 8
. I
-JQ O
2Q Q
gv o
•? jn
•7 C •?
f J *•
O ' v
•6;7 • 7
J "
v?^^1
/O • /
n = 2.5
1 .0
30.1
29. I
g'o
372
74-7
7T — TTj = 2 . O
2 .O
30.2
28.2
1 1
gy°
327
73-7
3-0
30.1
27.1
ii
w r o
234
72-7
4.0
30.1
26. I
9-5
w r
182
71.7
5-0
30.3
25-3
8.6
w c
157
70.7
6.0
30-3
24-3
7.0
w r
93
69.7
7.0
30-3
23-3
5-4
44
68.7
8.0
30.3
22.3
2.8
5-7
67.7
v
7S 8
i
28 •*
28. 2
1 1
y' r o
">A2
75 7
/ o * °
^0 . ^
i -(n-ni)
»0.32(>XlO-3.
p-n
Aug. 6, 5hi6m
25-7
4.2
76.7
0.335
21
0.318
24
5 25
25-7
4-4
76.7
.336
26
.319
28
Aug. 7, 10 oo
25-7
4-3
75-0
•339
24
•323
19
10 10
'25-7
3-7
75-9
•338
16
•323
II
10 20
25-7
4.1
75-9
•339
20
•323
15
3 5
25-7
4-2
75-7
•34°
21
.321
19
3 15
25-7
4.2
75-7
•340
21
.321
19
Aug. 8, 10 40
25-3
3-6
75-7
•335
14
• 317
19
10 50
25-5
4.0
75-7
•337
18
.320
18
II OO
26.0
4-9
75-7
•344
36
•327
24
5 40
25-9
4-9
75-7
•342
36
•325
28
25.6
4-3
75-7
•339
23
.321
21
Aug. 9, 9 30
25-6
3-8
75-8
•338
17
.321
15
9 40
25-8
4-2
75-8
•341
21
•324
14
4 oo
25-7
4-5
75-8
•340
27
•3i9
29
4 10
25-7
23-9
75-8
•340
2i8
•319
2O
4 20
25-7
5-i
75-8
•340
40
•3i9
42
1 Not cleaned by precipitation.
Hence in table n a larger fiducial value (dp — [TT— x1])/(p—i:') =0.335
was selected in turn, as the graphs in this part of the field (see arrow in
fig. 7) are more nearly straight. At the outset complete series of results
(August 10, n, and 12) were investigated; subsequently but three
observations in the neighborhood of the abscissa 0.335 fully sufficed.
The completed graphs are given in fig. 7 and marked VI to X. Their
position is throughout low as compared with III to V, for which there is
VAPOR NUCLEATION IN LAPSE OF TIME.
P
CO
e
P
I
S
.
o
B
c
V.
o
i
U)
2
3
ro
•t
P
r^
c
0
oq
o
3*
P
3
cr
fD
en
n
o «^~
3
fD
*/
^
/^.-O v
;^-<«-A ^fe-W'^1
»^3 ;
ULISK*-
\*
. /-1
26
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
now no reason referable to causes within the fog chamber, unless there
exists a singularly marked temperature effect, presently to be investi-
gated. Series VI alone is peculiar, showing a strong initial tendency to
return to the earlier set, III to V. Water nuclei were precipitated
before each observation. The data for n0 335 are also inscribed in fig. 8a
and fig. 86, where they are compared with the barometer and the tem-
perature of the fog chamber in a general way.
Table n also contains the corresponding values of dp/p and the
nucleations n derived from the new investigations in Chapter IV. From
these the values w-0 for
and n0_S45 for
are
derived to be used in the correlative summary in sec. 20. The nucleations,
wo.345> which suffice for the purpose, are given with the others in figs. 8a
and 86.
is cm.
30°
VTfo.
5/14345
100
50
0
27 Stpt. Z9 1 Oct. 3 S 1 9 11 13 If 11
FIG. 8b. — Changes of vapor nucleation of dust-free air, barometric pressure, and
temperature of the fog chamber in the lapse of time.
The data for n0 335 in figs. 8a and 86 sometimes follow the barometer,
sometimes depart widely from it; but coincidence will usually occur only
when both accompany the same temperature effect. As a rule there is a
rise of nucleation from morning to afternoon, suggesting the phenome-
non due to external radiation discovered by Wood and Campbell (section
i ) , but in these cases temperature is also apt to rise coincidently . The rise
in question fails to occur but 4 times out of the 13 observed in August,
but 7 times out of the 24 observed in September (2 being neutral), and
but 5 times out of the 13 observed in October.
VAPOR NUCLEATION IN LAPSE OF TIME.
TABLE n. — Time variation of the larger colloidal nucleation of dust-free wet air. Cor-
responding to table io, with allowance for temperature. Sp — p — p3; pm = o.i; p — p2 =
o.jjXdp.
,-jA
/,
t
^-(TT-TT,)
"(in.-s-s'X
$p
W0-3-K)X
io-3
Date, etc.
op.
P-
p-ic
n A i o
io-3
p
«Xio 3.
wn.348X
io-3
Aug. 10, g'^o™
4 40
4 20
4 30
4 40
Aug. n, 8 50
5 oo
25-7
25-7
25-7
25-7
25-7
25-3
26. 2
27.6
28.4
29. 2
27-3
25-1
25-7
27.0
28.2
29-3
30.2
25.3
25 7
3-9
3-9
4-4
4-4
4-4
3-7
5-7
'9.6
2II.O
3n-5
47-8
2-3
4-i
27-3
'10.6
'ii-S
gyo
3-0
4.4
75-8
75-6
75~6
75-5
75-4
0
26.0
26.0
28.0
28.0
28.2
28.2
28.2
28.2
28.2
28.2
25-8
25.8
25.8
26.0
26.0
26.0
26.0
26.0
0-323
•323
.321
.321
.322
.316
.328
•347
•359
•370
•347
•317
•325
•343
•359
•374
• 386
.320
. 12S
18
18
25
25
25
16
55
190
207
250
130
3
19
105
206
250
3i8
7
21?
1 (90)
1 <
1 105
[ V!. .
1 70
to
65
[VII. •
65
to
0-339
•339
•340
•340
•340
•335
•347
.365
•376
.386
.362
•332
•340
•358
•374
.388
.400
•336
. 1.4.O
13-3
13-3
18.5
18.5
18.5
"•3
39-o
185
280
320
IOO
2.6
15-2
83.5
253
320
5-5
i8.s
18.5
35
is '.5
35
15-2
40
18.5
78
27 I
47-1
7.4.4.
IOS
[ 80
-J CO
ST. s
28 S
3II .O
.1,61.
244
378
280
29.2
TO 2
3II
g- v
75-4
•373
.186
248
747
....
.387
. 402
280
....
1,1 O
£f V
.-log
348
411
Aug. 12, 10 oo
25-7
24. Q
3-1
2 . I
75-6
26.0
• 325
. 114
8
2 .4
75
• 340
7, TO
6-4
I .Q
6-4
7^
26 i,
36 T
777
6s
14.8
4Q .O
28 4
'lO. S
.362
IQS
.176
245
3 3«
29-3
25-3
26 8
3I2
2.6
7 .4
75-7
25.2
25.8
•374
.320
7.4.0
248
5
IOS
80
.388
•334
. ^54
360
3-7
86.0
30
SO
27 S
48.1
7. CO
14.2
^6^
122
28 4
2
IO. S
.362
2O7
. ^7S
24S
2Q 7.
3II . S
-274
248
.787
7.2O
74. 1
"IT
A A -I
41 5
AS.T.
4.6O
OT- • o
4.2 8
6T3
55Q
A CQ
. S6s
460
4 30
Aug. 13, 10 oo
30.1
25-9
26 6
7i3
3-9
SS.7
76.2
25-5
24-3
.385
.326
-2-2C
340
18
S6
I'56'!
•398
•340
. ^4Q
460
13-3
79.O
13-3
2S
27 . 1
57. 2
. ^45
I O4
j
.^?S8
80.5
3 30
25-8
26 7
3-7
6 s
75-9
24-3
.326
-I-J2
16
78
1 80 ,
•340
. 147
"•3
S9-O
"•3
4S
26 7
7 .O
.778
96
j
. 1S2
74 -O
Aug- 14, 9 30
25-5
26.0
3-5
6.4
75-4
23-9
•324
. 331
H
7S
} 80!
•338
•345
9-5
56.5
20
56.5
3 15
27.0
25-7
26. 2
26 7
"7-5
4.0
5-8
57.4
75-2
24. 2
•344
•329
•334
. 341
H7
19
57
104
I 1
n
• 358
•341
•348
• 355
89.0
14.2
41 .0
86.0
IO
30
Aug. 15, 9 40
25-6
26 . I
4-i
S. 1
75-4
23-3
.326
• ^^^
20
45
I65!
•339
•346
15-2
31.0
18
30
26 Q
87 "5
• ^44
116
i i
•357
89.0
'we.
2 WTO.
4wp. 5gy'o.
'gy-
8gBP.
28 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE ii. — Time variation of the larger colloidal nucleation of dust-free wet air — Continued.
^-(JT-TT,)
TO0.33sX
dp
W0.34oX
io— a
Date, etc.
op.
S.
P-
t.
p-n
»Xio 3
io-3
p
nX io 4
7J0.34sX
io-3
Aug. 15, 3hoom
25-5
26.0
3-9
S Q
75-4
0
23.8
0.324
• 3"U
18
4S
1 70 !
0.338
. T.4S
13-3
4-1 o
20
4.7
26.9
87 T
. T.A7.
116
\ \
. 3S7
77 . S
Aug. 1 6, 9 oo
25-7
26.1
3-7
S. I
76.0
23.0
• 325
. 1,1,0
16
40
167 1
•338
• 1,41,
"•3
27. s
18
•3.1,
27. I
'7 n
• ^44
117
J [
• 3S7
74.O
3 oo
25.8
26 2
3-7
^ 1
75-8
23.5
• 327
-1-12
16
4S
65 1
•340
^4S
n-3
^1 O
"•3
ii
27 .O
8- 1
• 1,4.1,
117
J 1
.^S6
83. s
o*
Aug. 17, 9 oo
25-7
26.2
3-5
4..Q
76.3
23.2
•323
• 1,1,0
12
17
1 80!
•337
• ^4^
9-5
24.6
15
38
26.8
4 2
• •^8
IOO
i i
. 3SI
80. =5
12 OO
25-7
2S.9
3-o
4 8
76.2
23.6
•323
.326
7-5
34
1 90I
•337
. 24.0
5-5
2^ . S
23-5
4S
26.9
$ I
- T^Q
116
i i
-2^-2
80. S
Aug. 23, 4 oo
25-7
2S- 7
4.8
4 8
75-2
25.0
.326
. 1,26
34
T.A.
1 75 1
•342
• ^42
23.5
23. S
15
3S
26.0
S 7
• 1,1,1
=56
. i46
39.0
27 .O
o • /
86 8
• 1,44
117
j i
. ^S9
66. s
Aug. 24, 9 30
25-7
26.2
3-i
S 4
76.1
23.1
•324
• 1,1,1
8.2
48
1 75 !
.338
• 1,44
6.4
1,2. 7
15
3S
27.0
87 n
• 1,4-2
117
i i
. 7SS
74 -O
3 oo
25.7
26.2
26.8
4.0
5-3
87 1
76.2
24.0
•323
•330
• 338
18
46
116
I'M
•337
•344
• SS2
14.2
31.0
86.0
20
40
Aug. 25, 9 oo
25-7
26.0
3-3
A S
76.6
22.5
•323
• 7.27
10
27
1 70!
•335
• ^39
7-7
19. s
2O
40
26.9
4 8
1.1.0
88
I i
. ^SI
66. s
3 oo
25-7
26.0
3-0
4.. 7
76.4
23.5
•323
• 1,27
7-i
32
|6o|
.336
• 340
5-5
22. 2
20
38
27 .O
•6 7
• 341
88
1 1
• 3SS
64.0
Aug. 26, 9 oo
25-7
26.0
3-3
4-3
76.2
23-7
•323
• 327
10.5
21.
1 '°f
•337
• ^4i
7-7
17.5
15
33
27.0
106.9
. ^41
IO5
J 1
• ^S4
69. s
4 oo
25-7
26. 1
4.0
S . I
75-9
23.6
• 324
. 1,1,0
18
40
1 ?°l
•338
. ^44
14.2
27. s
78
30
Aug. 27, 9 oo
27.0
25-9
26.4.
>°6.7
o4'8
"6.8
75-3
23.7
• 342
• 330
.1,1,6
105
34
89
1 75 1
.356
•344
. ^so
64.0
23-5
66.5
18
30
26.8
87 6
. i>42
116
J 1
. S56
04.0
3 oo
25-9
26.0
u5-3
86 ?
75-J
23-8
• 331
• 1,1,2
44
67
J 70 r
•345
• S46
31
52
20
31
Aug. 28, 9 oo
27.0
25-9
26.4
"7.6
4-i
"fi T
75-&
23.5
•346
•329
.336
"7
21
66
J 1
60 r
.360
• 342
• ^49
94
15-2
49
10
3O
27 .0
87 3
. ^44
H7
J 1
• SS7
83.5
3 oo
25.7
26 . 1,
4-5
S.8
75-6
23.4
• 327
• T^S
27
58
65 1
•340
. u8
19-5
41 .0
19-5
71
27. 2
137 6
• i,47
117
J 1
. ^560
94.0
Aug. 29, 9 30
25-9
26. 2
4-3
S.4
75-9
23.3
.328
• 1,1,2
24
48
1 70 f
•341
• H5
17-5
32. 7
13
32. 7
26.8
U7.2
• ^4O
104
J 1
• SSS
80.5
Sept. 7, 10 oo
25-7
26.O
3-8
S- i,
75-6
22. O
.328
• 332
17
44
60 !
•34°
• H4
12.3
3i
12.3
3S
26.8
U7.i
• 342
101
i i
• ^54
77-5
8gBP. »we.
10
gyo.
1 wy.
VAPOR NUCLEAT1ON IN LAPSE OF TIME. 2Q
ii. — Time variation of the larger colloidal nucleation of dust-free wet air — Continued.
^-(TT-Tr,)
'?0.33sX
dp
W0.34()X
io-3
Date, etc.
op.
.9.
/>•
.
/>— 7T
rcXlO 3.
io-3
p
iXio 3.
W0 34 8 X
io-3
Sept. 7, 3h45m
25.6
26 3
4-i
136 6
75-3
o
22 .O
0.327
• 3^7
2O
qo
1 70 !
0.340
-MQ
15.2
61 5
15-2
/in
^7 O
87 6
. ^47
117
I {
^SQ
QA. O
q.\j
Sept. 8, 9 oo
«/ •«"•
25.7
26 3
4.1
S Q
75-6
22.0
.327
. 3^6
20
62
1 55 r
•340
348
15-2
47 o
15-2
to
27 O
8
7 2
• 345
IOS
j {
-5C7
80 s
ow
4 oo
25-7
26 3
4.1
S 7
75-5
22.0
.328
. ^6
19
cc
1 ^ 1
• 340
. 348
15-2
-JQ
15.2
28
26 7
U7 6
. "342
IO4
] }
-2C4
04
Sept. 9, 9 30
25.8
26 3
3-8
S 4
75-4
21 .0
•332
- 338
17
48
1 3° !
• 342
. T.ACI
12.3
T>2 . 7
8
20
26 7
87 1
-34.4.
116
I i
^54
86
3 oo
25-7
26 3
4-4
6 o
75-2
22.6
.328
• ^7
25
64
1 55 1
• 342
. ^50
18.5
46
13
to
27 2
87 1
-240
117
i i
162
86
Sept. 10, 9 oo
25-8
26 5
4-5
6 8
75-4
22.8
• 329
338
27
87
| 65 r
• 342
. ^51
19-5
66.5
10
-JC
27 O
87 4
-3J.S
117
j 1
358
86
2 30
25-9
26 1
4-8
96 6
75-5
23.2
•330
•JTC;
35
82
1 7° f
•343
348
23-5
61.5
IO
•36
•"•• • o
27 O
87 8
• 345
117
J {
• 358
IOO
Sept. n, 9 oo
25-7
26 t
3-0
C 2
76.2
22. O
•325
-2-21
7
A.2
I 55 r
•337
^4S
5-5
29
15
•2Q
*u • o
27 I
87 o
• ^44
ios
J (
.356
74
2 30
25-8
26 ^
3-5
S 8
76.2
22. 2
.326
T. -2C
12
CO
1 55 !
•339
. 348
9-5
41
13
-JO
Sept. 12, 9 15
27.1
25-7
26 3
u7-4
3-8
A O
76 '.i
22. O
•344
•325
-2-2-3
105
17
VJ
j i
1 50 !
-356
•338
. ^46
86
12.3
24.6
15
25
27 O
87 3
• ^4^
117
I i
• 355
83-5
2 30
25-7
26 7
3-6
6 o
76.0
22. 2
.326
IIA.
14
64
1 65 i
.338
. ^46
10.5
46.0
18
40
Sept. 13, 9 oo
27.0
25.8
26 I
'7.2
3-6
^ 2
75-8
22. 2
•343
• 328
^^2
105
M
4-2
i I
55 r
-355
•340
• 344
80.5
10.5
29
10.5
33
27 O
8y j
- ^44
ios
j 1
•356
77-5
3 4°
25-7
26 3
3-7
S .6
75-6
22. O
.327
.336
16
53
1 5°i
•340
•348
"•3
36.7
H-3
25
27 C
77 2
. 74. s
105
J 1
• 357
80.5
Sept. 14, 10 oo
2.5-7
26 7
4.0
S 8
75-7
22. 2
• 327
. 335
18
57
1 ^ I
• 339
•347
14.2
41
17
33
*u • O
27 r
8-7
. "145
IOS
J |
• 357
77-5
3 30
^ / . k>
25-7
26 •}
4.c
s 8
75-5
22.2
.326
. ^34
18
S7
|6o r
•339
.346
14.2
41
18
35
•*u • c
07 r
87
^44
IOS
J |
.356
77-5
Sept. 15, 9 30
- / • *-
25.?
26 1
2-7
A J
76.
22. C
•323
^1
6
25
1 55 i
•336
•343
4.1
18.5
13
30
^u . ^
27 r
136
• ^4O
93
J 1
•352
64
2 30
25.?
o(S "
2.C
A /j
76.
21 .C
.326
-2T-2
7
25
40 r
•336
•343
5-i
18.5
13
3°
•*u • »:
27 2
U7 4
- 345
ios
J |
•355
86
Sept. 1 6, 10 45
25-c
26 =
2.C
A
77. c
19.8
•327
. 335
7
32
I30!
•336
•344
5-i
22.2
13
3°
-1-1 • ._
26 c
96
• 34O
89
i i
•349
56.5
7gy. 8gBP.
' wy.
13 wo.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE n. — Time variation of the larger colloidal nucleation of dust-free wet air — Continued.
dp-(n-7tl)
W0.33sX
dp
W0 • 340 X
io-3
Date, etc.
op.
J-.
£•
1.
P-K
ny, io-3.
io-3
P
nX io 3.
"0.318X
io-3
Sept. 17, 4b45m
25.8
26 2
3-0
4 .O
76.8
0
20.0
0.326
. 112
7
18
1 ^ 1
0.336
• ^41
5-5
H. 2
12
IS
26 Q
86 8
-24.1
9?
J 1
• ^SO
66. s
9 oo
25-7
26 2
2.8
•3 4
76.6
20.5
.325
772
6
12
1 3° I
•335
• 142
4-6
8.7
8
20
27 O
D
97 2
742
IO7
• "?S2
80 s
26.6
S . 2
. -277
43
• 347
20
4 oo
26.O
27 . 1
83'4
7 4
76.2
21 .0
• 331
. 348
II
117
) " 1
•341
.358
8.7
86
3
io
26 8
"7 o
74.2
96
J (
. ^S2
74
Sept. 18, 9 oo
25-5
26 A
3-0
S S
76.1
21 .O
• 324
777
7
C T
1 40 f
•335
. 147
5-5
IS
18
T.O
27. I
107 1
. 746
ICK
I \
•156
81. S
Sept. 20, 9 oo
25-6
26.7
3-8
»c s
75-9
22.2
• 325
. ^4O
17
ci
} 50 !
•337
. 3S2
12.3
IS
15
2S
27 O
(')
7,44
lO1^
i i
.3^6
4 oo
25-7
26 6
4-i
n7 4
75-6
23.0
• 327
•5 -JO
19
08
1 70 !
•340
. 1S2
15.2
86 o
15
4S
27 .0
147.9
. 144
1 40
I i
. 3S7
IOO
Sept. 21, 9 oo
25.8
26.3
4-5
136 8
75-5
23-5
.328
. ^S
27
87
I85 i
•342
• 148
19-5
66. s
3
40
26 8
147 9
742
IAO
I i
.3S6
IOT,
2 45
26.0
26.3
4.8
137-4
75-6
23.0
• 331
. us
34
98
98 1
•344
.348
23-5
86
IO
18
27 . 2
«7 7
. 347
117
J 1
. 360
97
Sept. 22, 8 45
25-9
26 . i
3-5
S 2
76. 2
22. O
•327
•J-JQ
12
42
1 6° 1
-340
• 341
9-5
29
9-5
C?)
27 .O
(U)
74.2
04
f }
. m4
3 15
25-9
26 I
3-5
c i
76.0
22. 2
.328
771
13
AO
1 " 1
•340
. 141
9-5
27 =;
10
4O
27 .0
U7.7
. 747
OO
J 1
• 1SS
07 .O
•+>_>
Sept. 23, 10 30
25-9
26.3
4.8
136.8
75-5
22.3
•331
.336
34
98
) SS {
•343
.348
23-5
66. s
IO
4O
27 O
87 c
7.J.6
I T 7
I \
1SS
89 o
5 oo
25-7
26 . 2
4.6
6 i
75-4
23
.327
7.7.4
29
66
} 70!
•340
. 147
20. 7
4Q
25
4O
26 8
86 o
7.47
1 04
I i
. 1SS
60 S
Sept. 24, 9 oo
25.8
26 4.
2.8
C I
76.3
21
• 327
316
6
40
1 35 1
•338
. 7,46
4-6
27 S
IO
2^
27 I
86 8
74S
IOS
I i
7 SS
66 s
3 oo
25.8
26 ^
3-5
A Q
76.3
20.8
.327
77.4
12
-27
43 f
•338
74 s
9-5
">A. 6
13
24 6
27 .O
H7.o
. T.44
9Q
j 1
. ^S4
74
Sept. 25, 9 oo
25-9
26. ^
2-4
4 2
77.1
19.6
.326
. ^2
3
22
1 ^ i
• 336
. ^41
3-0
16 i
15
AO
27 O
96 8
741
89
J 1
^so
66 s
T"
2 45
25-7
26 i
2-7
A A
77.0
19
• 325
777
6
2^
i 4° f
•334
742
4-i
18 s
15
IO
27 O
"* 5
742
82
J {
7 SI
SO O
,)v-'
Sept. 26, 8 40
25-9
26 . ^
2-5
-j.9
76-9
18.2
•329
• 114
4
17
1 2°{
•337
• 142
3-3
H-1
10
IO
27 O
." -*
"6.7
. 141
8s
j 1
. 1SI
64.0
2 50
25-7
26 T,
2-3
4. 2
76.7
20. 0
•325
T.T.T.
3
22
30
•335
. 143
2.6
16.1
12
21
27 ^
•6 1
T.A-J
7 S
J 1
.1^6
S6 s
'gy-
8gBP. swe.
Jgy o.
11 wy.
'wo.
14 wBrcor.
VAPOR NUCLEATION IN LAPSE OF TIME. 31
TABLE n. — Time variation of the larger colloidal nucleation of dust-free wet air — Continued.
»i.
^-(JT-TT.)
Jfu.3.isX
8P
W0.34oX
io-3
Date, etc.
op.
5.
>•
t.
P-7C
ny, 10 3.
io-3
P
«Xio 3.
wo.3.;sX
io-3
Sept. 27, 8h45m
25-9
26. 1
3-4
5-O
76.4
0
19.0
0.330
. 11$
1 1
1.8
1 40 f
0-339
7J.A
8-7
26 o
10
7O
27. I
137 i
746
OO
J {
7 ^ ^
77 ";
Ou
3 15
25-6
26.4
3-o
5- 2
76.3
19.5
.325
.336
7
42
1 4° i
•335
14.6
/ / • o
5-5
29 o
15
2^
26.8
7 • ^
742
116
J 1
1^1
8l 5
^0
Sept. 28, 9 oo
25-8
26.7
2.6
5.0
76.8
19.0
• 327
. 11Q
5
38
I ,5 f
•336
^48
uo • j
3-7
26 o
IO
20
27. I
96 6
. 144
8^
j 1
-i f-i
6l 5
3 15
25-7
26.6
3-0
"V 3
76.7
19-5
.325
. 117
7
45
] 40 f
•335
747
5-5
T. 1 O
15
25
27.O
96 6
-1AT.
82
j |
1^2
61 5
Sept. 29, 8 45
25-7
26. 2
2-7
-1 s
76.7
19. 2
.326
. ^"^^
6
•14
1 45 f
•335
-142
4.1
27 S
15
•1C
27.O
13- T
-I4.-2
no
J I
1^2
77 c
5 oo
25-7
26.6
3-2
5 • S
76.3
18.8
.328
^4O
9
ci
1 35 !
•337
14-Q
6.8
T C O
15
25
27.O
ii? T
. ^4S
no
i i
. 1^4.
77. 5
Sept. 30, 10 10
26.0
26.6
4.6
"6 6
75-8
19.0
•334
. 142
30
81
1 35 1
•343
.751
20.7
6l.5
IO
T,O
27.O
87 5
•
'US
117
i i
. 156
89 o
4 oo
25-7
26.6
3-6
136 8
75-9
19. 2
•330
742
14
9Q
J 45 f
•339
. l^i
10.5
66.5
15
4O
27 .O
77 1
^47
IO5
J 1
1^6
86 o
Oct. i, 9 45
25-7
26. 5
3-i
1 6
76.4
16.8
• 329
^40
8
10
! 20I
.336
. 7J.7
6.4
2O. 7
IO
20
27.0
U7 1
-24.7
no
i i
. "2.S4
86.0
3 oo
25-8
26.3
3-o
S.o
76.2
17.2
• 331
.118
7
17
i 25 f
•339
. ?4S
5-5
26.0
10
26
27 . 2
87 .0
T. SO
101
f i
. 157
74. 0
Oct. 2, 9 oo
25-7
25-9
2-3
T. . I
76.1
17.0
•331
-2-2-2
3
8
1 20!
•338
. ^4O
2.6
6.4
6.4
28
26.7
96 3
^44
71
i i
. -2^1
54- S
3 oo
26.0
26.5
4.4
5 • 7
75-9
iS.o
•335
. ^41
25
55
1 =5 f
•343
. 740
18.5
19-O
10
25
27 I
77 1
7 CQ
IO5
| 1
. ^S7
86.0
Oct. 3, 8 45
25-7
26.3
3-3
5- 1
76.0
18.5
• 329
. 117
10
4?
1 40 f
• 338
. 746
7-7
1i .0
13
28
27 .O
137. i
• 14-6
IOO
J 1
. 355
77- 5
3 oo
25-7
26.4
3-7
"6 8
76.0
20.5
• 327
• 117
16
87
60 f
•338
• 347
n-3
66.5
20
53
27 .O
77 «
. 145
ios
J i
• 355
IOO.O
Oct. 4,* 9 15
25-7
26. S
3-8
S- 5
76.1
20.5
•327
.11&
17
51
1 40 f
•338
• 348
12.3
35-0
15
28
26 o
137-3
. T.A.T.
IOI
J 1
• 1^1
83.5
3 oo
25-9
26 1
3-7
S .4
75-9
21 .O
•330
• 1l6
16
48
45 f
•341
• 347
ii -3
32.7
IO
25
27 7
158.o
•2XQ
I4O
J [
.360
108.
Oct. 5, o oo
25-7
26 6
3-5
"6.8
20.8
75-6
•329
. 741
12
93
J 50 1
•340
.352
9-5
66.5
9-5
3°
27 I
'7 8
. 148
140
J 1
•359
IOO
3 20
25.7
26 2
4.2
5 8
75-4
21 .O
• 330
. 117
21
S9
,40 f
•341
•348
16.3
41 .0
IO
3°
27 O
Q
7 ^
. 348
117
J 1
• 358
83-5
1 we.
'gy-
8gBP. »we.
1 wy.
13 wo.
15wPcor.
*Room heated hereafter.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE u. — Time variation of the larger colloidal nucleation of dust-free wet air — Continued.
£/>-(«:-»,)
"0.33..X
dP
W0.34flX
io-3
Date, etc.
op.
S.
/>•
t.
p-x
wX io 3.
io-3
P
wX io 3.
"o.34sX
io-3
Oct. 6, 9b0om
25-7
26 4.
4.6
136 7
75-1
O
20.5
0.331
7.4.1
29
92
1 5° (
0.342
• "?S2
20.7
64.0
10
7.S
26.8
"7-7
• 1,4-7
104
j 1
• 357
97.0
4 30
25-7
26. T,
4-9
I37.o
74-3
21 .O
•335
7, 4.7
36
97
1 35 I
•346
• ^S4
24.6
74-O
(?)
20
27 .O
^.O
• "^S3
175
j 1
• 363
152
Oct. 7, 9 30
25-8
26.1
4-9
136.6
74-9
21 .O
•334
.1,1,8
36
88
1 4°i
•344
• 348
24.6
61.5
(?)
30
27 .O
87 A
• ^so
H7
j 1
. T,6o
86.0
4 oo
25-9
26 T.
4-9
136 8
75-i
20.0
•335
7.41
36
87
1 " (
•345
. T.SO
24.6
66. s
(?)
2S
27. O
87 ,,
• ^SO
ill
\ 1
. ^60
80.5
Oct. 8, 9 oo
25-9
26. 7
3-0
A. 4
76.3
18.8
•331
W6
7
25
1 2°{
•339
- ^45
5-5
18.5
9
20
26 .9
96 f
744
65
\ (
• ^S3
49 -O
3 oo
26.0
26.7
3-5
6.1
76.4
21-5
•329
.1,1,8
12
66
1 45 f
•340
• ^49
9-5
49 .0
9-5
1,0
27 . 7
U7- S
•246
I 12
j 1
• ^S7
89.0
Oct. 9, 8 45
25-8
26 T,
3-8
S I
76.0
20.0
•330
777
17
4O
" {
•339
. ^46
12.3
27. S
13
25
26.9
6.8
• 14S
89
j 1
• ^S4
66.5
3 oo
25-7
26. T.
3-6
85 9
75-6
21 .O
•329
777
14
62
1 4S !
•340
• US
10.5
4S-O
IO
30
27 .0
'6.9
747
94
I i
• ^S7
69. S
Oct. 10, 9 oo
25-9
26.6
4-9
U7.S
75-2
19.8
•335
7.44
39
IOT,
1 40
•344
. 7.S4
24.6
89.0
(?)
30
26.2
96 7
770
71
• S48
S4- 5
27 O
87 2
7. SO
117
. 7 SO
80. S
3 30
25-9
26. T,
4-9
96 6
75-o
2O. O
.336
- T.42
36
82
1 30 1
•345
. 7.SI
24.6
61.5
(?)
2S
27.O
168.2
. ^SI
140
j 1
. ^60
117
Oct. ii, 9 15
25-7
26 .4
3-7
5 8
75-3
18.0
•333
-24-2
16
•59
25 1
•341
. 7^1
"•3
41 .0
7
20
27 O
U6 9
T.SI
IO2
j {
• T.S9
69. S
3 30
25-9
26 . T,
4-9
"6 ^
75-3
21 .O
• 330
. 770
36
74
45 f
•344
• ^49
24.6
56.5
(?)
30
27 .O
86.9
•34.8
OS
j
• SS9
69. S
Oct. 12, 8 45
26.0
26. 9
3-6
S. 2
76.6
I9.O
•331
7.47
15
47
1 3°{
•339
• T.SI
10.5
29.0
IO
20
27.4
87 1
740
118
1
•3^8
83.5
3 oo
26.1
26.6
3-8
c; i
76.6
I7.6
•334
-24O
17
4.0
\ "I
•341
. ^47
12.3
27. s
8
20
27 .O
S 8
•146
60
J (
7,S"?
41 .O
Oct. 13, 9 oo
26.0
26.4
2.3
4.6
77-4
18.0
.328
• ^^
3
30
1 30 f
.336
. ^41
2.6
20. 7
15
2S
27 .0
S . I
T.AI
46
J 1
. 74Q
1,1 .0
6 30
25-8
26.6
2.8
4. ^
77-3
20. o
• 324
77.S
6
28
1 30 f
•334
- ^44
4-6
19. s
13
2S
27 . I
6 7
7.4.1
8s
J 1
. -2CI
64.O
Oct. 14, 9 15
25-7
26.4
3-0
A. 7
77.1
20. o
•324
. 777
7
~12
1 40 1
•333
• 342
5-5
22. 2
15
28
27 . 2
6 2
. 74.4.
69
f 1
• 3S3
S2.O
Oct. 15, 9 oo
25-9
26. S
3-0
S O
76.7
20.4
•327
77.S
7
78
I 40 f
•338
• 346
5-5
26.0
IO
2T,
27 2
6 7
74.1;
8s
J 1
. 7SS
64.0
'we.
'gy-
8gBP. "we.
1 wy.
13 wo.
16wP.
EFFECT OF BAROMETER, TEMPERATURE, AND IONIZATION. 33
16. Effect of the barometer. — If we look more specifically at
the new data beginning with August 10, coincidences of minima and
maxima of the nucleation with maxima and minima of the barometric
pressure occur only on August 13, 25, and 27, and these are not pro-
nounced. In September there is no detailed similarity until September
1 6, but both curves have dropped somewhat toward the marked mini-
mum. After September 20, however, the apparent agreement of curves
is conspicuous up to September 24 and would be decisive if the run of
temperature were not similar. During the remainder of the month
there is no agreement— rather an opposition — and the two curves are
remarkably at variance during the unusually low barometer in the early
part of October. The peak of the barometric curves from October 4
to 8 has nothing to suggest it in the nucleation curve. We may conclude,
therefore, that a direct barometric effect is absent, that such coincidences
as seem to occur are referable to other causes, and that the method
used for the elimination of barometer discrepancies is to the same degree
vouched for.
17. Effect of temperature. — Throughout all of the observations the
tendency of temperature of the fog chamber to rise from morning to
afternoon is most probably to be regarded as the cause of a similar
tendency in the nucleation. There are exceptions, most of which, how-
ever, may be explained away. The curves show a similar general march
from August 10 to 23 and from here to August 29. From September
7 to 1 8 there is much detailed agreement, as, for instance, on September
8 to 10 and 15 to 16. The same is true after September 20, where markedly
coincident variation occurs.
So in October the agreement of curves is apt to be very close, as, for
instance, the effect from September 30 to October 3, the general fall
thereafter, and the effect from October 7 to October 9. All of this will
appear more strikingly when the observations are averaged for several
consecutive days, and most of the lack of synchronism is doubtless due
to the difficulty of finding the true value of nucleation.
18. Effect of ionization.— To find whether there is any relation of
the change of nucleation in the fog chamber in the lapse of time with a
state of ionization of the atmosphere, measurements were made of the
latter quantity by Miss L. B. Joslin, using Ebert's aspirator apparatus.
The data are given in table 12, where V denotes the fall of potential during
the fiducial time of aspiration (about 10 minutes), Q the charge per cubic
centimeter, and n the corresponding number of ions per cubic centimeter.
These data are constructed in the lower curves of fig. 9, together
with the cotemporaneous nucleations and temperatures of the fog cham-
ber, on a somewhat larger scale than heretofore. It would be difficult to
34 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 12. — lonization of the atmosphere in the lapse of time — Ebert's apparatus.
Date.
Time.
V.
Q.
«Xio-3.
Date.
Time.
V.
Q.
nXio~3.
Sept. 14
u.3h
9-3
+ 0.53
I.56
Sept. 29
10. Oh
6-7
+ 0.38
I . 12
8.2
•47
1.38
9-2
• 52
i-53
3-5
10.8
+ .61
1.76
Oct. i
IO.O
7-5
+ -43
1.26
12.6
•7i
2.01
8.9
- -5i
1.50
Sept. 15
10.4
8-3
+ -47
I .40
3-5
6.2
+ -35
1.05
IO. I
- -58
I.7I
4.8
- -27
•79
3-5
9-9
+ 5-6
1.65
Oct. 2
IO.O
6.5
+ -37
i .09
7-i
.40
1.18
9-6
- -55
1.62
Sept. 17
II .0
9.6
+ -55
1.62
3-5
i . i
+ .06
•19
9-4
•54
i-59
7.2
•4i
I .20
3-7
6.8
+ -39
1.14
Oct. 3
10.5
8-3
+ -47
I .40
7-7
•44
1.29
2.3
- -13
•38
Sept. 1 8
10.5
3-6
+ . 20
.60
3-0
7-7
+ -44
I . 29
3-9
— . 22
•65
7-i
- .40
1.18
3-5
4-5
+ -25
.76
Oct. 4
3-5
7-3
+ -42
I . 21
3-i
.18
•52
2.8
- .16
•47
Sept. 19
IO.O
7-5
+ -43
1.26
Oct. 5
10.3
6-7
+ .38
I . 12
7-7
•44
1.29
7-8
- -45
1.32
4.0
7-3
+ .42
I . 21
Oct. 6
10.5
4-5
+ .26
•76
2-4
•14
.41
2.8
- .16
•47
Sept. 20
10.3
5-6
+ -32
•94
Oct. 8
IO.O
14.0
+ .80
2-35
3-7
. 21
•63
10.6
- .60
1.78
3-5
7-i
+ .40
1.18
3-5
7-6
+ -43
1-25
5-i
.29
•85
5-3
- -30
.88
Sept. 21
IO.O
6.0
+ -34
i .00
Oct. 9
IO.O
3-7
+ .21
•63
6-9
- -39
1.14
4.2
•24
.70
3-o
5-6
+ -32
•94
3-o
4.0
+ . 22
.66
8.6
•49
1.44
1.8
. 10
•3i
Sept. 22
IO.O
5-0
+ .29
•85
Oct. 10
IO.O
7-8
+ -44
1.30
14.9
•85
2.50
3-3
- -19
•56
3-o
6-5
+ -37
i .09
3-5
7-5
+ -43
1.26
6-9
- -39
1.14
4.8
- -27
•79
Sept. 25
12.5
7.8
+ -45
1.32
Oct. 1 1
10.3
7-8
+ -45
1.32
5-8
- -33
•97
4-7
- -27
•79
3-5
3-9
+ . 22
•65
3-5
7-i
+ .40
1.18
1.8
. IO
•3i
2-5
.14
.41
Sept. 26
IO.O
8.9
+ -51
1.50
Oct. 12
3-5
5-9
+ -34
I .00
7-i
.40
1.18
7.0
.40
1.17
4-o
3-6
+ . 2O
.60
Oct. 13
"•5
6.7
+ -38
I . 12
6.0
•34
I. 00
"•3
• 65
I.9I
Sept. 27
IO.O
5-9
+ -34
I .00
3-5
4.6
+ .26
.76
•3 6
— . 20
.60
o • u
3-5
5-6
+ "32
•94
Oct. 15
IO. 2
8-3
+ ^47
I .40
2.8
.16
•47
2-3
•13
•38
Sept. 28
3-5
3-9
+ . 22
•65
3-5
10.4
+ -59
i-74
5-6
~ -32
•94
2.4
.14
.41
detect any detailed similarity in the two sets of results. Thus the maxi-
mum of nucleation on September 20 to 24 is in no way suggested by the
ionization. Both curves tend to descend toward the end of the month,
but this may be due to causes to which both are tributary. As such an
effect will appear again in the average results, it may be dismissed here.
Fig. 9 also contains the nucleations nosi5 for 0^/^ = 0.345 for com-
parison. Remarks may be made with reference to them similar to those
just stated. The enlarged scale admits of an easier comparison of
n0 335 and n0 345, which hold for different hypotheses.
EFFECT OF IONIZATION.
35
36 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
19. Mean results. — The most satisfactory criterion of the variation of
nucleation in the lapse of time would perhaps have been the slope of the
n lines as given by the three observations in terms of the abscissa,
x=(3p — [n — 7Ti])/(/> — ?r); but as these points lie on a graph whose
curvature is often marked, the curvature would in general be hard to
estimate and the ordinate «0.335 f°r :V = 0-335 ^as therefore been pre-
ferred and is summarized in table 13.
TABLE 13. — Summary of table 9. Observations a. m. and p. m.
>-TT) = 0.335.
Date.
Tem-
pera-
ture.
W0-33sX
io-3.
Date.
Tem-
pera-
ture.
«B.3»X
IO~3.
Date.
Tem-
pera-
ture.
W0-33sX
io-3.
o
o
o
Aug. 10
26
90
Aug. 25
22
70
Sept. 12
22
50
28
105
23
60
22
65
1 1
26
70
26
24
70
i3
22
55
26
70
24
70
22
50
12
26
75
27
24
75
H
22
55
26
80
24
70
22
60
13
24
56
28
24
60
i5
22
55
24
80
24
65
21
40
14
24
80
29
23
70
16
20
30
24
60
Sept. 7
22
60
20
45
15
23
65
22
70
i7
21
30
24
70
8
22
55
21
37
16
23
67
22
55
18
21
40
24
65
9
21
30
20
22
50
i?
23
80
23
55
23
70
24
90
10
23
65
21
23
85
23
25
75
23
70
23
98
24
23
75
n
22
55
24
95
22
55
The endeavor may be made to test the value of «0-335 for longer inter-
vals of time. As the series is often interrupted, 2-day to 4-day intervals
for the present suggest themselves. Consequently, if the data of table
13 (which is a summary of table n) be so compared, the values given in
table 14 appear.
If the results of table 13 be further corrected for dependence of the
precipitation on the changes of temperature of the fog chamber, data
given in an earlier report* and elsewhere are available.
At dp = 22 cm. the amount of water precipitated per cubic centi-
meter is at
/= 10° 20° 30°
wXio"= 4.2 5.5 6.7
Hence on the average the correction may be taken as — —^ -==2.3 per
5-5 X 20
cent of the values of m at 20° C.
*Smithsonian Contributions No. 1651, p. 135, 1905.
MEAN RESULTS.
37
Since n = 6ms3/xa3 approximately (where a is the optical constant
of coronas and 5 their angular diameter on a radius of 30 cm.) for a
given s, n varies as m. Therefore n must be increased to 2 .3 per cent
of its value per degree of temperature of the fog chamber above 20°
C. In this way the corrected data of table 14 were found.
TABLE 14. — Nucleations (averaged in groups of 2 to 4 days) in the lapse of time.
o-3 at dp/p = o.345,1 and at 8p-(n-7t1)/(p-n)=o.^5.
Date.
Tem-
pera-
ture.
Barom-
eter.
n0.335.
Cor-
rected
n0.33S.
n0.345.
Cor-
rected
^0-345.
lonization.
+ n.
— n.
°C.
cm.
Aug. 10-13
25-8
75-7i
77,000
87,OOO
37,600
43,ooo
• ...
14-17
23.8
7S- 71
72,000
78,OOO
^S.OOO
4.1,000
T^ /
23-26
\J
23.6
t \J I
76.07
/ i
73,000
79,000
%J t
35,900
~ J 7
39,100
27-29
23.8
75-50
68,000
74,000
31,400
34,400
Sept. 7-10
22.3
75-44
57,000
60,000
31,600
33,400
....
ii— i •?
22 .O
75.98
S6,ooo
S9,ooo
•*o, soo
32,000
o
14-16
21 . 2
t \j y
76.47
\J t
47,000
\J ./ 1
49,000
«J t \J
32,200
O )
33,200
1600
1570
17-20
21 .6
76.08
45,000
47,000
30,000
31,200
1090
900
21-23
22.5
75-72
75,000
79,000
40,000
42,500
970
1550
24-27
19.6
76.63
37,000
37,000
28,500
28,200
IOOO
790
28-30
I9.O
76-37
37,000
37,ooo
29,200
28,500
885
1230
Oct. i- 3
18.0
76. 10
32,000
30,000
25,40°
24,100
1040
I IIO
4- 5
20.8
75.75
44,000
45,000
28,300
28,900
1167
395
6- 7
20.6
74-85
40,000
41,000
27,500
27,900
760
470
8- 9
20.3
76.08
36,000
36,000
26,300
26,500
1 2 2O
920
IO-I I
19.7
75-17
35,ooo
35,ooo
26,300
25,100
I26O
640
12-13
18.7
76.97
27,000
27,000
22,500
21,800
960
I 2 2O
i4-J5
20. 2
76.90
40,000
40,000
25,500
25,600
1570
4OO
1 These will be considered in section 20.
Table 14 also contains the data for the corresponding averages of
temperature, barometric pressure, and ionization, and all data have
been further given in the graphs fig. 10, with the times (abscissas) laid
off on a smaller scale to bring out the relative variations. It is again
apparent that no relation of the nucleation curve to the barometer
curve or to the ionization curve can be made out. On the other hand,
the vapor nucleations of the dust-free wet air in the fog chamber agree
very fully with the cotemporaneous variations of the temperature of
the fog chamber (not of the temperature of the atmospheric air without,
of which they are also independent). It is even possible to make out
the rate at which nuclei are produced when the temperature of the fog
chamber increases. Taking the mean trend of both curves (nuclei and
temperature), it appears that nearly 8000 colloidal nuclei are generated
(apparently) in dust-free wet air, by a rise of temperature of i° C.
20. Nucleations depending upon dp /p. — In the above experiments
the nucleations were compared at a fixed value, 0.335, of the variable
[n— Ti^)l (p—Tc}. If, however, the corresponding value of the
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
relative drop dp/p (which assumes that all the water vapor is expanded
adiabatically without condensation) be computed, the latter will vary
with temperature in a way correlative with the vapor pressures con-
tained in the former. The nucleations computed for this particular
series of values of dp/p will also vary, and the rate was found to be about
6000 nuclei per degree. This is so near the temperature effect given
in section 19 that there must be a common cause underlying both.
FIG. 10. — Vapor nucleation of dust-free air, temperature of fog chamber, barometric
pressure, and positive and negative ionization (the former with small circles) in
lapse of time, averaged for period two to four days.
Hence in table n, n was also computed in its dependence on dp/p,
and advantage was additionally taken of the new values of n given in
Chapter III for the higher coronas. Two fiducial values of the variable
dp Ip were tested; the former, dp/p = o.T,4o, being, as a rule, too small,
the latter, dp/p = o.34$, was selected. The tables contain both of the
corresponding values of nucleation, n0 340 and w0345; but the last only
has been given on the charts (figs. 8, 9, and 10). The other does not
differ essentially from it. All values are summarized in succession in
table 15.
NUCLEATIONS DEPENDING ON RELATIVE DROP IN PRESSURE. 39
Fig. 8 contains an extended comparison of the old curve for w0 335 and
the new curve for w0 345, under the conditions which are given. In their
narrower variations the two curves are similar and the details already
specified for n0 335 need not therefore be repeated for n0 345. Pronounced
maxima and minima will in particular be found coincident.
The same will be observed in the case of fig. 9, where a larger scale is
introduced for n0 335. The question of greatest interest is now the com-
parison of mean data such as are given in table 14 in the lapse of time.
The data for n0 345 have been corrected for the effect of temperature
/, on the amount of water precipitated, by taking from the recent results
referred to the temperature coefficients dn/ndt, example of the values
for different relative drops being
§P/p= o.i 0.2 0.3 0.4 0.5
io3dn/ndt= 14 18 23 27 30
These data would not, however, seriously modify the trend of the
curves.
The graph (fig. 10), which also contains these nucleations, shows that
the effect of temperature in the lapse of time has not been eliminated
by replacing the extreme variable (dp — [TT — ^i]) / (p — rc) by the other
extreme variable dp/p. In other words, if the nucleation corresponding
to a fixed exhaustion op/p = 0.345 is studied in the lapse of time, the
successive nucleations* show a dependence on the temperature of the
fog chamber which can no longer be explained away. Both the details
and the general character of the graphs for n0 345 follow the fluctuations
of temperature to an extent which may be estimated from the figure as
an increment of about 2000 nuclei per rise of temperature of i° C. at
about 20° C. and for op/p = o. 345. Finally, there is no adequate reason
why the effect of cooling below a higher surrounding temperature should
be more efficient than the corresponding effect below a slightly lower
temperature ; for the rate of reheating would depend on the difference
of temperatures.
21. Possible suggestions as to the temperature effect. — To obtain a
suggestion as to the reason of the apparent increase of the size of col-
loidal nuclei with rise of temperature (cat. par.} effectively, therefore,
of their apparent increase in number at a given supersaturation, it
is expedient to recall the form of Helmholtz's modification of Kelvin's
vapor-pressure equation. If the ratio r of pressures at a convex surface
r and at a plane surface be pr/Pm, R the gas constant of water vapor,
$ its absolute temperature, s the density, and T the surface tension of
the liquid,
*American Journal, xxm, i9°7» IO. P- 2O9-
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 15. — Corresponding to table n, but containing nucleations for dp/p = 0.340
and df>/p = 0.345.
Date.
Tem-
perature
nO. 340 X
io-3.
W0'3«X
io-3.
Date.
Tem-
perature
M0.34flX
io-3.
TC0.34sX
io-3.
Aug. 10
26
18.5
35
Sept. 20
22. 2
15
25
28
18.5
35
23.0
15
45
ii
25-8
15-2
40
21
23-5
3(?)
40
26
18.5
38
23.0
10
38
12
26
6.4
33
22
22.0
9-5
25-8
30
50
22. 2
IO
40
13
24-3
13-3
25
23
22.3
10?
40
24-3
"•3
45
23.0
25
40
H
23-9
20
56
24
21
IO
25
24. 2
IO
30
20.8
13
25
i5
23-3
18
30
25
19.6
15
40
23.8
20
43
I9.O
15
30
16
23.0
18
33
26
18.2
IO
30
23-5
"•3
3i
20.0
12
23
17
23.2
15
38
27
I9.O
IO
30
23.6
23-5
45
19-5
15
25
23
25.0
15
35
28
19.0
10
20
24
23.1
15
35
19-5
15
25
24.0
20
40
29
19.2
15
35
25
22.5
20
40
18.8
15
25
23-5
20
38
30
19.0
IO
30
26
23-7
15
33
19.2
15
40
23.6
18
30
Oct. i
16.8
10
20
27
23-7
18
30
17.2
IO
26
23-8
20
3i
2
17.0
6.4
28
28
23-5
10?
30
18.0
IO
25
23-4
i9-5
33
3
18.5
13
28
29
23-3
13
33
20.5
20
53
Sept. 7
22. O
12.3
35
4
20.5
15
28
22. O
15-2
40
21 .0
IO
25
8
22. 0
15-2
30
5
20.8
9.5
30
22. 0
15-2
28
21 .O
IO
30
9
21 .O
8
20
6
20.5
IO
35
22.6
13
30
21 .O
....
20
10
22.8
IO
35
7
21 .O
....
30
23.2
10
35
2O. O
25
ii
22.0
15
30
8
18.8
8
20
22. 2
13
30
21-5
9-5
30
12
22. O
15
25
9
20. o
13
25
22. 2
18
40
21 .O
IO
30
13
22.2
10.5
33
22. 0
"•3
25
10
19.8
....
30
20.0
....
25
14
22. 2
17
33
ii
18.0
7
2O
22. 2
18
35
21 .O
30
15
22. 0
13
30
21 .O
13
30
12
19.0
10
20
16
19.8
13
30
I7.6
8
20
2O. O
12
35
13
18.0
15
25
20. o
13
25
17
20.5
8
20
21 .O
3
30
H
20. o
15
28
18
21 .O
18
. 30
15
20.4
IO
23
TEMPERATURE EFFECT CONCLUSION. 41
whence it appears that the increment of $ and R may replace each
other.
A small radius at a high temperature is as effective as a larger radius
at a low temperature #, and that is substantially what the above data
have brought out. Naturally the equation has been pushed beyond its
limits, for the meaning of T for particles not large as compared with
molecular dimensions is obscure; but it appears in other cases and is
probably true here that the suggestions of the equation are trustworthy
in a general way. Computing
by the aid of the adiabatic equation we may write ioV = i9.5/??1log10
(Pr/PaJ where Iog10 pr/P(X = o.8, and $1r = 2/io5, nearly. But ^ = 262°
if the gas is originally at temperature t — 2o°, whence r = y5/io9. Since
dr/r= —ddi/$lt an increment of the radius of but 0.038 under the
given conditions is equivalent to a rise of temperature of i° C. of the air
within the fog chamber or to 2000 more available nuclei, according to
the above figure.
22. Another suggestion. — The increment of about 2000 nuclei per
degree of temperature under the conditions given may also be looked
on as a parallel to what occurs in case of a radiant field like that pro-
duced by the X-rays. One may regard ionization as a state of dissocia-
tion sufficiently advanced to set free electrons and from this point of
view equivalent to a very high degree of temperature. One may thus
expect a passage of the vapor nuclei of wet dust-free air into the ions
through a continuous gradation of nuclei, and may note that vapor
nuclei and ions always occur together. True, the latter have been
associated with the radiation penetrating the atmosphere, with good
reason, but the possibility of a collateral cause of the ionization within
the fog chamber may nevertheless be entertained.
23. Conclusion. — It is shown by direct observation that the number of
nuclei caught in dust-free wet air at low barometer pressure is greatly in
excess of the number caught (cast, par.) at high barometer. This result may
be accounted for as a necessary consequence of the thermo-dynamics of
the experiment, however large and unexpected the variations appear.
The comparison of the nucleation of dust-free air with the cotempo-
raneous changes of atmospheric ionization shows no correspondence
whatever. This is curious, because the ions, though much fewer in
number, are larger in size than even the larger colloidal nuclei, and
therefore capture much of the moisture at low exhaustion. One must
conclude that the variations of the ionization are not sufficient to be
detected in the presence of the other nucleation.
42 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
For the same reason would it be unwarrantable to look for effects
due to variations of any external radiations. In other words, it is
improbable that Wood and Campbell's phenomena can be detected by the
fog chamber, and the results which seemed at first in accord with it
are due to a rise of temperature. The results show that dp/p is a suitable
variable for the comparisons of nucleations in a plug-cock fog chamber
like the above.
Finally the temperature conditions within the fog chamber produce
a very definite effect, amounting to an increase (cceteris par-ibus) of
about 2000 available vapor nuclei per degree centigrade near 20° and
the given exhaustion £/> 7^ = 0.345 or v1/v = i . 35. Estimating the average
number of efficient nuclei present at 25,000, this amounts to an incre-
ment of about 8 per cent per degree. Anomalous as it may seem that
rise of temperature should increase the number of efficient nuclei (ccet.
par.}, probably by increasing their size throughout, nothing has been
suggested to explain this result away. Virtually the same thing is done
by radiation, though in much more marked degree than by temperature,
so that one might regard ionization as a state of dissociation sufficiently
advanced to set free corpuscles, or equivalent to a high degree of
temperature. One might therefore expect a passage of the vapor nuclei
of wet dust-free air into the ions, through a continuous gradation of
nuclei; and in fact (granting that other valid explanations for the
occurrence of ions have been given) , they always occur together.
The present and a variety of other results made it necessary to re-
standardize the coronas in terms of the number of nuclei represented,
and the work will be given in the next chapter. Some of these data
have already been utilized in the above.
CHAPTER III.
THE NUCLEATION CONSTANTS OF CORONAS.
RESULTS WITH A SINGLE SOURCE OF LIGHT.
24. Introduction. — At this point it seemed essential to restandardize
the coronas in terms of the numbers of nuclei represented by a given
angular aperture and type of corona at a given exhaustion and tem-
perature. The measurements* carried out for this purpose in my
earlier memoirs were made under very different conditions; and though
reductions to the present results are feasible in a measure, it will ob-
viously be preferable to repeat the work anew. This is particularly
the case because the corrections referred to are liable to be large and
because the results in the following chapters will essentially depend
on the number of fog particles per cubic centimeter. This datum will
here as elsewhere be called the nucleation, and in dust-free wet air the
types of nuclei present will be the ions and the vapor nuclei only. These
will, as a rule, be inefficient in the presence of phosphorus nuclei.
25. Apparatus and methods. — The apparatus used is the same as
heretofore described in the Carnegie Institution of Washington Publica-
tion No. 62, p. 74, and is shown in fig. n. It consists of a large vacuum
chamber V connected with the relatively small fog chamber F, the
volume ratio being about v/V = o.o6. The latter was cylindrical in
form, with its long axis horizontal, so as to admit of the measurement of
coronas of large aperture. This angle may exceed 60° in the extreme
cases and there must be some depth (exceeding 5 inches) if the coronas
are to be sufficiently intense. The need of large fog chambers is there-
fore apparent and the plug-cock fog chamber seems to be the only
apparatus adapted to the present purposes.
The connecting pipe was about 18 inches long, 2 inches in diameter,
and the stopcock 2 inches in bore. Phosphorus nuclei wrere used. To
guard against subsidence and undersaturation, the cloth lining of the
fog chamber was fitted close to the walls and but two opposite narrow
horizontal strips were left open for the observation of coronas.
The method used was the one previously employed. The highly
nucleated medium ($X io8 phosphorus nuclei per cubic centimeter) was
successively expanded by a fixed amount, and the nucleated air removed
from the fog chamber was replaced by filtered air. The residual nuclea-
*Smithsonian Contributions, No. 1373, vol. 29, pp. i to 173, 1903; ibid., No. 1651,
vol. 34, pp. i to 226, 1905.
43
44 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
tion therefore varies in geometric progression with the number of ex-
haustions, apart from necessary corrections. The observations were
made in time series by two observers, Miss L. B. Joslin assisting me with
FIG. ii. — Fog chamber F, and vacuum chamber V.
the work. Details will be given in connection with the data. The
initial isothermal (T) pressures p and pf of the fog and vacuum chambers
and the final isothermal (T) pressure p3, when in communication after
exhaustion, were carefully determined previous to the experiment with
coronas. These were needed for the computation of the amount of
water precipitated per cubic centimeter in each of the series of exhaus-
tions. In addition to this the pressure [^>2] for finding the ratio of the
geometric sequence was necessary and found as follows: In each
exhaustion the stopcock was opened suddenly at the beginning of each
NUCLEATION CONSTANTS OF CORONAS. 45
minute and kept open for 5 seconds; it was then closed until the end
of the minute. Hence [p2] is the isothermal pressure observed in the
fog chamber under the given conditions, determining the density of air
and the nucleation left after each exhaustion. The ratio is therefore
(i)
where TT is the vapor pressure at the given isothermal temperature T of
observation.
As soon as the exhaust cock was closed the filter cock of the fog
chamber was opened, in order to evaporate the fog particles with the
least amount of subsidence or other loss. Observation of aperture was
made during the 5 seconds in question.
The relative number of nuclei for a series of coronas of decreasing
aperture is obtained in this way. It is furthermore necessary to stand-
ardize one of the coronas absolutely. This was done as described in the
earlier work (Smithsonian Contributions, No. 1651), and, if d denotes
the diameter of the fog particles and 5 the chord of the angular diameters
(f> of the corona observed with a goniometer with a radius of 30 cm.,
2 sin (f)/2 =5/30 (2)
* O \O /
was accepted when the eye and the source of light were at distances
Z} = 3o and 250 cm., respectively, on opposite sides of the fog chamber.
With a constant a selected we may then compute the nucleation n'
for the smaller white-centered or normal coronas as
n' = —s* ^
where m is the amount of water precipitated per cubic centimeter in the
exhausted vessel and n' the number of nuclei per cubic centimeter so
computed. The theory of diffraction would give a collateral approxi-
mation
6m m
26. Equations and corrections. — In the present experiment no cor-
rection was made for the time loss of nuclei, for convection losses
during influx and efflux (vortices washing against the walls of the
vessel), nor for evaporation loss (loss of water nuclei on evaporation such
as occurs with ions but not with solutional nuclei like those here pro-
duced by phosphorus, etc.). The justification of this was tested by
making series of measurements with widely different exhaustions,
[§p2], both as to the amount of the latter and number of exhaustions in
the series, as will be shown.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 16. — Coronas standardized. Phosphorus nuclei. Bar. 77.7 cm.; temp. 20°.
Cock open 5 seconds ; time between observations 60 seconds ; dp' =18.2; dp3= 17.0;
[dp2]=i6.2 at 5 seconds, 16.8 at 60 seconds; ^ = 0.779; 5=7.2; 0 = 0.0032;
0 = 30 cm. and 250 cm.
No.
Corona.
5-.
IO~3»' =
o . i gos3.
«0X I0~3
ratio.
«X io~3.
^ = 0.0183
Xn~l/*.
s*=*a/d.
i
Fog
4010
4010
0.000115
27.8
2
r'fog
30
....
3230
124
25-8
3
r' fog
....
....
2420
135
23-7
4
r' fog
1840
149
21-5
5
w c
1390
164
19-5
6
W V
1050
1 80
17.8
7
dkb
791
196
16.3
8
Gbp
H
....
594
220
H-5
9
g'bp
13
....
446
241
13-3
10
gy°
13
333
264
12. I
ii
yo
ii
....
248
291
I I .O
12
w c
10
....
183
321
10. 0
13
w p
8.1
....
132
359
8-9
14
gbp
7-5
....
91.8
406
7-9
15
w o
7.0
65
4090
62. 2
462
6-9
16
cor
6.1
43
4170
41-3
529
6.0
17
5-4
3°
4630
25-9
618
5-2
18
....
4-3
15
3960
15-2
738
4-3
19
....
3-2
6.2
3440
7.2
948
3-4
20
....
2 .O
i-5
3680
1.6
.001564
2.O
21
I .O
.2
2170
•4
2473
•1-3
TABLE 17. — Coronas standardized. Phosphorus nuclei. Barometer 77.7 cm.; tem-
perature 20°. Cock open 5 seconds; 60 seconds between observations; />'= 18.2;
^3=17-0; [df>2]=i6.2 after 5 seconds; 16.8 after 60 seconds. Distance 30 cm.
and 250 cm.; goniometer radius 30 cm.; ^ = 0.779; S = 6.8;1 ^ = 0.0032.
No.
Corona.
s.
IO"H' =
O. If)OS3.
n0X io~3
ratio.
nXio~3.
^ = 0.0183
Xn~l/3.
s' = a/d.
i
R'fog
5100
5100
0.000106
30.0
2
R'fog
30
3950
116
27.6
3
R'fog
....
....
3050
126
25-4
4
w R'
....
....
....
2350
138
23.2
5
w r
....
....
....
1790
151
21 . 2
6
w v
....
....
1360
165
19.4
7
st. b
....
....
IO2O
181
17-7
8
B. P.
....
....
....
769
202
15-8
9
gbp
....
....
....
579
220
14-5
10
gyo
13
....
435
241
13-3
ii
w o
11.7
....
....
32.7
265
12. I
12
w r o
10.5
....
....
241
295
IO-9
13
wP
9-0
....
176
327
9-8
14
g'BP
7-8
125
366
8.8
15
w o
7-5
80
4710
87
416
7-7
16
w b r
6.8
60
5160
59
470
6.8
17
....
5-9
39
5060
39
54°
5-9
18
(late)
4-9
22
4660
24.7
630
5-i
19
(early)
4-2
H
5200
13-7
766
4.1
20
3-4
7-4
5760
6-5
980
3-2
21
2-4
2.7
6530
2. I
.001430
2. 2
22
....
1.8
i . i
8260
•7
. 002030
1.6
'Use mean 5= 7.2 as in table 16.
NUCLEATION CONSTANTS OF CORONAS.
47
zzo
zco
FIG. 12. — Nucleation n, in terms of the apertures of coronas.
Small nucleation, moderate exhaustion.
IZOO
ft. Y4 16 IB
zoo
sooo
4000
3000
zooo
woo
tO 12 14 16 18 20 22 24 26 28 30
FIG. 13. — Nucleation n, in terms of the apertures of coronas. Large
nucleations, moderate exhaustions.
48 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The chief corrections are for subsidence of fog particles and for the
change of m with a drop of pressure and temperature. For a rectangular
vessel of height h, subsidence loss during a time t may be written vt/h,
where v is the rate of subsidence in centimeters per second. Since
io~sv and ds = a, it may also be written for the fixed time /
vt Sd~ 5
(5)
2
h a? s
where 5 is the subsidence constant for the loss during the fixed time /.
Hence for a rectangular vessel
— fc\ V (6>
h\ 18 /
and for a cylindrical vessel of radius r and horizontal axis
S=—l^—} (7)
*J V / /
7zr\ 18 /
equations which will be useful below.
In the present case we may therefore write the nucleation obtained
in successive identical exhaustions beginning with w0
/ S\ ,/ SW 5\
«o = noy> «! = w0j i- — «2 = w0/ i- — i- —
(8)
5\ / 5 \ T-r/ 5\
5V_i / ~ JL£ \ 52,
as further explained in the earlier volume. Again, since for normal
coronas nz is supposed to be given by w = 6w53/7ra3, 5 may be computed
by two successive exhaustions as
.
Hence the terms of the series
5N
j /
6m
may also be computed, and since nz = — ^ 532, the equation
6ms,3 i
(10)
NUCLEATION CONSTANTS OF CORONAS. 49
is available for computing the initial nucleation w0, and hence all sub-
sequent nucleations, absolutely. Naturally a number of observations
nz and sz will be used for computing w0 and 5. The equation shows very
well how the constants n0, S, a, m, are involved.
From nz the diameter dg of the sth fog particle may then be computed
dz = n-J/l?/6m/7r (n)
and similarly the 0th aperture sz will be, since ds—a
to be compared with the observed value of sz. It is clear that d and 5
will be independent of m, while n varies directly with it. Examples of
all these relations will be found in the following section.
27. Data for moderate exhaustions. — These data are given in tables
1 6 and 17. The drop of pressure is 17 cm. and the barometer unusually
high at 77.7 cm. Consequently the relative drop is dp3/p = o.2ig
and vl/v = i . 19, temperature 20° C. The symbols denote dp'=p — p',
dps=P — Ps< [$p2\ =P — [Pz]> as explained in sections 25 and 26, where the
meaning of y, a, S, D, etc., will also be found.
The first column shows the number z of the exhaustion, the second
and third the selected annuli of the coronas and their apertures s, meas-
ured to the outer edge of red or the first annuli. In the fourth column
n' = 6ms3/xa3, while the fifth shows successive values of n0 and their
mean. The sixth column gives the computed absolute nucleation, the
seventh the corresponding diameter of the fog particle, and the eighth
the computed aperture s. The data have been left as originally com-
puted, for their relations are chiefly of interest; but the value of
m = 3 . 2 X io~6 here used is too small and will be corrected in section 34.
These data are shown graphically in figs. 12 and 13, the computed
values of s being taken as abscissas, the computed n as ordinates. To
admit the enormous range of the nucleation n the ordinates are appro-
priately changed in the scale of 10. The observed data are given in
the same diagram, but with a different designation for the points.
28. Remarks on the tables and charts. — One may observe at the
outset that the initial nucleation n is about the same in both cases,
being n = 5. 100,000 and 4,010,000 smaller in the second. The same
order of values will be found for the nucleations n in very different orders
of exhaustions in the succeeding tables.
The following values of 5 were computed as shown in equation 9
from the data of tables 1 6 and 1 7 :
\
lui ^Yi
I
50 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
s=J.O 6.1 5.4 4.3 3.2 2.0 i.o
S= 7-4 3-9 10-4 8.7 6.9 3.3
s = 7-5 6.8 5.9 4.9 4.2 3.4 2.4 1.8
5= 2.0 7.6 9.1 4.8 5.8 5.8 2.9
Leaving out the smallest coronas and those which are no longer normal,
the data 5 = 7.2 and 5 = 6.8 were taken as fair averages in the two
cases. The data for «0 show that the first table (16) is somewhat over-
compensated, while the second (17) is undercompensated by the values
of 5 entered. The high value of [o_£>2] = i6.8 was accepted with mis-
givings, but there is no evidence against it. It is interesting to com-
pare with the above values of 5 those which may be computed from sub-
sidence data in the way given in equation 7. From this it appears that
5 = 1.7 for t = 5 seconds of subsidence of fog. Now, the time needed for
complete evaporation was about 15 or 20 seconds, whence it follows that
5 must be of the order of 5 to 7 , agreeing therefore very well with the
datum computed from coronas. For the very small coronas subsidence
is too rapid to enter into any correction of this kind.
The selection of a constant 0 = ^5 = 0.0032 is the weakest part of the
above deduction. It is based on the earlier memoir and obtained from
the subsidence of observed coronas. Since the theory of diffraction
for an angular radius '= 10.7; 3=io.o;
9.2; ^ = 0.873; 5 = 6.8; 0 = 0.0032.
No.
Corona.
^.
IO3»' =
O.I28.T3.
w0Xio~3
(ratio).
nX io~3.
d = o.oi6i
x«-1/3.
s' = a/d.
i
Rfog
30
2540
2540
0.000118
27
2
JH°g
26
....
2 2OO
124
25-9
3
5Jog
25
1880
131
24.4
4
o °g
22
....
1630
137
23-3
5
Rfog
22
....
1400
144
22. 2
6
wR'
19
....
I2IO
15°
21-3
7
! wR
17
....
....
1030
159
2O. I
8
! w c
16.5
....
163
19.6
9
:w c
15.5
....
748
177
18.1
10
lv
....
....
635
1 86
17.2
ii
Blue
H-5
....
537
199
16.1
12
gBP
H
....
....
454
209
15-3
13
gBP
13-8
383
222
14.4
14
gBP
I3.8
322
233
13-7
15
gy o
13-5
....
....
271
247
12.9
16
'gyo
13-5
....
228
264
12. I
17
yo
12.5
....
....
191
278
"•5
18
yr
ii. 5
....
1 60
298
10.8
19
w c
10.5
....
....
132
3l6
10. 2
20
w P cor
9-7
....
....
1 08
335
9.6
21
gBP
8.1
....
88
362
8.8
22
gBP
7-6
....
....
68.7
393
8.1
23
....
7-3
53-o
428
7-5
24
....
6.9
42.O
2650
40-3
470
6.8
25
....
5-8
25.0
2IOO
30.2
5i8
6.2
26
....
5-4
20. I
2430
21 . I
584
5-5
27
4.8
14.2
2560
14.1
665
4.8
28
....
4-i
8.8
2590
8.6
785
4-i
29
....
3-3
4.6
2580
4-5
976
3-3
30
....
2-7
2.6
2880
2-3
.001220
2.6
31
2.0
I .0
1810
i-4
1438
2. 2
32
....
I .O
. I
2970
•9
1660
i-9
33
.0
.0
4850
•5
2038
1.6
II. Same. Bar. 75. 4 cm.; temp. 24° C.; 5 = 4.9.
i
Fog
2 I 2O
0.000125
25.6
2
Fog
30
....
....
I850
131
24-3
3
Fog
24
....
....
1610
138
23.2
4
Rfog
23
....
....
1390
144
22.2
5
Rfog
21
....
....
I2IO
150
21.3
6
Rfog
18
....
IO4O
1 60
2O. O
7
Rfog
17
• • . .
893
168
I9.O
8
Cfog
16
....
....
767
176
18.2
9
Cfog
15
....
658
185
17-3
10
v-c
H
....
561
195
16.4
ii
Violet
T4
....
477
207
15.5
12
B
H
....
....
406
218
14.7
13
g-b
14
....
....
346
230
13.9
14
gbp
14
....
....
294
241
13.3
15
g'bp
14
....
251
256
12.5
16
gy °
13
....
....
213
268
ii. 9
17
gyo
13
....
....
181
288
ii . i
1 Mixed colors.
54 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 18 — Continued.
No.
Corona.
s.
IO3W' =
0 I28.T3.
w0Xio~3
(ratio).
«Xio-3.
/>' = 27.1; ^3=20.5;
25.o; j/ = o.656; 8 = 6.5 assumed; 0 = 0.0032.
No.
Corona.
s.
w'io~3 =
O. 24.2S3.
«.0Xio-3.
«X io~3.
d = n~l/3X
0.0199.
s'^a/d.
I.
i
Rfog
20
2320
2320
0.000150
21.3
2
w c
15
....
1500
173
18.5
3
violet
15-5
955
202
15-8
4
Gbp
15
608
235
13.6
5
gyo
H
387
273
11.7
6
w r
10.5
....
246
317
10. I
7
P cor
8.6
....
152
373
8.6
8
w o
7-4
98
2510
90.8
442
7-2
9
cor
5-8
42. 2
2080
\ 52-5
532
6.0
10
Jcor
4-9
28.5
2370
\ 27.9
657
4-9
ii
cor
4.8
26.6
(4610)
13-4
840
3-8
II.
i
Fog
....
2470
2470
0.000148
21.6
2
R'fog
23
....
1610
170
18.8
3
Fog
1040
197
16.3
4
gbp
16
....
673
227
14.1
5
g'o
....
430
264
12. I
6
yo
ii. 8
....
272
307
IO-4
7
w P cor
9-3
....
....
170
359
8.9
8
w y
7.2
90.3
2160
103
424
7-5
9
cor
6-3
60.5
2520
593
5io
6-3
10
cor
5-3
36.1
2730
32.6
624
5-i
1 1
xcor
4-6
23-5
(3530)
16.4
783
4.1
12
D. F. air
6.1
54-9
....
....
....
....
III.
I
Fog
23
2270
2270
0.000152
21 .O
2
Rfog
....
....
1470
175
18.3
3
violet
i?
....
951
202
15.8
4
gbP
15
....
610
235
I3.6
5
gy o
13.6
388
273
ii .8
6
w r
10.6
....
....
246
317
10. 1
7
w P cor?
8.0
....
152
373
8.6
8
w o
7-3
94.1
2390
89-5
445
7-2
9
cor
5-6
42.6
1880
5i-4
535
6.0
10
cor
25-o
29.7
2530
26.7
666
4-8
1 Nuclei of dust-free air and water nuclei remain constant.
2 Nuclei of dust-free air in presence of water nuclei.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The preceding data are shown in fig. 16, with a distinction between
the observed and computed values of s. The usual difficulties due to
impure colors are apparent. In view of the high exhaustions many
typical coronas do not appear and the small coronas are lost by the
efficiency of vapor nuclei as stated.
4- 6 8 fO as
in table 20 and then reducing all data to 24°. The results are of no
marked advantage over the earlier data and are therefore omitted.
NUCLEATION CONSTANTS OF CORONAS.
57
10
8
FIG. 17. — Nucleation n, in terms of the apertures of coronas. Low nucleation,
moderate exhaustion.
15 n
27 Z9 31
FIG. 1 8. — Nucleation n, in terms of the apertures of coronas. High nucleation,
moderate exhaustion.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 20. — Coronas standardized with phosphorus nuclei. Bar. 76.2 cm.; temp.
24° C.; cock open 5 seconds; 60 seconds between observations. />'=! 8.1 cm.;
^/>3=I7-1; [dp2\= 1 6- 3 after 60 seconds; distances 40 cm. and 250 cm.; goniometer
arms 30 cm.; ^ = 0.78; 5 = 6.5; ^ = 32.
No.
Corona.
s.
IO3H/ =
O. 2IOS3.
rc0Xio-3
(ratio).
«Xio-3.
d=n-V*
Xo.oig.
s' = a/d.
I.
i
Fog
(30)
5302
5302
0.000108
30.0
2
Fog
25
....
4110
119
27. 2
3
w o
i/
....
....
3180
129
25.0
4
w o
17
....
....
2470
141
23.0
5
w o
17
1900
153
21 . I
6
w r o
16
....
1470
167
19.4
7
V
....
....
....
895
198
I6.3
8
b
16
....
....
686
216
15.0
9
bg
16
524
235
I3.8
10
w y o
15
....
397
258
12.5
ii
w r o
13
....
301
284
II.4
12
w c
". 5
226
312
IO.4
13
wP
10
....
....
167
345
9-4
H
cor
8
122
383
8-3
15
....
7
72.0
4470
85.5
43i
7-5
16
6-5
57-7
5300
57-8
491
6-5
17
....
5-7
38.8
54io
38.1
564
5-7
18
....
4-9
24.8
5530
23.8
oho
4-9
19
4.0
13-4
5260
13-5
800
4.0
20
3-2
6-9
5840
6-3
0.001027
3-2
21
....
2.6
3-7
11070
1.8
1560
2 . I
22
....
i-5
• 7
597°
.6
3170
i-5
No.
Corona.
5.
io3n' =
O.2IOS3.
«0=io-3.
»X io~3.
3 =
17-
8p,~
10.
dp3=:
•0.5.
»P»-
17-
Mean
JXio8
and s.
dXio6.
s.
dXicf.
s.
rfXio6.
S.
dXioK.
S.
Violet (2). ..
190
170
17.0
18 .5
190
200
17.2
16 o
zoo
15.8
200
1 80
I6.3
17 . S
191
16.8
2OO
IS. 8
Green (2). . .
220
230
14.4
14.4
220
240
14.4
13-3
230
230
2^O
13-6
14.1
13.6
230
22O
13.8
14.6
228
14.0
Green (3) ...
410
370
7.8
8.6
390
420
8.1
7.6
4IO
390
4IO
7-9
8.2
7 • Q
380
4OO
8.3
8.0
398
8.1
Green (4.} .
1 Computed with n'= o. iggs* and y= 0.786, the latter being more in keeping with table 20.
60 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
To find, however, in how far the results themselves are trustworthy,
it will be necessary to find the computed values in the different series
of the diameter of the particles producing a given corona. For this
purpose the violet and green coronas are suitable. There are three of
the latter, the two upper being very brilliant. In the former report
the diameters of particles were estimated as d = 0.000460 cm. for the
middle green corona. Ratios of 4, 3, and 2 were usually apparent,
the data being multiples of a diameter something larger than d = o. oooi 5 ,
the corona for which is not producible. In the present experiments
the values of d and 5 for the green coronas are given in table 2 1 .
While there is considerable fluctuation, the data approach very closely
to a common mean, remembering that the color itself necessarily has
a certain latitude and wide differences of exhaustion are involved.
The ratio 2, 3, 4 of diameters of fog particles is not as well suggested
in the present result as in the former, while the absolute sizes themselves
are throughout smaller. It is nevertheless convenient to retain the
ratio for the division of coronas into successive series. If these may be
considered as beginning with deep red and ending with violet the fol-
lowing group may be postulated:
TABLE 22. — Showing cycles.
v, (d =0.000 n cm.) v2, d = o. 00019 cm. i>3, d = 0.00033 cm. ^4> ^ = 0.00044 cm.
g, ( 13 cm.) g2, 23 cm. g3, 40 cm. g,, 52 cm.
r, 16 cm. r2l 32 cm. rs, 48 cm. r4, 64 cm.
Only the red and crimson of the first series are certainly observable
with the above apparatus. Their aperture is about 60°, their rings
diffuse, and their disk filmy, so that in a small apparatus they would
be mistaken for clear air. The second series is producible and vivid
throughout, and the same is even more true of the third. The fourth is
already closely packed, while the fifth and subsequent series merge into
each other too rapidly for separation.
Series 3 and 4 were obtained in great number in my work with at-
mospheric nucleation. Selecting some twenty or more cases the mean
ratio i/53 : 1/54 = 0.146 : o.2o6=c?3 : d4. Hence the ratio of 3 : 4 is
very well sustained. The goniometer distance from the fog chamber
was nearly a meter in this case. In the present experiments, however,
the short goniometer distance (£ = 30 cm.), though adapted for the
best seeing, is not so suitable for measuring diameters. Apart from
this, the former experiments were made with plate-glass apparatus.
In cylindrical apparatus, as in the present case, there must have been
appreciable refraction due to differences of thickness. Hence it is
probable that the series i is actually the first occurring, although the
smallest active particles (violet) must exceed o.oooi cm. in diameter.
The same terminal conditions are suggested by the axial colors of the
NUCLEATION CONSTANTS OF CORONAS.
61
steam jet. It seems curious that the diffraction phenomenon should
begin with particles of the order of three times the wave-length of light.
Using the method of contact of coronas from two sources described
below, the ratio of diameters of the first four series is much more nearly
as i, 2, 3, 4, for the green coronas for instance, than in the present
experiments.
34. Insertion of new values for m. — The values of m used in the
above tables were throughout obtained from the earlier experiments.
As the relations of n are not affected and as m does not influence d and 5
(see equations, section 26) the latter will be left in this form. The nuclea-
tion n varies as m. Since that time, however, new data for m were
investigated compatibly with Chapter II. Inserting these in tables 16
and 17 and agreeing that n shall hold for dp/p — 0.219 and 20°, io8 ra =
3.2 must be replaced by io6 m = 3.6. In table 20, similarly, for
dp/p = o.224 and 20° C., io6 m = 3.6 must be replaced by io8 7^ = 3.7.
These results have been compiled in table 23, which is adapted for
practical purposes. The results are nearly coincident. These data will
be used in preference for the computation of nucleation.
TABLE 23. — Values of -y and n referred to new values of m.
Table 16.
Table 17.
Table 20, i.
Table 20, n.
s.
w-XiO-3.
s.
wX io~3.
nXio-3.
s.
nXio~3.
r' 27.8
4490
r' 30.2
57io
r' 30.0
5460
r' 27.0
4163
r' 25.8
3620
r' 27.6
4400
r' 27.2
4233
r' 24.8
3223
r' 23.7
2708
r' 25.4
3420
o 25.0
3276
r' 22.8
2482
r' 21.5
2064
r' 23 . 2
2630
o 23.0
2545
r 20.9
1916
c 19-5
1558
r 21.2
2010
O 21 . I
1957
c 19.2
1473
v 17.8
1176
v 19.4
1520
ro 19.4
1514
v 17-5
1123
b 16.3
886
b' 17-7
II4O
v 16.3
922
bg 16. i
861
g H-S
665
B 15-8
86 1
b 15.0
707
g 14-6
654
g' 13-3
500
g H-5
649
bg 13-8
540
gy 13-3
495
gy 12. i
373
gy 13-3
487
yo 12.5
409
0 12.2
372
y o ii .0
278
O 12. I
366
r o 11.4
310
r 10.9
276
C IO.O
205
ro 10.9
270
c 10.4
233
C IO.O
204
P 8.9
148
p 9.8
197
P 9-4
172
9.0
148
g 7-9
103
g' 8.8
140
8-3
126
8.0
107
o 6.9
69.6
o 7.7
97
7-5
88.
7-o
76.6
6.0
46.3
br 6.8
66
6.5
59-5
6.1
50.6
5-2
29.0
5-9
43
5-7
39-2
5-4
31.8
4-3
17.0
27.6
4-9
24-5
4-5
19.0
3-4
8.1
4.1
15-3
4.0
13-9
3-6
IO. I
2.O
1.6
3-2
7-3
3-2
6-5
2.6
3-7
I .3
•4
2.2
2-3
2. I
i -9
i . i
•3
1.6
.8
i . 5
.6
•5
•03
IO8W =
'3-6
....
3-6
....
3-7
....
3-7
....
9p/P =
. 219
.219
.224
....
.224
1 /a
d =
0IQOM.--1/3
Oiqow""1/3
....
.OI92W.""1/3
....
,oig2n~1/a
....
j =
. i68»V8
....
. i68«1/3
....
. I67W1/3
....
. i67n'/»
....
62
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
To reduce the other tables to the same standards (remembering that
n varies as m, while d and 5 are independent of it), is not necessary for
the present comparisons. In table 18, however, 10 we = 2.i should be
replaced by io6 w = 2 .3, where dp/p = o. 133. In table 19, dp/p = 0.273,
io6 w = 4.i is to be replaced by io6 7^ = 4.3. In all cases the initial
nucleations are thus increased. The new values for m are referred to
20° C. and the temperature coefficient is about 2 per cent per degree.
35. Wilson's* data and conclusions. — The following table (24) con-
tains Wilson's exhaustions (vt/v) at 18° to 19° C. and the correspond-
ing disk colors as I interpret them. It also contains the equivalent
relative drop of pressure dp/p used above. From these and the colors,
the diameters of fog particles (d} may be estimated, provided the series
in which these colors lie is known ; hence d.A^ refers to the probable case
of the occurrence of the third and second series, d2 1 to the very im-
probable case of the occurrence of the second and first series. Hence
if the values m be found for the corresponding temperature and ex-
pansions (dp/p) the nucleations n3 2 and n2 1 respectively follow. Wilson
gives but a single series between green coronas. There are two such
series and three definite green coronas producible, and I shall assume
that the very vivid upper one is meant. The first series is not pro-
ducible by any means known to me, except in the lower red coronas.
Hence I ignore n2 1 and take «3 2, in which case the data are distributed
similarly to my own, so far as the slope of the curves is concerned.
TABLE 24. — Estimation of the nucleation and size of nuclei corresponding to Wilson's
colors for wet dust -free air. Temp. 18° to 19° C.
From d.
From color.
Vi/V.
io3X
dp/p.
Disk
color.
dg.j.Xio5.
dvl X io5.
n3)SXio-3.
«2,iXio-3.
K3)2XlO-8.
w2llXio-3.
.410
384
g
40
23
1 60
870
I9O
870
.410
384
g
....
• 413
386
g
....
.416
388
bg
....
....
....
.418
389
b
.419
390
V
33
19
290
1460
'265
1500
.420
390
V
....
1 .420
390
r p
....
....
1 .426
394
r
32
16
325
2650
320
2150
1.429
396
rg
....
....
....
....
1-436
400
y w
....
1.448
401
w
....
1.469
418
gw
23
12
910
6500
9IO
7000
i-373
360
Fog limit.
i-3i
31?
+ ions, condensation limit.
1-25
270
— ions, condensation limit.
*Phil. Trans. Roy. Soc., vol. 189, p. 265, 1897. Cf. p. 285.
NUCLEATION CONSTANTS OF CORONAS. 63
There is another way in which the estimate in question may be made.
Let the nucleations corresponding to the colors be taken and reduction
made for the different drops of pressure in question. This is merely
a corroboration of the method of computation. The coincidence is as
close as may be expected, as the methods of approach are widely differ-
ent and the nucleation varies as the cube of the inverse diameter.
Wilson's views of the nature of the phenomena are quite different
and lead to enormous nucleation, even as compared with the improbable
n2l. He says (loc. cit., p. 301):
When all diffraction colors disappear and the fog appears white from all points of
view, as it does when [the expansion] v2/vl amounts to about i . 44, we can not be far
wrong in assuming that the diameter of the drops does not exceed one wave-length in
the brightest part of the spectrum, that is, about 5 X io~5 cm. That the absence of
color is not due to the inequality of the drops is evident from the fact that the colors
are at their brightest when v2/vi '1S only slightly less than i . 44 and from the perfect
regularity of the color changes up to this point.
Taking the diameter of the drops as 5Xio~5 cm., we obtain for the volume of each
drop about 6 X io~H c. cm., or its mass is 6 X io~14 gram.
Now, we have seen that when the expansion is such as produces the sensitive tint
(when v2/vl = i .42), the quantity of water which separates out is about 7.6Xio~6
gram in each cubic centimeter. With greater expansions rather more must separate
out. We therefore obtain as an inferior limit the number of drops, when v2/v1= i .44,
7 . 6 X io8/6 X io~14= io8 per cubic centimeter.
In my data the smallest green corona corresponds to a diameter of
particles of about d4 = 0.0005 2 cm., the next to d3 — 0.00040 cm., the
next to J4 = 0.00023, the first (which I have not been able to produce
by any means whatever, however large the nuclei) should correspond
to dl = 0.00013 cm., and even this calls for particles nearly three times
as large as Wilson's estimate (0.00005 cm.). In a small tube but 2 cm.
in diameter, like Wilson's test-tube apparatus, it is improbable that the
d2 green corona, which is about 27° in angular diameter, could look
otherwise than greenish white, whereas the filmy disk of the large
crimson coronas (the largest producible, ^=0.00016, with an angular
diameter of about 39°) would be mistaken for colorless. I shall venture
to believe, therefore, that Wilson's large greenish-white coronas corre-
sponded to about o . 9 X io6 rather than to io8 nuclei per cubic centimeter,
and that the maximum nucleation would not exceed io7 even if colors of
the unapproachable first order were produced.
36. Longer intervals between observations. Conclusion. — Finally, experi-
ments were made with longer intervals of time, 2 minutes and 3 minutes,
between the observations. The object in view was the avoidance of
distortion of the higher coronas due to the absence of homogeneous nucle-
ated wet air in the fog chamber. But the longer intervals did not improve
the coronas and the data were for this reason discarded.
64 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
Using the method of successive equal exhaustions for standardization
and a single spot of light as the source of diffractions, the coronas of
cloudy condensation were overhauled in the above chapter with special
reference to the use of an efficient plug-cock fog chamber. The ratio
of the section of the exhaust to the section of the fog chamber was about
one to six. The useful equations are summarized. The chief difficulty
encountered is the extreme sensitiveness of the coronas produced to
any lack of homogeneity in the nucleation of the air.
Given types of coronas, like the green pattern, for instance, seem to
recur for the ratios of 4, 3, 2, i in the diameters of the fog particles.
The results as a whole show fairly good agreement with the earlier
results below the middle green-blue-purple corona, but above this the
divergence of values has not been much improved. In the definite
region specified, corrections need be made for subsidence only. The
fiducial value of the nucleations of normal coronas has been accepted as
heretofore.
It does not seem probable that fog particles as small as o.oooi cm.
are ever measurably encountered in the fog chamber. This is larger
than Wilson's estimate made in terms of the wave-length of light; but
detailed comparisons are unsatisfactory, because of the difficulty of
identifying his colors as to their place in the observed cycles of colors.
NUCLEATION CONSTANTS OF CORONAS. 65
DISTRIBUTION OF VAPOR NUCLEI AND OF IONS IN DUST-FREE WET
AIR. CONDENSATION AND FOG LIMITS.
37. Introductory. — It will, in the first place, be desirable to gather cer-
tain of the older data together for the comparison of fog limits. There
is, in fact, quite a serious discrepancy between Mr. Wilson's results and
mine when reduced to the same scale. Mr. Wilson's supersaturations
for negative ions and cloud are distinctly higher, which seems to mean
nothing less than that my fog chamber, instead of being inferior, is in
these regions superior to his own. Thus, in moderately ionized air my
condensations begin at a drop of about 18.5 cm. from 76 cm. as com-
pared with 20. 5 in Wilson's apparatus; similarly, my fogs begin at the
drop 20.3, Wilson's at 27.7. Furthermore, at low ionization even the
vapor nuclei of dust-free wet air become efficient in the presence of ions.
It seems impossible .therefore, that any positive ions should fail of capture.
38. Notation. — The whole case may best be represented graphically,
but the tables will also be given. In my apparatus, however, the adia-
batic volume expansion v1/v is a troublesome datum to compute accu-
rately; it appears as
vl P (
where p and p' are the pressures in the fog and vacuum chambers before
exhaustion, p3 their common pressure when in communication after
exhaustion, always at the same temperature. The volume ratios of the
chambers is [v/V] =0.064; the TT'S denote the different vapor pressures
and k and c the specific heats. With a large vacuum chamber the
approximation
may be used, so that if dp=p—p3, the convenient variable for the com-
parison of exhaustions is the relative drop dp/pa. This is used in the
diagram with the approximate equivalent of the volume expansion v1/v.
(Cf. Chapter I.)
39. Data. — In table 25 results are given for the conditions observed
near the fog limits of dust-free air, and of dust-free air weakly ionized
by the beta and gamma rays (coming from a closed tube containing
radium placed on the outside of the fog chamber) and strongly ionized by
the X-rays (at a distance D from the fog chamber) . The data for ionized
air are nearly coincident, but dust-free air requires higher supersatura-
tion. The notation is as above, p, p—dp' being the pressures of the fog
and vacuum chambers before, p— Sp3 the common pressure after ex-
haustion. The relative drop in pressure is x, the angular diameter of the
coronas 5/30, the number of nuclei per cubic centimeter n, the volume
66
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 25. — Fog limits of non-energized air, of air energized by weak radium, and by
intense X-rays. J9 = 35 cm., anticathode to axis of fog chamber.
dp'.
»P»
J.
op3/p.
wXio-3.
VT-
Bar. 76.
2 cm.; t<
:mp. 26°
to 28° C.
Radium
21 . I
IQ. 7
4. S
O. 2S9
22
. 2^7
Air
21-3
20. o
2O. 2
21,. T,
19.8
18.4
18.9
21 . 5
4-2
li
i-5
I -7
. 260
. 242
.248
.282
18
O. 2
0.6
I . 2
.238
.217
. 224
.26=5
X-rays
22.8
21 .9
21.3
2O.4
(21. I)
20.3
19.6
19.4
I . 2
'r
0.0
4- I
• 277
.266
.257
• 2SS
0.4
O. 2
O.O
17
• 259
. 246
• 234
. 2^2
l8-9
19.6
2O. O
2O.4
17.2
18.0
18.4
19. 2
0.0
o.o
1.8
3-8
. 226
•236
. 242
.252
O.O
o.o
i-3
i-3
.199
. 211
.217
.228
Bar. 7
5.8 cm.;
temp, ic
B.6°C.
Radiation.
spa.
s.
$p3/p.
nXio~3.
iij-v.
it?, X io-3.
Radium
20 6
6 2
O 272
60
T 2 >J2
^o
X-rays, 0 = 150 cm. ..
X-rays, with radium . .
X-ray, D = $o cm. and
radium, 0 = 50 cm. .
Radium
18.6
18.6
18.6
} 18.4
I 18.7
18 7
r
r
2r
2r
i-9
r
•245
•245
•245
•243
.247
2J.7
0.2
0. 2
O. 2
O. 2
1.5
O 2
i . ^ J^
. 221
. 221
. 221
.218
.223
22"?
ow
0.2
O. 2
O.2
0.2
i-3
O 2
Do
21 6
37 0
28s
8q
• **o
I 269
7 . s
X-rays, D = 50
2O 7
49 S
277
2IO
I 2S4
176
• *ot
'No corona visible; scattered rain. 2 Coronas gradually increasing. 3wy. 4wc.
TABLE 26. — Dust-free wet air energized by weak radium acting from £^ = 35 cm.
Bar. 75.8 cm.; temp. 27° C. Wet glass walls.
dp'.
dp3.
5.
dp3/p.
nXio-3.
•vj-v.
25.6
24. i
4-3
0.318
23
1.312
24.6
23.0
3-9
• 304
i?
1.293
23.2
21.8 3.9
.288
16
1-273
21.8
20.5
3-8
.271
H
1.252
21 . I
19.8
2.5
.261
3-6
1.239
2O. 2
18.8
r
.248
0. 2
1 . 224
2O. I
18.8
o
.248
O.O
1 . 224
21 .9
20. 6
3-8
.272
H
1-253
24.0
22.3
3-7
.294
H
1.280
25-5
23-9
3-8
• 315
17
1.308
27-5
25-7
4.6
•339
28
1-342
29. 2
27-5
5-5
•363
50
1-377
31.2
29.0
a7-5
•383
133
i .408
1 w o.
NUCLEATION CONSTANTS OF CORONAS.
expansion on exhaustion vl/v. Tables 26 and 27 contain corresponding
results for air energized by the weak radium at a distance D = 35 or 40
cm. from the fog chamber. The difference observed in the curves of
successive identical experiments was found to be referable to the wet
or dry condition of the inside of the glass walls of the fog chamber.
Freshly wet walls are apparently essential.
TABLE 27. — Dust-free wet air energized by weak radium acting from D = 4O cm.
Supplementary data. Bar. 76. 2 cm.; temp. 24° C. Dry glass walls.
dp'.
ap*
s.
8PJP.
wXio-3.
vjv.
KojXlO-3.
25.6
24.0
3-9
0.315
i7
1.308
16
26. 1
24-5
3-9
.322
17
1.318
16
26. 7
25.0
3-9
• 327
J7
1-325
16
27. 2
25-5
3-9
•334
18
1-335
17
28.1
26.5
4-2
•346
23
1-352
21
28.9
27. 2
5-2
• 356
4i
1-365
39
30.1
28-3
6-5
•371
86
1-389
81
28.6
27.1
5-o
•354
37
1.364
35
28.5
26.8
4-9
• 350
34
1-357
32
21.8
20.6
3-6
.270
12
1.250
1 1
21 . I
19.9
2.0
.261
2
1-239
2
20. 6
19.4
r i .0
• 255
O. 2
1.232
O. 2
20.6
19.6
r i .0
•257
0. 2
1-234
O. 2
Repeated. Glass vessel clean and wet.
27. 2
25-7
4-5
0-337
27
1-339
26
28.3
26.7
5-0
•349
36
I-356
34
26.4
24.7
4-2
•323
21
i-3J9
20
25-7
24.0
4.2
•315
21
1.308
20
24-5
23.2
4.0
•304
18
1.293
17
24.0
22.3
3-8
. 292
15
1.278
16
22. O
20. 6
3-6
.270
12
1.250
12
21 .0
19.9
2.4
. 261
3
1.239
3
In table 28 the ionization is slightly intensified by affixing the radium
tube to the outside of the walls of the fog chamber. In table 29 there is
further intensification, obtained by acting upon the fog chamber with
the X-rays at £ = 50 cm.
TABLE 28. — Dust-free wet air ionized by weak radium (10 mg. 10,000 X) on glass fog
chamber. Bar. 74.9 cm., 75.0 cm.; temp. i7.7°C.
•h
s.
•vt.
«X,o-.
vjv.
»>,
s.
WP.
-X-o-
V*.
20.5
6-5
0.273
69
1-254
24.1
6-9
0.321
92
I.3I6
19.4
3-4
• 259
IO
1-237
26.0
6.8
-347
93
1-352
17.9
18.3
19.9
22.3
.0
r i .0
5-5
6-9
• 239
.244
.265
.297
0
0. 2
40
86
i . 214
i . 219
1.244
1.284
29.4
32.5
39-4
42.8
6-9
6-9
Diffuse
Diffuse
• 392
•433
-525
•571
1 06
112
I-423
1.496
I-695
1.823
Fog limit below ^ = 0.7 56 at 18°, equivalent to ^=1.22, equivalent to a drop
(adiabatically) of />= 18.6 cm, (about ) at 76 cm., 2 cm. below Wilson's dp = 20. 5 cm.
68
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 29. — Dust-free wet air ionized by X-rays at I? = 50 cm. Bar. 75.9 cm.;
temp. 21.3° C.
9p»
s.
WP.
raXio-3.
T>1/V.
dps-
S.
Wp.
nXio~3.
•ojv.
18.4
18.9
19.6
r
2-4
5-2
0.242
.249
.258
0. 2
3-3
32
I.2I8
1.225
1.236
2O. 2
19.4
19.0
'S.i
5-0
i-9
o. 266
•255
.250
125
29
i-5
1-245
1.232
i . 226
'\vp corona.
-/-39 MC MS
.Zi
.39
FIG. 20. — Nucleation n of dust-free air and of ionized air in terms of relative adiabaticfl
drop in pressure dp/p and of volume expansion vjv. Enlarged scale for n. Region^
for ions.
FIG. 21. — Nucleation n in terms of relative adiabatic drop of pressure dp/p, and of
volume expansion "vj-v for dust-free air not energized, and for dust-free air acted on
by the beta and gamma rays of radium and by the X-rays from different distances D.
W refers to C. T. R. Wilson's condensation and fog limits, B to my own; T shows
J. J. Thomson's results referred to scale of the diagram. Several older series, V to X,
are given for dust-free air.
40. Graphs. Dust=free air. — The charts (figs. 20, 21, and 22) con-
tain a number of curves showing the nucleation in different scales (com-
puted from the angular diameter of coronas) in terms of the exhaustion.
In figs. 20 and 21 typical cases are given, in their lower parts only. Fig.
22 contains full curves on a smaller scale. Thus the curve for the vapor
nuclei of dust-free air begins appreciably below dp/p = o.26 (v1/v = i .24,
NUCLEATION CONSTANTS OF CORONAS.
69
70 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
adiabatic drop from 76 cm., 19.8 cm.), but it hugs the axis until about
0.33, after which it sweeps upward far beyond the chart into the hun-
dred-thousands. The position of Wilson's negative ions and positive
ions is indicated at 0.27 and above 0.31. Wilson's fog point would lie
at 0.36 in the chart and there would be an air curve to the right beyond.
Series III to X are taken from my earlier report (Carnegie Institution
of Washington Publication No. 62, 1907, p. 67). The serial number is
marked on the curve.
41. Weak radiation. — If a weak ionizer (radium io,oooX, 100 mg.,
sealed in an aluminum tube) is placed at D = 40 cm. from the glass fog
chamber, the air curve rises slightly above dp/p = o.2$, becomes nearly
constant slightly above 0.27 until above 0.35, after which it also begins to
sweep with great rapidity into the hundred-thousands of nuclei. That is,
at weak ionization the vapor nuclei of dust-free wret air become efficient
in the presence of ions. There are but two steps in the curve, the initial
one scarcely leaving the axis, the other at about n = 15,000 to 20,000.
42. Moderate radiation. — Let the radium tube be attached to the outer
surface of the fog chamber. The curve which is obtained begins appre-
ciably slightly above dp/p = o. 24 (v1/v = i . 21, adiabatic drop from 76 cm.
about 18.4 cm.), but it scarcely rises until above 0.25. From this point
it also sweeps upward but can not get much above 70,000 to 80,000
nuclei per cubic centimeter, which condition is reached at about 0.28.
To make this curve rise into the hundred-thousands, i. e., to make the
vapor nuclei of dust-free wet air efficient in the presence of the ions,
the exhaustion must be carried to about o. 50, much beyond the lateral
limits of the diagram ; but the fog is then intense and without coronas.
Again there are but two steps, one very near, the axis not appreciably
influenced by the greater ionization and the other above « = 70,000.
Persistent nuclei are not produced, however long the exposure.
43. Strong radiation. — If an ordinary X-ray bulb (4-inch spark) is
placed at a distance of about 50 centimeters from the fog chamber, the
condensation produced begins appreciably somewhat below 0.24 (v1/v =
i . 21 ; adiabatic drop from 76 cm. about 18 cm.) ; but the graph scarcely
rises until nearly 0.25, when the upward sweep into the hundred-thou-
sands begins. Exposure of a few seconds produces fleeting nuclei only ;
exposure of one or more minutes produces persistent nuclei. In spite
of intense ionization, the first step near the axis has scarcely risen; the
other is indefinitely high beyond the reach of coronas.
44. Other nucleations. — I have ventured to place the data of J. J.
Thomson (Phil. Mag., vol. v, 1903, p. 349) at T in the same chart.
They must be interpreted, however, relatively to Wilson's points (nega-
NUCLEATION CONSTANTS OF CORONAS. 71
tive ions vt/v = i .25, positive ions 1.31, cloud i .38). In relation to the
other curves of the chart Thomson's graph must be shifted bodily toward
the left until the lower and upper steps of the curve correspond with the
other cases. In none of the experiments made with my apparatus does
the initial step (which should correspond to the branch for negative
ions) rise much above the horizontal axis, no matter how intense the
ionization. This rise begins at about 0.25 in the chart and continues
thereafter in a way to correspond with the ionization. The diagram
also shows J. J. Thomson's second group of experiments, in which the
initial step (^/v < i .33) lies at an average height of n = 8$X io3 and the
second step at an average height about twice as large.
Fig. 22, which contains most of the earlier results reduced to the
present scale, shows the variation of nucleation obtainable at different
times to which reference has already been made. The high position of
the X-ray curve is particularly noticeable. All data except C. T. R.
Wilson's are given as if the coronas had been observed at 27°, for which
case the least amount of reduction was needed. The Wilson line should
therefore be depressed about 8X2 = 16 per cent in nucleation to be
comparable with the others.
45. Temperature effects.— It was demonstrated in Chapter II that
the vapor nucleation of dust-free air varies in marked degree with tem-
perature, if the relative drop in pressure be computed as x=(dps — [n-
7ij])/(p — TT). Computed relatively to dp3/p, there is a much more mod-
erate variation with temperature outstanding, suggesting that the appar-
ent variation may be associated with the occurrence of the vapor density
TT in x. To throw light upon this subject from a different point of view,
the condensation limits of dust-free air and of ionized air were determined
at temperatures between 13° and 30° and table 30 contains the results.
The notation being as above, it is only necessary to refer to the final
column for dp3/p and the volume expansion vjv = (p/[p— dp3])lly>
computed therefrom.
The results of table 30 being summarized by giving expansions corre-
sponding to the fog limits both for [v1/v] = (i—x)11^ and v1/v=(i-
dps/pyif, show clearly that vjv, computed from dp3/p, is independent
of temperature, whereas the other datum [vjv] varies with temperature
in a way referable to the values of n involved. It follows that the fog
limits are not changed by temperature in a way found by the nucleation
itself in Chapter II. The mean fog limit for dust-free air vjv = i .252
agrees with Wilson's data. The fog limit for ionized air is, however,
decidedly below this, and thus below Wilson's value. Finally, [vjv] is
always less than vjv and under ordinary temperatures from i to 2 per
cent less.
72
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 30. — Temperature comparisons. Radium on top of fog chamber. D = o.
Tem-
Tem-
dp'.
OpS-
S.
.X«r-.
pera-
ture and
barom-
dp\/p.
dp'.
dp3.
.r.
nXio-3.
pera-
ture and
barom-
•vj-v
§p3/p.
eter.
eter.
Ions due to radium.
Vapor nuclei. Wet dust-free air.
22.6
21-5
20. 3
21 .6
20. 1
19.0
6.8
o.o
80
O. I
14.0°
76. i cm.
i . 226
0.250
25.6
24.6
22 . 7
4.6
3-6
3.6
28.6
13-9
30.0°
75.7 cm.
20. 6
22.5
21-5
19-5
21.5
20. 1
2. I
6.6
5-0
2.O
74
29
30.0°
75 .7 cm.
I . 222
r o . 246
....
21 . I
20. I
2O. 3
2-5
o.o
3-8
o.o
O. I
1.247
Jo. 265
\ 0.268
20. i
18.4
1 -7
I .0
. . . .
1 0.243
20. o
18.7
o.o
0.0
13.2°
18.6
"^ I O
O. I
*-*
18.4
o.o
o.o
21 .9
20.3
o.o
0.0
76. 8 cm.
22.9
21 .6
o.o
o.o
18. 6
19. 2
2O. O
19.4
17-5
18.0
18.8
3-2
0.0
o.o
o.5
7-5
0.0
0.0
O. I
13.2°
76.8 cm.
I . 220
0.245
J3.8
23-3
22.8
22. I
21 .9
21-5
^
0:5
O. 2
0. 2
O. I
* * * "
1.263
[0.285
\ 0.280
Vapor nuclei.
Ions due to radium.
21.8
20.4
0-5
O. I
14.0°
1.247
19. 2
I8.I
0.0
0.0
14.0°
1 . 226
22.4
21 . I
I.O
O. 2
76.0 cm.
r 0.268
19.8
18.6
0.0
0.0
76 cm.
/ 0.245
....
20.3
0.0
0.0
|\ 0.267
20.6
19.4
strong
O. I
lo-255
SUMMARY OF RESULTS.
Ionized air.
Dust-free air.
vjv.
""l/V.
Differ-
ence.
vjv.
vjv.
Differ-
ence.
14°
30
13
H
Mean. .
i . 226
i . 220
I . 220
I . 226
I . 214
I . 196
I . 212
I . 214
O.OI2
.24
.08
. 12
1.247
1.263
1.247
I . 222
1.252
1-257
0.025
.on
.010
1.223
1.252
....
46. New investigations. — In tables 31,32, and 33 data were investigated
for X-rays of different strengths and for dust-free air. In the latter
case the coincidence of data is not as close as was anticipated, different
apparatus showing a somewhat different behavior. The results are all
given in fig. 23. The drop in the upper X-ray curve is probably due to a
breakdown in the X-ray bulb, as it is not sustained by the other curves.
Fig. 23 also contains Wilson's series, under the supposition that the
coronas begin with the green of the third and end with the green of the
second series. In such a case the present results lie in a region of lower
supersaturation than Wilson's. The slopes throughout are similar. If
Wilson's colors are of the second and first series, the green alone will
appear in the diagram, the other nucleations being too high. In such a
case Wilson's line will intersect the graphs of the present paper, as shown
by the graphs of the point g2 1-
NUCLEATION CONSTANTS OF CORONAS.
73
74
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 31. — Weak X-rays. App. II. Bar. 75.68 cm., 75.86 cm 75.8 cm;
temp. 25.0° C. February 18, 1907.
dp.
s.
Cor.
dp3/P-
nXio~3.
Cor-
rected
nXio~3.
sp.
s.
Cor.
.
«Xio-3.
Cor-
rected
nXio-3.
(1)17.6
0
0.232
0
o
(034.6
.0
0-457
594
6/7
18.6
2.5
cor
•245
3
4
3i-i
. I
y
. 410
562
638
19-5
5-2
0
•257
32
35
28.5
•4
y
•376
529
598
19.7
7.0
c
. 260
83
92
25-3
•5
y
•334
490
549
19.9
7-o
o
.263
90
IOO
23.0
.0
o
•3°3
403
450
20. o
7-4
gy
.264
97
108
20.8
9-5
p
•274
211
234
20.5
9.2
c
.271
191
212
19.1
3-9
cor
.252
14.6
16.1
21.8
9-3
c
.287
207
230
19.9
7.0
o
.263
84
93
25.5
ii .0
o
.336
467
523
20. o
7-3
g
. 264
94
104
30.0
1 1 .0
....
•396
550
622
20.4
8.7
P
. 269
155
172
TABLE 32. — Strong X-rays. App. II. February 21, 1907. Bar. 75.1 cm.; temp. 27.4° C.
sp.
5.
Cor.
§p3/p.
20° C.
nX io~3.
Cor-
rected
ioXn~3.
sp.
5-.
Cor.
op3/p.
20° C.
nX io~3.
Cor-
rected
10 Xn~3.
(2) 18.6
19-5
2-4
7.0
cor
o. 248
. 260
3-2
83
4
X-rays off. Dust-free air. Bar. 75.5;
temp. 27. 2° C.
20.4
10.8
w o
.272
307
357
21-4
12.
gy
.285
557
648
(3)37-6
13
bg
0.500
1130
1380
21 .9
....
gy
. 292
566
662
34-9
13
g
• 465
969
1170
23.0
g
.306
654
765
32-8
....
g'
•437
834
1007
24.1
....
g
.321
766
902
30.1
13
gto
.401
713
856
25-9
g!
•345
904
1071
gy
33-7
13
Vi O
•449
650
784
27-9
10
r
•372
367
437
33-6
12
w o
.448
650
784
25-8
4-7
cor
• 344
30.8
36
39-9
small-
w o
• 532
640
782
24.0
3-2
cor
.320
8.9
10
er
22.7
2-5
cor
.302
4-2
5
TABLE 33. — Strong X-rays. App. I. Bar. 76.5 cm. temp. 22.5° C. February 22, 1907.
Cor-
Cor-
sp.
s.
Cor.
dp/p.
20 C.
nXio~3.
rected
nXio~3.
dp.
S.
Cor.
vp/p.
20 C.
nXio~3.
rected
»Xio-3.
(4) !9-4
o
0.254
o
0
X-rays off . Dust-free air. Bar. 76.7;
19.7
4-9
.258
28
29
temp. 22.4° C.
20.5
8.8
c
.268
161
170
21.4
10.7
w o
.280
357
357
22. 0
12.8
yo
.288
436
460
(5)34-2
....
g
0.447
1060
H34
23-4
24-5
13-5
gyo
gy
.306
.321
584
680
617
721
31.0
27.7
'sis
w/bg
• 405
-362
899
187
960
199
24.8
....
g'
-324
766
812
25.6
2-5
....
•335
4-5
5
29.7
....
g
.388
988
1052
23.6
1.8
....
• 309
i-5
1.6
34-6
g
•452
1066
1140
22.2
I . 2
....
. 290
• 4
•4
NUCLEATION CONSTANTS OF CORONAS. 75
47. Conclusion. — The new results lead to about the same conclusions
as the older data given above. The endeavor to obtain the negative and
positive steps of the ionization fails in my apparatus. Sometimes there
are suspicious breaks in the nucleation curve supporting such a tendency ;
but it is not sustained.
What I always get is division of the totality of ions into two groups—
a numerically small group with large nuclei, and a numerically large
group with relatively small nuclei containing all the ions. This occurs
even in such cases where I catch the vapor nuclei of dust-free air in
presence of the ions (radium at D = 4o cm.), and hence all ions, positive
and negative, must have been caught in an earlier stage of the exhaustion.
The slopes of the air graph and the strong X-ray graph represent the
initial branches of a general law of distribution of molecular aggregates
such as is given by the theory of dissociation. They may therefore be
expected to be similar in their slopes, as they actually are. The results
therefore bear on the molecular structure of vapors.
The question is finally to be asked why I catch the negative ions, etc.,
at an apparently much lower supersaturation than C. T. R. Wilson. I
have entertained doubts whether the inertia of the piston in his appara-
tus is initially quite negligible; whether in any apparatus the computed
adiabatic temperatures were actually reached. Nobody has proved it,
and the case should be worst for small tubes. Moreover, in every appa-
ratus there must be a limit at which the smaller nuclei of a graded system
can no longer be caught in the presence of the larger nuclei. There is a
remote possibility that, whereas in the plug-cock fog chamber the exhaus-
tion starts rapidly but ends off with retardation, in Wilson's apparatus
it may start with relative slowness but finish with accelerated rapidity.
If the lower limits of condensation were due to emanations of metallic
or other material coming from the vessel, the effect should vary with
the intensity of the ionization, which it does not. If it were due to the
use of filtered air in place of stagnant air, as in Wilson's apparatus, it
should be equally evident with non-ionized air, where the limit of con-
densation agrees with Wilson's point for negative ions.
The chief results of this section will be found in the charts, corre-
sponding points of which have been connected with straight lines with
no attempt at smoothing. In case of the air lines, results made at
long intervals of time apart have been summarized.
CHAPTER IV.
THE NUCLEATION CONSTANTS OF CORONAS— CONTINUED.
ON A METHOD FOR THE OBSERVATION OF CORONAS.
48. Character of the method. — In the usual practical experiments
with the large coronas of cloudy condensation (the largest types having
angular diameter of nearly 60°), the source of light is placed in the
equatorial (vertical) plane of the fog chamber and remote from it.
The eye and goniometer are put as near it as possible whenever sharp
vision is essential. The diffracted rays in such cases come from the
fog particles at the ends of the chamber, as in fig. 24, a, and are liable
FIG. 24. — (a) Diffractions from fog particles at a, b, c, and a single source S, reaching
the eye at e. (6) Diffractions from fog particles at a, b, c, and two sources S', S",
with coronas n n' and n' n", in contract at n', reaching the eye at c. (c) Diagram
showing the relation of S, s', s, R, r, 6. (d) Case of two sources and coronas in con-
tact at n' drawn to scale.
to be seriously distorted by the refraction of the glass walls. Further-
more, the limit will be reached sooner or later, in which the fog particles,
to which the diffractions are due, lie at or beyond the ends of the fog
chamber, after which the features essential to the measurement will no
longer appear. Moreover, one eye only can be used in the measure-
ments. In fig. 24, a, with a source at 5 and an eye at e, the diffractions
of the fog particles a, b, c overlap.
76
NUCLEATION CONSTANTS OF CORONAS. 77
It occurred to me, therefore, to invert the phenomenon by using two
sources, which may be moved symmetrically towards or from the
equatorial plane, as in fig. 24, b, and to observe the contact in this plane
of the two identical coronas produced. In this way the oblique refrac-
tions are diminished as far as possible, coronas of all sizes are observable,
and both eyes are available for observation, increasing sharpness of vision
and lessening the eye strain. The contact method is in itself more
sensitive, seeing that the eyes may be placed all but in contact with the
fog chamber. In fig. 24, b, with two sources at 5' and S" and the coronas
nn' and n'n" in contact at n' at the edge of a given annulus, the diffrac-
tions of the fog particles a, b, c overlap.
49. Apparatus. — Fig. 24, d, shows a general disposition of the appa-
ratus. S' and 5" are the two circular sources of light lying in the same
horizontal, and movable in opposite directions in equal amounts, at the
control of the observer at the fog chamber F. S' and 5" are therefore
always symmetrical with respect to the vertical plane SR. The diffrac-
tion of rays due to the fog particles in F produces coronas seen at nn' and
n'n", and the lamps S'S" have been adjusted at a distance 5, so that
the selected annuli of the coronas are in contact at n'. The angular
radii of the coronas, marked 6 or shaded in the diagram, are nearly
equal and 2R tan 6 = 5, where R is the distance of the axis of the fog
chamber from the track 5.
On a double track, at 5, the two carriages for the lamps S'S" are
moved with sprocket and chain or in a similar manner, and provided
with a scale stretched between them, reading to centimeters. This scale
is a lath of wood about 3 meters long, with one end fastened at S', the
other free, while the scale moves across an index at 5". A pole at R, with
the end in the observer's hand, moves the two central sprockets and at
the same time serves for the measurement of R, should this vary.
50. Errors. — Fig. 24 shows clearly that the angle of diffraction cor-
responding to the fog particles a, b, c, nearer and farther from the eye,
will not be the same, and that this effect will vanish as the coronas are
smaller, as the diameter or thickness of the fog chamber is less, and as
the distance R from the source is greater. Slightly different annuli
overlap; but the effect is much less here than in the case of a single
source, where the active fog particles lie oblique to the axis. (See fig.
24, a, and fig. 24, b, at a, b, c.) In practice this effect is probably negligible
if the dimensions of apparatus and disposition of parts are properly
chosen, particularly so since the fog particles themselves are not usually
so nearly of a size as to imply less overlapping. In fact the true corona,
if large or even of moderate size, is seen but for an instant immediately
after exhaustion. It thereafter shrinks rapidly, as may be gathered from
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
the incidental data shown in table 34, obtained with fog particles about
0.0002 cm. in diameter, belonging to the large yellow -blue corona.
TABLE 34. — Contraction of coronas during subsidence. Bar. 75.2 cm.; temp. 27° C.;
factor 1.56; temp, factor 0.027.
t.
5.
••
nX io~3.
t.
S.
s.
nXio~3.
I. sec
II sec
0
12. 0
14.4
920
0
12.5
15.0
1140
30
IO. 2
12.2
600
30
10.8
13.0
730
60
8.4
10. I
350
60
8.8
10.6
400
90
7-3
8.8
220
90
7-4
8.9
230
The coronas shrink as the fog particles increase in number and de-
crease in size at an accelerated rate. The initial rates must be estimated
at a decrement of number
greater than i . 4 per cent per
second, supposing that no
water is added from other
sources than the evaporation
of smaller particles. In 100
seconds about 80 particles
have escaped out of each
100. The case is much more
serious for larger coronas, so
that these are characteristic-
ally fleeting and must be ob-
served at once. It may not be
impossible that rapidity of
evaporation itself sets a limit
to the largest coronas pro-
ducible. The nuclei, however,
are not lost as a rule. They
occur as water nuclei and are
ZOO
Sec.
zo
40
60
80
100
FIG. 25. — Nucleation n, computed from aperture
s of the coronas, gradually shrinking during
the subsidence within 100 seconds after ex-
haustion.
available for the next coronas, if not removed.
It follows, then, that for these cases the method of subsidence is not
applicable, as the corona changes totally before measurable subsidence
is recorded. Hence an instantaneous procedure like the goniometer
method or the present method is alone available.
51. Data. — In table 35 I have inserted results obtained with phos-
phorus nuclei, leaving out the initial fogs. It is seen at once that large
coronal diameters are actually measurable, a result not possible hitherto.
Reduced to the goniometer method, the present results may be written
0.12 5=5', for small coronas; but for large coronas, if 6 is the an-
NUCLEATION CONSTANTS OF CORONAS.
79
TABLE 35. — New apparatus. Two coronas in contact. Bar. 75.6cm.; temp. 24.7° C.;
S=2R tan 6; # = 250 cm.; cock open 5 seconds; interval i minute. df>3=ij.6;
[3p2]=i6.8; phosphorus nuclei, ^=0.771; dp3/p = o. 233; m = 4.2g/cra3; 0 = 0.0032;
Exp.
No.
S.
Cor.
.$•.
io~3n' =
0.244^.
M! X IO~3.
«Xio~3.
£ = 0.16
Xn1'3
r' = o . 1 2S.
cm.
i.
i
?2IO
o'
19-3
....
....
3660
24.6
2
185
o
16.7
....
....
2770
22.4
• ...
3
165
r o
15-4
....
....
2080
20.5
....
4
H5
c
H-3
....
....
1560
18.6
....
5
130
stone bl.
13-3
....
....
1160
16.8
6
120
g'
12.5
....
....
862
15-4
7
113
gy
11.9
....
....
636
13.8
....
8
104
gy
ii . i
....
....
467
12.4
9
97
yo
10.5
....
....
34i
II . 2
10
90
o
9-9
....
247
IO.O
....
ii
78
c
8.8
....
....
178
9.0
....
12
65
g
7-4
98.8
2880
125
8.0
13
60
gy
6.9
80.0
3430
85-1
7.0
....
H
55
r
6.4
63.9 4130
56.5
6.1
15
45
cor
5-3
36.4 3633
36.6
5-3
....
16
36
cor
4-3
19.4
3265
21.7
4-5
....
i?
30
cor
3-6
11.4
3830
10.9
3-6
18
23
cor
2.8
5-4
4720
4-2
2.6
....
19
18
cor
2. 2
2.6
1750
• 5
i-3
....
20
0
absent
0.0
0.0
....
o.o
....
2.
i
?2IO
o'
19
....
....
22OI
20.8
25.0
2
198
o
18.6
....
1679
19.0
23.8
3
185
c
17.9
....
....
1278
17-3
22.2
4
174
w'
18.1
....
973
15-8
22. I
5
158
st. bl.
16.1
....
....
740
14-5
19.0
6
135
g
H-3
559
I3-1
16.2
7
118
gy
12.8
....
....
420
12. O
14-2
8
101
o
II .2
....
....
3U
10-9
12. I
9
88
r
IO.O
....
....
230
9.8
10.6
10
75
r
8.6
....
....
167
8.8
9.0
ii
65
gyo
7-6
118
7-9
7.8
12
58
r
6.8
84.0
2269
81.5
6-9
7-0
13
5i
cor
6.0
55-6
2250
54-4
6.1
6.1
H
45
cor
5-3
38.5
2452
34-6
5-2
5-4
15
35
cor
4.2
18.1
1927
20.7
4-4
4-2
16
28
cor
3-4
9.6
2IO6
IO.O
3-5
3-4
i?
21
cor
2-5
3-8
2462
3-4
2.4
2-5
18
?i5
very
1.8
i-4
2680
i . i
1.6
1.8
small
3-
i
?2IO
o'
19.0
....
2010
20. i
25.0
2
195
0
18.4
....
....
1534
18.4
23-4
3
175
w'
17.2
....
Il67
16.8
21 .O
4
158
V
16.1
885
15-4
ig.O
5
145
g
15.0
670
14.0
17.4
6
133
gy
14.1
....
505
12.7
16.0
7
120
y o
13.0
379
"•5
14.4
8
1 06
o
11.7
282
10.6
12.7
9
88
c
IO.O
209
9-4
10.6
10
74
g
8.5
....
....
151
8-5
8.9
ii
60
g
7.0
91 .0
1708
107
7.6
7-2
12
57
r
6.6
76.6
2133
72.2
6.7
6.8
13
49
cor
5-7
50.0
2105
47.8
5-8
5-9
H
40
cor
4-7
27.0
1813
29.9
5-o
4.8
15
33
cor
4.0
15-6
1898
16.5
4-i
4.0
16
27
cor
3-2
8.0
2104
7-5
3-i
3-2
17
21
cor
2.5
3-8
3881
2.1
2.O
2.5
18
• • • •
just
....
....
.6
I .O
....
visible
8o
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
gular diameter, S = 2R tan d, s = 2r sin 6, or 5 = 8.3 s/\/i — s2/4f2>
5=0.12 5/Vi +S2/4^2, ^ = 250 cm., r = 3o cm. Fig. 24, c, shows the
relation of these quantities. Since the elementary diffraction equation
may be put
sin 0 — i .22
for the first minimum
5 =(2. 44 R l/d)/\/i—(i.22 l/d)2
and 5 would therefore appear to be less immediately adapted for the
equation than s. It does not follow, however, that this 5 and the one
observed at the goniometer work are the same. In fact they are not,
the latter being larger for reasons involved in the more recondite theory
of the experiment, or else due to irregular refractions at the remote
ends of the chamber. In practice 5 will usually be preferred to s.
In table 35, y = 0.Tji = (p— [dp2]— TT)/(/>— TT) ; = 0.233; ioem =
3.80 at 20°; therefore at 25°, 10 per cent higher or io6m = 4.i8 grams
per cubic centimeter. Hence nf = 6mss/ita? — o. 244 53/io3. The value of
TABLE 36. — New apparatus. Two coronas in contact. Bar. 76.4 cm.; temp. = 27° C;
S=2R tan 0; ^ = 250 cm.; cock open 5 seconds; interval i minute. o()3=g.g.
g.2. Phosphorus nuclei. of>3/p — o . 1 20 ; ^ = 0.875; io6wz = 2.33; £' = 6.5.
Exp.
No.
S.
Cor.
s' = 1 2.S.
IOSK' =
0.136^.
WjX io~3.
«X io~3.
5 = o.i94»1/3.
4-
i
>2IO
o-fog
25.0
1888
24.0
2
2O I
o
24.1
....
1635
23.0
3
194
o
23-3
1414
21.8
4
188
0
21.4
....
1222
20.9
5
173
r
20.8
1053
19.9
6
1 60
c
19.2
907
18.9
7
146
c
17-5
....
779
17.9
8
131
v'c
15-7
667
17.0
9
116
V'
13-9
567
16.2
10
105
v'g
2.6
479
15-2
ii
98
y'g
1.8
402
14.4
12
98
v'g
1.8
....
335
13-5
13
98
g
1.8
280
12.8
14
95
gy
1.4
233
12. O
15
94
y o
i-3
194
n-3
16
94
yo
i-3
161
10.6
17
88
w r
10.6
133
9-9
18
88
w c
10.6
no
9-4
19
80
w p
9-6
90.3
8.8
20
72
cor
8.6
73-2
8.2
21
67
g'
8.0
58.5
7-6
22
61
gy
7-3
....
46. i
7.0
23
54
w r
6-5
37-4
1995
35-4
6-4
24
48
r
5-8
26.5
1913
26. i
5-8
25
42
cor
5-0
17.0
1748
18.4
5-2
26
37
cor
4-4
12. O
1895
12. O
4-5
27
28
cor
3-4
5-2
7.0
3-7
28
22
cor
2.6
2-5
2-5
2-7
29
I/
cor
2.O
I . 2
....
0.9
1-9
30
O
O.O
O
0.3
i-4
NUCLEATION CONSTANTS OF CORONAS. 8l
the subsidence constant 5' = 6 . 5 is taken as the mea value of the above
data. To compute s = cm1/3/(6w/7r)1/3, the reduced values are 5 = 0. i6w1/3.
In table 36 the exhaustion ^ = 0.771 is smaller and the temperature
27°. The constants have the corresponding values shown at the head of
the table.
52. Remarks concerning the tables, and conclusion. — The first series in
table 34 contains data both for 5, 0.12 5=5' and s, and leads to a cu-
rious consequence. The computed chords of the coronas, 5 = a(7rw/6m)1/3,
is not proportional to s = 2r sin 0 but to S = 2R tan 0, where 26 is the
angular diameter of the coronas. This implies a diffraction equation read-
ing tan 6=1 .22 Xjd.
These results are shown in fig. 26, where 5 aw1/3 is laid off as the
abscissas and 0.12 5 oc tan 0 and o. i25/\/i +^S2/4^2 oc sin 6, as or-
dinates. If we confine our attention to values within 5 = 14, where the
readings are more certain, and where there is less accentuated over-
lapping of coronas, the graph 0.12 5 oscillates between two straight
lines as the coronas change from the red to the green types. The slopes
of these lines are respectively as 1.08 = 73.2^/0 and 0.99 = 73.2^/0,
whence ^ = 0.000047 and ^2 = 0.000043 cm. These should be blue and
violet minima.
Fig. 26 shows, moreover, that compared with the graph for 0.12
5 = 6o tan 6, the curve for sin 6 is in series i quite out of the question,
as already specified. Hence in the remaining series of observations in
tables 35 and 36, 0.12 5 was used in place of 5. The results for the
series 2, 3, 4, are also given in fig. 26, in the same way. Curiously
enough, series 2 and 3, which should be identical with i, fail to coincide
with it in the region of higher coronas. In these series the graph 5 oc sin 0
would more nearly express the results, though the agreement is far from
satisfactory. Series 4 again corroborates series i, needing the s' ex tan 6
graph for its nearest expression; but in this series there is a curious
horizontal part corresponding to observed coronas of the fixed type
in the middle region of green coronas (5 = 10 to 12), showing that the
periodicity has been exaggerated.
It is exceedingly difficult to account for this difference of behavior.
One may suppose that the phosphorus nuclei, which are here solutional
water nuclei, are not quite of the same size. This may happen if the
air is unequally saturated, for instance. In such a case the coronas
would be largest when the air is most nearly homogeneous and the
nuclei gradient within narrow limits (series 2 and 3), whereas in less
favorable cases (series i and 4) smaller coronas would appear. As the
abscissas, s = a (nTC/dm}1/3, where nz=yz~lK and the ordinates s (ob-
served) are independent of each other, the equality of 5' and 5 will in a
measure check the work apart from the constant a which determines «0.
This is actually the case for the lower series of coronas below 5-10.
82
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
Si SI
NUCLEATION CONSTANTS OF CORONAS.
On the other hand, it is the observational value of the aperture of the
given coronas which varies. Thus in fig. 26 the green coronas vary from
5 = 12 to 5 = 17 in the different series. Very probably mixed coronas
are being observed. To this must be added the subjective error or
personal equation which enters into the determination of contacts.
Finally, the tendency of a corona to shrink at once after the formation
of droplets makes it difficult to catch the time at which coronas should
be observed soon enough. Under other circumstances there is even
liable to be an oscillation of the coronal aperture in the lapse of time.
All these difficulties are accentuated as the coronas become larger, for
here not only are the droplets more volatile, but the coronas overlap,
and there is an unlooked-for tendency for them to flatten at the point
of contact. The dark rings are liable to invade the bright.
The green coronas in table 34, series i and 2, and table 35, series 3,
show the following average values:
Series
Computed.
Observed.
Computed.
Observed.
SB.
S2.
S3.
S2.
I09d3.
io6oL
ioed3.
io6d,.
i
2
3
8
8
8
16
H
13
8
8
8
H
15
13
400
400
400
200
230
250
400
400
400
230
210
260
Mean values are thus
£3 — 8.0 I O6<^3 = 400 52=I4-3 IO6a2 = :
agreeing pretty well with the above data (Chapter III, section 33), where
53= 8.1 10^3 = 398 s2=i4.o io6^2 — 228
I may summarize, in conclusion, that the present section has developed
the method of observation by which data are obtained from the distance
apart of two sources of light when certain fiducial rings of the coronas
are put in contact. This method is superior to the above method with a
single source of light, although its full value has not been evidenced,
because of the extreme sensitiveness of the coronas to differences in the
distribution of the density of the nucleation. There is a second difficulty
inherent in the phenomenon itself, viz, the shrinkage or oscillation in
the size of coronas following the instant of their formation. It is prob-
able that the number of fog particles actually decreases by evapora-
tion, though the phenomenon is complicated by the coincident variation
of temperature. After relatively long waiting, a somewhat similar
shrinkage takes place throughout the period of subsidence, and in case
of large coronas the apparent nucleation may thus be reduced to one-
fifth of its original value.
84 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
DISTRIBUTIONS OF VAPOR NUCLEI AND OF IONS IN DUST-FREE
WET AIR.
53. Behavior of different samples of radium. New fog chamber.—
It was my hope to be able to obviate the need of using the trouble-
some and inconstant X-ray bulb by replacing it by a strong sample of
radium. It also seemed possible that the fog chamber might be stand-
ardized in this way; but the attempts proved quite abortive, as indeed
might have been expected. The coronas were but slightly increased on
intensifying the original activity of radium I, 100 nig. io,oooX , equiva-
lent to say io6, by adding radium II, 10 mg. 2oo,oooX, equivalent to
2Xio6; radium III, 100 mg. io,oooX, equivalent to iXio6; radium
IV, 100 mg. io, ooo X , equivalent to i X io6; radium V, 100 mg. 20,000 X ,
equivalent to 2Xio6; on the whole, therefore, about seven times.
Obviously the radium must be kept sealed in tubes of aluminum or of
very thin glass, as otherwise the fog chamber would become infected,
which would be fatal to experiments of the present character.
The reason of the relative inefficiency of the radium is given by the
equation —dn/dt = a — bn2, where a is the number of ions generated per
second and bn2 the number which decay per second. Hence for the
case of equilibrium a/b = n2, where a varies as the activity of the radium.
If the five samples in question be taken together, therefore, the
equilibrium nucleation n would be, for any fixed distance of the radium
from the fog chamber,
Now, n varies as S3 (if 5 be the angular diameter of the coronas) in a
general way, and therefore the resultant
a (X. S6
Consequently enormous increases of the nucleation bring about but
slight changes of the angular diameter of the coronas. This estimate
is not quite correct if the values of b vary, as seems to be the case, with
the nucleation; but for the larger nucleations here in question such
an effect is not observable. If it can be controlled a new method of
standardizing the fog chamber for moderate coronas would be suggested.
54. Data — Results of this character are given in table 37, where 5 is
the double tangent of the corona on a radius of 250 cm., n the nucleation
corrected for the exhaustion v1/v = i.28f. In addition to the effect
of aggregating the radium tubes, their position on the outside of the
fog chamber is indicated as follows: a denotes that the tubes are placed
on the outside of the walls of the horizontal glass cylinder, above its
middle or equatorial parts; b that they are similarly placed near the
brass cap at the exhaust end; c that they are placed near the remote
NUCLEATION CONSTANTS OF CORONAS.
TABLE 37. — Radium I, 100 mg. io,oooX, and radium II, 10 mg. 2oo,oooX compared.
Bar. jG.ycm.; temp. 20° C.; 3p3= 22 .9 cm.; 3p3/p = o. 299; i>,/-u= i . 287.
S.
3.IlS = S'.
7iXlO~3.
io-6w2.
Zn2.
CO II
[44
45
l42
[46
I45
50
152
\ 5-3
} -
} «••
39
42
61
1,520
1,810
3,720
3,330
v1/ *••••
I
I and II at a .
(2) The same, on different parts of chamber. Bar. 76.3; temp. 18° C; dp3/p = o.2gg.
II at c
f6i
\62
/ 60
\ 60
(65
67
[ 44
I 44
MI
I 38
(47
149
46
57
55
65
67
} 7'3
} 7'2
} -
} 5-3
} 4-7
J 5'7
5-5
} 6.7
} "'
104
101
129
39
29
50
44
80
129
10,820
10,200
16,640
i,52i
841
2,500
i,936
6,400
16,640
21,000
2,360
1 at c
I and II at c
II at b
I at b
I and II at b
I and II at b
at ti
at c
(3) II kept in old place o ; I placed on chamber at c nearer glass end ; observation at c.
TJ
Bar. 76.3 cm.; temp. i9°C; df>3=22.g; />3//> = o . 300 ; ^ = 1.288.
V at c
/66
1 66
[62
59
59
59
66
66
(7I
1 7i
7-9
7-9
7-4
7-i
7-i
7-i
7-9
7-9
8-5
8-5
129
129
92
89
89
89
129
129
162
162
> 16,600
} 8,300
1 7,900
! 1 6, 600
26,400
16,200
32,800
IV at c
Ill at c
Ill and IV ate . . ....
Ill IV and V at c
glass end. Observations were made with both eyes below c, as this posi-
tion showed the largest coronas. The marked reductions of size for the
other positions of the eyes are probably distance effects, though there are
necessarily a variety of complications. Table 37 shows, however, the
extreme need of placing all the radium as nearly as possible on the same
spot, the importance of which was not at first adequately appreciated
(compare series 2). Radium placed at c produces over eight times as
86 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 37 — Continued.
5.
o. i2S=.y'.
nX io~3.
IO~W.
Sw2.
(4) Further comparisons, all
at
c. B
ar. 76. 2;
temp. 20° C
- ; 8p3/p =
3.300.
II
66
1 8.0
I T.Z
18,200
I
68
69
/
} 8.4
i S7
24,600
V
7i
6?
? 8.3
I S2
2^,100
Ill
7i
60
J
i 7-5
III
12,300
IV
65
62
J ' °
} 7-4
IO7
11,400
I + II + III + IV + V
61
82
/
> IO.O
266
70,800
80,600
I + III + IV + V
85
r72
J
] 8.8
I7S
30,600
71,400
III + IV + V
175
r 73
1 8.<;
162
26,200
46,800
III + IV
t°9
72
8.6
1 66
27,600
23,700
many nuclei than when placed at b and over twice as many than when
placed at a, and the rate of production of ions would be as the square of
these numbers. The effect is enhanced by the fact that the lateral rays
have to pass obliquely through the glass; but this appears to be a minor
disturbance. In all the experiments an aluminum gutter was cemented
to the top of the fog chamber and the sample tubes of radium placed
between given marks within it.
300
£00
too
27
o
100 ZOO
300 400
FIG. 27. — Aggregated effect of beta and gamma rays of different samples of radium,
I, II, III, IV, and V, observed and computed in terms of nucleation n produced.
Table 37 contains the values of 2w2 for the four series of experiments
given, and in fig. 27 these data are additionally shown by mapping out
the observed n as abscissas and the computed w =
2 as ordinates.
There is considerable divergence from the straight line which ought to
NUCLEATION CONSTANTS OF CORONAS.
appear, reasons for which are outstanding. As a rule smaller values of
n are observed than should occur, particularly for the larger coronas.
As a means of standardizing the fog chamber, therefore, this method is
again inapplicable ; moreover, strictures are cast on the present theory
by Chapter VI, where — dn/dt = a — bn2 is called in question.
55. Distributions of vapor nuclei and of ions. — In tables 38 and
39 I have collected data for the number of nuclei and of ions found in
apparatus II, under different conditions. Not only is a new fog chamber
used here, but the method employed is the one described in the present
chapter. Contact is therefore made between the fiducial annuli of two
coronas, and the distance apart of the sources of light or the double
tangent S, on a radius of 250 cm., at which contact occurs, is measured.
Special work was also done to determine the fog limits; and in case of
the vapor nuclei of dust-free air, the initial region of ions is explored in
detail (table 39). The table contains the adiabatic expansion v1/v and
the relative adiabatic drop dp3/p.
TABLE 38. — Certain distributions in apparatus II. Bar. 76cm.; temp. i8°C.
dp,.
S.
0.125 = ^'.
'nXio-3.
vjv.
.
(i) Radium I + II
22.8
72
8.6
167
.288
0.300
26.6
70
8.4
176
• 357
• 350
26.6
7i
8-5
182
•357
.350
24.7
67
8.0
144
.322
.325
23.0
72
8.6
1 66
. 292
• 303
21 . I
65
7-8
119
.260
.278
19.2
10
I . 2
0.4
.230
• 253
19. 2
10
I . 2
0.4
1.230
.253
Fog limit. Radium I + II and X-rays. Bar. 76.1 cm.; temp. 2i°C.
(2) Radium I + II
18.5
o.o
O.O
o.o
i. 218
o. 243
19-5
o.o
O.O
o.o
1-233
.256
20.4
(?)
(?)
(?)
1.247
.268
20.4
17
2.0
2-5
1.247
.268
Bar. 76.0 cm.; temp. 2i°C.
(3) Radium I + II
18.3
0
O
o.o
. 216
o. 241
18.8
o
O
0.0
.222
.247
19-3
9
II
0-3
.231
• 254
19-3
9
II
0.3
.231
• 254
(4.} X-rays • D = i. s . ,
19. S
22
26
4.6
•234
.257
18.9
IO
12
0.3
.225
.249
D = io
19. i
!3
16
0.9
.227
• 251
18.5
O
o
o.o
. 219
• 243
1 Ions under radiation not lost by exhaustion.
88 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 39. — Distributions of vapor nuclei in dust-free air. Bar. 75.9 cm.; temp. 21. 5° C.
spa.
5.
s'.
n.
WP-
vj-v.
dp3.
S.
s'.
n.
ops/P-
v v.
(I)
19-3
20.3
20.8
21.2
21.7
22. O
22.3
22.8
23-3
23.6
24.4
25-3
26.4
27.1
26.9
27.6
28.1
28.9
29. I
29-5
3°-5
31.0
32.0
32.0
33-5
35-4
38.0
o
13
H
14
15
H
15
15
17
19
19
26
30
52
45
y6g
72
81
C97
r 102
y 129
g' li !8
g' 140
g 136
g H7
v'? 140
v'? 140
o.o
1.6
i-7
i-7
1.8
i-7
1.8
1.8
2 .O
2-3
2-3
3-i
3.6
6.2
5-4
8-3
8.6
9-7
ii. 6
12.2
15-5
15-4
16.8
16.3
17.6
?I7.0
?i8.o
0.0
0.9
I . 2
I . 2
1-4
I . 2
i-5
i-5
2 .O
3-3
3-4
8.6
14-7
74.0
47.0
176
194
289
480
560
I2IO
1225
1533
H31
1780
1670
2090
0.254
.267
• 275
.279
.286
. 290
.294
.300
• 307
•3"
-322
•333
.348
•357
•355
•364
•370
.381
•383
•389
.402
.410
.422
.422
.442
.466
.500
.231
. 246
.256
.262
.270
•275
.280
.288
.297
.302
.318
•333
•354
.368
•365
1.378
1.388
1-405
i .408
1.418
1.440
•454
.476
.476
•5i3
.561
1-635
Radium removed from the room. Bar.
75.1; temp. 22° C. Vapor nuclei.
(2)
19.4
20. i
20.3
o
IO
IO
o
I . 2
I . 2
o.o
0.4
0.4
0.258
.268
.270
1-235
1.248
1.250
X-rays. D=io; bar. 75.1 cm.; temp. 22° C.
(3)
18.5
19-5
20.8
20.9
21-7
21 .9
22.4
23.0
23-4
25.0
30-0
35-1
? 10
26
r 89
ybus
g'o 135
g 130
g I31
g' 136
131
132
134
136
I . 2
3-i
10.7
13.8
16.2
15.6
15-7
16.3
15-7
15.8
16.1
16.3
0.4
7-i
303
654
1074
959
1017
1130
1058
1107
I31/
1486
o. 246
. 260
.277
.278
.289
. 292
.298
.306
.312
•333
.400
.467
I . 222
1.238
1-259
I . 26O
1.274
1.278
1.285
I . 296
1.304
1-333
1-437
1-563
56. Remarks on the table. — These results are constructed in figs. 28
and 29 in different scales, the nucleation of fig. 29 being on a scale 100
times greater, so that it may be in keeping with the very low nuclea-
tions. As a whole the figures are very closely like the above, though a
different apparatus was used. The line for dust-free air and vapor nuclei
here showed a tendency to transcend large green coronas, distinctly
entering the violet of the first series; but as the coronas are filmy the
measurement is correspondingly difficult. Over 2,000,000 vapor nuclei
are registered by the present method in the extreme case.
In general, however, apparatus II shows fewer nuclei than apparatus
I under like conditions of exhaustion. Thus at ^3/^ = 0.375, n — 250,000
for I and n = 500,000 for II; at higher exhaustions, dp3/p = o.T,g, n =
800,000 to 900,000 for I, w = 600,000 for II; at op3/p = o.4o, n — 900,000
to 1,000,000 for I and n= 1,200,000 for II; but here apparatus I is
already losing efficiency.
Fig. 28 also shows the small nucleations due to radium I + 11 and
radium I to V, as compared with the enormous effect of X-rays in
proper positions. In the case of the intense X-rays, the striking rapid
upward sweep of the curve is noticeable in case of apparatus I as
compared with apparatus II. The asymptote is reached much more
NUCLEATION CONSTANTS OF CORONAS.
89
p
tO
tt>
fD
3*
o>
Qrq
H-t»
O
O
a
s
PS
o
a?
o
3
p
en
S.
n
v> n
22
srg
*3
M
o
P.'
C to
W 00
3
1
n"
2,w 5"
3
C ,0
re en
p a* p <"*•
?. o 3 5'
3 in
S § 3 3
H? 3 n> M
S S p o
ag B "•
OaTfTg
S p. O-
Xrt o P'
M 2 a cr
o £.3 P
I ^cr cr.
xjjp^ n
• O. >-t D.
PPM
^^'o ao
Zr7 5"°
o CL a o
p* PB,
(T r^-
^s-s
o
?^^
fsfg
M^
H'n P"^
a P *p
^ ^3 D.
3 ^3 r*
T3 K, a-
rt- ft, O. fD
D "i *-•
™ 3 f?o
"HH _.. O> C
„ 3 g a
8 «r 8 B.
3 n w 2
'SS.^^
S-g >
^ w tr >-.
^§«
r?P « O
>> 5 M ~
' H 3
So^^S
•^ « A
3 °
s: o
dpa.
dp3.
*
sp3/p.
,,.
P'-
SX»r-.
At 24°
n2Xio~3.
I. Cock open 30°. Bar. 76 cm.; temp. 24.2° C.; £' = 52.4 cm. Original ions,1
s = 6. 9; n= 1 10,000.
76.0
76.0
63-9
64.0
68-7
68.8
59-8
61 .9
O.O
0.0
12. I
12. 0
7-3
7-2
16.2
14.1
22. I
22. 2
22.9
22.9
22-9
22.6
23.2
23.2
4-5
4-7
5-5
5-4
5-3
5-2
5-2
5-2
0.291
. 292
. 169
2. 170
.227
.224
.117
.147
59-9
53-8
53-4
52.8
52.8
54-4
....
30.4
34-8
3i
29-3
37-5
34-8
17.4
22.3
II. Higher exhaustions. Ions, «= 130,000.
76.0
62.0
67.9
67.8
76.0
0.0
14.0
8.1
8.2
o.o
26.3
26.5
26. 2
26. 2
4-6
25-3
4-5
0.346
. 202
.267
.266
•339
49-7
49-5
49.8
49.8
50.2
48.9
38.9
33-5
39-3
39-o
35-9
III. Miscellaneous. Ions, n= 137,000.
Cock open 60° . .
Cock open 90° . .
Radium in place
Ions
76.0
76.0
76.0
76.0
0.0
o.o
0.0
o.o
25-9
25-9
25-9
25-9
5^6
7-o
0.341
•341
•341
50.1
50.1
50.1
50.1
48.9
....
50.9
50.9
67-9
129.0
IV. Bar. 75.9 cm.; temp. 26° C. dp' = 27.1 cm.
Cock open 60° . .
75-9
61.1
o.o
14.8
25-7
26.5
5-3
6.0
0-339
.191
50.2
49-4
48.8
57
46
60
47
V. Low pressure. dp = 22.icm. Original corona, ^ = 6.4; w = 86,ooo.
75-9
64.7
64.0
0.0
II . 2
11.9
20. 7
21.5
21.5
35'3
0.273
•159
.150
55-2
54-4
54-4
53-8
45
24
23
47
86
81
VI. Bar. 76.0 cm.; temp. 14° C. Original corona on radium ions, s==6.g;
» = 97,ooo. Cock open 30°. dp' = 27. 5 cm.
Radium in place
Ions
60.6
55-9
76.0
76.0
20. 1
0.0
0.0
26.8
26.9
25-7
25-7
6.2
5-6
6-5
6.9
0.188
. 122
•338
-338
49.2
49.1
50-3
50.3
48.5
24.9
1 08
127
42
21
82
97
1 Loss by subsidence.
5gbp.
IOO CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 42. — Sizes of residual water nuclei — Continued.
P.
dpa.
9p»
j-
8p3/p.
P*
/>'•
n2x io-3.
At 24°
n2Xio-3.
VII. Bar. 75.7 cm.; temp. 29.5° C.
Ions
75-7
75-7
75-7
58-2
58.8
75-7
0.0
0.0
o.o
17-5
16.9
0.0
28.1
27.1
27.4
28.0
28.0
27.4
6.9
'6.2
24-3
4-7
4-7
4-4
0.371
•358
.362
.180
.189
.362
47.6
48.6
48.3
47-7
47-7
48.3
46.7
141
5IO2
634-5
20.9
22. 2
36.8
159
"5
39
23
24
42
VIII. Same. Lower pressures. Bar. 75. 7 cm.; temp. 29.5° C.
(Ions') .
75-7
53-8
75-7
64.0
53-6
75-7
0.0
21 .9
O.O
ii. 7
22. I
O.O
34-4
35-2
34-4
35-i
35-5
34-4
4.8
5-0
4.6
5-0
5-6
6-9
0-454
.247
•454
.366
.250
• 455
4i-3
40.5
4i-3
40.6
4O. 2
39 3
59-7
34-3
52.6
52.0
49.1
176
68
38
60
59
54
20 1
1 Radium in place; ions active in presence of water nuclei.
2 Radium off.
When the relatively large nuclei are caught at the very low drop
of pressure, a higher drop applied in turn always reveals a relatively
large number of water nuclei, apparently too small to have been caught
in the first exhaustion. This evidence must also be used with caution,
because evaporation in the filmy coronas, observed in the first instance,
is liable to be a marked feature.
If the graphs of fig. 31 be prolonged until they intersect the axis at
about # = 0.05, the limiting superior diameter of water nuclei may be
estimated from the Kelvin-Helmholtz equation. Regarding the super-
saturation to be about 5 = 1.15, the amount of adiabatic cooling as far
as 9°, the maximum diameter for the present series would be about
d = 2 X io~6 cm. In the above cases where the condensation began below
2 cm. (say at about i cm.) the maximum diameter than d = 25 X io~6 cm.
One may notice, however, that the effect of temperature enters abso-
lutely into Helmholtz's equation, so that if the minimum volume of
expansion could be found it would be worth while to compute d carefully.
5 decreasing rapidly implies a corresponding rapid increase of d.
In series VII and VIII, made at a somewhat later date, high exhaus-
tion and (incidentally) relatively high temperatures occur. The data are
also given in fig. 2, but they show no definite tendency. There remain
for discussion series IV and V, in each of which the filter cock was open
as widely as permissible and in which the number of water nuclei result-
ing from more rapid evaporation is often twice as large as heretofore.
In each of these cases the nucleation decreases very definitely and
rapidly with the exhaustion, as the numbers of nuclei were not only
large, but their sizes distributed over a wide range of values.
RESIDUAL WATER NUCLEI.
101
The values of table 42 refer to different numbers of initial ions. The
initial coronas are usually the same (w y o) ; but being obtained at
different exhaustions, this corona implies greater nucleation as the
exhaustion is higher. The number of ions in the tables has been com-
puted by supposing the exhaustion to be faster than the reproduction of
ions; i. ., the number of ions found for the exhausted vessel is always
multiplied by the volume expansion, apart from the correction for the
increased quantity of water precipitated. It may be questioned whether
this hypothesis is justified, but there is no way of testing it. It is also
very difficult to understand why the corona remains constant, while the
exhaustion, after all ions are caught, continually increases over enormous
ranges.
In table 43 the data of table 42 are summarized, but without referring
them to the same initial ionization, as these reductions would be uncer-
tain. X = op3/p. Notwithstanding the care given the work, the results
are far from satisfactory. All series show, however, that the number of
residual water nuclei present after the evaporation of a fog originally
containing about 100,000 ions per cubic centimeter is smaller as the
exhaustion is smaller, as if the water nuclei within certain ranges were of
all sizes.
TABLE 43. — Summary of table 42. Filter cock open 30°. Data referred to 125,000
ions, originally present.
XX io-3.
nX io-3.
XX io-3.
«X I0~3.
Series I. Ions 110,000. Bar. 76.0
cm.; temp. 24° C.; £' = 52. 4 cm.
Series VI.1 Ions 97,000. Bar. 76cm.;
temp. 14° C.; £' = 48. 5 cm.
291
292
169
170
227
224
117
147
30
35
3i
29
37
35
17
22
188
122
42
21
Series VII. Ions 160,000. Bar. 75.7
cm.; temp. 30° C.; />' = 46.7cm.
362
1 80
189
362
39
23
24
42
Series II. Ions 130,000. Bar. 76
cm.; temp. 24° C.; ^' = 48. 9 cm.
Series VIII. Ions 200,000. Bar. 75.7
cm.; temp. 30° C.; £' = 39. 3 cm.
346
1 86
202
267
266
339
39
45
33
39
39
36
454
247
454
366
250
68
38
60
59
54
'Made at an earlier date. The filter cock may have been too widely open.
102
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The effect of the low pressure under which the water nuclei are stored
does not clearly appear; nor can the effect of temperature be stated.
The most consistent results are those of series I, in which the lowest
exhaustions were applied. One-third to one-half of the original ions
or vapor nuclei are represented by the residual water nuclei, the number
TABLE 44. — Decay of residual water nuclei.
Exciter.
dp>s and
Spa/p.
s.
nX io~3.
t.
df>3 and
dp3/p.
s'.
n' X IO-3.
Ratio.
I. Bar. 76.2 cm.; temp. 15° C.; radium and water nuclei, dp>' = 24.0 cm.; vapor
nuclei, dp' = 29.3 cm.; Sp/p = 0.297 and 0-362; 7^/z; = i . 284 and 1.375;
not corrected for temperature.
Radium . .
22.6
6.9
86
90
22.6
4-6
26
0.30
8p/P = 0.297
86
90
.297
5-o
32
-37
86
i So
....
5-o
32
•37
86
1 80
....
5-0
32
•37
86
300
....
3-7
H
.16
86
600
....
3-9
16
• 19
II. Wet air.
None
27 .6
J7.S
I SO
1 20
22 .6
S . 3
38
O. 2S
0.362
"6.2
88
1 80
.297
4.2
20
•23
36.9
117
300
5-i
34
.29
"6.9
117
600
....
4-8
29
.25
III. Repeated. Identical pressures (dp' = 28.3 cm.) throughout. Always same
rate of influx (partially open cock). Temp. 22° C.; bar. 76 cm.; 1^/7; =
1-363-
None
26.9
6-3
9i
600
26.9
4-2
2?
0.30
Radium . .
•354
6-4
94
600
•354
46.3
(9i)
•97
6.6
IO2
600
....
3-6
17
-17
IV. Repeated. Bar. 75.2 cm.; temp. 19° C.; rvl/-v= i .362; />' = 28 . 3 cm.
None
(26.5
I -352
u.,
107
660
[26.5
I -352
),4
H
0.13
None
(26.7
I -355
}36-9
116
720
(26.7
I -355
} 3-5
16
.14
Radium . .
"6.7
107
600
3-5
16
•15
Radium . .
....
6.6
IO2
600
....
3-3
13
-13
None
....
'6.9
116
690
3-8
20
.18
'gbp.
2wr.
'wog.
4Radium in place.
increasing with the rapidity of evaporation. As the evaporation is
accentuated, the graduation of sizes lies within larger ranges. Ions are
efficient in the presence of water nuclei, indicating the small bulk of the
latter.
RESIDUAL WATER NUCLEI.
103
63. Persistence of water nuclei.— If there is a difference between
the water nuclei obtained after evaporation of fog particles precipitated
upon ions and those precipitated upon vapor nuclei, this should show
itself in a corresponding difference in the length of life of the types of
water nuclei in the two cases. Incidentally the number of nuclei dissi-
pated upon evaporation must appear in the graphs.
The data of the experiments are given in table 44, where n shows the
number of nuclei in the original fog precipitated upon ions or on vapor
nuclei and n' the number of residual water nuclei after the evaporation
of the first fog. In series I the filter cock was open after the measurement
of the first corona and the exhaustion used in the precipitation upon vapor
0 100 100 300 400 SOO 600 100 800 900
FIG. 32. — (a) Persistence of residual water nuclei obtained from the evaporation of
fog particles precipitated upon ions and vapor nuclei. The curve shows the number
n of water nuclei left i seconds after evaporation, (ft) Comparison of water nuclei
obtained from evaporation of fog particles precipitated upon phosphorus nuclei and
ions, in successive identical exhaustions. (Note the conspicuous loss in evaporation
between the first and second precipitations.)
nuclei was greater than it was in the corresponding case for ions. These
objectionable features were removed in the second and third series, where
identical exhaustions occur throughout and the graduated filter cock (fine
screw-valve) was opened to a definite number of degrees (30°). After
about 60° the resistance of the long filter prohibited a more rapid influx.
The results are all shown in fig. 32, a, with the series suitably dis-
tinguished by crosses, and they are referred throughout to an initial
nucleation of 86,000 per cubic centimeter. The data show, in the first
place, that somewhat more than one-third of the original number of
ions or of vapor nuclei are represented by these residual water nuclei,
104 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
the remainder having been dissipated during the first evaporation. This
agrees with the above results. The loss of nuclei in the lapse of time is
thereafter relatively slow, not more than one-half vanishing in the
ensuing 10 minutes. From the nature of the experiments it is idle to
endeavor to make out a numerical value for the rates, but they are of
the value of those obtained on shaking very dilute solutions, for instance.
Under the influence of radium, about the same number of water
nuclei occur after 10 minutes, no matter whether the initial dp3 is 26.7
or 22.6. Temperature corrections would not modify the conclusions
drawn. When the fog is precipitated under the same exhaustions with
identically initial coronas (this is possible because the vapor nuclei are
efficient in the presence of the ions), on either ions or vapor nuclei, the
persistence of the water nuclei obtained on identical evaporation is
about the same. From this one may argue that the water nuclei which
persist, cat. par., are roughly independent of the nature of the original
nuclei. Finally in fig. 32, b, the persistence of water nuclei in successive
exhaustions is shown for comparison, the data being anticipated from
the next section. Water nuclei precipitated on ions vanish much more
rapidly than for the corresponding case of phosphorus nuclei.
64. Summary. — Fogs when characterized by identical initial coronas
evaporate naturally, or under compression, to about the same number of
residual water nuclei, no matter whether the precipitation takes place
on ions or on vapor nuclei. The method, however, is rough. In the most
favorable cases about one-half of the original number of ions are repre-
sented by the residual number of water nuclei. If the drop of pressure is
continually decreased the number of residual water nuclei caught
decreases with the pressure, rapidly below dp/p — o.i to 0.2. In view
of the small amount of water precipitated and of the extremely filmy
coronas obtained as a consequence, measurement is difficult. There is a
lower limit to which the drop of pressure may be reduced unless a huge
fog chamber is constructed specially for these experiments. For small
exhaustions, coronas are liable to remain of the same type even though
dp /p decreases over wide ranges.
The persistence of residual water nuclei is not appreciably different
when this precipitation of fog particles to be evaporated takes place on
ions or on water nuclei. It is, however, enormously different, cast, par.,
from the case of phosphorus nuclei. It appears that this difference is
not of the nature of a time loss, but of a true evaporation loss. When
water nuclei are obtained from fog particles precipitated upon ions or
upon vapor nuclei, the chief loss of water nuclei accompanies each
evaporation of the fog particles, and over one-half of the total number
of ions may fail of representation in the number the nuclei present after
the first evaporation. This incidental observation will be systemat-
ically considered in the next section.
RESIDUAL WATER NUCLEI.
105
THE PERSISTENCE OF WATER NUCLEI IN SUCCESSIVE EXHAUSTIONS.
65. Standardization with ions. — A curious behavior appeared in an
attempt to standardize the coronas by aid of the ions due to gamma
rays penetrating the fog chamber. These were obtained from a sealed
sample of radium of strength io,oooX and weighing 100 mg. The coronas
were produced by successive exhaustions of the same value, the fogs
being dissipated by evaporation as soon as possible. The data given
in the above way in table 45 show an enormously rapid initial loss. To
obtain large coronas, the exhaustion to catch the ions was higher (drop
of pressure 3p3 = 22 . 6) than to catch the water nuclei resulting from the
evaporation of fog particles (^3 = 17.1). Hence, in the two cases
dp3/p = 0.293, volume expansion v1/v = i.28, and dp3/p = o.22j, V1/v =
i .20, whence nX io~3 = o. 268s3 and nX io~3 = o. 2I553.
80
FIG. 33. — Residual water nuclei obtained from evaporation of fog particles precipitated
upon ions. Curve (a) shows number of nuclei computed and observed found in
successive identical exhaustions ; curve (6) the corresponding relations of nucleation
n and coronal diameter s; (c) the corresponding behavior of phosphorus nuclei
compared with the ions.
io6
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The attempt to find the subsidence constant 5 fails; as, for instance,
•*=4-7 3-3 2.0 i.o
5= 12.2 7.9 3.4
4-4 3-o 1.8
11.5 6.6
showing a well-marked progression of data. Similarly, the attempt to
find n0 in the table fails, as the progression is here equally manifest. In
other words, with the evaporation of the first fog (on ions) more than half
the nuclei are lost, whereas in subsequent evaporations the behavior of
the remaining nuclei is more like phosphorus nuclei.
TABLE 45. — Coronas standardized. Ions from gamma rays (radium). Bar. 75.2 cm.;
temp. 25° C. ; 90 seconds between observations. Cock open 5 seconds. For ions
dp' = 23. 6 cm.; <5/>3=22.ocm.; ^' = 0.71; 8p3/p = o. 293 (factor, o. 268s3); for water
nuclei, dp = 1 8 . i ; ^3=17.1; [/>2] = 1 6 . 5 ; dp3/p = o. 227; ^ = 0.774. AssumeS = 6.5.
No. of
exhaustion.
Corona.
j.
n'Xio~3 =
0. 2I5-T3.
No. of
exhaustion.
Corona.
s.
«'Xio-a =
o. 215-y3.
(Ions) i
w r
6 6
'76 9
(Ions) i
w r
6.6
'76.0
(Water nuclei) 2
4-7
22.3
(Water nuclei) 2
4.4
18.3
3
3-3
7-7
....
3-0
5-8
4
....
2.O
1-7
....
1.8
I . 2
5
....
I .O
O.2
....
O.O
O.O
6
....
O.O
0.0
n'= o.268s3.
These data are shown in fig. 33, where io~3n' = o. 21 $s3 indicates the
number of nuclei actually present in the exhausted fog chamber and n
the number which presumably ought to be present. The discrepancy is
obvious and in large measure due to the losses in the first evaporation.
Thus, taking the second residue (nX io~3 = 5o.6) as the initial number
the results, in thousands per cubic centimeter, show that over one-half
are lost on first exhaustion.
Nuclei
Should be
Nuclei
Should be
present.
present.
present.
present.
Ions
76 Q
76 Q
Ions
76 Q
76 Q
After i evaporation
22.3
50.6
After i evaporation
I8.3
50.6
After 2 evaporations
7-7
8.0
After 2 evaporations
5-8
6.2
After 3 evaporations
i-7
0.9
After 3 evaporations
I . 2
0.4
After 4 evaporations
O. 2
O. I
After 4 evaporations
O.O
O.O
The same result may be inferred by laying off the nucleation in terms
of the number of the exhaustion as in fig. 33. In fact, the phosphorus
nucleation, as taken from table 20 for corresponding initial nucleations,
vanishes per exhaustion more slowly throughout.
66. Further data. — Thus it appears that the water nuclei obtained
by evaporating fog particles precipitated on ions vanish more rapidly,
at least in the beginning, than may be accounted for as the combined
result of the exhaustion applied and the subsidence. New results were
RESIDUAL WATER NUCLEI.
I07
therefore investigated in table 46, by aid of the method of two sources,
5 being their distance apart on a radius ^ = 250 cm., where S = 2R
tan 6/2, if 6 is the angular diameter of the coronas. The number of
water nuclei must be increased by the exhaustion, but not the initial
number of ions in the exhausted fog chamber. The data for n are
taken from the observed sizes of coronas as investigated above.
TABLE 46. — Fog chamber standardized with ions from radium. Bar. 76.0 cm.; temp.
20° C.; 60 seconds between observations ; subsidence 5 seconds.
Series and
exhaustion number.
5.
0.12S = S'.
nXio~3
(exh.).
nX io~3.
Calculated
nXio-3.
For ions, ^' = 24.0 cm.; §p3=22.g cm.; [2] = 22.4 cm. For water nuclei,
^' = 24.0 cm.; (J/>3=22.9 cm.; [dp2] = 22.4 cm.; dp3/p = 0.301; 5 = 6.5.
i.
2. •
'
' (Ions) i
gy 72
39
27
21
y' 17
72
42
30
21
18
y' 70
40
29
20
8.6
4-7
5-2
2-5
2.O
8.6
5-0
3-6
2-5
2. 2
8.4
4.8
3-5
2-4
28
8.5
4-i
2. 2
32
I3-I
4-i
2.9
29
12
3-7
166
36
1 1
5-3
2.8
166
42
17
5-3
3-7
157
38
15
4.8
(Water nuclei) . 2
3
4
(Air) . . . s
(Ions) i
(Water nuclei) . 2
3
4
(Air) . s
(Ions) i
(Water nuclei) 2
3
4
The same.1 For ions, £/>' = 24.0 cm.; 8p3=22.g cm.; [d/>2] = 22.4 cm.; dp3/p =
0.301. For water nuclei, />' = 18.5 cm.; Sp3=i7-7 cm.; [Sp2]=i-j.o cm.;
8p3/P = o-233', y = o.7ji.
4-'
5-<
6. <
(Ions) i
71
47
33
24
H
o
72
40
30
20
13
O
72
42
33
25
15
0
8.5
5-6
4.0
2.9
1-7
o.o
8.6
4.8
3-6
2-4
1.6
0.0
8.6
5-0
4.0
3-0
1.8
0.0
162
45-7
18.6
6-3
I . 2
O.O
1 66
29-3
I3-I
3-7
i .0
0.0
1 66
33-6
17.7
6.9
1.4
o.o
162
114
69
32
5-5
0.9
166
117
64
25
9
4
167
117
66
30
6-5
1.4
(Water nuclei) 2
3
4
5
i 6
' (Ions) . . .1
(Water nuclei) . 2
3
4
5
6
f (Ions) i
(Water nuclei) 2
3
4
5
6
'Water nuclei removed by exhaustion, but the ions are not.
108 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 46 — Continued.
Series and
exhaustion number.
S.
o.i2S=.y'.
nXio-3
(exh.).
nx io~3.
Calculated
«X io~3.
The same, with ions from X-rays. Bar. 76.1; temp. 21° C. Ions, dp' = 24 cm.;
8f>3= 22.9 cm.; [df>2] = 22.4 cm.; df>3/p = 0.301. Water nuclei, dp' = 18. 5 cm.;
^3=17-7 cm.; [Sp2]=i7.o cm.; 3//> = o. 233.
f dons') . . .1
O IO2
12.2
47 S
475
(Water nuclei) 2
50
6.0
*
" / *-*
57
" / \j
350
3
40
4.8
29
221
7-
4
30
3-6
....
13
122
5
19
2-3
....
3-2
47
6
O
o.o
....
o.o
18
i
O IO2
12.2
....
475
475
2
54
6.5
....
74
350
8.-
3
4i
4-9
....
30
228
4
30
3-6
....
13
128
5
17
2.O
....
2. 2
49
r (Ions) i
g y 124
14.9
8l3
813
(Water nuclei) 2
O J
63
~ ^
7-6
\J
115
\J
607
3
\J
46
/
5-5
....
*J
44
/
415
9-<
4
33
4.0
....
17.6
245
5
23
2.8
....
5-7
112
6
13
1.6
....
i-9
16
7
0
0.0
....
o.o
2
(Ions) i
g' 1 23
14.8
813
813
(Water nuclei) . . 2
O *J
66
^
7-9
«J
128
vJ
607
3
49
5-9
....
53
419
IO. '
4
38
4.6
....
26
263
5
27
3-2
....
8-5
140
6
17
2.O
2.2
37
(Ions) i
g' 128
I S -4
IIOO
IIOO
(Water nuclei) 2
O
66
V ~
7.9
128
823
3
47
f X
5-6
46
568
ii.1
4
35
4-2
2O
348
5
26
3-i
....
8.0
174
6
17
2.O
2.2
50
(Ions) i
128
I S .4
I IOO
IIOO
(Water nuclei) . . . 2
7i
j ^
8.5
....
162
823
3
50
6.0
....
57
580
12. •
4
39
4-7
28
366
5
29
3-5
....
ii. 7
199
6
18
2.O
....
2.8
72
7
o
O.O
....
0.0
26
In the first, second, and third series the exhaustion was somewhat
above the condensation limit of air, so that the coronas do not vanish.
But as the vapor nuclei are relatively inactive as compared with the
ions, the initial fall of nucleation is well brought out. The exhaustion
is here identical for ions and for water nuclei.
In series 4, 5, and 6 the exhaustion for water nuclei is below the con-
densation limit of air and the coronas vanish in successive partial evacua-
tions. It is necessary, therefore, to make the exhaustion for ions (only)
above the fog limit of air, as otherwise too few would be caught. The
observed march of data is, however, similar to the preceding experi-
ments, as is shown in fig. 34.
RESIDUAL WATER NUCLEI.
ICQ
These results were now varied by bringing to bear stronger radiation
obtained from an X-ray bulb placed at successively decreasing distances
D from the fog chamber. In series 7 and 8, £ = 40, in series 9 and 10,
D = 2o cm. and in series n and 12, D = i2 cm. (about) from the axis of
the fog chamber. The enormous initial radiations drop off rapidly in
the same way as in the preceding case. All the series are consistent,
except the eleventh, in which the initial drop is too large compared with
the others. It was customary to keep the exhaust cock open for 5
seconds, after which the filter cock was opened to dispel the fog, i minute
being allowed between the exhaustions. The results are shown in detail
in fig. 34, a, b, c, together with similar data for vapor nuclei and for phos-
phorus nuclei.
TABLE 47. — Vapor nuclei. Fog chamber standardized.
Series and exhaustion number.
5.
O. 12 S = Sr.
«X io~3.
Calculated
nXio~3.
Bar. 76.0 cm.; temp. 20° C. For vapor nuclei, 8p' = 33.1 cm.; ^3=31.3 cm.;
[2] = 30.8 cm.; dp3/p = o.^i2. For water nuclei, Sp' = i8.5 cm.; ^3=17.7
cm.; [o>2] = i7.o; dp3/p = o. 233.
i. <
2. •
(Vapor nuclei) i
y "7
so
67
52
39
28
19
10
y 116
pcor 72
r 61
50
37
26
20
10
14.0
9.6
8.0
6.2
4-7
3-4
2-3
I . 2
13-9
8.6
7-3
6.0
4-4
3-i
2.4
I .2
J905
234
135
66
27.7
10.9
3-3
0-3
X905
1 66
103
57
23-7
8
3-7
0-3
905
674
482
333
214
116
39
13
905
673
473
319
2OI
103
26
6
(Water nuclei) 2
3
4
5
6
7
8
' (Vapor nuclei) i
(Water nuclei) 2
3
4
5
6
7
8
Bar. 76. i cm.; temp. 21° C. For vapor nuclei, ^3=28.3 cm.; dj>3/p= i . 233. For
water nuclei, Sp3/p = o.T,72.
3- <
4-
[ (Vapor nuclei) i
6.8
5-2
4.0
2-7
i-7
o.o
7-i
5-i
4-3
3-3
2-5
8.2
6.2
4-8
3-2
2.0
0.0
8-5
6.1
5-2
4.0
3-0
172
66
29
9-1
2. I
0.0
191
61
35
17-7
6-9
172
1 20
77
42
12
4
191
134
85
49
22
(Water nuclei) 2
3
4
5
6
f (Vapor nuclei) i
(Water nuclei) 2
3
4
I 5
'Water nuclei removed by exhaustion, but not the vapor nuclei.
no
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
RESIDUAL WATER NUCLEI.
Ill
67. Data for vapor nuclei. — Table 47 contains similar data for the
vapor nuclei of wet dust-free air. In series i and 2 large coronas or high
nucleations are met with at the start, and they are compared in fig.
34, c, with a corresponding case for ions. In series 3 and 4 lower initial
nucleations are contained, and these data are compared in fig. 34 with the
corresponding cases of ions and phosphorus nuclei. Corrections for
subsidence should have been added to the graphs for ions and for vapor
nuclei, but these are not large enough to modify them materially, so far
as the figures go. *Q
4
FIG. 35. — Relative difference of nucleation (n' — n) /n of water nuclei from fog particles
precipitated upon phosphorus nuclei and on ions, in terms of i/n. The serial number
of the initial nucleation is attached to each curve.
68. Remarks on the tables. — The graphs in figs. 34, a, to 34, c, show
unmistakably that the water nuclei obtained from the evaporation of
fog particles precipitated on ions vanish in the successive exhaustions
faster than in the corresponding case with the vapor nuclei of dust-free
air; while the water nuclei from fog particles precipitated on vapor
nuclei vanish much faster than is the case for the corresponding solu-
112 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
tional nuclei obtained with phosphorus emanation. It is thus necessary
to examine in detail the three more obvious causes for the decrease in
nuclei, which are as follows: (i) The exhaustions, applied alike in all
cases; (2) the subsidence of fog particles during the short time of their
suspension, i. e., between the exhaustion and the evaporation by influx of
air; (3) the occurrence of electrical charge in the case of ionized nuclei,
whereby the charged water nuclei may be brought to coalescence.
Probably the best method of reaching a numerical result will consist
in eliminating the effect of exhaustion and subsidence, as was done above
for phosphorus nuclei, thus leaving the new losses of nuclei alone out-
standing. If
where y is the exhaustion ratio and the product n(i — S/s2z_1), the
correction for subsidence, the data marked n' calculated in the table may
be obtained. They are such as apply for solutional nuclei produced by
phosphorus, but they are throughout enormously in excess of the values
n observed for vapor nuclei and for ions. If we suppose that there is a
second cause of dissipation with each exhaustion we may therefore write
(abbreviating the products n)
n'z = n1yz-1xz~lU
merely to get a numerical statement of the case. The values of the frac-
tion or coefficient of survival x so found show a gradual increase of value
as the numbers of exhaustions increase or the nucleations decrease, indi-
cating that the greatest dissipation of nuclei is during the first exhaustion.
If these values of x, as summarized in table 48, be constructed in
terms of n, they show that x is considerably in excess for vapor nuclei
as compared with ions. Thus, at an average (nl + n2)/2, very roughly,
-ii — ?= 100,000 vapor nuclei ions, < °
= 50,000 vapor nuclei ions, { x~
I -45
= 10,000 vapor nuclei ions, <
results which are too irregular for further comparison.
A simple term like (n' — n)jn is preferable in other respects, and in
order to put the larger and more certain data on the diagram, (»' — n)/n
may be constructed in terms of i/n. If it wrere a question of time loss
merely, some further theoretical progress might be made, but the results
are not sufficiently smooth to give much assistance here. Hence in fig.
35- (n' — n)/n is shown in terms of ioe/w, both for ions and for vapor
nuclei. In both cases the curves rise higher as the parameter n is greater.
The initial ascent is not very different for ions and for vapor nuclei.
The dissipations up to (or due to) the first exhaustion are similar in
amount. But thereafter the curves for ions rise more rapidly than the
RESIDUAL WATER NUCLEI.
corresponding curves for vapor nuclei, showing that the water nuclei in
the latter case are more persistent under successive exhaustions and
evaporation than the ions.
TABLE 48. — Summary of table 46. Ions.
Series.
Observed
«Xio-3.
Computed
n'Xio-3.
I08/W.
(n'-ri)/n.
xXio2.
x, x', x", etc.
d'Xio5.
4-
162
162
6
0
38
46
114
22
2.O
40
0.40
57
19
69
54
3-8
52
.68
80
6
32
159
5-i
59
•7i
no
i
6
830
4-5
69
i . i
190
5-
1 66
166
6
0
• • • •
• • • •
37
29
ii7
34
3-0
25
0.25
67
13
64
76
3-9
45
.80
89
4
25
267
5-7
53
•75
133
i
10
IOOO
8-5
80
2.7
200
6.
166
167
6
0
37
34
117
3«
2-4
29
o. 29
64
18
66
56
2.7
5i
.90
80
7
30
H5
3-3
61
.89
107
i
6
690
3-6
68
•9i
1 80
7-
475
475
2
o
• • * i
26
57
350
17
5-i
16
o. 16
53
29
221
34
6.6
33
.69
67
13
122
77
8.4
45
.84
89
3
47
312
14.0
5i
.80
140
8.
475
475
2
o
....
26
74
350
13
3-7
21
0.21
49
30
228
33
6.6
33
•52
65
13
128
77
8.8
44
•77
89
2
49
450
46
•53
160
9-
810
813
i
0
21
"5
607
9
4-3
19
o. 19
42
44
415
23
8.4
48
•58
58
18
245
57
12.5
52
•65
80
6
112
175
18.5
47
•7i
114
10.
810
813
i
0
....
....
22
128
607
8
3-7
21
O. 21
41
53
419
19
6.9
51
.62
54
26
263
38
9-i
56
.76
70
8
140
118
15-4
50
.61
IOO
1 1.
IIOO
IIOO
i
o
21
128
823
8
5-4
16
o. 16
41
46
568
22
11.4
43
• 51
57
20
348
50
16.4
49
•7i
/6
8
174
125
21
46
.81
103
12.
I IOO
I IOO
I
O
....
21
162
823
6
4-1
20
o. 20
38
57
580
17
9.2
46
•5i
53
28
366
36
12. I
53
•77
68
12
199
85
16.0
49
.76
92
114 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 48 — Continued. — Summary of table 47. Vapor nuclei.
Series.
Observed
wXio~3.
Computed.
n' X io~3.
io6/n.
(n' — n)/n.
xXio2.
x, x', x", etc.
dXio5.
i.
905
905
i
o.o
23
234
674
4
i-9
35
o-35
33
i35
482
7
2.6
53
.80
40
66
333
15
4.0
58
•7i
52
28
214
36
6.7
60
• 65
68
n
116
92
9-5
•73
94
3-3
39
300
n
....
.90
140
2.
905
905
i
o.o
....
23
1 66
673
6
3-o
25
-25
37
103
473
10
3-6
47
.88
44
57
319
18
4.6
56
.82
53
24
2OI
42
7.8
59
.67
73
8
103
125
11.9
•65
103
4
26
270
....
....
i-7
134
3-
172
172
6
0.0
39
66
I 2O
15
0.8
55
0-55
52
29
77
34
i-7
62
.69
67
9
42
no
3-6
60
•58
IOO
2
12
450
4-8
66
.82
1 60
4-
IQI
191
5
o.o
38
61
134
16
I . 2
"46
0.46
53
35
85
29
1.4
64
.89
62
18
49
56
i-7
7i
.88
80
7
22
145
2-5
75
.86
107
Finally, the best method of interpreting the above results is in terms
of an equation of the form (if n1 be the initial nucleation)
nz =
x' x"
n
where nz is the nucleation of the 2th exhaustion, y the exhaustion ratio,
II the subsidence correction, and x, x', x", etc., the successive coefficients
showing the relative survival x, or the corresponding loss i — x, of nuclei,
accompanying the evaporation of fog particles. This equation asserts
that the loss is different in the successive evaporations, and this is
actually the case, as has been fully shown in table 48. The data x, x',
x", etc., have been constructed in fig. 36, a, b, c, d, in terms of the number
of successive identical exhaustions for the case where the nuclei are ions,
and in fig. 36, e, f, for the case of vapor nuclei. The ordinates thus show
the fraction of the total number of fog particles evaporated, surviving as
nuclei after the particular evaporation given (in turn) by the abscissas.
It is not probable that more than three or four successive data will be
trustworthy, because with the rapidly decreasing size of coronas the
errors are cumulative.
Fig. 36, a, b, c, d, shows that the effect of the first evaporation is
always preponderating and that it is more destructive as the original
RESIDUAL WATER NUCLEI.
number of ions is greater. Thus when n = 160,000, i—x or 60 to 70 per
cent are lost during the first, and only about i — x' or 20 percent during
the second and subsequent evaporations. If n = 900,000 to 1,100,000
where the fog particles are very much smaller, the first destroys about
3 4- 1 Z 3 4
/ & 3 4-
FIG. 36, a, b, c, d e, f. — Charts showing the rate of survival of nuclei in each successive
identical evaporation of fog particles precipitated upon ions, x is the relation of
the number of nuclei after the given evaporation of fog particles to the number of
nuclei before it. The abscissas show the number of evaporation in the series.
80 per cent, the second 40 per cent, the third 30 per cent of the number
which happen to be present just before the respective evaporation.
Hence for large values of n the loss due to evaporation is appreciable
throughout many repetitions.
n6
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The results (fig. 36, e, /) for fog particles precipitated upon the vapor
nuclei of dust-free air are similar, but in no case does the coefficient of
survival x increase after the second exhaustion, as was the case with
1-00
•20
40 60 80 20 40 60 80 100
37
ZO 30 40 SO 40 60 80 100
FIG. 37, o, b, c, d, e. — The same as fig. 36, showing x, x', x", in terms of the diam-
eters d of fog particles evaporated.
ions. (Compare fig. 36, c, d, with fig. 36, e, f, all of which apply for high
original nucleations of about io6 per cubic centimeter.) Contrasting
the case of ions with the case for vapor nuclei, by comparing a with e
and c, d with /, in fig. 36, specifically, the coefficient of survival is always
RESIDUAL WATER NUCLEI. 117
decidedly smaller for ions in the first exhaustion than for vapor nuclei.
The charged nuclei are therefore destroyed in greater number by the
evaporation of fog particles precipitated on them. When the number
of nuclei is large (iofi) this is also true in subsequent evaporations, though
the contrast is less marked.
Another question which comes up for settlement is this: Whether
the fog particles which are represented by nuclei after evaporation are
above a certain critical size, and those particles which vanish are below
it. This is hardly probable, because all the fog particles contributed to
the same corona and because it implies an enormous inequality in the
fog particles of the first exhaustion, considering that 45 to 85 per cent
of these vanish in the different cases cited. For the present purpose it is
sufficient to write Js' = o.oo32, where s' may be taken from tables 46
and 47. These results for the diameters of fog particles are given in
table 48. They are constructed graphically in fig. 37, a, b, for ions, and
in fig. 37, c, d, for water nuclei.
Fig. 37, a, containing series 4 to 8 for ions and small nucleations below
500,000, suggests that x may change abruptly when d = 0.0006 cm.;
while fig. 37, b, for ions and large nucleations, io6 has the same appear-
ance at d = 0.0005 cm- ^ is seen, however, that this is nothing more
than the transition from the first to the second evaporation, the former
being so much more efficient.
Fig. 37, c and d, for large and small nucleations of vapor nuclei, has
the same character. In c, for instance, there is an abrupt change below
40,000 nuclei. But the case is again one instancing the paramount
importance of the first evaporation. There is, however, no doubt of an
outstanding effect due to the number or the size of nuclei. The co-
efficient of survival x decreases as the number of nuclei increases, or
better, as their size diminishes. Thus, if the comparison be restricted
to the first evaporation fig. 37, e,
Ions.
Vapor nuclei . .
38 37 37
io2Jt: = 4O 25 29
iosd= 39 38
io?x= 55 46
26 26
16 21
23 23
35 25
21 22
19 21
21 21 centimeters.
16 20
centimeters.
from which the increase of x with the size of particles is put beyond
question and the larger coefficient of survival for vapor nuclei as com-
pared with ions is again apparent. Whether the peculiar features of the
curve (fig. 37, c), which reappears in each case, have a definite meaning
must be left to conjecture; but in most of the curves a, b, c, d, e, the
occurrence of maximum x is in evidence.
69. The loss of nuclei actually due to evaporation. — It is finally to
be shown that the peculiar loss of water nuclei resulting after evapora-
tion of fog particles precipitated upon ions is due to this evaporation
n8
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
(or its equivalent) and not due to the dissipation of the water nuclei in
the lapse of time. It might be supposed, for instance, that water nuclei
obtained from the fog condensed on the ions are smaller and therefore
diffuse more rapidly than water nuclei obtained by other methods.
If so, then if the time between the successive exhaustions is doubled,
trebled, etc., the loss should be correspondingly increased.
TABLE 49. — Successive exhaustion after different time intervals. Ions due to gamma
rays. Bar. 76.1 cm.; temp. :8°C.; ^3=22.9 cm. For ions, dp3/p = o.j,oi; 8ps=
17. 7 cm. For water nuclei, [Sp2] = 17.0 cm.; 8p3/p = o. 232; •vl/v=i.2i.
Series.
Time.
S.
Exhausted
wXio-3.
ttXio-3.
Series.
Time.
5.
Exhausted
n X io-3.
nXio~3.
I.
min.
o
i
'73
38
i?5
22
175
27
Radium left in place except during
exhaustion.
26
6.6
8 o
3
17
1^6
tj . \.r
2.0
4
0
0.0
0.0
VI.
0
'o
170
170
i
46
36
44
II.
0
>72
1 66
1 66
2
33
14.6
17.7
i
46
36
44
3
23
4-7
5-7
2
30
n. 6
14.0
4
12
0-5
0.6
-J
22
3.8
4.6
o
4
12
O
0.5
AJ.
0.6
Bar., 76 cm.; temperature 21° C.
III.
0
172
1 66
1 66
2
49
44
53
4
30
10.8
13.0
VII.
0
76
196
196
6
20
3-i
3-7
4
38
22
27
8
10
0-3
0-3
8
23
4-7
5-7
12
12
0.5
0.6
IV.
o
'68
146
146
3
42
27
33
VIII.
O
70
157
157
6
25
5-7
6-9
6
39
23
28
9
15
I . 2
i-4
12
22
3-8
4.6
18
12
0.5
0.6
V.
o
66
129
129
4
32
12.7
15-4
8
20
3-i
3-7
12
12
• 5
0.6
1 g to gy corona.
Table 49, constructed on the above plan but containing the time
interval t, in minutes between the exhaustions, shows that the time effect
is secondary. The table gives n with correction for the exhaustion or
volume increase vl/v.
The data are represented in fig. 38, the abscissa being the time in
minutes, the ordinates showing the nucleation. The curves indicate
a steady progression toward the right as the time interval increases,
showing that the time losses, although not necessarily absent, are not of
serious importance. In fact, in fig. 39 the group for i -minute and 6-
minute intervals constructed in terms of the number of exhaustions
(ignoring lapse of time) are virtually coincident. Again, the curve for
RESIDUAL WATER NUCLEI.
2 -minute intervals actually shows less loss (due to favorable exhaustion
conditions) than the curve for i -minute interval.
In series 6 radium was left in place except during the exhaustion,
(for ions are efficient in presence of water nuclei). It is seen, however,
that the water nuclei stored in this ionized field do not decay more
rapidly than in ordinary dust-free wet air.
/ 2 3
4-
180
160
FIG. 38. — Nucleation of residual water nuclei in successive identical exhaustions made
at different intervals of time apart. Fog particles precipitated upon ions.
FIG. 39. — The same, constructed for successive exhaustions and ignoring the time
intervals.
All the results might be made more striking by reducing them to the
same initial nucleation or ionization. Just how differences in these
values arise is difficult to affirm, but all the after effects in the successive
exhaustions are usually consistent. It does not follow, however, that
the correction is to be made by proportionately increasing all the low
nucleations by the amount required in the primary nucleation. Series
7 and 8 were therefore added specially with a view to normally large
initial nucleations.
. •<_ . - ,J
<5,\
,*<8». --^'-
LH
120 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
70. Conclusion. — When fog particles are precipitated upon solutional
nuclei, like those of phosphorus, the losses in successive identical ex-
haustions are due to the magnitude of this exhaustion, to subsidence,
and (in a small measure) to time losses or decay.
On the other hand, when fog particles are precipitated on ions or
vapor nuclei, there is an additional and usually very large loss, accom-
panying the evaporation of the fog particles to water nuclei. Fully 50
to 80 per cent of the nuclei may be lost after the first evaporation. The
time between the evaporations is of little consequence. More nuclei are
lost for the cases of ions than for the cases of vapor nuclei, other things
being equal. All this is very well brought out by the figures.
The loss decreases as the number of the exhaustion increases, or as
the number of nuclei present is smaller, or better, as their size is larger.
If, apart from subsidence, the nucleation nz of the zih identical ex-
haustion of ratio y be put
x' x"
the fractions x, x' ', x", etc., make an increasing series and may be called
the successive coefficients of survival characteristic of the sizes of fog
particles in each of the successive evaporations. The values of x increase
from about o . 2 for large and o . 5 for small ionization in the initial
evaporation to about o . 8 in the latter evaporations. For particles of like
size x is larger for vapor nuclei than for ions. The x values of the initial
evaporation distinctly increase with the respective size of particles in all
cases.
CHAPTER VI.
THE DECAY OF IONIZED NUCLEI IN THE LAPSE OF TIME.
71. Introduction. — The attempt was made in an earlier paper to
standardize the coronas by aid of the decay curves of radium. The
method is apparently very simple and requires the knowledge merely of
the coronas appearing under given circumstances when the radium tube
is in place d on the outside of the fog chamber, in comparison with the
coronas observed under the same circumstances when the radium has
suddenly been removed for different lengths of time before condensation.
From electrical observations the equation
dn/dl=—bn2 or i/« = i/n' + b (t—t'}
is found to be adequate if n and n' denote the ionizations occurring at
the times t and t', and the same would appear to be the case with the
corresponding nucleations. Moreover, if the relative nucleations n'/n for
two coronas obtained at a given exhaustion are known (for instance by
the above method of geometric sequences) the absolute values of the
nucleations will follow. With a radium ionization at t and tf seconds
after its removal
But the attempt to carry out this apparently straightforward method
leads to grave complications. If n be reckoned in thousands per cubic
centimeter, the electrical value of b may be taken as 6 = 0.0014, while
the value of b found from the decay of ions is more than two times as
large as this, increasing, moreover, very rapidly as the nucleation is
smaller. True, it is possible that the above method for finding the
nucleations absolutely may be at fault. Relative values seem to be
trustworthy, but absolute data are not to the same degree substantiated;
but even if this were granted, the march in the values of b would be
unaccounted for and seems to be a new phenomenon.
72. Data. Exhaustion above the fog limit of air.— In table 50 the
adiabatic drop of pressure dpa is somewhat larger than the fog limit
of dust-free air, as is shown in the second section of the table. The
column 5 gives the angular diameter of the coronas at a time / in seconds
after the sudden removal of radium from the outer walls of the glass fog
chamber. The relative drop in pressure x = dp3/p and the nucleations
n follow. The initial coronas are small, as the radium is weak (10,000 X ,
100 mg.).
121
122
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 50. — Fog chamber standardized with radium. Bar. 76. 2 cm.; temp. 25.7° C.;
water nuclei precipitated. Exhaustions above the fog limit of dust-free air. dp3/p =
o . 290 to o . 293 ; factor i . 22-1 . 23.
o>3.
S.
'•
»*
nXio-3.
Successive
b.
Mean
b.
cm.
cm.
sec.
Radium
18 4.
o
o
o. 242
o
* *-' • *T
20.6
'6.4
o
.270
65
....
....
I
22 . 2
]6 . 9
o
g
O OO ^ ^ I
•3
. i
'6.8
5-3
0
5
• 293
. 290
82
38
> 0.0029
. i
5-3
5
. 290
38
> . 002 i
. i
4-7
10
.290
27
. i
4-7
10
.290
27
1
. i
3-8
20
. 290
I5- l
\ -0033
....
. 2
3-7
20
. 292
13-9
j
. 2
. 2
3-7
3-3
20
30
.292
. 292
13-9
9-5
.0042
....
. 2
. 2
3-2
2.6
30
60
. 292
. 292
8.4
4.6
] -0035
....
. 2
. I
2.6
1.6
60
I 2O
. 292
. 290
4.6
0.9
.0150
....
. I
1.6
I 2O
. 290
o-9
....
....
. 2
6-7
0
. 292
79
....
. 2
6.8
0
.292
82
....
....
II. Air2.
22 . I
I .0
290
I . 7
. I
:?
. . . .
. 290
/
I .2
. .. .
....
20-7
r'
....
.272
0. 2
....
....
20-4
r'
.268
O. I
....
....
'wrcor. 2Radium removed. Corona glimpsed at j)P— 20.4.
These data are given in fig. 40,* which also contains the observed
values of i / n and the corresponding computed values of i / n if b = o . oo 1 4.
If the values of b are computed from the means of successive pairs of
measurements at different times /, the data under b "successive" are
obtained. A somewhat irregular increase is observed as n decreases.
If the first observation be combined with the fourth, etc., the values are
«=o.29 6=0.0029
34
36
4i
or a mean value 6 = 0.0033, if the last observation be ignored, since
the coronas are just visible here.
If the electrical datum 6 = 0.0014 be correct, the present nucleations
n are to be increased on the average, 0.0003/0.0014 = 2.3 times; if the
last datum for b were included, much more. This is quite unreasonable.
One must conclude, therefore, that b for nuclei is larger than b for ions
or that an ion, acting as a nucleus in a saturated atmosphere, decays
*The data of fig. 40 are constructed from an earlier computation not differing essen-
tially from table 50.
RESIDUAL WATER NUCLEI.
123
(dn/dt = — bn2) several times as rapidly as the same ion in a dry atmos-
phere when tested by the electrical conduction of the medium.
If but a part, n, of all the ions are captured, n' escaping, we may write
—dn/dt — dnf /dt = bn2 + 2 bnn' + bn'2
so that both dn/dt and dn'/dt are larger than bn2 and bn'2. If n = n',
—2dn/dt = 4bn2 or — dn/dt = 2bri*
If but one-third of all the ions, 3^, are captured, — dn/dl = g bn2; etc.
Hence if but i/m of all the ions are captured, the coefficient of decay
FIG. 40. — (a) Decay of ionization in fog chamber in
lapse of seconds, n being number of nuclei per cubic
centimeter. (b) i/n in the lapse of seconds ob-
served and computed with 6 = 0.0014 when n is ex-
pressed in thousands per cubic centimeter.
being as found should be about m times too large as compared with the
true values. This does not explain, however, why the coefficient 6
increases when t is larger and n is smaller; if it were additionally assumed
that the ions decrease regularly in size as they decay more and more,
124
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
so that they withdraw more and more fully beyond the given range of
supersaturation applied, the second part of these occurrences would also
be accounted for; but the assumption is not probable.
73. Exhaustions below the condensation limit of dust=free air.—
It would follow from what has just been stated that if the drop of
pressure is lower, the values of b obtained must be larger ; for not only are
few of the ions caught, but the diminution of bulk (virtually) which may
accompany the decay would place them sooner out of reach of the given
!0
20
10 fa* 20
FIG. 41. — (a) Decay of ionization in fog chamber in
lapse of seconds, n being number of nuclei per cubic
centimeter. (6) i/n in the lapse of seconds ob-
served and computed with 6 = 0.0014 when n is ex-
pressed in thousands per cubic centimeter.
exhaustion as the interval of decay increases. Table 51 contains ex-
periments of this kind, and they are reproduced in fig. 41, the data,
however, being again constructed from an older computation which
suffices for the present purposes. The relative drop in the first series
is about at the fog limit of dust-free air, while in the second series it is
RESIDUAL WATER NUCLEI.
much below. The successive values of b show an outspoken march into
larger values as the time / increases.
If we combine the first observation with the fourth, etc., in series i,
x = o.2j, 6 = 0.0038, 0.0041, 0.0057, °-°I34> or a mean value of b =
0.0045, if the last observation is ignored. But to ignore this value is
here quite inadmissible, as the data for series 2, where # = 0.25, viz,
6 = 0.021, 0.177, fully show.
TABLE 51. — Fog chamber standardized with radium (10 mg. io,oooX). Bar. 76.1
cm.; temp. 25. i° C.; water nuclei precipitated. Exhaustions practically below the
fog limit of dust-free air. §{>/p = o.268 to o. 272; distances 40 and 250 cm.
dp3.
s.
t.
nXio~3.
Successive
b.
Mean
b.
cm.
cm.
sec.
I. Radium
2O. 7
6 4.
o
66
.6
.6
6-3
5-o
o
5
63
30
\ o . 0036
o . 0045
•4
.6
5-o
4-4
5
10
30
21.4
.0031
....
• 5
•5
4-2
3-6
10
20
19-5
12. I
.0042
• 5
•5
3-4
3-i
20
30
10. 0
7-4
J .0044
....
•5
• 5
3-i
2-3
30
60
7-4
3-0
\ . 0066
....
•5
2-3
60
3-o
.0180
•4
1-5
1 20
0.7
.6
i-5
1 20
0.7
....
Air
.6
o
o o
Radium at 325 cm.
.6
r
....
0. 2
....
....
Bar. 76. 2 cm.; temp. 24.0° C.; 8p/p = o. 254-0.256.
II
IQ 4.
•3 o
o
6 i
•4
3-2
o
7.5
> 0.0206
O.O2I
• 5
2.5
5
3-9
]
•5
•3
2.6
i-7
5
10
4.1
i . i
} -I770
....
•3
i-7
10
i . i
....
....
74. Data for weak ionization. - -In the above work the initial
intensity of radiation was the same. It was suggested that the average
size of a nucleus might decrease in the lapse of time. Thus a variety
of further questions arise: (i) Whether weak radiation produces a
smaller average nucleus; (2) whether a stronger radiation does the
reverse; (3) whether the limit of b decreases as the exhaustion increases
and finally approaches b = o . ooi 4, etc. The experiments of the following
tables show that b varies with the number of nuclei present, no matter
whether a given nucleation is due to weak radiation or to decay from
a stronger radiation, or finally to low exhaustion; or that the nuclei
probably break to pieces as a whole.
126
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 52. — Decay of weak ionization. Radium at D = ^o cm. Bar. 76.3 cm.; temp.
24-o°C.; #£3=22.3; dpa/P = 0.292. Above fog limit of air. ' = 23 . 8 cm.
5.
5-.
t.
Exhausted
nX io~3.
nXio~3.
b.
cm.
sec.
i. Radium
M s
A 2
o
1 f 20. o
O ' O
'3.6
T"
4-3
0
I 21.5
. . . .
23-9
4-7
0
2 J27.3
....
24.o
3-0
3-i
3-i
3-0
4.8
3-6
3-7
3-7
3-6
0
5
5
10
10
\28.9
12.9
13-9
13-9
12.9
(24-4)
16.5
17.8
17.8
16.5
0.0017
.0015
.0052
•0055
2.8
3-4
15
10.7
13-7
....
2.8
3-4
15
10.7
13-7
....
2.6
3- 1
20
7-9
IO. I
2.4
2-9
20
6-3
8.1
2. 2
2.6
30
4.6
5-9
.0041
2. I
2-5
30
4-i
5-2
1.8
2. 2
60
2.8
3-6
1.8
2. 2
60
2.8
3-6
Air
1.6
I .0
I 7
s
• /
1 Subsequent.
2 Initial.
60
QjSec. to ZO 30 40 50 60
Otec, 10 ZO 30 40 50
FIG. 42. — Decay of ionization n in fog chamber in lapse of seconds for different initial
ionizations and different exhaustions.
FIG. 43. — Coefficients of decay referred to thousands of nuclei per cubic centimeter for
different initial exhaustions n0.
FIG. 44. — Decay of ionization in fog chamber in lapse of seconds for different initial
ionization.
RESIDUAL WATER NUCLEI.
127
In table 52 weak ionization is obtained by placing the radium tube
at 40 cm. from the fog chamber. The data, moreover, are investigated
by the new method of two sources of light 5 cm. apart, at a distance R
from the fog chamber. The number of nuclei n, computed for the
exhausted fog chamber, is corrected by multiplying by the volume
expansion v1/v = i . 25. Finally, b is computed from pairs of observations
about 20 seconds apart, as suggested by the brace. Water nuclei were
always precipitated before each test. In table 52 the exhaustion is
above the fog limit of air and the data are constructed in fig. 42 in com-
parison with cases for stronger radiation and of weaker radiation (by
decay) in table 51. Together they form a coherent series of curves,
since it is the number n present which determines the value of 6, no
matter whether the small number is due to low exhaustion (dpz/p near
the fog limit) ; or to decay of ions in the lapse of time (exhaustion /
seconds after removing the radium from the fog chamber), or due to
TABLE 53. — Decay of weak ionization. Radium at D = 40 cm. Bar. 76.9 cm.; temp.
i8.o°C. ; />3=2i .o cm.; dp^/p = o.2j2- Practically below fog limit of air. R =
cm. Exhaustion i . 25 =i>1/i>.
S.
O. I2S = S'.
t.
Exhausted
Corrected
b.
«X io~3.
•M ^^ T ("I — "
» fr /*\ J. tJ •
sec.
2. Radium
-zi
-i. . 7
o
j , 2
'(16. S)
o
29
o /
3-5
o
ii . i
\*** • O/
KI3.9)
. ...
28
3-4
o
IO. 2
'(12.8)
25
23
25
3-0
2.8
3-0
5
5
10
6-5
6^5
8.1
6-4
8.2
0.0043
043
25
22
3-o
2.6
10
20
6-5
4-7
8.2
5-8
135
22
2.6
2O
4-7
5-8
18
2. 2
25
2-7
3-4
....
22
2.6
25
4-5
5-7
18
2. 2
30
2-7
3-4
....
15
1.8
30
1.4
1.8
....
15
1.8
60
i .4
1.8
13
1-5
60
0.8
I .0
....
The same; stronger radiation. Radium at D = o from walls.
•i .
4-S
c .4.
o
1.8. T.
1(47-9)
TU
46
o • T-
5-5
0
O O
41 .0
\T^ / 7 /
'(51-3)
]
. 37
4-4
5
22. 2
27.7
1 0.0047
38
4-5
5
23-5
29.4
[0.0053
29
3-5
10
I I . I
13-9
J
29
3-5
10
I I . I
13-9
....
25
3-0
20
6.4
8.0
....
24
2.9
2O
6.0
7-5
....
25
3-0
30
6-4
8.0
....
46
5-5
30
41 .0
51-3
....
1 Ions under radiation not lost by exhaustion like the rest.
128 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
lower radiation (radiation at some distance, 40 cm., from the fog cham-
ber). Thus in fig. 42 curve c introduces low exhaustion dp3/p, curve b
low radiation, all of them the time effect.
In fig. 43 the results of tables 50 and 51 have in fact been summarized,
the table giving — b = (dn / dt') / n2 and the nucleation n from which the
decay takes place. One may note the rapidly increasing values of b
when n is smaller and their tendency towards constant values when n is
larger, remembering always that the ionization is throughout low.
75. Further experiments. — Table 52, containing exhaustions above
the fog limit of air, fails to show the usual high values of b, for the ionized
nucleation eventually emerges into the vapor nucleation of dust-free air.
In table 53, however, the exhaustion is low enough to catch but few
vapor nuclei, while being high enough to insure large coronas due to
ions. The data are shown in fig. 44. Series II for low initial nucleations
is somewhat irregular, for reasons, as I afterwards learned, connected
with the precise position of the radium tube on the top of the fog cham-
ber. Series III for higher nucleations is smoother. Both, however,
confirm the occurrence of large values of b associated with small values
of n, no matter how the latter are obtained.
If the true equation of the decay curve, dn/dt, were known, it would
be worth while to reduce all these data to a common scale. But fig. 43
shows that the values of b rather suddenly increase below io3w0 = io, so
that a simple relation is not suggested for the reduction.
The question arises incidentally whether the ions may not vanish by
accretion, i. e., their number may be reduced because individual ions
cohere. In such a case the fog limits should be reduced, which is con-
trary to the evidence. There seems to be a second cause for decay
entering efficiently when the nucleation becomes smaller. We may
therefore pertinently inquire whether for large nucleation the decay of
ions in the fog chamber approaches the electrical value.
76. Case of absorption and decay of ions. — The most promising
method of accounting for the above results has been suggested by the
work in connection with the behavior of phosphorus nuclei.* There may
be either generation or destruction of ions proportional to the number
n present per cubic centimeter, in addition to the mutual destruction on
combination of opposite charges. In other words, the equation now
applicable now is
— dn/dt = a + en + bri*
where a is the number generated per second by the radiation, en the
number independently absorbed per second, and bn2 the number decay-
*Barus, Experiments with Ionized Air, Smiths. Contrib. No. 1309, 1901, pp. 34-36.
RESIDUAL WATER NUCLEI. 129
ing by mutual destruction per second. Here c is negative for generation
and positive for absorption. If a is zero,
—dn/dt = cn + bn2
or
n »0
where the nucleation n and n0 occurs at the times t and t0, respectively.
If 6-0,
if c = o, the equation reverts to the preceding case, where — dn/dt = bn2.
Hence when c becomes appreciable,
dn/dt c
• = — -f- b
n2 n
or the usual decay coefficient increases as n diminishes, becoming
infinite when n = o. This is precisely what the above tables have brought
out. The value of b does not appear, except when n is very large. Since
6 is of the order of io~6, if c is of the order of 3 X io~2 (as will presently
appear), c/n will not be a predominating quantity when n is of the order
of io6 (c/w = 3X io~8); but it will rapidly become so as n approaches
the order of io4 (c/n = 3 X io~6), which again is closely verified by the
above data.
Finally, if the decay bn2 is temporarily ignored and if the ions are
supposed to be absorbed with a velocity K at the walls of the cylindrical
fog chamber of length / and radius r,
I . 2 XT . K . n = I . nr2 . en or K = cr/ 2
if c = 3 . 5 X i o ~2, r — 6 cm. , K = o . i cm/sec. , which is not an unreasonable
datum. It is not improbable, however, that absorption occurs within
the fog chamber in view of the presence of water nuclei. Finally, if the
ends of the fog chamber be taken,
v- r r
'a(i+r//)
quite apart from the effect of internal partitions. Hence K estimated
at o. i cm. /sec. is an upper limit.
Again, if —dn/dt= — a + bn2 + cn, the conditions of equilibrium are
modified and become (since dn/dt = o)
a = en + bn2
where a measures the intensity of radiation. It no longer varies with n2.
Thus
2&V
The complicated relation of n and a was not suspected in my earlier
work, where distance effects due to X-rays were observed.
130 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
77. The absorption of phosphorus nuclei.* — The method of the pre-
ceding paragraph applied to the data obtained in the given paper with
phosphorus nuclei leads to striking results. It shows the possibility of
computing nucleation by passing a current of highly ionized air through
tubes of known length and section into the steam-jet apparatus there
developed. In these experiments, made a long time ago, the value of the
absorption velocity K was found to be 0.3 cm. per second, with the
condition that decay by the mutual destruction of phosphorus nuclei is
negligible. The equations here are
where v is the velocity of the air current bearing phosphorus nuclei
and flowing through a tube of radius r, and where n0 and n are the
nucleations at the ends of the tube of length x.
If V and V are the volumes of air in liters per minute of lengths
x and o, discharging equal numbers of nuclei per second into the steam
jet,
If decay can not be ignored, as is now to be assumed, the equation is
more complicated; for
-(v/K')dn/dx = 2Kn/K'r + n2
or
n(£2K(x-Xo)/rv(2K + K'rn0) — K'rn0) =
where K' is the decay coefficient; or since ^ = 1000
n
itR=K'/2K=b/2C.
For the same clear blue field seen in the steam-jet apparatus, the incom-
ing volume per second of nucleation must be constant. Hence nV =
n'V', and if x = o,
0 0 V
If V = V0 corresponds to xf = o (or the absence of the tube)
eKrx/2.65VlL + Rr\_Rr =
\W0 /
The equation therefore reduces to
V /V0+i
e rX/2'65V=:i+Rrn0+I
whence
i / V/V0-i
I T
n — -T-* ' z.-'*^- /« A^T/ A
* Experiments with Ionized Air, Smiths. Contrib., 1309, pp. 34-36, 1901.
RESIDUAL WATER NUCLEI.
It is well worth while to compute n from the results stated, and this
has been done in table 54. To do so it is necessary to accept the values
TABLE 54. —Initial phosphorus nucleation, n0, from steam-jet measurements (Smith-
sonian Contrib. No. 1309, pp. 34-36, 1901). Assumed 6=io-6; £ = 0.0356; b/2c=
i4Xio-6 = /?. Fin liters per minute. n0 = ~ ^ krx/a 6°~. '— - i J
X.
V.
IO-6M0.
x com-
puted.
X.
V.
IO-X-
x com-
puted.
I. Absorption pipe gray rubber. 2 r =
V. Absorption pipe brown rubber.
0.64 cm.; 1/0 = 0.75.
2r = o.35 cm.; V0 = 6.
cm.
cm.
0
0.7
0
0.7
....
125
3-1
3-3
120
50
i-5
7-i
....
295
4-7
3-6
291
IOO
1.9
6.4
....
455
6.5
4.6
555
150
2.3
6.6
0
0.8
2OO
2.8
7-8
....
250
3-i
7-7
300
3-5
8-4
II. Same. ^ = 0.75.
O
0.6
cm.
VI. Absorption pipe lead. 2r = o.63
0
0.5
....
....
cm.; V = o.6.
85
2. I
i-9
49
125
2.8
2.7
97
295
5-2
4-4
360
cm.
455
6.9
5-3
624
o
0.5
IOO
2-3
3-0
200
4.2
5-9
300
4-6
4.6
III. Absorption pipe brown rubber.
400
4-7
/-» Q
3-4
....
2r = o.35 cm.; F0 = o.6.
o
O . o
cm.
VII. Same.
o
0.5
....
JOO
1 -3
4.6
150
i-7
4-7
cm.
200
2. 2
5-9
o
0-5
....
250
300
350
2.6
3-3
4.2
6.4
9.0
13.0
....
34
68
IOO
200
I . 2
2.O
2.6
3-8
i .6
3-2
4-i
4.6
....
300
4-3
3-9
....
0
0.6
....
....
IV. Absorption pipe glass. 2^ = 0.29
to 0.32 cm.; l/0 = o.8.
VIII. Absorption pipe lead. 2^=3.2
cm.; F0 = o.7.
cm.
o
0.8
....
50
I .2
2.5
....
cm.
IOO
1.4
2. I
0
o-7
....
....
150
i-9
3-7
50
i-4
4.8
....
0
0.8
IOO
i-7
4-i
....
150
2.O
4-4
132 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
for Kr and K, and these_are taken from section 79, where b = K = io*
and c = K" = o.o356, fairly reproducing the data obtained with ions in the
fog chamber.
Naturally it is hazardous to accept the constants for ionized air and
apply them to the case for phosphorus emanations. Hence the order
of values of n in table 54 is surprisingly good. For similar values of n
are obtained with the fog chamber where the initial nucleation has been
found by the totally different method of successive exhaustions.
There is an observable increase of n with the volume of nuclei-bearing
air (V liters per minute) passing through the tube in a given time. But
this is not unreasonable, because when the velocity of the current is
greater, fresher phosphorus emanation reaches the mouth of the absorp-
tion tube. Moreover, since the criterion of an efflux of fixed total nuclea-
tion (nV) per minute is the color of the field of the steam tube, a better
general agreement must not be anticipated. Finally, the activity of
phosphorus in producing ionized emanations varies with temperature
and V0 is very difficult to obtain closer than yo = o.5 to 0.8. The
constants b and c are thus provisional values.
The high results for brown rubber are clearly due to low values of
V0 found in the experiment. Thus if V0 = o.8 had been taken instead
of V0 = o.6 the following values would have resulted:
III [ ^~ I-3 I-? 2-2 2'^ 3' 3 4'2 liters per minute.
\ io8»0= 2.0 2.4 3.6 4.0 6.0 8.8
v f V= 1.5 1.9 2.3 2.8 3.1 2.5 liters per minute.
\ioe«0= 4.0 4.0 4.0 5.2 5.2 6.4
These are much nearer the other values, showing that the great diffi-
culty of finding V0, the influx in the absence of an absorption tube,
is the outstanding discrepancy which is principally responsible for the
fluctuation of data. There seems to be no effect due to either diameter
of tube or substance of walls.
In Series I and II, a few of the tube-lengths are computed for a mean
constant n0 = 3, 600,000. The agreement is admissible in case of series I
but not in series II, since a tube-length of 10 cm. makes an appreciable
difference in V.
In the above equations, since nV = n0V0, it is therefore possible to
pass at once to the nucleations by writing C = n0V0, or
Krnx/2.$6C _ l^o
It is therefore well worth while to try the experiment with dust-free
air ionized by radium or the X-rays, in which case the complications met
with in case of phosphorus nuclei will be avoided. The steam tube,
which is ordinarily fed with atmospheric air, may, however, have to be
modified.
RESIDUAL WATER NUCLEI.
133
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
78. Data. — Experiments were made with special reference to the
views just given and are found in table 55. It is not possible, however,
from results of the character of the present, to discriminate sharply
TABLE 55. — Decay of ions under high ionization (strong radium and X-rays). dp/p =
0.305. Bar. 75. 3 cm.; temp. 27° C.; df> = 22.g cm.
Radium I-IV.
,-v Successive
Cor- „„,,
n Successive
Cor- _8,,
Time.
5.
s' = recte
o . 1 25 n X
d
Time.
5.
s' — recte
o . 1 25 n X
d
io-3.
io-3.
5 sec.
20 sec.
5 sec. 20 sec.
o
SfO 71
88 '178
20
77
4. O 23
o
e'o 71
8.8 ^78 ....
2S
20
3 . S l6 I . IO I .08
5
51
6.1 81 1.26
... •
25
35
4-2 27
c:
S2
62 87 ....
2S
77
4..O 23
10
46
5-5 58 1.32
....
30
29
3.5 16 2.66 2. 02
10
44
5-3 5
i
30
30
3.6 17
15
35
4-2 27 3.44
....
60
21
2-5 5-5 4-i 3-30
15
37
4-4 30
60
21
2-5 5-5
20
35
4.2 27 0.86
1.72
0
71
8.5 '165 22.25
II. X-rays. £>=ioo. Sf>/ £ = 0.300. Bar. 75.6cm.; temp. 27° C.
Cor-
Succes-
Cor-
Succes-
Time.
5.
^ = 0.125.
rected
sive
Time.
5.
Sr = O. 125.
rected
sive
n X io-3.
6Xio«.
nXl°~3
&Xio8.
0
we 89
10.7
332i
1.50
40
25
3-0
8.9
2.40
0
87
10.4
3 299
40
25
3-0
8-9
....
10
45
5-4
53
1.63
50
23
2.8
7-4
10
46
5-5
56
50
23
2.8
7-4
20
37
4-4
29.7
2-43
o
88
10.6
33i6
20
36
4-3
28.1
5
58
7.0
119
30
30
3-6
16.9
5-23
5
54
6-5
95
....
3°
30
3-6
16.9
....
III. X-rays. D = 5O. <5/>//> = o. 299. Bar. 76.0 cm.; temp. 25° C.
Cor-
6Xio«
Cor-
6Xio6
Time.
5.
Sf = O. 125.
rected
succes-
Time.
5.
Sr =O. 125.
rected
succes-
nXio-3.
sive.
«Xio-3.
sive.
o
w r 91
10.9
337
1.17
40
28
3-4
H
o
90
10.8
331
40
27
3-2
ii
....
IO
49
5-9
69
1.76
50
23
2.8
7-5
....
10
48
5-8
66
50
24
2.9
8.2
....
20
40
4.8
38
2.68
5
57
6.8
107
....
40
40
4-8
38
....
5
52
6.2
84
....
30
33
4-0
23
3.91
0
wr 86
10.3
288
....
30
30
3-6
17
....
Corrected for expansion, 231, 231, 215. 2Mean. 3 If corrected for expansions, 414, 385, 407.
RESIDUAL WATER NUCLEI.
TABLE 55 — Continued.
'35
IV. X-rays. £>=i5- (?/>//> = 0.299. Bar. 76.ocm.; temp. 27° C.
Time.
Cor- frXio6
S. ,y'=o.i2S. rected succes-
«Xio~3. sive.
Cor- &Xio"
Time. 5. s' = o.i2S. rected succes-
nXio~3. sive.
o
10
10
ybm 13.4 625 1.38
49 5-9 69
47 5.6 60 2.03
20 36 4.3 28
20 36 4.3 28
o g' 116 14.0 750
V. X-rays. D=i5cm. c?/>//> = o. 297. Bar. 76.4001.; temp. 26° C.
Time.
5.
S' = O.I2S.
Corrected
«Xio-3.
Time.
S.
Sf = 0 . 1 2.S.
Corrected
nX io~3.
o
10
10
gy 124
54
49
14.9
6-5
5-9
620
93
68
50
50
30
26
28
3-4
3-7
10
14
18
20
2O
35
4-9
4-2
40
26
30
10
34
4.1
6.1
24
78
30
30
40
29
32
27
3-5
3-8
3-2
15
19
1 1
5
5
o
wo 70
70
gy 133
8.4
8.4
16.0
200
200
990
40
27
3-2
ii
between c and 6, and the endeavor will have to be made to select the
best values from inspection.
The data of table 55, both observed and computed, in accordance with
section 76, are shown in the charts (figs. 45 to 49). In fact, the data of
table 52 also appear therein in a new light, the whole being summarized
in table 57.
79. Remarks on tables. — In these series the constants obtained for
different intervals of t — 10 directly are as follows:
TABLE 56.— i/n- i/w0=(i/«0+ &/c)(y(<-'o)- i).
Series.
t-t.0.
io36.
c.
io36/c.
Temper-
ature.
Pressure.
seconds.
o
'••!
o, 15; 15, 30
5, 15; 20, 30
0.00239
.00286
— 0.0177
— .0196
-0.135
. 146
} *
75-3
n.j
o, 20; 20, 40
10, 30; 30, 50
.00082
. 00088
+ . 0448
• 0315
- .0183
.0281
f "
75-6
m. \
o, 20; 20, 40
10, 30; 30, 50
. 0006 I
. 00056
.0411
.0399
.0149
.0140
1 1
76.0
IV.
0, 10, 20
.00107
.0388
.0275
27
76.0
Mean data, series II to IV, 6 = 0.000,00079, 0=0.0392.
CONDENSATION OF VAl'OK AS INIH'CKP UY NUCLEI AND IONS.
There is a curious consistency in the constants so determined, even
when the compensating values of b and c are of different signs, as, for in-
stance, in scries I. The reason is not apparent, but the fact is note-
worthy. These constants will necessarily be correct at three values of /,
but the computed values of ;; are no better as a whole than will be the
case if the first set of constants of series IT, for instance, are used.
200 .
WO
J<>
CO
70
i/ 10 ;a> 30 40 vi' ui- ;v
FIG. 48. — Decay of ionization in fog chamber in lapse of seconds,
observed and computed.
In fact, the constant b may be arbitrarily put as a reasonable estimate*
o.oooooi with (7 = 0.0356 and a fair reproduction of the observations
*To\vnsend, McClung and Langevin find b= i.i X io~9 about, using electrical methods.
See Rutherford's Radioactivity, pp. 41, 42, 1905.
RESIDUAL WATER NUCLEI.
obtained. This is shown in table 57 and the charts (figs. 45 to 49),
in which the values of the earlier table 52 have been incorporated.
The charts (figs. 45 to 49) show, however, that in all cases the fall of
computed curves, while not quite rapid enough at t — /„< 10, is somewhat
too rapid for the higher time intervals. It follows that 6 is less than
io~8 and c greater than 0.035. ^ we take the mean of the positive
values in table 56, 6 = 0.00079, £ = 0.039; but the provisional constants
in table 57 are in much better agreement with the observations than the
direct values.
TABLE 57. — Estimated constants b = ID-*, 0=0.0356. n given in thousands per cm3.
Series.
t.
io~3Xn
observed.
io~*Xn
computed.
Series.
/.
io-8 Xn
observed.
io~3Xw
computed.
i
0
24.4
24.4
2
0
310
310
5
17.2
18.3
5
107
107
10
17.2
14.2
10
55
60
15
13-7
1 1 . i
20
29
28
20
9-i
8.9
3«
17
16
30
5-5
5-6
40
9
10
60
3-6
1.8
50
7
6
2
O
"•5
".5
3
0
334
334
5
7-2
9-i
5
95
no
10
8.2
7-3
10
67
61
20
5-8
4.9
20
38
28
25
4-5
4.0
30
20
16
30
2.6
3-3
40
12
10
60
i.4
i . i
50
8
6
3
0
39-6
39-7
4
0
625
625
5
28.5
28.1
JO
65
70
10
? 13-9
20.8
20
28
3i
20
? 7-7
12.4
30
8.0
7-9
5
O
620
620
IO
81
70
i
0
178
178
20
33
3i
5
84
82
30
17
17
10
54
50
40
ii
ii
15
28
34
50
>I2
7
20
25
25
30
21
»7
2.5
22
19
IO
78
70
30
17
H
5
200
135
60
5
4
1 Continued after i hour's rest. Too high.
The question finally arises whether any systematic error in the
standardization of coronas, and hence in the values n, could have pro-
duced an effect equivalent to the occurrence of the constant c. The
equation may be written
— I
.fc
-
rta&er
RESIDUAL WATER 1'CLEI.
obtained. This is shown in table 57 ai the charts (figs. 45 to 49),
in which the values of the earlier table 5 been incorporated.
The charts (figs. 45 to 49) show, howe r, that in all cases the fall of
computed curves, while not quite rapid :— /„< 10, is somewhat
too rapid for the higher time intervals, t follows that 6 is less than
io~* and c greater than 0.035. If w< an of the positive
values in table 56, 6 -=0.00079, c = 0.039 >ut the provisional constants
in table 57 are in much better agreer -\ 'Starvations than the
_t val-
TABLE 57.— Estimated c
>« it)"*, c- • < n in thousands per cm*.
.— ('/a.
„ . io~»X» io-*X«
Series. observed, computed.
r.
i o 24.4 24.4
1 5 »7-t *
10 17.2
14.2
IO
15 iJ-7
ill
20 9- I 8.9
30 5.5 56
40
1.8
2 0 MS > 1 -5
0
io 8.2 7-3
[O
20 5.8 49
20
25 45 4-o
30 2.6 3-3
40
14 I.I
50
.
o 6
3"
o
tf
5
i
IO
to
20.8
20
20
It. 4
30
8.0
79
o
10
I
•
5
10
178
178
5°
"
13
20
3°
60
28
17
5
m
The question
standardiza4'
duced an
equation
io-*Xn
io-' Xn
served.
computed.
3'° 3'°
107 i<>7
55
29
28
17
16
9
IO
"
6
334
334
95
no
67
61
38
20
16
I 2
IO
-
6
625
625
65
70
28
M
620
620
8l
70
1
17
17
1 1
7
r in the
have pro-
nt c. Tie
CONDENSATION OF VAPOR AS INDUCED
BY NUCLEI AND IONS
THIRD REPORT
BY CARL BARUS
Hazard Professor of Physics, Brown University
WASHINGTON, D. C.:
Published by the Carnegie Institution of Washington
1908
' 1BRARY