UC-NRLF
fiSl
OF THE
JNIVERS1TY
OF
3ICS
CONDENSATION OF VAPOR AS INDUCED
BY NUCLEI AND IONS
THIRD REPORT
BY CARD BARUS
Hazard Professor of Physics^T^rown University
WASHINGTON, D. C.:
Published by. the Carnegie Institution of Washington
1908
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
aSSICS UBRARY
^. 7 1
U BRAKY
PREFA'CE.
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 io 5 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
M663474
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 2 -{-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.
1 . Introduction T
2. The variables. Table i x
3. Approximate computations of /> x and p 2 . Table 2; fig. i 3
4. Definite computations of p t and p 2 . Table 3 6
5. Computation of vjv. Table 3 ; fig. 2 7
6. Approximate computation of j^ 8
7. Approximate computation of p 2 9
8. Rate of reheating of the j:og_chamber. Table 4; fig. 3 Io
9. Definite computation of r lt p lt r 2 , 2 , etc. Table 5 ll
10. Conclusion X 3
CHAPTER II. Changes of Vapor Nucleation of 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.
n. Introduction. Table 6; fig. 4 J 4
12. Data. Tables 7 and 8 ; figs. 5 and 6 J 7
13. Explanation. Table 9 2l
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
18. 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 4 1
23. Conclusion 4 l
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 5 1
30. Data for high exhaustions. Table 19; fig. 16 54
31. Standardization with ions 5 6
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 OF 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 6 5
v
VI CONTENTS.
Page
40. Graphs. Dust-free air. Figs. 20, 21, and 22 68
41 . Weak radiation 7
42. Moderate radiation 7
43. Strong radiation 7
44. Other nucleations 7
45. Temperature effects. Table 30 7 l
46. New investigations. Tables 31, 32, and 33; fig. 23 72
47. Conclusion 75
CHAPTER IV. The Nucleation Constants of 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 1 1 1
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 1 20
CHAPTER VI. The Decay of Ionized Nuclei in the Lapse of Time.
7 1 . Introduction 1 2 1
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
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
2 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, n vapor pressure, is to be considered.
The ratio of volumes of the fog and vacuum chambers was about
TABLE i. Notation. Drop of pressure dp = p-p 3 , observed; dp = p-p 2 , computed.
St^ e Fog chamber.
i
Vacuum chamber.
Remarks.
i i p
p
T
7t
P'
P'
r
71
Initial states; cham-
r
bers separated.
2
Pi
Pi
T!
X
P\
P'l
T',
n\
Adiabatic states,
after exhaustion;
chambers commu-
nicating.
7
Pi
Pi
T!
TTj
P*i
P'l
^i
77,
The same, after con-
densation of water
in fog chamber.
4
P,
Pz
T
1C
P' 2
P' Z
"
71
Chambers separated
before condensa-
tion ensued ; orig-
inal temperature
regained.
5
P2
T
~
P T 2
P 7 !
T
71
Chambers separated
after condensa-
tion ; original tem-
perature regained.
6
Ps
P3
T
7C
P*
P&
T
n
Chambers communi-
cating after ex-
haustion; original
temperature re-
stored.
i
At the beginning (case i), the fog chamber is at atmospheric pressure
p (nearly), the vacuum chamber at the low pressure p 1 ', and both at
the absolute temperature r. 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 r,
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)=Rp-c. This gives
eleven equations, some of which may be simplified. Corresponding
quantities in groups i and 2, as, for instance, r/r 1 , 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 n are supposed to be given by the corresponding T,
though at high exhaustions the lower limit of known data, TT = /(T), is
often exceeded, at least in case of vapors other than water vapor.
3. Approximate computation of p t and p 2 . It will first be necessary
to compute p 2 , 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
* lk and r/r\
at the outset, in correspondence with Boyle's law, and thereafter to
correct for the temporary introduction of n 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 n, 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 p 2 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 p 2 . (Sections 5 and 9.)
The solution when the air in both chambers is continually saturated
leads to transcendental equations for the adiabatic pressures pi=p'i,
4 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
which can therefore only be obtained approximately. If the vapor
pressures ^ and n\ correspond to p^ and p\, the results would be
, cjk==
Pl ~~ ~~~-
-x) (i+v/V)
, _ _. \c/k
where approximate values must be entered for n lt n\, p lt in the denom
inator on the right side of the equation.
Similarly
- ( *- e)/ *
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/ F = 0.064; P~76', t=2OC.\
7r=i.7 cm.; t refers to degrees C., T to absolute temperature, dp denotes the
drop in pressure. r/r 1 =(p/p l ) l - c/k and T/T' I )<=(/>//> / I ) I -C/& assumed.
Observed. 1
Computed. 2
P.
/V
/V
/>',-
Pi-
P\.
/V
V*
P 2 .
43-5
5i-5
59-5
45-5
52-5
59-7
47-9
54-3
?62.2
45-6
46.1
52.5
59-3
46.!
52.5
59-3
54-7
59-6
64.6
44-9
52.0
59-4
49-9
55-5
61.5
,.
*v
ffj.
^
^.
t\.
*P*-
p-ps-
9P*~
P-P 2 -
*P/9P*
o.o
. 2
5
2.2
1-9
i-7
0.7
9
i.i
o
-17.8
- 8.3
+ .8
+ 5-2
9-4
12.7
+ 24.1
21.3
19.8
0.0
16.3
23-5
30-5
0.0
11.4
16.4
21.3
[lo.7o
J 0.69
1 These observat[ons merely illustrate the equations. No attempt made at accuracy. See chart.
s The values of Pi/Pi = 0.91, 0.93, 0.95, respectively.
The corrections, (p 2 p 3 ) varying with (p p a ), 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, xxn, p. 342, .1906.
EFFICIENCY OF PLUG-COCK FOG CHAMBER.
*Q* 45* 25
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 ' = 45 cm. and p = 6j
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/TJ is here an approximation.
A few incidental results deserve brief mention. The first of these is
the nearly constant difference of about dp 2 = 2 cm. between the observed
value p 2 (nominal) and p 3 . Since for dry air or not
(p' 2 -x) +v/V (/v-*) = (/Y-*) +V/VJ
is constant for a given exhaustion, dp' 2 = v/V - op 2 . Hence if
dp 2 = 2 cm., since v/V = 0.064, dp' 2 = o .064X2 =o .13 cm., nearly.
This case is illustrated graphically for p f = 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 p 2 , the large vacuum chamber is only a millimeter
short of them when the cock is again closed. The constancy of the
observed difference p 2 p 3 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 ^' = 59.5 cm., are direct errors of observation. On the other hand,
however, since within the ranges of observation p = a, P 2 = a 2 + b 2 p',
Pz = a a + b 3 p' very nearly, it follows that (p p 2 ) / (p p 3 ) may approxi-
mately be written A+Bp', where a, 6, A, B, etc., are constant. Fre-
quently B is negligible, so that (p 2 p s )/(p p 3 ) is constant, in which
case the graphs for p 2 p 3 varying with p p 3 pass through the origin.
4. Definite computation of p 1 and p 2 . If the adiabatic equations be
written without approximation
T j f i +
and
TI
the equations for p l and p 2 become
-
and
Pt-xJ V
from which p l may be found after putting an approximate form for p l
(p 3 nearly) into the vapor-pressure term of the second member. A
single approximation usually suffices.
From these equations
follow at once. Subsidiary equations
and
s ,
remain as before in section 3. To compute v/V in this way high ex-
haustion is essential, otherwise p' and p 3 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.
7
5. Computation of v t /v. Since (v 1 /v) k/c = p/p l , the volume expan-
sion is a cumbersome datum to compute rigorously, and it appears as
7t
where an approximate value of p l (nearly p s , observed) must be placed
60
FIG. 2. Same as fig. i, if the temperature ratio is corrected
and reads T/ T I == (/>//>I) I ~ C/A;
in the vapor-pressure terms of the second member. For distinction [v/ V]
here denotes the volume ratio of fog and vacuum chambers. The terms
involving vapor pressure may often be neglected, whereupon the equation
v f p
/(l-c/fc)
+v/V*p
P_y*
pj
reappears, if the equivalent of p t be inserted. In these cases p l may
again be replaced by p 3 .
8 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
The data for p ly etc., are given in table 3, and are shown in the graphs
of fig. 2, whence their differences from fig. i may be ascertained. The
respective pressures holding for ^' = 45 cm. are also shown in a notched
curve and will be further elucidated. The ratio dp 2 /dp 3 of the isothermal
and adiabatic drop is here (table 3) about 0.68, or of the same order as
in table 2.
TABLE 3. Definite computations corresponding to table 2. p~j6 cm.; t=2O;
7r=i.7; r/T l ='(p/p l ) 1 -c / k i and r/T r l =(p/p' i y-e'k assumed.
*,.
*v
,
P'-
/>,
P, t,
r,
P,
P'z-
v*.
Pi/P-
O. I
2-4
0.6
43-5
45-5
46.4 19.0
25.6
55-1
44-9
1.416
0.920
.2
2.O
Q
52-5
52.6 - 9.6
21.9
60. i
52.1
1.292
939
5
i.7
i.i
59-5
59-7
59-3 - -2
19.8
64.9
59-3
1.181
958
T,.
P*
Pi-
I0 x.
*
W ,
^3-Or-Kx)
P-P 2 .
^3 =
P-P
Ratios
dp 2 /dp a .
/>-^
4-9
50.8
47.2
5-6
30-5
0.401
0.389
0.0
0.0
1
9.0
56.6
53-5
4-7
23-5
309
.297
ii . i
16.3
10.677
12.7
62.3
60. i
3-6
16.3
.214
.203
15-9
23-5
J .690
20.9
30-5
J
6. Approximate computation of T X . To find the temperature of
the fog chamber after the adiabatic temperature r l has been raised by
condensation of fog to r ly it is apparently necessary to compute p 2
first, and then proceed by the method used by Wilson* and Thomson.
When the vacuum chamber is large, however, its pressures vary but
slightly, and therefore the pressure observed at the vacuum chamber
after exhaustion, p 3 , when the two chambers are in communication, is
very nearly the adiabatic pressure of the fog chamber, p v This result
makes it easier to compute not only T I} but incidentally the water, m,
precipitated per cubic centimeter (without stopping to compute the
other pressures), with a degree of accuracy more than sufficient when
the other measurements depend on the size of coronas.
To show this, let d, L, and n refer to the density, latent heat of
vaporization, and pressure of water (or other) vapor; let p, k, c, T,
denote density, specific heat at constant pressure, specific heat at con-
stant volume, and absolute temperature of the air, the water vapor
contained being disregarded apart from the occurrence of condensation.
As above let the variables, if primed, belong to the vacuum chamber,
otherwise to the fog chamber. Let the subscripts, etc., also be similarly
interpreted, so that d is the known density of saturated water vapor at
T absolute.
*C. T. R. Wilson: Phil. Trans., London, vol. 189, p. 298, 1897.
EFFICIENCY OF PLUG-COCK FOG CHAMBER. 9
Assuming the law of adiabatic expansion to hold both for gaseous
water vapor and for wet air in the absence of condensation, it is con-
venient in a plug-cock apparatus of fog and vacuum chamber (where
pi is nearly given by p a ) to reduce to adiabatic conditions; whence
where m is the quantity of water precipitated per cubic centimeter of
the exhausted fog chamber. Finally d, the density of saturated water
vapor, must be known as far as r, so that an equation df(r) is addition-
ally given. Here 7i t the vapor pressure at r lt is usually negligible (about
0.5 cm.) as compared with p lt and p t may in practice (where great
accuracy is not demanded) be replaced by p 3 , which like p is read off,
while TT holds at T, which is also read off. In the next section I
give a numerical example, taken from table 2, for ' = 43.5 cm.
If the original equation (isothermal) is taken, m = $. 36X10 ~ 6 grams
per cubic centimeter. If the above equation is taken, w = 5 . 35X io~~ 6 .
If the same equation is taken and p 1 replaced by p 3 , m = $ -3oX io~ 6 ,
the error being i per cent of the true value, which is near enough in
practice or admits of easy correction.
7. Approximate computation of p 2 . Since the plug stopcock can
not be closed before the water condenses in the fog chamber after
sudden exhaustion, the pressure observed in the fog chamber when the
room temperature reappears is smaller than p 2 . An excess of air has
passed to the vacuum chamber, so that the pressure within the fog
chamber is eventually p 2 , or less. The equation for p l and p\ remains
as in section 3, or better, as in section 4.
The new quantities are
ri
where p l is the density of air at r t . The ratio pj p v may be found when
T is known as
Pi (PiKj (TI/
where r\ and T^, n\ and n\, p l and p\ are nearly the same. The last
equation may usually be written
10 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
and the small quantity involving the vapor pressures n treated as a
correction. It amounts to about i per cent of the large quantity. The
values of p 2 are also given in the table and chart. This shows that p 2
observed is always smaller than p 2 computed, even when allowance
is made for the condensation of water; i. e., the fog chamber begins to
appreciably heat itself above the temperature T I before the cock can be
closed again, so that when isolated it contains less than its proper
quantity of air. Only the initial and the final (both chambers com-
municating) pressures may therefore be taken at the fog chamber.
(Cf. section 9.)
8. Rate of reheating of fog chamber. There is a final question
at issue, relating to the rate at which heat flows into the adiabatically
cooled fog chamber. Experiments may be made by opening the exhaust
cock for stated lengths of time t. The vacuum pressure being p f = 48 . 6,
the datum for t = o second may be computed as ^2 = 57.8 cm., or after
condensation ^ = 52.4 cm. Table 4 contains the results, and they are
fully mapped out in chart, fig. 3. The notched curves show the suc-
cessions of pressure in both chambers. Neither p 2 nor p' 2 may be ob-
served, since the chambers communicate during the opening of the stop-
cock for a period certainly longer than o . i second. Observable pressures
are shown on the vertical line below p 2 and above p' 2 . Hence within
a quarter of a second the final isothermal pressure (/ = oo , chambers
communicating) is already regained to more than 60 per cent, and this in
spite of the fact that the capacity of the fog chamber is over 6 liters.
Hence the attempt to observe p 2 (isothermal temperature after con-
densation) at the fog chamber is idle. It practically reaches p 3 if the
exhaust cock is open about 10 seconds. The pressure p 2 is never reached,
yet p 2 is exceeded, owing to the counteraction of the vacuum chamber.
Finally p may be virtually read off in case of a large vacuum chamber
by adding a slight correction for p 3 . This is one of the advantages of the
method.
TABLE 4. Rate of heat influx. Barometer, 76.0 cm.
t.
'
l *V
Observed
P*
P' 3 -
P*
sec.
cm.
cm.
cm.
cm.
cm.
0.25
48.6
50.2
53-2
50-3
50.6
i
48.6
50.2
52.0
50.2
50.5
2-5
48.6
50.4
51-5
50.4
50.5
5
48.6
50.2
50-9
50.2
50.3
5
48.6
50.2
52.7
50.2
50.2
From chart ' = 48.6; 3=57.8; 2=52.4 cm,
'Ftom the chart /> / 1 = 5o.2; '3=50.0.
EFFICIENCY OF PLUG-COCK FOG CHAMBER.
II
O*' /
FIG. 3. Observed value of apparent isothermal pressure p 2 , after lapse of different
seconds of time after exhaustion; also corresponding drop of pressure df> 2 from
atmospheric pressure.
9. Definite computation of r lt p t , r 2 , p 2 , etc. In view of the
equation
the density of saturated vapor at the temperature r becomes
" c/ * c -
where d 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
If the coefficient of d in the above equations be written x,
where a and b are constant, so that r is the temperature at which the
line J, 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 ^ and ^ may be used. Table 5 contains a series of
useful data for m, dp (if = 76), dp/p, v 1 /v, / lf and / r
TABL,E 5. Water precipitated at different exhaustions and temperatures.
= 76 cm.; dp 3 =p p 3 cm.
a
y
dp
P
dp.
At 10 C.
At 20 C.
At 30 C.
wXio 6 .
/ 1 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'sf 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 dp is the observed fall of pressure
(P~p3)> P the pressure of the fog chamber before, p 3 the pressure after
*Carnegie Institution of Washington Publication No. 62, chap, vi, 1907. Cf. Science,
xxm, p. 952, 1906; xxiv, p. 180, 1906.
fWood and Campbell: Nature, LXXIII, p. 583, 1906.
14
CHANGE OF VAPOR NUCLEATION IN LAPSE OF TIME.
exhaustion with fog and vacuum chamber in communication, all at the
same temperature; 5 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.
Date, etc.
Apparatus I.
Apparatus II.
dp,.
s i-
P.
s\.
n Xio- 3 .
3P
S 2 .
s z .
w 2 Xio~ 3 .
July 12, 8 h 50 ra
27.1
3-9
76.2
3-9
19
25-5
2-9
3-3
IO
3 45
27.2
5-i
76.2
4-9
37
25-5
2.6
3-o
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
IO
5 30
27.2
5-o
76.0
4-7
33
25-6
2-5
2-4
3-7
July 14, 8 41
27.2
5-6
76.0
5-3
46
25-4
2.6
2.O
2. I
3 20
27.2
5-o
75-9
4.6
30
25-6
2-4
2-3
3-o
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-o
7-4
3 30
27.2
5-6
75-9
5-2
43
25.2 j 2.6
3-5
12.7
5 25
27.2
5-2
75-9
4.8
35
July 1 6, 9 oo
27-3
5-5
75-7
4-9
37
25-5
2.9
2.9
"6.7
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-o
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 18, 9 51
27.2
5-5
75-8
5-o
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
i-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.
16 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
16
78
30
ZO
to
cfycvro
P
A
fVeib
10
7 July 9 11 13 tJ" 77 13 21
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 1 1 . 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 r l is the low (absolute) temperature obtained by
sudden expansion adiabatically from r the ratio TJ/T should be wholly
dependent upon the corresponding pressures; and yet, for the same
ratio, more nuclei are obtained as T is larger. This difference of be-
havior is maintained for larger and smaller ratios of r 1 /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 = 0.06,
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 p 3 , when in isothermal communication after exhaustion;
p 2 and p\, 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
p m 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 = Pp m p 3 , and the drop of pressure
takes place from p = Pp m adiabatically to p lt isothermally to p 2 if the
fog chamber were isolated as specified, or isothermally to p 3 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 p m , i. e., by
starting with a partially exhausted fog chamber and a vacuum chamber
at fixed exhaustion p' ', which implies a nearly fixed p z \ or by keeping
p m constant (small, nearly zero), thus starting with the fog chamber
about at atmospheric pressure, and determining p' of the vacuum
chamber and therefore p 3 .
Briefly, then, the condensational effects of a given difference dp when
lying between different pressures p and p 3 , 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 p 3 nearly constant
*Am, Journ. Sci., xxn, p. 136, 1906.
i8
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
and varying p m (lower pressure limit, p, variable) and second by keeping
p fixed and varying p' and p 3 (upper pressure limit variable). Tables
7 and 8 show these data, the latter for a wider range of coronas than the
v
FIG. 5. Nucleation of dust-free air for different drops of pressure dp = p p. 2 ; [dp]'
denoting that the upper limit, [dp^ that the lower limit of the drop of pressure dp
is varied. Also corresponding nucleation referred to the exhaustion dp/p. Four
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=pp 2 , 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
[^]i = I 7-4 an d [dp]' = 19 -4 cm. in fig. 6, where all data (table 8) were
obtained in one series of experiments.
7. Effect of varying p in
P-pm. v/V = o.o64; p-p
Chamber II. Bar.
dp; 71=2.3; ^=25
P.
P*.
*>-/>
#.
S.
Cor.
ttXio- 3 .
dp/p.
P-
I
7C 7
1 O 2
27 7
27 I
6 Q
2' B P
2 io5
O. ^SQ
7C c
. I
I .O
2 .O
5
5
. -2
4
26.5
2S . ^
6.9
7.0
S . I
g'BP
g'B P
2 io6
104
7Q
.362
.355
344
75-6
71.7
77.7
II
7tr 7
2.O
3-o
3-o
4.0
4.0
6.0
3 I
.6
.6
7
.8
7
.6
27 6
25.6
24.6
24-7
23-8
23-7
21.6
27 S
6.4
4-5
4.2
2-5
2.4
i-5
Q. S
w y
w r
72
27
21
4-3
3-5
1.4
190
.348
339
340
332
331
311
.364
73-7
72.7
72.7
71.7
71.7
69.7
75.6
4.0
I.O
6 o
!e
.8
23-7
26.6
21.8
2.4
7-i
1.8
g'BP
3-9
116
1.6
331
356
.313
71.7
74-7
69.7
I'
7C c
I.O
O 2
.6
24.. Q
26.6
24. 7
7-5
i . 7
g'BP
116
1.8
.356
.328
74-7
75-3
t 21 4 C
2^ 6
oc 4.
-\ 6
1 1;
. -IT.J
JT ! I Q
26 4.
26 2
5 6
C7
348
;r-7r 1 = 1.4.
IP
4 76.2
. 2
25. Q
2^. 7
3- 2
cor
9-5
338
76.0
*=2 3 C.
7T = 2.1.
71 71-^= 1.6.
5 I
7 e c
2
26.9
27.4
28.7
29.4
30.5
33-5
24. Q
26.7
27.2
28.5
29.2
30.3
33-2
24. 7
6.4
6.8
10.2
12
13?
13?
I .7
wp
gB P
w r
yr
gBP
Do
76
120
210
310
380
4IO
1.8
.351
359
375
.384
399
437
.328
75-3
4 = ,2~0p
2 c 6
2 c j.
i 6
15
337
* *o v*.
^O "
26 A.
26 2
^ 6
53
348
7T 7T!= 1.6.
^ u "4-
1 Water nuclei not precipitated. 4 From Carnegie Institution of Wa.shin^ton
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 l r 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 dp = p p z \ [dp]'
denoting that the upper limits, \dp\ 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. Data 1 corresponding to table 7 for larger ranges of dp.
21
P.
m-
P-P*
=
-#.-
S.
Cor.
nXio~ 3 .
/>
III
7S 8
O. I
27 6
27 5
91
w r
1 7Q
7 c 7
7T =2.5
/ O ' *-*
* 1 *\J
28.5
* / 3
28.4
l
ii. 5
2 w r o
1 / y
244
/ /
7T TTj = 2 . O
29.1
29.0
n. 8
2 w r o
332
29.9
29.8
g
375
26.8
26.7
8.0
139
25-4
25-3
4-3
2 4
26.6
26.5
7-3
H5
IV. ...
7S 8
. I
-IQ O
2Q Q
fir v o
"^ilO
7 c 7
71 =2.5
/ O u
1.0
O" **
30.1
* Z7 " V
29.1
5 J *-*
g'o
OH-*- 1
372
/ /
74-7
7T 7T 1 2 . O
2.0
30.2
28.2
ii
gyo
327
73-7
3-o
30.1
27.1
ii
w r o
234
72.7
4.0
30.1
26.1
9-5
w r
182
71.7
5-o
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-o
30.3
23-3
5-4
44
68.7
8.0
30.3
22.3
2.8
5-7
67.7
v
7q 8
i
28 *
28.2
1 1
y' r o
j. \j
24.2
75 7
7T =2.5
/
. i
^o . ^
25-3
25.2
2-9
***
6.6
/ O /
7T 7T t = 2 . O
1 Color distortion. The value of s corresponds to g y at least.
2 Fog chamber cleaned of water nuclei after each observation.
13. Explanation. It will next be necessary to endeavor to coordinate
the two curves for [dp] t and [dp]'. If the absolute temperatures of the
air within the fog chamber before and after exhaustion are r and r t
(adiabatic pressure p t ) then apart from the condensation of water vapor
at the original vapor pressure n at r, we may write as one extreme case,
With a large vacuum chamber the difference between p 1 and p 3 is very
small relatively to p l and p 3 , so that for the present purposes p p d =
p Pi = dp (nearly), whence
dp (TT Trjyfc-c)/*
P-X /
Similarly we may write as a second extreme case,
or the degree of sudden cooling from a fixed temperature T to the adia-
batic temperature r l depends primarily on dp /p. This would in any case
be permissible for comparison in table 6, where a continuous series of
experiments is made at the same temperature. The moisture error is
thus a constant throughout. Hence the apertures of coronas s, and the
nucleation n, will be a function of dp/p to the degree specified.
22 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
In table 9 I have, therefore, arranged the data for n with reference to
the corresponding values of dp/p, both for the cases of I, II, III, and V,
where the upper pressure limit of the drop dp (curve [dp]'), and cases
F, .IF, IV, where the lower pressure limit of the drop dp (curve [dp]^,
are varied. This result is also given in the chart (figs. 5 and 6) and the
mean results of the latter are suggested by the dotted line in the former.
In fig. 5 the curious result is obtained that the data for [dp]' are now
liable to lie even above those for [dp^ which is the inversion of the former
case. As a whole, however, and with due regard to the subtleties in-
volved, the two sets of data practically belong to the same curve, for
the departure of either in the long run is seen to be positive as well as
negative. The results of fig. 5 (as has been stated) were obtained in a
single series of observations, all at the same temperature. If they be
compared with fig. 5 (dotted line), containing observations made at
other times, they lie distinctly above the graph of the figure, no matter
whether [8p/p]' or [dp/p^ is in question. Hence it is again probable
that something else besides mere variation of the barometer is in question
and is not accounted for in the correction. Thus it is next necessary to
inquire into the effects of vapor pressure, which in series I and II would
differ from series I' and IF, though in series I, II, III, IV, and V the
temperatures are so nearly alike that shifting of graphs due to this
disturbance is not appreciable.
TABUS 9.
Summary of table 7. Summary of table 8.
.
dp/p.
nXio- 3
1' and II'.
dp/p.
nXio~ 3 .
I and II.
dp/p.
wXio- 3 .
Ill and V.
dp/p.
wXio- 3 .
IV.
0.328
2
0.3II
i
0-333
7
0.329
6
337
15
313
2
334
2 4
339
44
337
15
331
3
350
H5
338
10
....
353
139
349
93
348
53
331
4
358
157
.348
53
332
4
364
179
364
182
351
76
339
27
373
242
373
234
359
120
340
21
375
244
375
210
344
39
383
246
^382
327
384
310
348
72
394
375
390
372
399
380
355
104
395
340
395
340
437
4IO
356
116
356
116
359
105
362
106
364
190
14. The effect of vapor pressure. The second extreme limit,
may now be used and the data for nucleation, n, expressed in terms of
dp~(nn l )/(p7r) as the variable for comparison. Remembering
EFFECT OF VAPOR PRESSURE. 23
that the total variation of pressure to bring out the coronal phenomenon
does not much exceed 3 cm., and that the observations below will be
made within a single centimeter, the precipitation of moisture may be
treated as depending on T/TJ, the ratio of the initial and the final tem-
perature of adiabatic cooling if the former is nearly constant and if the
same medium is retained, though the case is in reality more complicated.
These data are also given in table 9 and have been inserted in fig. 7.
FIG. 7. Nucleation found at different drops of pressure. Second extreme case.
The graphs III, IV, and V are now even more coincident, whereas I
and II, V and II' differ from each other and from III and V in the same
sense as above. Hence, apart from barometric pressure, some other
cause must have influenced these nucleations.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
I conclude, therefore, that by far the greater part of the dependence
of the vapor nucleation upon the barometer is the necessary result of
the thermodynamics of the case, but that conclusive evidence of the
absence of other causes either within or without the fog chamber on the
time variation of its nucleation, though extremely difficult to make out,
seems as yet to be outstanding.
15. New data for vapor nucleation in the lapse of time. In table 10
results of the same character as the preceding have been collected.
Moreover, by choosing a particular dp (TT nJKp 7^=0.320 and
reducing all data for n to this value, the result so found (w 0-320 X io~ 3 )
should be independent of atmospheric pressure, etc., and respond to
external radiation if such exists. The data are shown in fig. 8a. They
are not out of keeping with Wood and Campbell's phenomena as a whole,
but they do not follow the barometer. The correction of n is about i . 7
per o.oo i of the pressure ratio, but it is too uncertain in this region,
since the graphs are of pronounced curvature.
TABLE 10. Time variation of the larger colloidal nucleation of wet dust-free air.
Conical filter. Apparatus II with 2-inch pipes, cleaned by precipitation before
observation. p m = o.i; p = Pp m ', p p 2 ==I 9-9-
Date, etc.
dp.
s.
P.
dp/p.
nXio~ 3 .
dp-fr-Kj
^O.KioXlO- 3 .
p-n
Aug. 6, 5 h i6 m
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
340
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
H
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
Au g- 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
319
29
4 i-o
25-7
2 3-9
75-8
340
2 i8
319
20
4 20
25-7
5-i
75-8
340
40
319
42
1 Not cleaned by precipitation.
Hence in table 1 1 a larger fiducial value (dp [TT 7rJ)/(/> ?0 =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 fullv 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 OP TIME.
% rf^N
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 w 0-335 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>340 for _/?/ = 0.340 and n 0>345 for dp/p = o.34$ are
derived to be used in the correlative summary in sec. 20. The nucleations,
w o.345> which suffice for the purpose, are given with the others in figs. 8a
and 86.
isc/m.
30
' 77
',11.
33
27 Sift 29 1 Oct. 3 S 1 9 11 13 \5 11
FIG. 86. Changes of vapor nucleation of dust-free air, barometric pressure,
temperature of the fog chamber in the lapse of time.
and
The data for n 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.
ii. Time variation of the larger colloidal nucleation of dust-free wet air. Cor-
responding to table 10, with allowance for temperature.
= p p
p 2 =
^>
A
/.-(*-*,)
"033,X
dp
io- 3
Date, etc.
op.
S.
P-
.
P .
io- 3
P
W io- 3
Aug. io, 9 h 3o m
25-7
3-9
75-8
26.0
0.323
18
1 (90) r
0-339
13-3
18.5
4 40
25-7
3-9
....
26.0
323
18
(
339
13-3
35
4 20
25-7
4-4
75-6
28.0
.321
25
340
18.5
4 30
25-7
4-4
28.0
.321
25
340
18.5
....
4 40
25-7
4-4
28.2
.322
25
105
340
18.5
18.5
25-3
3-7
75.6
28.2
.316
16
335
ii. 3
35
26.2
5-7
28.2
.328
55
VT <
347
39-o
27.6
'9.6
28.2
347
190
V 1. '
365
185
....
28.4
2 II.O
28.2
359
207
376
280
....
29.2
11.5
....
28.2
370
250
.386
320
Aug. ii, 8 50
27-3
75-5
25.8
347
130
70
362
IOO
15-2
25-1
2-3
....
25.8
317
3
to
332
2.6
40
25-7
4.1
25.8
325
19
65
340
15-2
27.0
3 7-3
....
26.0
343
105
VII.
358
83.5
....
28.2
4o.6
....
26.0
359
206
374
253
....
29-3
2 ii-5
....
26.0
374
250
388
320
....
30.2
gyo
26.0
.386
318
.400
5
25-3
3-0
75-4
26.0
.320
7
: 65 :
336
5-5
18.5
2 c 7
44,
/y f
to
^4-0
18.5
38
O /
27 I
*r
*7 T.
1,4.4.
IOS
1 80 '
OT"
A ^ O
83.5
o
* / *
28.5
I o
3 II.O
^6^
244.
'378
^O O
280
29.2
75-4
373
T"T"
248
J
* O /
.387
280
....
or y
386
T.AT.
AO2
31.0
6 J
gy
* % 3<-> x -'
398
OT~O
348
....
.411
....
. .
Aug. 12, io oo
25-7
3- 1
75*6
26.0
325
8
75
340
6.4
6.4
24 9
2 . I
^14
2.4
-7 OQ
1 .9
33
26.3
2 6.i
'^ ^
65
.348
49 .0
28.4
'10.5
^362
w O
195
* OT^
376
245
....
29-3
3 I2
....
25.2
374
248
....
.388
360
3 30
25-3
2.6
75-7
25.8
.320
5
80
334
3-7
30
26.8
4 7 ' 4
....
. . . .
340
105
....
354
86.0
50
27-5
....
. . . .
350
142
....
363
122
28 4.
2 io.5
.362
207
375
245
....
*'*-' . <-|
29-3
3 n-5
....
* O
374
248
.387
320
....
-JA 'I
' r 1
44 ?
4.1 c
453
460
OT- ' .
t.
/-(*-*.)
P-71
X io- 3 .
W 0.336X
io- 3
dp
P
tXio- 3 .
W 0.34 X
io- 3
W 034 8 X
I0~ 3
Sept. 7, 3 h 45 m
Sept. 8, 9 oo
4 oo
25-6
26.3
27.0
25-7
26.3
27.0
25-7
26 3
4.1
13 6.6
7.6
4.1
2
4.1
e 7
75-3
7s'-6
75-5
O
22 .O
22. O
22.0
0.327
337
347
327
336
345
.328
336
20
90
117
20
62
105
19
re
I'M
n
1 ss \
3.340
349
359
340
348
357
340
^48
15.2
61.5
94-o
15-2
43-o
80.5
15.2
-3Q
15-2
40
15-2
30
15-2
28
26 7
U 7 6
^4-2
IO4.
l \
j CA
QA
Sept. 9, 9 30
3 oo
Sept. 10, 9 oo
2 30
25-8
26.3
26.7
25-7
26.3
27.2
25-8
26.5
27.0
25-9
26 *
3-8
5-4
8 7-4
4-4
6.0
8 7-4
4-5
6.8
8 7-4
4-8
9 6 6
75-4
75-2
75-4
75-5
21 .0
22.6
22.8
23.2
332
.338
344
328
337
349
329
338
345
330
335
17
48
116
25
64
117
27
87
117
35
82
n
n
I'M
70 !
342
349
354
342
350
362
342
351
358
343
.348
12.3
32-7
86
18.5
46
86
19-5
66.5
86
23-5
61.5
8
20
13
30
10
35
IO
35
Sept. n, 9 oo
2 30
zu.^
27.0
25-7
26.3
27.1
25-8
26 ;
8 7-8
3-0
5-2
8 7 .o
3-5
c 8
7 6 '.2
7 6 '.2
22.0
22.2
345
325
333
344
326
77C
117
7
42
105
12
CO
1
55 |
358
337
345
356
339
.348
IOO
5-5
29
74
9-5
41
15
30
13
3O
Sept. 12, 9 15
2 30
Sept. 13, 9 oo
27.1
25-7
26.3
27.0
25-7
26.3
27.0
25-8
26.1
27 O
"7-4
3-8
4-9
8 7-3
3-6
6.0
'7.2
3-6
'I' 2
7 6 '.I
76.0
75-8
22. O
22. 2
22.
344
325
333
343
326
334
343
328
332
344
105
17
37
117
14
64
105
14
4 2
105
S M
KM
n
356
338
346
355
338
346
355
340
344
356
86
12.3
24.6
83-5
10.5
46.0
80.5
10.5
29
77-5
15
25
18
40
10.5
33
3 40
25-7
26.3
27 O
3-7
,;
75-6
22. O
327
336
345
16
53
105
n
340
348
357
ii. 3
36.7
80.5
"3
25
Sept. 14, 10 oo
25-7
26 3
4-c
5.8
75-
22.
327
335
18
57
!"(
339
347
14.2
4i
17
33
27 C
87
34 S
ios
J 1
357
77-5
3 30
Sept. 15, 9 30
2 30
25-7
26.3
27. c
25-*
26.2
27. c
25.
26 i
4-c
4: s
2.
13 6^
2.
75-
76'.
76'.
22.
22.
21 .
326
334
344
323
331
340
326
. -277
18
57
105
6
25
93
7
2 5
H
55 i
40 (
339
346
356
336
343
352
336
343
14.2
4i
77-5
4.1
18.5
64
5-i
18.5
18
35
13
30
13
30
27 c
11 7
. 34 S
105
[
355
86
Sept. 16, 10 45
25-9
26.'
26. c
2.
9 6!
77-
19-
327
335
340
7
32
89
I'M
336
344
349
5-i
22.2
56.5
13
30
7gy. 8gBP. 8 W6.
wy.
13 WO.
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE ii. Time variation of the larger colloidal nucleation of dust-free wet air Continued.
ty-Or-TO
w . 335 X
dp
W 0.34(>X
io- 3
Date, etc.
dp.
S.
/>
t.
p-lt
wX io- 3 .
io- 3
P
X io 3 .
0.8X
io- 3
Sept. 17, 4 b 45 m
9 oo
25-8
26.2
26.9
25-7
26 2
3-o
4-0
9 6.8
2.8
7 A
76.8
76^6
2O. O
20.5
0.326
332
.341
.325
2-22
7
18
95
6
12
n
30
0.336
341
350
335
.342
5-5
14.2
66.5
4.6
8.7
12
35
'&"
20
27.0
26 6
7-J
c 2
342
. "3^7
103
4.7
1
352
347
80.5
2 9
4 oo
26.0
27-3
26 8
3-4
,7-4
9 7 O
76.2
21.0
331
348
. 342
II
117
96
n
341
358
.352
8-7
86
74
3
30
Sept. 1 8, 9 oo
25-5
26 A
3-0
e c
76.1
21 .O
324
177
7
CJ
|40 J
335
347
5-5
75
is
7O
Sept. 20, 9 oo
27.1
25-6
26 7
<3
5-1
75-9
22.2
346
325
74.0
105
17
ci
150 r
356
337
.352
83-5
12.3
7,S
15
25
4 oo
27.0
25-7
26 6
(')
4-i
"7 4
75-6
23.0
344
327
. "^Q
105
19
Q8
L
356
340
.352
15-2
86.0
15
45
27 o
14 7 Q
. ^44
I4-O
j
357
IOO
Sept. 21, 9 oo
25-8
26 7.
4-5
13 6 8
75-5
23-5
328
. 335
27
87
J8 5
342
.348
19-5
66.5
3
4
2 45
26.8
26.0
26 3
14 7-9
4.8
13 7 4
75*6
23.0
342
331
77C
140
34
08
J9S j
356
344
.348
103
23-5
86
IO
7,8
Sept. 22, 8 45
3 15
27.2
25-9
26.1
27.0
25-9
26 i
r.'
3-5
5-2
( u )
3-5
c i
76^
76.0
22.0
22.2
347
327
330
342
-328
. ^I
117
12
42
94
13
40
r{
) 55
360
340
343
354
340
343
97
9-5
29
9-5
27.5
9-5
(?)
10
4
27 O
U 7 7
. ^4-^
qq
j
355
97.0
Sept. 23, 10 30
25-9
26 3
4-8
13 6 8
75-5
22.3
331
.336
34
Q8
)8 5
343
348
23-5
66.5
10
4
27 O
8 7 <5
.746
1 17
J
358
89.0
5 oo
25-7
26 2
4.6
6 i
75-4
23
327
. "}^4
29
66
ri
340
347
20.7
49
25
40
26 8
8 6 o
. "343
104
i i
355
69.5
Sept. 24, 9 oo
25-8
26 4
2.8
c . i
76.3
21
327
.736
6
4
35
338
.346
4.6
27.5
IO
2 5
27 I
6 S
i^c
ICK
. 35S
66.5
3 oo
Sept. 25, 9 oo
25-8
26.3
27.0
25-9
26 3
3-5
4-9
"7.0
2.4
A 2
76.3
77-i
20.8
19.6
.327
334
344
326
. ^2
12
37
99
3
22
43
45 {
338
345
354
336
34 1
9-5
24.6
74
3-
16.3
13
24.6
15
4
27 O
9 6 8
- ^4-1
89
1
.350
66.5
2 45
Sept. 26, 8 40
25-7
26.3
27.0
25-9
26 3
2.7
4-4
9 6-5
2 -5
3Q
77-o
76.9
19
is. 2
.325
333
342
329
774
6
25
82
4
17
40 I
20 1
334
342
351
337
.342
4.1
18.5
59-o
3-3
13.3
15
30
10
3
27 O
9 6 7
747
85
j |
.351
64.0
2 50
25-7
26 3
2-3
A 2
76.7
20.0
325
. "3^3
3
22
30
335
343
2.6
16.3
12
23
27 1
6 1
. 347
75
j 1
356
56.5
'gBP.
we.
>gyo.
wy.
"wo.
14 wBrcor.
VAPOR NUCLEATION IN LAPSE OF TIME.
3 1
TABLE n. Time variation of the larger colloidal nucleation of dust-free wet air Continued.
Date, etc.
dp.
s.
/>
t.
'/> (TT TTj)
-*
rcXio- 3 .
"0.335 X
io- 3
dp
P
*Xio- 3 .
"0.340X
io- 3
" .34 8 X
I0~ 3
Sept. 27, 8 h 45 m
3 i5
25-9
26.3
27.1
25-6
26.4
3-4
13 5 '
13 7.i
3-o
5. 2
76.4
76^3
O
19.0
19.5
0.330
335
346
325
.336
ii
38
99
7
42
} 4 (
1 4
0-339
344
355
335
34.6
8-7
26.0
77-5
5-5
2Q O
IO
30
15
2S
26.8
7.3
^42
116
} i
. "3SI
8^ s
Sept. 28, 9 oo
25-8
26.7
27 I
2.6
%l
76.8
19.0
.327
339
^44
5
38
8^
25 i
.336
348
-2 era
3-7
26.0
61 s
IO
20
3 i5
25-7
26.6
27 O
3-0
M
76.7
19-5
.325
337
. ^4"^
7
45
82
4 f
335
347
. 3S2
5-5
31.0
61.5
15
25
Sept. 29, 8 45
25-7
26 2
2.7
4.8
76. 7
19.2
.326
^^
6
34
145 f
335
342
4.1
23. S
15
35
27 O
13 7.i
. ^4^
99
j 1
.352
77-5
5 oo
25-7
26 6
3-2
5-5
76.3
18.8
.328
. 340
9
51
35
337
349
6.8
35.0
15
25
27 O
U 7.i
. 34S
99
J 1
354
77-5
Sept. 30, 10 10
26.0
26.6
***
75-8
19.0
334
. 742
30
81
J35 J
343
.351
20.7
61.5
10
3
4 oo
Oct. i, 9 45
3 oo
27.0
25-7
26.6
27.0
25-7
26.5
27.0
25-8
26.3
"7.5
-il
7 7-4
3-i
4.6
"7-4
3-o
5.0
75-9
76*4
76^2
19.2
16.8
17.2
348
330
342
347
329
34
347
331
.338
117
14
99
105
8
30
99
7
37
} 45 (
I""'
I"
356
339
351
.356
336
347
354
339
345
89.0
10.5
66.5
86.0
6.4
20.7
86.0
5-5
26.0
15
40
IO
20
10
26
Oct. 2, 9 oo
27.2
25-7
25-9
26 7
7.0
2-3
*3
76 '.i
17.0
350
331
333
-24.4.
103
3
8
71
H
357
338
340
.351
74-o
2.6
6.4
54-5
'6.4
28
3 oo
26.0
26 5
4-4
c . 7
75-9
18.0
335
74.1
25
SS
25
343
349
18.5
39-
10
25
27 I
7 7-4
. "3 SO
105
357
86.0
Oct. 3, 8 45
25-7
26 3
3-3
S 3
76.0
18.5
.329
. 337
10
45
4 o
338
34 6
7-7
31.0
13
28
27 O
13 7.i
.346
IOO
355
77-5
3 oo
25-7
26 4
#2
76.0
20.5
.327
337
16
87
r(
.338
347
ii. 3
66.5
20
53
27 O
7 7 8
O4.c
ios
j i
355
100.0
Oct. 4,* 9 15
3 oo
25-7
26.5
26.9
25-9
26 3
3-8
!3 7 ; 3
3-7
5 A
76.1
75-5
20. 5
21 .O
327
338
343
330
.336
17
5i
101
16
48
n
45
.338
.348
353
341
347
12.3
35-0
83.5
3
32-7
15
28
IO
25
Oct. 5, 9 oo
3 20
27-3
25-7
26.6
27.1
25-7
26.2
27 C
15 8.c
3-5
"6.8
l 7-8
4.2
5-8
8 ? ^
20. g
75-4
75-6
21 .C
349
329
341
348
330
337
.348
140
12
93
140
21
59
117
i i
n
n
.360
340
352
359
341
.348
358
108.
9-5
66.5
IOO
16.3
41 .0
83-5
9-5
30
10
30
r gy-
8 gBP.
we.
11 wy.
13 W0 .
15 w P cor.
*Room heated hereafter.
32 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE ii. Time variation of the larger colloidal nucleation of dust-free wet air Continued.
dp- (---,)
M 0.335X
dp
M 0.34oX
io- 3
Date, etc.
dp.
s.
P>
t.
p-x
wx 10 *.
io- 3
P
wXio 3 .
W 0.34sX
io- 3
Oct. 6, 9 h oo m
4 30
Oct. 7, 9 30
4 oo
25-7
26.4
26.8
25-7
26.3
27.0
25-8
26.1
27.0
25-9
26.3
4.6
"6.7
"7-7
4-9
18 7.o
J 9.o
4-9
13 6.6
8 7-4
4-9
13 6 8
75-i
':'
74-9
75-i
20 : 5
21 .O
21 .O
20.0
0.331
341
347
335
343
353
334
338
350
335
-14.1
29
92
104
36
97
175
36
88
117
36
87
n
n
40 f
35 1
0.342
352
357
346
354
363
344
348
.360
345
"^SO
20.7
64.0
97-0
24.6
74-o
152
24.6
61.5
86.0
24.6
66.5
10
35
(?)"
20
(?)"
30
(?)"
2S
27 .O
8- ^
^so
in
1
. ^60
80. S
Oct. 8, 9 oo
3 oo
Oct. 9, 8 45
25-9
26.3
26.9
26.0
26.7
27-3
25-8
26.3
3-o
4:1
3-5
6.1
ll 7-5
3-8
S- 1
76.3
76^4
76.0
18.8
21.5
20. o
331
.336
344
329
338
346
330
337
7
25
65
12
66
112
17
4
n
n
1 35
339
345
353
340
349
357
339
346
5-5
18.5
49-0
9-5
49-o
89.0
12.3
27.5
9
20
9-5
30
13
2 5
3 oo
26.9
25-7
26.3
27 O
6.8
3 ' 6
9 5-9
7 6 9
75^6
21.0
345
329
337
-24.7
89
H
62
94
}"{
354
340
348
. 3S7
66.5
10.5
43-0
69. 5
IO
30
Oct. 10, 9 oo
3 30
Oct. ii, 9 15
25-9
26.6
26.2
27.0
25-9
26.3
27.0
25-7
26.4
4-9
n 7-5
"6.3
* 7 .2
4-9
"6.6
16 8.2
3-7
5-8
75-2
75-o
75-3
19.8
20.0
18.0
335
344
339
350
336
342
351
333
343
39
103
71
117
36
82
140
16
59
1 40
:;{
" i
344
354
348
359
345
351
.360
341
.351
24.6
89.0
54-5
80.5
24.6
61.5
117
"3
41.0
(?)
30
(?)"
25
7
20
27 .O
H 6 Q
-3 CJ
IO2
1
. 3S9
69.5
3 30
25-9
26.7
4-9
8 6 4
75-3
21 .O
330
T.T.Q
36
74
45
344
349
24.6
56.5
(?)
3
Oct. 12, 8 45
3 oo
27.0
26.O
26.9
27-4
26.1
26.6
27.0
"6.9
3-6
'1:1
3-8
5-i
5.8
76.6
76^6
19.0
i' 7 '.6
348
331
343
349
334
34
346
95
15
43
118
17
40
60
1
3
'"I
359
339
351
358
341
347
353
69-5
10.5
29.0
83-5
12.3
27-5
41.0
IO
20
8
20
Oct. 13, 9 oo
6 30
Oct. 14, 9 15
Oct. 15, 9 oo
26.0
26.4
27.0
25.8
26.6
27.1
25-7
26. 4
27.2
25-9
26.5
27 2
2-3
4.6
5-3
2.8
4-5
6-7
3-0
4-7
6.2
3-o
5-0
6 7
77-4
77-3
77.1
76 '-7
18.0
20.0
20. o
20.4
.328
333
341
324
335
341
324
333
344
327
335
-14.5;
3
30
46
6
28
85
7
32
69
7
38
85
,
30
.,,
n
336
341
349
334
344
351
333
342
353
338
346
355
2.6
20.7
31.0
4-6
19-5
64.0
5-5
22.2
52.0
5-5
26.0
64.0
15
25
13
25
15
28
IO
23
gy-
? gBP.
11 wy.
13 wo.
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 1 6. 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 1 2 , 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.
rcXio- 3 .
Date.
Time.
V.
Q.
*Xio- 3 .
Sept. 14
ii -3 h
9-3
+0.53
.56
Sept. 29
IO.O h
6-7
+0.38
I. 12
8.2
- -47
38
9.2
- .52
i-53
3-5
10.8
+ .61
76
Oct. i
IO.O
7-5
+ .43
.26
12.6
- -7i
.01
8-9
- -51
50
Sept. 15
10.4
8-3
+ -47
.40
3-5
6.2
+ .35
05
10. I
- .58
71
4.8
- .27
79
3-5
9-9
+ 5-6
.65
Oct. 2
IO.O
6-5
+ .37
.09
7-i
- .40
.18
9-6
- -55
.62
Sept. 17
II .0
9.6
+ .55
.62
3-5
1. 1
+ .06
19
9.4
- -54
59
7-2
- .41
.20
3-7
6.8
+ -39
.14
Oct. 3
10.5
8-3
+ -47
.40
7-7
- .44
.29
2-3
- .13
38
Sept. 1 8
10.5
3-6
+ .20
.60
3-o
7-7
+ -44
29
3-9
. 22
65
7-i
- .40
.18
3-5
4-5
+ -25
.76
Oct. 4
3-5
7-3
+ .42
. 21
3- 1
- .18
52
2.8
- .16
47
Sept. 19
10.
7-5
+ -43
1.26
Oct. 5
10.3
6-7
+ -38
. 12
7-7
- -44
1.29
7-8
- -45
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
1. 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
i-44
1.8
. 10
.31
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
3-0
6-5
+ -37
1.09
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. ii
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
.10
3i
2-5
- .14
.41
Sept. 26
IO.O
8-9
+ .51
1.50
Oct. 12
3-5
5-9
+ -34
1. 00
7-i
- .40
1.18
7.0
- .40
1-17
4.0
3-6
+ .20
.60
Oct. 13
ii. 5
6-7
+ -38
I. 12
6.0
- -34
i .00
ii. 3
- -65
I.9I
Sept. 27
IO.O
5-9
+ -34
i .00
3-5
4.6
+ .26
.76
3-6
. 20
.60
3-5
5-6
+ .32
94
Oct. 15
10.2
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 n OS45 for <^>/ = 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
n 335 and n 345 , which hold for different hypotheses.
EFFECT OF IONIZATION.
35
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=($p [n 7rJ)/(/> ri)\ 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 w 0335 for # = 0.335 nas therefore been pre-
ferred and is summarized in table 13.
13. Summary of table 9. Observations a. m. and p. m.
Date.
Tem-
pera-
ture.
io- 3 .
Date.
Tem-
pera-
ture.
"o.SSsX
io- 3 .
Date.
Tem-
pera-
ture.
"-0.335X
io- 3 .
o
o
o
Aug. io
26
90
Aug. 25
22
70
Sept. 12
22
50
28
105
23
60
22
65
ii
26
70
26
24
70
13
22
55
26
70
24
70
22
50
12
26
75
27
24
75
14
22
55
26
80
2 4
70
22
60
13
24
56
28
24
60
15
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
17
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
17
23
80
23
55
23
70
24
90
IO
23
65
21
23
85
23
25
75
23
70
23
98
24
23
75
ii
22
55
24
95
22
55
The endeavor may be made to test the value of n 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 ii) 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
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 = 6ms 3 /xa? 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.
wXio~ 3 at J 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 [p 2 ] 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 r 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 s the chord of the angular diameters
(j) of the corona observed with a goniometer with a radius of 30 cm.,
2 sin 0/2=5/30 (2)
^5 = 0.0032 (3)
was accepted when the eye and the source of light were at distances
D = 3o and 250 cm., respectively, on opposite sides of the fog chamber.
With a constant a selected we may then compute the nucleation n f
for the smaller white-centered or normal coronas as
, 6m 3 (4)
Vl/ x o
xa
where m is the amount of water precipitated per cubic centimeter in the
exhausted vessel and n f the number of nuclei per cubic centimeter so
computed. The theory of diffraction would give a collateral approxi-
mation
6m m
= 71(73.2 v0 3== 0.205(10*!?
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,
[dp 2 ], both as to the amount of the latter and number of exhaustions in
the series, as will be shown.
4 6
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; dp s = 17.0;
[d/>J=i6.2 at 5 seconds, 16.8 at 60 seconds; ^=0.779; S=j.2; = 0.0032;
D = 30 cm. and 250 cm.
No.
Corona.
s.
I0 - 3 n' =
o. igos 3 .
w Xio- 3
ratio.
wXio- 3 .
^=0.0183
Xw~ 1/3 .
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
we
....
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
gyo
13
....
333
264
12. I
ii
yo
ii
....
248
291
II.
12
we
10
....
183
321
10.
13
w p
8.1
....
132
359
8. 9
H
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
4i-3
529
6.0
17
5-4
30
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
17. Coronas standardized. Phosphorus nuclei. Barometer 77.7 cm.; tem-
perature 20. Cock open 5 seconds; 60 seconds between observations; dp' =18.2;
dp 3 =ij.o; [dp^\=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 3 n f =
0. igos 3 .
w Xio~ 3
ratio.
wXio- 3 .
^ = 0.0183
Xw~ 1/3 .
s f = 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
wR'
....
....
2350
138
23.2
5
wr
....
....
....
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
T 4
g'BP
7.8
....
....
125
366
8.8
15
w o
7-5
80
4710
87
4 l6
7-7
16
wb r
6.8
60
5160
59
470
6.8
17
....
5-9
39
5060
39
540
5-9
18
(late)
4-9
22
4660
24-7
630
5-i
19
(early)
4-2
14
5200
13-7
7 66
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
x Use mean 5= 7.2 as in table 16.
NUCLEATION CONSTANTS OF CORONAS.
47
zzo
00
o
10
FIG. 12. Nucleation n, in terms of the apertures of coronas.
Small nucleation, moderate exhaustion.
10 ft 44- 16 IB
200
1000
10 1Z 14 16 18 20 22 24 26 2Q 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~ 8 v and ds = a, it may also be written for the fixed time t
h a 2 ~5 2
where 5 is the subsidence constant for the loss during the fixed time t.
Hence for a rectangular vessel
1
and for a cylindrical vessel of radius r and horizontal axis
equations which will be useful below.
In the present case we may therefore write the nucleation obtained
in successive identical exhaustions beginning with n
(8)
as further explained in the earlier volume. Again, since for normal
coronas n z is supposed to be given by n = 6ms 3 /xa 3 , S may be computed
by two successive exhaustions as
Hence the terms of the series
6m
may also be computed, and since n z = - 3 s 3 z , the equation
nd
6ms z i
W " = (10)
NUCLEATION CONSTANTS OF CORONAS. 49
is available for computing the initial nucleation , and hence all sub-
sequent nucleations, absolutely. Naturally a number of observations
n z and s z will be used for computing n Q and 5. The equation shows very
well how the constants n , S, a, m, are involved.
From n z the diameter d z of the 2th fog particle may then be computed
d z =n~ I/ li/6m/7: (n)
and similarly the 2th aperture s e will be, since ds = a
to be compared with the observed value of s z . 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 dp 3 /p = o.2ig
an.dv 1 /v = i.ig, temperature 20 C. The symbols denote dp'=p //,
dp3 = P Pai [$p2\ = P [Pz]> as explained in sections 25 and 26, where the
meaning of y, a, 5, 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' = 6ms*/na 3 , while the fifth shows successive values of n Q 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~ 8 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 5 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 S were computed as shown in equation 9
from the data of tables 1 6 and 1 7 :
50 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
5 = 7.0 6.1 5.4 4.3 3.2 2.0 i.o
5= 7-4 3-9 10.4 8.7 6.9 3.3
*=7-5 6.8 5.9 4.9 4.2 3.4 2.4 1.8
S= 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 = y.2 and 5 = 6.8 were taken as fair averages in the two
cases. The data for n 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 [dp 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 = 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 a = cfc = o.oo32 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 of the coronas gives
sin ^> =5/60 = 1.22 X/d (13)
for the first minimum annulus of wave-length X, and ds = a,
a = 73. 2 ^ (14)
whence a = o . 0032 would correspond to blue violet. With an eye at but
30 cm. from the fog chamber, the equation for sin is certainly not quite
true and a must be variable with X, except perhaps for the smaller normal
coronas, which are so closely packed that a mean value of X is suggested.
If m be taken as 3.2Xio~~ 6 , equation 4 shows ^' = 190 s 3 . Equation
1 4 incorporated in equation 4 would imply for i o 6 m = 3 . 2
_
=
6ms 3
7r( 73 .2 /I)
n' = 0*036 s w 1 =
according as the first red, orange, or violet minimum were used, data which
merely imply an order of values, as equation 13 is not fully applicable.
Tables 16 and 17 and figs. 12 and 13 show a satisfactory order of
agreement between the observed and computed values of 5 and the
corresponding data computed for n as far as 5 = 7 to 10 cm., where the
middle green coronas enter. The agreement thereafter improves again
until the higher green coronas are passed, when further divergence is
marked. I will not enter into this here, as the subject has been discussed
NUCLEATION CONSTANTS OF CORONAS. 51
in the earlier memoir. It is necessary, moreover, to investigate some
other method of obtaining 5 for the very large coronas, such as is given
in Chapter IV. In the present memoir the discrepancy is accentuated
by the short periods of i minute between the observations. This is not
sufficient for the complete mixture of the inflowing air and the nucleated
air within the fog chamber. As a result there are apt to be color dis-
tortions and bands of color before the real corona appears, while the
latter is not quite sharp. It was thought that longer intervals of waiting
between the exhaustions would have introduced other discrepancies
or losses of nuclei. Experiments made under these conditions did not,
however, much improve the irregularities, as may be seen in section 36.
Furthermore, in the larger coronas it is difficult to determine the actual
limits of the diffused annuli by the present single-source method. The
same difficulty will appear in the next section. Finally the d and s
values computed from equations n and 12 show
^ = 0.0183 n~ 1/3 s = o. 175 ni/ 3
For the lower coronas these s values agree with the observed data
quite within the errors of observation, remembering that the coronas
were not perfectly sharp. For the higher coronas they are probably
close to the truth, provided the green and blue coronas be measured
to the purple rings. Both d and s will be discussed below and another
reduction will be attempted.
29. Data for low exhaustions. Inasmuch as the only correction
added was for subsidence, it is necessary to test in how far convection
losses of nuclei upon evacuation, losses on evaporation, and losses in
the lapse of time (decay) are relatively small. This may be done by
comparing the data for very low exhaustions with the data for relatively
high exhaustions. In the former case many exhaustions must be made
and a longer time will elapse between the first and last of the equal
intervals than in the second case, where there will be relatively few
exhaustions and a relatively small lapse of time. If the errors in question
are negligible, the same initial nucleation and the same diameter of fog
particles for the same coronas will be obtained. The subsidence constant
5 appears as follows:
* = 6. 5.8 5-4 4-8 -4-i 3-3 2.7 2.0 i.o
15.4 2.6 5.5 6.7 6.8 3-9 3-9
6.2 6.0 5.3 4-5 4-o 3-3 2.5 1.7
5= 4.1 7-6 8.4 3-8 5-8 5-5 4-i
The mean values are ^ = 6-8, 5 2 = 4-9- Hence 5 = 5-9 was taken.
Experiments showed [dp 2 ] for 5 seconds of opening of the exhaust cock
to be equivalent to ? = 0.873. The computed diameter
52 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
iO
1ZOO
3000
ZOOO
1000
8 9 10 11
FIG. 14. Nucleation n, in terms of the apertures of coronas. Low nucleations;
low exhaustions.
FIG. 15. Nucleation n, in terms of the apertures of coronas. High nucleation;
low exhaustion.
NUCLEATION CONSTANTS OF CORONAS.
S3
18. Coronas standardized. Phosphorus nuclei. Bar. 75.1 cm.; temp. 26;
60 seconds between observations; cock open 5 seconds. dp'=io.']\ dp 3 =io.o;
9-2; ^=0.873; 5 = 6.8; a =
No.
Corona.
s.
I0 3 W' =
O.I28.J 3 .
w Xio~ 3
(ratio) .
wXio- 3 .
Xw 11 / 3 .
s'=a/d.
i
Rfog
30
2540
2540
0.000118
27
2
Rfog
26
....
2 2OO
124
25-9
3
Rfog
25
....
....
1880
131
24.4
4
Rfog
22
....
1630
137
23-3
5
Rfog
22
I4OO
144
22.2
6
wR'
19
1210
150
21.3
7
! wR
17
1030
159
2O. I
8
! we
16.5
....
163
19.6
9
*w c
15-5
'748
177
18.1
10
1 v
....
....
635
186
17.2
ii
Blue
14-5
....
....
537
199
16.1
12
gBP
H
....
....
454
209
15-3
13
gBP
13-8
....
....
383
222
14.4
14
gBP
13-8
....
....
322
233
13-7
15
gyo
13-5
....
271
247
12.9
16
'gyo
13-5
228
264
12. I
17
yo
12-5
191
2 7 8
n-5
18
yr
ii. 5
....
....
1 60
298
10.8
19
we
10.5
....
....
132
316
IO. 2
20
wP cor
9-7
....
....
108
335
9.6
21
gBP
8.1
....
....
88
362
8.8
22
gBP
7-6
....
68.7
393
8.1
23
7-3
53-0
428
7-5
24
....
6.9
42.0
2650
40.3
470
6.8
25
5-8
25-0
2100
30.2
6.2
26
5-4
20. I
2430
21 . I
584
5-5
27
4.8
14.2
2560
I4.I
665
4-8
28
8.8
2590
8.6
785
29
....
3-3
4.6
2580
4-5
976
3-3
30
....
2-7
2.6
2880
2-3
.001220
2.6
31
....
2.O
1 .0
1810
1.4
H38
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
2120
O.OOOI25
25-6
2
Fog
30
....
1850
131
24-3
3
Fog
2 4
....
....
1610
138
23-2
4
Rfog
23
....
....
1390
144
22.2
5
Rfog
21
....
I2IO
150
21-3
6
Rfog
18
1040
1 60
20.0
8
Rfog
Cfog
17
16
....
....
893
767
168
176
19.0
18.2
9
Cfog
15
....
658
185
17-3
10
v-c
14
....
561
195
I6. 4
ii
Violet
....
....
477
207
15.5
12
B
14
....
406
218
14.7
13
g-b
....
346
230
13.9
H
gbp
14
....
294
241
13.3
15
g'bp
14
....
....
251
256
12-5
16
gyo
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.
io 3 w' =
128S 3 .
w Xio- 3
(ratio) .
wXio- 3 .
d=o.oi6i
XM -l/3
s'=a/d.
18
wo
12.0
....
153
O.OOO3OI
10.6
19
wo
ii. 3
129?
322
9.9?
20
we
10.7
109
335
9.6
21
w c
IO.O
9i
358
8-9
22
wP
9.0
75
382
8.4
23
g'bp
8.0
62
407
7-9
24
g'bp
7-5
50
438
7-3
25
w r
6-7
38^5
2060
40
47i
6.8
26
we
6.2
30.5
2090
30-9
513
6.2
27
cor
6.0
27.6
2490
23-5
563
5-7
28
cor
5-3
19.1
2290
17.7
617
5-2
29
cor
4-5
ii. 6
1930
12.8
688
4-6
30
cor
4.0
8.2
2070
8.4
793
4.0
31
cor
3-3
4-6
1910
5-i
936
3-4
32
cor
2-5
2.0
1720
2-5
.001180
2.7
33
cor
i-7
.6
2690
5
2040
1.6
34
cor
.0
.0
. i
3500
9
The data of table 18 are arranged as above for table 16. The adiabatic
drop of pressure is 10 cm. from 75.1 cm. and the relative drop therefore
dp 3 /p = o. 133 and the volume expansion about v 1 /v = i . 107. The water
precipitated per cubic centimeter is about m 2 . 2 grams per cubic
centimeter, in both series at 26 and 24. Hence w = 0.12 8s 8 . A more
recent value of m will be inserted for definite purposes in section 34.
These data are given in the charts (figs. 14 and 15) with a usual
distinction between observed and computed values of the coronal
apertures 5. The divergence again begins in the region of green coronas,
but is here on opposed sides of the line computed for the two series. The
reason of this is the lack of homogeneity of the wet nucleated air, when
the interval between observations is but i minute. The colors of coro-
nas are mixed and the individual observations to this extent uncertain.
With these differences the periods occur in the usual way.
An interesting result of this series is the occurrence of crimson and red
coronas of the first order, above the violet. In other words the initial fogs
soon dissolve into true coronas. But their size is difficult to estimate
in case of the single-source method, because of their filmy character.
One may note that the initial nucleations ^0 = 2,320,000 and 2,470,000
correspond to the values of the table 19.
30. Data for high exhaustions. The corresponding results for an
adiabatic drop of pressure of 27 . i cm. from 75 cm. are found in table 19.
There are three series. The relative drop of pressure is ^3/^ = 0.273,
the volume expansion v 1 /v 1.2^4. Hence, in the absence of phos-
phorus nuclei, precipitation will take place, in the given apparatus, on
NUCLEATION CONSTANTS OF CORONAS.
55
the nuclei of dust-free air, which are within reach of the exhaustion to
the extent of about n = 57,000. Coronas can not be brought to vanish,
but up to the final limit the water nuclei are alone active. The amount
of water precipitated per cubic centimeter at 25 was taken as w =
4.iXio~ 6 . Hence n' = 0.242 s a . The subsidence constants appear as
^=7.4 5.8 4.9
S= 14.6 2.7
7-2 6.3 5.3
i.i 3.6
4.6
7-3 5-6 5-0
16.4 2.0
an irregular series of values, due to the increasing efficiency of the vapor
nuclei of dust-free air. The values of 5 found in tables 16 and 17 are
therefore taken in preference. The observed drop [3p 2 ] corresponds to
y = 0.656. The diameter of particles is d = o.oi^gn~ l/3 . The value of
m taken will be replaced by a more recent value in section 34.
TABLE 19. Coronas standardized. Phosphorus nuclei. Bar. 75.0 cm.; temp. 25;
60 seconds between observations; cock open 5 seconds, dp' = 27.1; dp 3=20.5;
25.0; ^ = 0.656; 8 = 6.5 assumed; = 0.0032.
No.
Corona.
w'io~ 3 =
O. 24.2S 3 .
w Xio- 3 .
wXio~ 3 .
rf = W -l/3 X
0.0199.
s' = a/d.
I.
i
Rfog
20
2320
2320
0.000150
21.3
2
we
15
1500
173
18.5
3
violet
15-5
955
202
15-8
4
Gbp
15
....
608
235
13-6
5
gy
H
....
387
273
11.7
6
w r
10.5
....
....
246
317
IO. I
7
Pcor
8.6
....
....
152
373
8.6
8
w o
7-4
9 8
2510
90.8
442
7-2
9
cor
5-8
42.2
2080
1 52-5
532
6.0
10
*cor
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
10.4
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
ii
x cor
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
21.0
2
Rfog
1470
175
18.3
3
violet
J 7
....
95i
202
15-8
4
g b P
15
....
610
235
13-6
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
2 5-0
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 10
600
soo
4 6 6 10 ft 14- 16 18 20 22 4
FIG. 16. Nucleation n, in terms of the apertures of coronas. High exhaustion.
31. Standardization with ions. The endeavor to standardize the
coronas by precipitating the fog particles upon ions lead to peculiar
results, which makes it necessary to discuss the subject independently in
Chapter V. In fact, about one-half of the water nuclei which should be
present after the first evaporation of fog particles vanishes independently.
Half the ions are thus not represented by fog particles, except in the
first precipitation. The remainder in the subsequent exhaustions behave
more normally.
32. Further data. Results obtained in case of the intermediate
exhaustions dp z = ~L h j cm. are liable to be most serviceable for the con-
struction of a practical table, and two further series were therefore
investigated under atmospheric conditions different from the above.
These results are given in table 20 and in figs. 17 and 18. In both series
the agreement between the observed and computed values of 5 within
5 = 10 is surprisingly close. The attempt was, moreover, to compute
tables 1 6 and 17 under modified suppositions, putting [p 2 ] = I ^-3 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
FIG. 1 7. Nucleation n, in terms of the apertures of coronas. Low nucleation,
moderate exhaustion.
15 17 13 Z1 Z3 If
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. <^>'=i8.i cm.;
dpa = l l l > [$p2\ = J 6 3 after 60 seconds; distances 40 cm. and 250 cm. ; goniometer
arms 30 cm.; y = o.j8; 5 = 6.5; ds=^2.
No.
Corona.
ioV =
1 0.2I0^ 3 .
w Xio~ 3
(ratio).
wXio~ 3 .
d = n~V s
Xo.019.
s' = a/d.
I.
i
Fog
(30)
5302
5302
0.000108
30.0
2
Fog
25
4110
119
27.2
3
w o
17
3180
129
25.0
4
w o
17
2470
141
23.0
5
W
17
1900
153
21. I
6
wr o
16
1470
167
19.4
7
v
895
198
I6. 3
8
b
16
686
216
15.0
9
bg
16
524
235
13-8
10
wy o
15
397
258
12-5
ii
wr o
13
301
284
xi. 4
12
we
u-5
226
312
10.4
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
660
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
5970
.6
3170
i-5
No.
Corona.
s.
I0 3 W' =
o.2io-y 3 .
n =io~ 3 .
wXio- 3 .
d = n~V 3
Xo.oi9.
s' = a/d.
II.
j
Fog
4040
4040
O.OOOI2O
27.0
2
wr'
(is) '
3130
130
24.8
3
we
....
....
2410
138
22.8
4
! w r
17.0
....
1860
154
20.9
5
w c
16.5
....
1430
168
19.2
6
V
....
....
1090
184
17-5
7
bg
16.5
....
....
836
202
16.1
8
g
16.0
....
....
635
221
14.6
9
gy
481
242
13.0
10
w o
14.0
361
267
12. 2
ii
w r
ii .0
268
295
IO.9
12
w c
IO.O
198
326
IO.O
13
cor
9.0
144
363
9-0
H
7-9
....
....
104
404
8.0
15
....
7-i
75-2
4200
72.4
456
7.0
16
....
5-8
41 .0
3370
49.1
520
6.1
17
....
5-3
31-3
4090
30.9
60 5
5-4
18
....
4-5
19.1
4160
18.5
717
4-5
19
3-5
9.0
3710
9.8
888
3-6
20
2-7
4-2
4710
3-6
0.001240
2.6
21
i-7
1 .0
3
2840
i . i
22
....
r
03
6130
5
23
....
o
....
.0
.0
NUCLEATION CONSTANTS OF CORONAS.
59
33. The violet and green coronas. The object of the series of experi-
ments made at very low exhaustions (dp = 10) and compared with a series
for high exhaustions (^ = 20.5) was an estimation of the importance
of the time effect and of the convective effect in causing loss of nuclei.
If the latter series be reduced to the former by modifying the constants
in terms of pressure and temperature the coincidence of the graphs is
complete, as shown in fig. 19. This indicates that the method of reduc-
tion is reliable.
600
3000
ZOOO
1000
4 6 8 tO 12 14- 16 18 ZO 2Z Z4-
FIG. 19. Nucleation n, in terms of the apertures of coronas. Results in tables
1 8 and 19 compared.
TABLE 21. Violet and green coronas, d and s values.
Table
and ]
3 16
7- 1
Table
18.
Table
19-
Table
2O.
Color.
a/S =
17-
*.-
10.
*Pt<
Jo. 5.
#-
17-
Mean
d =0.00019 cm. ^3. d = 0.00033 cm. v 4 , d = o. 00044 cm.
g, ( 13 cm.) g 2 , 23 cm. g 3) 40 cm. g 4 , 52 cm.
r, 16 cm. r 2 , 32 cm. r 3 , 48 cm. r 4 , 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/s s : 1/5-4 = 0.146 : o.2o6=J 3 : d 4 . 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 (D = ^o cm.), though adapted for the
best seeing, is not so suitable for measuring diameters. Apart from
this, the former experiments w r ere 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.
6l
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 rn. 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 = o.2ig and 20, io 6 m =
3.2 must be replaced by io 6 m = 3.6. In table 20, similarly, for
p/p = o. 224 and 20 C., io 6 m = 3 . 6 must be replaced by io 6 m = 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 s and n referred to new values of m.
Table 16.
Table 17.
Table 20, i.
Table 20, n.
s.
.Xior..
s.
.XKrt
s.
.Xlrt
s.
Xio- a .
r' 27.8
4490
r' 30 . 2
5710
r' 30 . o
5460
r' 27.0
4163
r' 25.8
3620
r' 27.6
4400
r' 27.2
4233
r' 24.8
3223
i' 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
2OIO
O 21 . I
1957
c 19.2
H73
v 17.8
1176
v 19.4
1520
ro 19.4
v 17-5
1123
b 16.3
886
b' 17.7
II4O
v 16.3
922
bg 16.1
861
g J 4-5
665
B 15.8
861
b 15.0
707
g 14-6
654
g' 13-3
500
g H-S
649
bg 13-8
540
gy 13-3
495
gy 12. i
373
gy 13-3
487
yo 12.5
409
O 12.2
372
y o ii .0
278
O 12. I
366
ro 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.
7.0
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
10. I
2.O
1.6
3-2
7-3
3-2
6-5
2.6
3-7
I . ^
4
2.2
2-3
2.1
1.9
I.I
3
....
1.6
.8
1-5
.6
5
03
IO 9 W =
3-6
....
3-6
3-7
....
3-7
....
dp/p=
d =
.219
.oigow- 1 / 3
.219
.oigow" 1 / 3
.224
.OI92W" 1 / 3
.224
.OI92W- 1 / 3
s =
. i68rtV 3
. i68V 3
. i67V
....
. I67W 1 / 3
....
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 w 6 = 2.i should be
replaced by io 6 m = 2 .3, where dp/p = o. 133. In table 19, dpjp 0.2 73,
io 6 m = 4.i is to be replaced by io 8 ^ = 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 (v^/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 2 refers to the probable case
of the occurrence of the third and second series, d 2 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 Ip) the nucleations n 32 and w 21 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 w 2>1 and take w 3>2 , in which case the data are distributed
similarly to my own, so far as the slope of the curves is concerned.
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.
io 3 X
dp/p.
Disk
color.
d 3 , 2 Xio 5 .
d 2>l X io 5 .
w 3 , 2 Xio- 3 .
n 2)l X io- 3 .
3)2 Xio- 3 .
n 2>1 X io~ 3 .
.410
384
g
40
23
1 60
870
190
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
.420
390
r p
.426
394
r
32
16 325
2650
320
2150
.429
396
rg
.... ....
436
400
y w
.448
401
w
.... ....
.469
418
gw
23
12 910
6500
910
7000
373
360
Fog limit.
3i
3 T 7
-fions, condensation limit.
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
n 21 . 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] v 2 /v 1 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 5Xio~ 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 1^2/^1 is 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~ 14 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 v 2 /'Vi == I -4 2 )> the quantity of water which separates out is about 7.6X10"'
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 lyfy = i . 44,
7 . 6 X io 8 /6 X io~ 14 = io 8 per cubic centimeter.
In my data the smallest green corona corresponds to a diameter of
particles of about d 4 = 0.0005 2 cm., the next to 0/3 = 0.00040 cm., the
next to d 4 = 0.0002 3, the first (which I have not been able to produce
by any means whatever, however large the nuclei) should correspond
to ^ = 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
d 2 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, 6^ = 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 io 6 rather than to io 8 nuclei per cubic centimeter,
and that the maximum nucleation would not exceed io 7 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 v l /v is a troublesome datum to compute accu-
rately; it appears as
where p and p' are the pressures in the fog and vacuum chambers before
exhaustion, p 3 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 p 3 , the convenient variable for the com-
parison of exhaustions is the relative drop dp/p 3 . This is used in the
diagram with the approximate equivalent of the volume expansion v 1 /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, pdp' being the pressures of the fog
and vacuum chambers before, p8p 3 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. > = 35 cm., anticathode to axis of fog chamber.
w.
*.
s.
M.
nX io~ 3 .
vjv.
Bar. 76.
2 cm.; t
emp. 26
to 28 C.
Radium . .
21 I
IQ 7
4. ">
O 2^Q
22
2 77
21.3
I 9 .8
4-2
.260
18
2 3 8
20.0
18.4
*r
.242
O. 2
.217
20.2
18.9
i .5
.248
0.6
.224
Air
2 o <7
21 . 5
I . 7
.282
I 2
26 s
22.8
(21. I)
I .2
.277
0.4
259
21 .9
20.3
l r
.266
0.2
.2 4 6
21.3
19.6
0.0
257
0.0
234
X-rays
2O.4.
19.4
4- I
17
. 272
18.9
17.2
0.0
.226
0.0
.199
19.6
18.0
0.0
2 3 6
0.0
. 211
20.0
18.4
1.8
.242
1-3
.217
20.4
19.2
3-8
.252
.228
Bar. 7
5.8 cm.;
temp. i<
3.6C.
Radiation.
dps-
s.
dps/p*
wXio- 3 .
vjv.
n^ X io- 3 .
Radium
20 6
6 2
O 272
60
2 eo
18.6
T
245
0.2
.221
0.2
X-rays, D = 1 50 cm . . .
18.6
r
245
0.2
.221
0.2
X-rays, with radium . .
18.6
2 r
245
0.2
.221
0.2
X-ray, D = ^o cm. and
radium, D = 50 cm . .
1 18.4
I 18.7
2 r
243
247
O. 2
1-5
.218
223
0.2
1-3
Radium
18 7
r
24.7
O 2
227
O 2
Do
21 6
3 7 O
28=;
80
260
7 ^
X-rays, D 50
2O 7
4 Q S
277
2IO
2 ^4
176
No corona visible; scattered rain. 2 Coronas gradually increasing. 3 w y . 4 w c.
26. Dust-free wet air energized by weak radium acting from
Bar. 75 . 8 cm. ; temp. 27 C. Wet glass walls.
*y.
*/v
J.
*PJP-
nXio- 3 .
*!/
25.6
24.1
4-3
0.318
23
.312
24.6
23.0
3-9
304
17
293
23.2
21.8
3-9
.288
16
273
21.8
20.5
3-8
.271
H
.252
21. I
19.8
2-5
.261
3-6
239
20.2
18.8
r
.248
0.2
.224
20.1
18.8
.248
0.0
.224
21.9
20.6
3-8
.272
H
253
24.0
22.3
3-7
.294
14
.280
25-5
23-9
3-8
3i5
17
.308
27-5
25.7
4.6
339
28
342
29. 2
27.5
5-5
.363
50
377
31-2
29.0
x 7-5
.383
133
.408
= cm.
NUCLEATION CONSTANTS OF CORONAS.
6 7
expansion on exhaustion vjv. Tables 26 and 27 contain corresponding
results for air energized by the weak radium at a distance > = 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.
TABUS 27. Dust-free wet air energized by weak radium acting from = 40 cm.
Supplementary data. Bar. 76.2 cm.; temp. 24 C. Dry glass walls.
9?.
#
s.
9pt/p.
wXio- 3 .
Vi/V.
n^ X io~ 3 .
' 25.6
24.0
3-9
0.315
17
-308
16
26.1
24-5
3-9
.322
17
.318
16
26.7
25.0
3-9
327
J 7
325
16
27.2
25-5
3-9
334
18
335
17
28.1
26.5
4.2
346
23
352
21
28.9
27.2
5-2
356
4i
.365
39
30.1
28.3
6-5
371
86
389
81
28.6
27.1
5-o
354
37
364
35
28.5
26.8
4-9
350
34
357
32
21.8
20.6
3-6
.270
12
.250
ii
21 . I
19.9
2.0
.261
2
239
2
20.6
19.4
r i .0
255
O. 2
232
O. 2
20.6
19.6
r i .0
257
O. 2
234
O. 2
Repeated. Glass vessel clean and wet
27.2
25-7
4-5
0-337
27
339
26
28.3
26.7
5-o
349
36
356
34
26.4
24.7
4.2
323
21
319
20
25-7
24.0
4.2
.315
21
.308
20
24-5
23.2
4.0
304
18
293
17
24.0
22.3
3-8
.292
15
.278
16
22. O
20. 6
3-6
.270
12
.250
12
21 .O
19.9
2.4
.261
3
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 2 9 there is
further intensification, obtained by acting upon the fog chamber with
the X-rays at d = $o cm.
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. 17.7 C.
tyf
s.
8PJP-
wXio- 3 .
Vi/V.
*P*
s.
*P/P-
nX io- 3 .
v i/ v -
20.5
6-5
0.273
69
254
24.1
6-9
0.321
92
.316
19.4
3-4
259
10
237
26.0
6.8
347
93
352
17.9
.0
239
O
.214
29.4
6.9
392
1 06
423
18.3
r i.o
.244
O.2
.219
32.5
6.9
433
112
.496
19.9
22.3
5-5
6-9
.265
297
40
86
.244
.284
39-4
42.8
Diffuse
Diffuse
525
571
695
.823
Fog limit below ^ = 0.756 at 18, equivalent to ^=1.22, equivalent to a drop
(adiabatically) of dp= 18.6 cm. (about ) at 76 cm,, 2 cm. below Wilson's ^ = 20.5 cm.
68
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 29. Dust-free wet air ionized by X-rays at > = 5o cm. Bar. 75.9 cm.;
temp. 21.3 C.
2ZQ
i
9P*
s.
8P*/P>
wXio~ 3 .
vjv.
9p
S.
8pjp.
rcXio- 3 .
oj-v.
I
18.4
r
o. 242
O. 2
1. 218
20.2
^.I 0.266
125
1.245
18.9
2-4
.249
3-3 1-225
19.4
5-o .255
29
1.232
19.6
5-2
.258
32 ; 1.236 19.0 i .9 .250 i .5
i . 226
1 1;
1 !
wp corona.
.Z7 .28 .29 .30 .3\1 .32 JB ./ J'J" .JP .?7 .38 .J9
FIG. 20. Nuclealion n of dust-free air and of ionized air in terms of relative adiabatic
drop in pressure dp/p and of volume expansion vj-v. Enlarged scale for n. Region
for ions.
FIG. 21. Nucleation n in terms of relative adiabatic drop of pressure Sp/p, and of
volume expansion v t /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 (v 1 /v = i . 24,
NUCLEATION CONSTANTS OF CORONAS.
K> ft
' 8.
?
1
CTcn
. 3
3"
If
O o'
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 o . 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 = 4o 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 wet 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 = 0.24 (ujv = 1.21, 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 n = 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 (vjv =
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
live ions v 1 /v = i .25, positive ions i .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^/v < i . 33) lies at an average height of n = 8$ X io 3 and the
second step at an average height about twice as large.
Fig. 22, w r hich 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=(dp 3 [n
nJ)/(P 7r )- Computed relatively to dp 3 /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 dp a /p and the volume expansion v l /v=(p/[p <^ 3 ]) 1/T ,
computed therefrom.
The results of table 30 being summarized by giving expansions corre-
sponding to the fog limits both for [v 1 /v] = (i x) l/ v and vjv=(i-
dp3/PY ly , show clearly that vjv, computed from dp 3 /p, is independent
of temperature, whereas the other datum [vjv] varies with temperature
in a way referable to the values of TC 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.
CONDENSATION OP VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 30. Temperature comparisons. Radium on top of fog chamber. D = o.
Tem-
Tem-
pera-
.
pera-
.
dp'.
dp,.
S.
nXio \
ture and
barom-
$P S /P-
8P'.
#.-
s.
ttXio .
ture and
barom-
dp,/ p.
eter.
eter.
Ions due to radium.
Vapor nuclei. Wet dust-free air.
22.6
21.5
20.3
21.6
20. I
I9.O
6.8
o.o
80
O. I
14.0
76. i cm.
1.226
0.250
25-6
24.6
4-6
3-6
28.6
13-9
30.0
75. 7 cm.
22 7
-2 6
13 . i
20. 6
19.5
2. I
2.0
22.5
21.5
20. i
21-5
2O. I
I8. 4
18.6
6.6
5-0
74
29
I.O
O. I
30.0
75 .7 cm.
I . 222
[0.246
1 0.243
20. o
21 . I
2O. I
20.3
18.7
2-5
o.o
o.o
3-8
o.o
O. I
0.0
' ' ' 'o
1.247
Jo. 265
\ 0.268
18 4.
o o
o o
21 .9
20.3: o.o
0.0
76.8 cm.
22-9
21.6 0.0
0.0
18.6
19.2
20.0
19.4
17.5
18.0
18.8
3- 2
0.0
0.0
0.5
7-5
0.0
o.o
O. I
13 '-2
76.8 cm.
I .220
0.245
-'3-8
23-3
22.8
22. I >I.O
21.9 > i .0
21-5 0.5
0.2
O. 2
O. I
::;;
i .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
18.1
o.o
0.0
14.0
1.226
22.4
21 . I
I.O
0.2
76.0 cm.
f 0.268
19.8
18.6
o.o
O.O
76 cm.
; 0.245
20.3
o.o
0.0
\ 0.267
20. 6
19.4
strong
O. I
10.255
SUMMARY OF RESULTS.
Ionized air.
Dust-free air.
v\h>
-vj-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 3i,32,and33 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 g 2l .
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.oC. February 18, 1907.
Cor-
Cor-
dp.
s.
Cor.
dp 3 /p.
wXio~ 3 .
rected
9p.
s.
Cor.
dpa/p.
wXio- 3 .
rected
wXio- 3 .
wXio- 3 .
(1)17.6
0.232
o
o
(034-6
II .0
0-457
594
677
18.6
2.5
cor
245
3
4
II . I
y
.410
562
638
19-5
5-2
257
32
35
2S'.l
11.4
y
376
529
598
19.7
7.0
c
.260
83
92
25-3
n-5
y
334
490
549
19.9
7-o
o
.263
90
100
23.0
II.
o
303
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
I 4 .6
16.1
21.8
9-3
c
.287
207
230
19.9
7.0
263
84
93
25.5
ii .0
o
.336
467
523
20. o
7-3
g
. 264
94
104
30.0
ii .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.
Cor-
Cor-
dp.
s.
Cor.
WP.
20 C.
n X io- 3 .
rected
io Xw- 3 .
dp.
s.
Cor.
3PJP-
20 C.
wXio- 3 .
rected
io Xw~ 3 .
(2) 18.6
19-5
2.4
7.0
cor
o. 248
. 260
3-2
83
.
4
96
X-rays off. Dust-free air. Bar. 75.5;
temp. 27.2 C.
20.4
10.8
W
.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
7i3
856
25-9
g!
345
904
1071
gy
33-7
13
w 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-
o r\
Cor-
dp.
s.
Cor.
dp/p.
20 C.
wXio- 3 .
rected
wXio- 8 .
dp.
S.
Cor.
dp/p.
20 C.
wXio- 3 .
rected
wXio- 8 .
(4) 19-4
o
0.254
o
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
.280
357
357
22.0
12.8
yo
.288
436
460
(5)34-2
g
0.447
1060
"34
23-4
13-5
gyo
.306
584
617
31.0
g
405
899
960
24-5
gy
.321
680
721
27.7
'*-5
w/bg
-362
187
199
2 4 .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
1.2
....
. 290
4
4
NUCLEATION CONSTANTS OF CORONAS. 7$
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 Z) = 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
d
FIG. 24. (a) Diffractions from fog particles at a, b, c, and a single source S, reaching
the eye at e. (b) Diffractions from fog particles at a, b, c, and two sources S', S",
with coronas n n' and n' n", in contract at n f , 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.
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, 6, with two sources at S' and S" and the coronas
nn f and n'n" in contact at n f 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 S" 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 S" 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 f and
n f n" , and the lamps S'5" 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 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 S". A pole at R, with
the end in the observer's hand, moves the tw r o 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, 6, 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.;
0.408; factor i. 56; temp, factor 0.027.
/.
5.
S.
wXio~ 3 .
t.
S.
s.
nXio- 3 .
I. sec
II sec
o
12.
14.4
920
12.5
15-0
1140
30
IO.2
12.2
600
30
10.8
13.0
730
60
8. 4
IO. I
350
60
8.8
10.6
400
90
7-3
8.8
220
90
7-4
8.9
230
1000 N
600 _X_>
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
400
ZOO
0&e C . ZO 40 BO
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
o.i 2 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. dp 3=17. 6',
[/> 2 ]=i6.8; phosphorus nuclei, ^=0.771; dpa/p = o.233; w=4.2 g/cm 3 ; = 0.0032;
5'-6.5.
Exp.
No.
S.
Cor.
s.
o-*n' =
0.244* 3 .
n x X io- 3 .
wXio- 3 .
= 0.16
Xw 1/3
' = O . 1 2S.
cm.
i.
i
?2IO
o'
19-3
....
3660
24.6
2
185
16.7
....
2770
22.4
3
165
TO
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
H3
gy
ii. 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
1-3
....
20
o
absent
0.0
0.0
o.o
....
....
2.
i
?2IO
0'
19
22OI
20.8
25.0
2
198
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
22.1
5
158
st. bl.
16.1
....
740
14.5
19.0
6
135
g
14-3
....
559
13-1
16.2
7
118
gy
12.8
....
420
12.0
14.2
8
101
II. 2
....
313
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
gy
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
14
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
2106
IO.O
3-5
3-4
17
21
cor
2-5
3-8
2462
3-4
2.4
2-5
18
?i5
very
1.8
1.4
2680
i.i
1.6
1.8
small
3-
i
?2IO
o'
19.0
2010
20.1
25.0
2
195
o
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
I9.O
5
145
g
15.0
....
....
670
14.0
17.4
6
133
gy
14.1
....
505
12.7
16.0
7
I 2O
y o
13.0
....
379
ii. 5
14.4
8
106
ii. 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
J 3
49
cor
5-7
50.0
2105
47.8
5-8
5-9
14
4
cor
4-7
27.0
1813
29.9
5-0
4.8
15
33
cor
4.0
15-6
1898
16.5
4.1
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
2.0
2-5
18
....
just
....
....
.6
1.0
....
visible
8o
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
gular diameter, S = 2R tan 0, s = 2r sin 6, or 5 = 8.3 s/\/i s 2 /4r 2 ,
5=0.12 5/Vi +5 2 /4^ 2 , ^ = 250 cm., ^ = 30 cm. Fig. 24, c, shows the
relation of these quantities. Since the elementary diffraction equation
may be put
sin = i .22 XI d
for the first minimum
5 =(2. 44 R */d)/Vi(i.22 XI d)*
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 5.
In table 35, ^ = 0.771 = (p[dp 2 ]n)/(pK) ; 0^3/^-0.233; io e w =
3.80 at 20; therefore at 25, 10 per cent higher or io 6 m = 4.i8 grams
per cubic centimeter. Hence n' = 6ms 3 /xa 3 = o. 244 s 3 /io s . The value of
TABLE 36. New apparatus. Two coronas in contact. Bar. 7 6. 4 cm.; temp. = 2 7 C;
S=2R tan 0; ^ = 250 cm.; cock open 5 seconds; interval i minute. d
2 ] = 9.2. Phosphorus nuclei. dp 3 /p = o.i2O', ^ = 0.875; io 6 w=2.33;
6.5.
Exp.
No.
s.
Cor.
S r = I 2S.
IO 3 ' =
0.136^.
MjXlO- 3 .
wXio~ 3 .
s = o.i94w 1/3 .
4-
i
> 2IO
o-fog
25.0
1888
24.0
2
2OI
o
24.1
....
1635
23-0
3
194
o
23-3
....
1414
21.8
4
1 88
o
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
12.6
479
15.2
ii
98
v'g
ii. 8
402
14.4
12
98
v/ g
ii. 8
335
13-5
13
98
g
n. 8
280
12.8
H
95
gy
11.4
233
12.0
15
94
yo
ii. 3
194
ii. 3
16
94
yo
ii. 3
161
10.6
17
88
w r
10.6
133
99
18
88
we
10.6
no
9-4
19
80
wp
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
....
46.1
7.0
23
54
w r
6-5
37-4
1995
35-4
6.4
24
48
r
5-8
26.5
1913
26.1
5-8
25
4 2
cor
5-0
17.0
1748
18.4
5-2
26
37
cor
4-4
12.0
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
17
cor
2.0
I . 2
0.9
i-9
30
....
0.0
O
....
0-3
i-4
i
NUCLEATION CONSTANTS OF CORONAS. 8l
the subsidence constant S' = 6 . 5 is taken as the mea value of the above
data. To compute 5 = an 1 ' 3 / (6m/ ?r) 1/3 , the reduced values are 5=0. i6n 1/3 .
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, s = a(nn/6m) lf3 ,
is not proportional to s = 2r sin 6 but to S = 2R tan 6, where 26 is the
angular diameter of the coronas. This implies a diffraction equation read-
ing tan 6 = 1.2 2 X/d.
These results are shown in fig. 26, where s cc n 1 / 3 is laid off as the
abscissas and 0.12 5 oc tan 6 and o. i25/Vi + S 2 /4-R 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 S oscillates between two straight
lines as the coronas change from the red to the green types. The slopes
of these lines are respectively as i .08 = 73 . 2 X^ja and 0.99 = 73 . 2 >l 2 /a,
whence ^ 1 = 0.000047 an( ^ ^2 = - 000 43 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 s. 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 s oc sin
would more nearly express the results, though the agreement is far from
satisfactory. Series 4 again corroborates series i, needing the s f oc tan
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 (n^r/am) 1 / 3 , where n 2 =^ 2 - J n and the ordinates s (ob-
served) are independent of each other, the equality of s' and 5 will in a
measure check the work apart from the constant a which determines n .
This is actually the case for the lower series of coronas below 5 = 10.
82 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
\
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. Th$ 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:
Computed.
Observed.
Computed.
Observed.
vSeries
,,
S 2 .
s s .
S 2 .
io^ 3 .
,oV,
,0^
i
8
16
8
14
400
200
400
230
2
8
H
8
15
400
230
400
2IO
3
8
13
8
13
400
250
4OO
260
Mean values are thus
5 3 = 8 . o i o e .I2S = .f'.
nXio-*.
io-V.
2w a .
44
(l) II
45
5-3
39
1,520
42
I ....
46
45
5-4
42
1,810
I and II at a
50
52
6.1
61
3,720
3,330
(2) The same, on different parts of chamber. Bar. 76.3; temp. 18 C; ^3/^ = 0.299.
II at c
61
62
7-3
104
10,820
I at c
60
60
7.2
TOI
10,200
I and II ate
65
67
7-9
129
16,640
21,000
II at b
44
44
5-3
39
1,521
I at 6
4 1
38
4-7
29
841
I and II at b
47
49
5-7
50
2,500
2,360
I and II at b
46
5-5
44
i,936
....
at o
57
6.7
80
6,400
1 55
at c
(65
167
7-9
129
16,640
(3) II kept in old place a ; I placed on chamber at c nearer glass end ; observation at c.
Bar. 76.3 cm.; temp, 19 C; ^3=22.9; dp z /p= 0.300; ^ = 1.288.
V ate
66
66
7-9
7-9
129
129
16,600
....
IV at c
62
59
7-4
7-i
92
89
8,300
Ill at c
59
59
7-i
7-i
89
89
7,900
Ill and IV ate
66
66
7-9
7-9
129
129
16,600
16,200
Ill, IV, and V at c
7i
7i
8.5
8-5
162
162
26,400
32,800
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.
S.
0.125=.?'.
nX io- 3 .
io-w 2 .
Sw 2 .
(4) Further comparisons, all at c. Bar. 76.2; temp. 20 C; dp a /p = 0.300.
II
1
i
66
68
69
7i
67
7i
60
65
62
61
82
85
'72
175
73
[69
72
8.0
8.4
8.3
} r.a
7-4
IO.O
8.8
8.5
8.6
135
157
152
in
107
266
175
162
1 66
18,200
24,600
23,100
12,300
11,400
70,800
30,600
26,200
27,600
89,600
71,400
46,800
23,700
I
V
Ill
IV
I + II + III + IV + V
I + III + IV + V
III + IV + V
III + IV
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
too
WO 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 ^n 2 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 n = \ / ^n 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 bn 2 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 5, 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 v 1 /v and
the relative adiabatic drop dp 3 /p.
38. Certain distributions in apparatus II. Bar. 76 cm.; temp. 18 C.
9P
5.
0.125 = .?'.
'wXio- 3 .
v i/ v '
Spz/p.
(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
IQ. 2
10
1.2
0.4
.230
.253
19.2
10
I . 2
0.4
.230
.253
Fog limit. Radium I + II and X-rays. Bar. 76.1 cm.; temp. 2iC.
(2) Radium I + II
18.5
o.o
O.O
0.0
i. 218
0.243
19-5
0.0
0.0
0.0
1-233
.256
20.4
(?)
(?)
(?)
1.247
.268
20.4
17
2.O
2-5
1.247
.268
Bar. 76.0 cm.; temp. 2iC.
(3) Radium I + II
18.3
o
o.o
.216
o. 241
18.8
o
O
o.o
.222
.247
19-3
9
II
0.3
.231
254
19-3
9
II
0.3
.231
254
(d.~) X-ravs D = i s . .
19-5
18.9
22
10
26
12
4.6
o-3
234
.225
257
.249
D 10
IQ I
13
16
0.9
.227
.251
I8. 5
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. 2i.5C
8p
S.
S*.
n.
*Pl/P.
vjv.
dp*.
5.
s'.
n.
*PJP-
V V.
(I)
i9-3
20.3
20.8
21.2
21.7
22.0
22.3
22.8
23-3
23-6
24.4
25-3
26.4
27.1
26.9
27.6
28.1
28.9
29.1
29-5
30.5
31.0
32.0
32.0
33-5
35-4
38.0
o
13
14
H
15
H
15
15
17
19
19
26
30
52
45
769
72
81
97
r 102
Y 129
g' 128
g' 140
g 136
g H7
v'? 140
v 7 ? 140
o.o
.6
7
7
.8
'.8
.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
?!7-0
?i8.o
o.o
0.9
1.2
I . 2
1-4
I .2
i-5
1.5
2.O
3-3
3-4
8.6
14.7
74.0
47.0
176
194
289
480
560
I2IO
1225
1533
1431
1780
1670
2090
0.254
.267
.275
.279
.286
.290
.294
.300
307
311
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
378
388
405
.408
.418
.440
454
.476
.476
513
.561
635
Radium removed from the room. Bar.
75.1; temp. 22 C. Vapor nuclei.
(2)
19.4
20. i
20.3
10
10
I .2
1.2
o.o
0.4
0.4
0.258
.268
.270
i 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
ybiis
g'o 135
g 130
g 131
g'i36
131
132
134
136
1.2
3-i
10.7
13-8
16.2
15.6
15.7
16.3
15.7
15.8
16.1
16.3
o.4
7-i
303
654
1074
959
1017
1130
1058
1107
I3i7
1486
0.246
.260
.277
.278
.289
.292
.298
306
.312
333
.400
.467
.222
2 3 8
259
.260
274
.278
285
. 296
304
333
437
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, dp s /p = o.^g t n =
800,000 to 900,000 for I, n = 600,000 for II; at dp s /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.
8 9
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
suddenly in case of the new results, and it is perhaps higher than in the
old. No progress above the green corona could be obtained, but on the
other hand there was no decrement of nucleation at very high exhaus-
tions, such as is often obtained.
57. Condensation limits and fog limits. Conclusion. The conden-
sation limits, or the exhaustions at which condensation begins, are best
gathered from fig. 29, which also shows the nearly constant low nuclea-
tion (due, as C. T. R. Wilson has proved, to ions), which precedes the
region of vapor nuclei in the case of dust-free wet air.
Series.
Condensation limit.
-vj-v.
9PJP-
Radium I + 11
II
II
IV
V
V
I
II
III
i . 240
(higher)
. 226
.225
.223
.238
.241
.222
o. 262
.250
.249
.247
.261
.263
.246
X-rays, D=io cm
Radium I + 11
X-rays Z? = 35 cm
D= io cm
Vapor nuclei
Do
X-rays, D = 10 cm
D is the distance from which the X-ray tube acts.
It appears certain from these results that the condensation limit
decreases slowly as the intensity of radiation increases; also that it is
lower for ionized air, even under weak radiation, than for dust-free
normal air. Coronas may be obtained in succession, in these instances,
after they have completely vanished in the preceding case of weaker
radiation. Rain is naturally accompanied by a definite corona. If we
reckon the intensity of the radiation as the square of the maximum
radiation producible, or the height of the asymptote, the following data
may be adduced from figs. 28 and 29:
wXio- 3 .
n\
Ratio.
apJP-
vjv.
*(V").
Wet air (dust-free)
Radium I + 11
i-5
100 to 150
2
I tO 2XlO 4
i
I0 4
0.26
25
1.240
I 225
0.0
.OI5
X-rays D=o ....
IOOO
IO 8
IO 8
24.5
I . 22O
.020
Thus, while the intensity of radiation changes from the natural radia-
tion in dust-free air, i, to io 4 for beta-gamma radiations, and from i to
io 6 for X-rays, the volume expansion at which condensation takes place
shifts over decrements of 0.015 and 0.020 or 15/1240 and 20/1240,
i. e., 1.2 per cent and i . 6 per cent.
NUCLEATION CONSTANTS OF CORONAS.
In conclusion, it may be interesting to adduce mean values for the
condensation limits as obtained in Chapter III, with the former appara-
tus I. They are shown in the table below, and they agree well with
the present set, remembering that the values would be slightly below
these data if taken from the chart.
dp 3 /p.
Vj/Vj.
Air alone . . .
O 26s
I 24. "*
Air actuated
by radium
.246
I . 22"?
Air actuated
by X-rays
. 24.^
I . 2 2O
The results of the chapter may be summarized as follows. The
endeavor to standardize the fog chamber by a number of distinct but
similar samples of radium, used in succession, runs counter to a great
difficulty, inasmuch as the effect produced at the line of vision depends
upon the position of the radium tubes on the outside of the fog chamber.
Moreover, the aperture of the coronas varies only with the sixth root of
the rate of production and is therefore not a sensitive criterion.
The results for vapor nuclei and ions are best seen from the chart.
The deductions are similar to those already given at the end of Chapter
III. The positions of the condensation and the fog limits have just
been stated. These terminal points, as well as the graph as a whole, are
reached at lower exhaustions than was the case in Wilson's experiments.
CHAPTER V.
RESIDUAL WATER NUCLEI.
PROMISCUOUS EXPERIMENTS.
58. Historical. A nucleus obtained from a partial evaporation of fog
particles will be called a residual water nucleus or, briefly, a water nucleus.
C. T. R. Wilson,* in his experiments with ultra-violet light, found
that nuclei were spontaneously producible on long exposure of dust-free
air saturated with water vapor to the radiation. He explained this as
being due to the probable production and solution of hydrogen peroxide,
wherefore the vapor pressure at the surface of the minute solvent water
droplets would be diminished. Such droplets would therefore grow in
the saturated environment. Wilson also encountered water nuclei pro-
duced by evaporation, but he expressed no opinion of their nature, merely
treating them as an impurity to be removed to make the air dust-free.
J. J. Thomson, f in his famous experiments, encountered similar dif-
ficulties with water nuclei. He states that
When .... the number of ions is large, experience shows that they are not all
brought down by the first cloud formed by sudden expansion after the
first cloud has subsided, [and] another expansion be made, a second cloud
is formed
On page 531, moreover,
The first expansion .... though it does not bring all the ions down, seems to
increase the size of those left and makes them more permanent, .... these modified
ions are able to cause a cloud to settle with an expansion of less than i . 25 . . . .
secondary clouds .... are but little affected by the electric field, ....
From this it seems that Thomson did not regard these secondary
clouds as precipitated upon water nuclei derived from the evaporation
of the fog particles of the first cloud.
In 1902,1 and more at length in my memoir on the structure of the
nucleus, I gave a detailed account of the behavior of the residual water
nuclei and showed by direct experiment that the merest trace of solute
in the fog particle evaporated left a persistent water nucleus behind.
The water nuclei of pure water seem by comparison to be evanescent.
The reduction of vapor pressure due to solution compensated the in-
creased vapor pressure due to curvature.
*Phil. Trans., p. 428, vol. 192, 1889.
fPhil. Mag. (5), 1898, vol. 46, p. 528 (cf. pp. 529 and 531) .
JPhil. Mag. (6), iv, pp. 262-269, 1902.
Structure of the Nucleus, Smithsonian Reports, No. 1373, 1903, Washington.
92
RESIDUAL WATER NUCLEI. 93
In 1903 J. J. Thomson* gave a general account of condensation nuclei,
at the end of which he formulates succinct reasons for the persistence
of water nuclei, even when derived from the evaporation of fog particles
of pure water. He says "on the view of the relation between surface
tension and the thickness of water films, to which Reinold and Rucker
were led by their experiments with very thin films, drops of pure water
of a definite radius might be in equilibrium with saturated water vapor
even if they were not charged," a proposition which is thereafter proved.
A further deduction of J. J. Thomson's which may be of use below is
that "the efficiency of an ion as a nucleus for condensation depends
upon the maximum size of the aggregation, while the velocity of the
electric field depends upon the average size." Thus the "average size
of a negative ion may easily be less than that of a positive ion, "
while the negative nucleus is larger than the positive, other things being
equal. I may also add that J. J. Thomson computes the radius of a vapor
nucleus to be io~ 7 /i . 9 cm., whereas the radius of the ionized nucleus is
io~ 7 /3 . i, so that the vapor nuclei are slightly larger than the ions.
Furthermore, Thomson shows that vapor nuclei are probably aggrega-
tions of water molecules, and elsewhere that "in a space far from satura-
ted with water vapor, .... drops will be formed, and that the size of
these drops diminishes only very slowly as the quantity of water vapor
in the surrounding air diminishes . . . . "
In 1905 the Transactions of the St. Louis International Electrical
Congress were published, which gave a review of the present state of our
knowledge of condensation nuclei by C. T. R. Wilson, f This contains
the most recent contributions relating to water nuclei. In view of the
investigations of Langevin and of E. BlochJ on the occurrence and
behavior of slow-moving ions, Wilson finally summarizes the results
bearing on nuclei as follows:
(i) The ions proper, requiring a fourfold or sixfold supersaturation to cause water
to condense on them, and having a mobility exceeding i cm. per second in a field of
one volt per second. (2) Loaded ions, requiring little or no supersaturation to make
water condense on them, and having a mobility generally less than a thousandth
part of that of the ions proper. (3) Uncharged nuclei, resembling the second class and
requiring little or no supersaturation in order that visible drops may form upon them.
59. Purpose, plan, and method. My purpose in the present paper
is to determine whether there is any difference in the sizes of residual
water nuclei obtained in the evaporation of fog particles under different
conditions; for instance, whether the fog particles of large coronas
*Conduction of Electricity through Gases, Chapter VII, Cambridge, 1903.
tTrans. of International Electrical Congress of 1904, p. 365 (cf. p. 378), St.
Louis, 1905.
tRecherchessurlaconductilite^lectri q uedel'air,etc., Paris, 1904 (quoted by Wilson) .
94 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
evaporate to the same nucleus as the fog particles of small coronas; or,
more pertinently, whether the fog particles precipitated on ions evapor-
ate to the same nucleus as the fog particles precipitated on the vapor
nuclei of wet dust-free air. A number of allied questions will be treated.
A variety of methods were tested, as follows:
I. The endeavor was made to find if from fogs characterized by
identical coronas the number of residual nuclei was the same after the
natural evaporation during subsidence, no matter whether the original
precipitate occurred on ions or on the vapor nuclei of dust-free air.
II. Identical coronas were produced on ions and on vapor nuclei,
respectively; but the evaporation of fog particles was accelerated by
keeping the influx valve open by a definite amount. The number of
residual nuclei was then tested by a second exhaustion, the amount of
which was varied. This was done both by starting with different press-
ures in the vacuum chamber for full barometric pressure in the fog
chamber and by starting with different partial exhaustions in the fog
chamber for the same pressure in the vacuum chamber.
III. The persistence of the residual nuclei was studied by measuring
their decrease in number in the lapse of time. Incidentally the loss due
to evaporation was estimated and the distribution of sizes considered.
Finally, in the second part of this chapter the method of successive
exhaustion, which is found to be most productive, is brought to a definite
conclusion.
In all cases the ions were produced by a weak sample of radium in a
sealed aluminum tube, attached to the top of the fog chamber. This
was removed during the examination for water nuclei, inasmuch as the
ions are efficient in the presence of the latter. The corona obtained
from the radium was always the same, care being taken to precipitate all
residual water nuclei in these cases, and to have a pressure difference
sufficiently high to catch all the ions, or at least the same fraction of the
total number. To produce the same given corona with the vapor nuclei
of dust-free air is easily accomplished after a short preliminary trial.
Moreover, these coronas may be obtained at the same pressure when-
ever the asymptote for the ions has been reached. The eye is always
40 cm. and the source of light 250 cm. from the axis of the fog chamber.
60. Residual water nuclei after the natural evaporation of fog par=
tides. The results obtained from these experiments are given in table 40.
Here = 76 and p dp' a are the initial pressures of the fog and vacuum
chambers; p dp a the final pressure, when in communication after
exhaustion; s a /$o the angular diameter of the corona, observed for
ions and vapor nuclei in dust-free air, as specified. Again, p = dp f b ',
p dp b denotes the initial pressure of the fog chamber and vacuum
chamber before exhaustion; p dp c the final common pressure after
RESIDUAL WATER NUCLEI.
95
exhaustion, when the fog particles corresponding to s a have subsided,
leaving (by natural evaporation) the residual water nuclei corresponding
to the corona of any diameter 5^/30, behind.
40. Experiments with residual water nuclei. Bar. 76 cm.; temp. 14 C.
Natural evaporation.
Precipitation on
dp'a.
Spa.
Jo.
(
*/>//>.
WaXlO" 3
'
* v
Vapor nuclei
28 *
26 7
3c
^
> "* ^1
Rad ions
29.3
29-3
2Q "3
27-5
2 7 .8
07 7
'6.9
2 6-9
IA Q
' oo 1
.385
.385
-jOc
1 06
1 06
infi
* 1
2 7 ;8
u. y
oo
2 7 7
Precipitation on
*.
dpc.
V
dp c
p~
'Pc-dp h
11
bX io~*.
Vapor nuclei
26 s
2 'I
o
j An
^ 6
Rad ions
II- 9
no
26.8
26 7
2-7
3Q
.232
211
4.2
c 6
*J L
- u
x wo; 2 gbp.
Table 40 shows that for initial coronas of the same size, 5 = 6.9, "the
residual coronas 5 = 2.7 an d 3.0 do not differ sufficiently to make the
evidence decisive. Less than one-tenth the original number of ions are
represented by water nuclei, the remainder having vanished by sub-
sidence with the fog particles or otherwise. There does not seem to be
any certain difference between the behavior of vapor nuclei and of ions,
so far as these experiments go. The large number surviving in the first
instance (small initial corona), as compared with a smaller number in
larger coronas, is striking.
61. Rapid evaporation of fog=particles. In table 41 the filter cock
is left slightly open in order that the water nuclei may be increased.
The fog-chamber is initially at barometric pressure. The initial pressures
of the vacuum chamber are ^ = 76.7 23.6 cm., to catch the ions
produced by weak radium and numbering about 100,000. The pressure-
differences are then reduced successively to the values to catch the water
nuclei left after the accelerated evaporation specified. The exhaustion
drops from p and p dp' as initial pressures in fog chamber and in
vacuum chamber to pdp 3 , the final common pressure in both, while
dpzlP is a convenient datum for the comparison of the water nuclea-
tions n. These have been corrected for the temperature / of the fog
chamber, more water being precipitated as / is higher and for volume
expansion from v at / to v l at / r
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLB4L Sizes of water nuclei. Radium ionizer. Slightly open filter cock ;
t several minutes.
9?.
9P+
s a .
dPz/P-
Wlfj.
m'l).
w 2 Xio~ 3 .
At 20.
w 2 Xio~ 3 .
Ions originally ;j= 7.0 (w o); n= 115,000. Bar. 76.7 cm.; ' = 53. i cm.; temp. 2i.oC.
I.
23-6
22.2
4-5
0.289
30.2
3i
23-6
22.2
l 5-o
.289
....
40-3
'4i
23-6
22.2
2 4-4
.289
....
28.7
*2 9
23-6
22.2
4.6
.289
32.1
33
13.0
12.4
3 5-4
.162
27.8
28
16.7
16.0
4 5-2
. 209
32.5
33
17.0
16.2
4 5-2
. 211
32-8
33
6.0
5-9
6 7-i
.077
30.2
3i
23-6
22.2
4-7
.289
34-4
35
23-6
22.2
4 5-5
.289
....
54-2
55
Ions. . .
22 . 2
7 O
28Q
1 14. 7
117
Bar. 75.9 cm.; temp. 26 C. Original corona, .9 = 6.4; ^ = 95,000; dp' = 22.i cm.
II.
5-0
4-9
5 7-5
0.065
30.3
32
1-9
i-9
9 .2
.025
....
23.1
24
22.1
20.8
3 6-4
.214
....
83.5
95
Ions . . .
10.3
10.
3 5-4
.132
22.5
24
Bar. 76.2 cm.; temp. 25.5 C.; ions, n= 115,000.
III.
I .O
I.O
7 8.6
0.013
9-5
IO. I
18.0
17.0
3-3
. 2 2 3
9-2
7 io-3
....
2.2
8 7-5
.029
....
13.0
13-8
....
22.1
2.2
.290
....
3-6
7 4-i
....
1.9
8 7-5
.025
....
12.3
13.0
....
17.0
2.8
223
....
5-5
7 6.2
3-o
7-5
039
....
18.3
19.4
22. 2
2. 2
.291
3-6
7 4-i
Radium not removed. 2Cock open late. 3 gbp. 4 wo.
Subsequent exhaustion to catch the water nuclei left after first exhaustion.
gbp.
s gyo. Hvc.
we to gbp, very faint.
The data are given in fig. 30, w in terms of the relative drop in pressure,
x = dp 3 /p. Though the experiments were made with great care and
apparently satisfactory, the results are disappointing; but this is prob-
ably to be expected when the water nuclei are only obtainable by
evaporations lasting as much as a fraction of a minute, during which
there must be both subsidence and probably also a washing-out of
nuclei by the disturbance produced during the influx of air. In the first
series, where there are 115,000 ions, not more than 30,000 or 40,000 water
nuclei (about one-third), are obtainable. On opening the filter cock
RESIDUAL WATER NUCLEI.
97
wider and as wide as permissible to insure filtration, the number of
water nuclei was increased to over 50,000, or to about one-half the num-
ber of ions. In the second series about 90,000 ions were
available, because of the lower drop dp 3 , and less than 30,000
were represented by water nuclei, again about one-third.
-,140
FIG. 30. Number of residual water nuclei obtained from rapid evaporation of fog
particles and found at different small adiabatic drops of pressure dp/p.
FIG. 31. Number of residual water nuclei obtained from rapid evaporation of fog
particles in a partially exhausted fog chamber and caught at different small adiabatic
drops of pressure dp/p.
When the drop dp 3 is as low as 2 cm., the number of water nuclei
is relatively small, though at 5 cm. the maximum is already reached.
Unfortunately, therefore, the range of marked variation of n lies below
a few centimeters of dp 3 , wherefore the coronas are too filmy and large
to admit of easy identification, unless a special immense fog chamber
is constructed for small exhaustions. So far as these experiments go,
however, the appearance is rather such as recalls the distribution curves
for ions and for dust-free air; in other words, the water nuclei are prob-
ably of all sizes within certain limiting dimensions, like the ions.
In the third series of table 41 the attempt is made to further study
these large, filmy coronas. They may be recognized with certainty here
and are throughout of the green-blue-purple type, corresponding to
about 100,000 nuclei under normal expansions. At the low exhaustions
used, however, they correspond to 10 or 15 thousand nuclei per cubic
98 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
centimeter, since but little water is precipitated. In this series a second
large exhaustion was made to catch the nuclei left by the first exhaus-
tion in each of the four cases. But few nuclei were found, however,
perhaps because considerable time (5 minutes) was needed between the
exhaustions; but the reason for this is not clear. One may notice in
conclusion that the numbers found for the nucleation depend essentially
upon computation, as the coronas are large. There is one correction,
m/m 27 , to allow for the small quantity of water precipitated; another
for the volume increase on exhaustion; a third for temperature, etc.
The coronas themselves naturally increase as the expansion is larger,
but they do not keep pace with the corrections.
62. Continued. In the experiments of table 42 the filter cock was
again left slightly open; but the vacuum chamber was kept at the
same initial pressure p dp'. The low drops of pressure were secured by
successively reducing the pressure of the fog chamber, as shown under
P P a- This is a much more convenient method of experiment, though
the computation is more troublesome. The final common pressure after
exhaustion is p dp 3 . All other data have the same meaning as before
and corrections are added for the precipitation of water, m' /m\ for the
volume expansion v l /v and for temperature. The table contains six
series of results for different exhaustions and differently opened filter
cock. Data are reproduced in fig. 31.
Naturally the same evaporation difficulties are again obtained, but
the curves as a whole are more definite. In series I and II the number
of ions which survive in the water nuclei is again about a third in each
case; but if the filter cock is opened wider, about half as many water
nuclei occur relatively to the original number of ions. If radium is left
in place (series III, VI) the ions are still efficient in presence of the
increased number of nuclei.
The curves corresponding to the distribution of water nuclei in series I
again suggest the distribution curve of ions and of vapor nuclei in dust-
free air. In other words, all sizes of nuclei within a certain range of
dimension seem to be present. Series II has not been carried far enough,
for the experiment places a lower limit at which the method necessarily
breaks down. Series VI, however, is of a similar character to series I.
The distinctive feature of these experiments is the occurrence of
reduced nucleation at very much higher drops of pressure than above.
One would naturally associate this with the fact that the water nuclei
are stored before the precipitation of fog upon them, in a partially
exhausted vessel. Yet the evidence is not clear on this point. The
smallest nucleation occurs at the lowest pressure attainable, viz, 59.8 to
61.9; but in series II higher values of n appear at 62.0 to 62.4 cm. A
larger drop of pressure is here applied adapted to catch the smaller nuclei.
RESIDUAL WATER NUCLEI.
TABLE 42. Sizes of residual water nuclei.
99
P.
8 pa.
*p
S 2 .
*P*/P-
P
/>'
n 2 Xio~ 3 .
At 24
w 2 Xio~ 3 .
I. Cock open 30. Bar. 76 cm.; temp. 24.2 C.; ' = 52.4 cm. Original ions, 1
y== 6.9; n=no,ooo.
76.0
76.0
63-9
64.0
68.7
68.8
59-8
61 .9
0.0
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
o. 291
.292
169
2 .i7o
.227
.224
.117
.147
59-9
53-8
53-i
53-i
53-i
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, n= 130,000.
76.0
62.0
67.9
67.8
76.0
o.o
14.0
8.1
8.2
o.o
26. 3
26.5
26.2
26.2
25-8
4-6
2 5 ' 3
2 5-i
5-i
4-5
0.346
. 2O2
.267
.266
339
49-7
49-5
49.8
49.8
50.2
48.9
38.9
33-5
39-3
39-0
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
o.o
o.o
0.0
0.0
25-9
25-9
25-9
25-9
5-i
5-i
5-6
7.0
0.341
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. ^'=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.i cm. Original corona, s = 6 . 4 ; n = 86,ooo.
75-9
64.7
64.0
o.o
II . 2
II.9
20.7
21.5
21.5
I 5 ' 3
I 5 ' 2
3 5-2
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, 5 = 6.9;
n = 97,000. Cock open 30. ' = 27.5 cm.
Radium in place
Ions
60.6
55-9
76.0
76.0
15-4
2O. I
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
5i-5
24.9
108
127
42
21
82
97
i Loss by subsidence. 2 w o.
gbp.
100 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
TABLE 42. Sizes of residual water nuclei Continued.
P.
dpa.
*/,.
S 2 .
dp 3 /p.
P
P'-
M 2 X io- 3 .
At 24
w 2 Xio~ 3 .
VII. Bar. 75.7 cm.; temp. 29.5 C.
Ions
75-7
75-7
75-7
58.2
58.8
75-7
O.O
0.0
0.0
17.5
16.9
0.0
28.1
27.1
27.4
28.0
28.0
27.4
6-9
1 6.2
2 4-3
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
6 I02
6 34-5
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
0.0
11.7
22. I
0.0
34-4
35-2
34-4
35-1
35-5
34-4
4.8
5-0
4.6
5-o
5-6
6.9
0.454
.247
454
.366
.250
455
41-3
40-5
41-3
40.6
40.2
39 3
59-7
34-3
52.6
52.0
49.1
176
68
38
60
59
54
201
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 caugftt
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.
S 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. e., 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 = dp 3 /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.
43. Summary of table 42. Filter cock open 30. Data referred to 125,00x3
ions, originally present.
XX io- 3 .
nX io- 3 .
XXio- 8 .
Xio- 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
H7
30
35
3i
29
37
35
17
22
188
122
42
21
Series VII. Ions 160,000. Ear. 75. 7
cm.; temp. 30 C.; ' = 46. 7 cm.
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
iMade 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 3 and
tpjp.
s.
wXio- 3 .
t.
dps and
*PJP.
s f .
W'XIO- 3 .
Ratio.
I. Bar. 76.2 cm.; temp. 15 C.; radium and water nuclei, >/>' = 24.0 cm.; vapor
nuclei, dp' = 29. 3 cm.; dp/p = 0.297 and 0.362; v l /'v= 1.284 an d 1-375 1
not corrected for temperature.
Radium. .
22.6
6-9
86
90
22.6
4.6
26
0.30
dp/p = 0.297
86
90
.297
5-o
32
-37
86
1 80
....
5-o
32
37
86
1 80
....
5-o
32
37
86
300
....
3-7
14
.16
86
600
3-9
16
19
II. Wet air.
None
27.6
17 ?
I SO
1 20
22 6
C T.
*8
O 2S
0.362
2 6.2
88
1 80
297
4-2
20
23
3 6. 9
117
300
5-i
34
29
3 6. 9
117
600
4.8
29
25
III. Repeated. Identical pressures (' = 28. 3 cm.) throughout. Always same
rate of influx (partially open cock). Temp. 22 C.; bar. 76 cm.; vj-v
1-363-
None
26.9
6-3
9i
600
26.9
4-2
27
0.30
Radium . .
354
6-4
94
600
354
4 6-3
(9i)
97
6.6
102
600
3-6
17
17
IV. Repeated. Bar. 75.2 cm.; temp. 19 C.; vjv=i .362; dp' = 28.3 cm.
None
(26.5
\ -352
h.
107
660
f 26.5
I -352
J3,
H
0.13
None
(26.7
I -355
} 3 6-9
116
720
(26.7
I -355
} 3-5
16
.14
Radium . .
8 6. 7
107
600
3-5
16
15
Radium . .
6.6
IO2
600
3-3
J 3
13
None
'6.9
116
690
3-8
20
.18
J gbp. 2 wr. 3 wog. 4 Radium 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
100 0.00 300 400 SOO 600 100 800
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 t seconds after evaporation. (6) 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 dp 3 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. 32,6, 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 Ip 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, c&t. 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 dp 3 = 22 . 6) than to catch the water nuclei resulting from the
evaporation of fog particles (^3 = 17.1). Hence, in the two cases
dp 3 /p=o.293, volume expansion v 1 /v = i.2&, and dp 3 /p = o.22'j, v 1 /v =
i . 20, whence nX io~ 3 = o. 268s 3 and nX io~ 3 = o. 2I5-S 3 .
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,
,S=
3-3 2 -o i.o
12.2 7.9 3.4
4-4 3-0 i.
11.5 6.6
showing a well-marked progression of data. Similarly, the attempt to
find n 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. ; d/> 3 =22.ocm.; ^' = 0.71; dp 3 /p = o. 293 (factor, o.268.y 3 ); forwater
nuclei, dp=i8. i ; dp^ij.i', [dp 2 ]=i6.5; dp 3 /p = o.22j; y = o. 774. AssumeS = 6.5.
No. of
exhaustion.
Corona.
s.
w'Xio- 3 =
0.2I5S 3 .
No. of
exhaustion.
Corona.
s.
w'Xio~ 3 =
0.215-y 3 .
(Ions) i
w r
6 6
*76 Q
(Ions) i
w r
6 6
*76 Q
(Water nuclei) 2
4-7
22.3
(Water nuclei) 2
4-4
18.3
3
....
3-3
7-7
....
3-o
5-8
4
....
2.0
i-7
....
1.8
I . 2
5
....
1.0
0.2
....
0.0
0.0
6
....
0.0
0.0
These data are shown in fig. 33, where i o~ 3 n' = o. 2 i$s 3 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 (wX 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
present.
Should be
present.
Nuclei
present.
Should be
present.
Ions
76 Q
76 Q
Ions
76 Q
76 9
After i evaporation
After 2 evaporations
After 3 evaporations
After 4 evaporations
22.3
7-7
i-7
0.2
50.6
8.0
0.9
0. I
After i evaporation
After 2 evaporations
After 3 evaporations
After 4 evaporations
18.3
5-8
I . 2
O.O
50.6
6.2
0.4
0.0
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.
I0 7
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.
o.i2S = .y'.
n X io~ 3
(exh.).
wXio- 3 .
Calculated
wXio- 3 .
For ions, dp' = 24.0 cm.; dp 3 =22.g cm.; [d/> 2 ] = 22.4 cm. For water nuclei,
dp' = 24.o cm.; dp 3 =22.g cm.; [d 2 ] = 22.4 cm.; d/> 3 //? = 0.301; =6.5.
i.
2.
3-
(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
2.0
8.6
5-o
3-6
2-5
2. 2
8. 4
4 .8
3-5
2.4
28
8-5
4.1
2.2
32
I3-I
4.1
2.9
29
12
3-7
1 66
36
n
5-3
2.8
1 66
42
17
5-3
3-7
157
38
15
4.8
(Water nuclei) 2
3
4
(Air) . . 5
(Ions) i
(Water nuclei) 2
O
4
(Air) . . s
(Ions) i
(Water nuclei) 2
3
4
The same. 1 For ions, ' = 24.0 cm.; dp 3 =22.g cm.; [dp 2 ] = 22.4 cm.; dp 3 /p =
0.301. For water nuclei, ^=18.5 cm.; ^3=17.7 cm.; [dp 2 ]=i7.o cm.;
^3/^ = 0.233; ^ = 0.771.
4-
5-
6.
si : f
r (Ions) . . .1
71
47
33
24
14
72
40
30
20
13
o
72
42
33
25
15
8-5
5-6
4.0
2-9
i-7
0.0
8.6
4.8
3-6
2-4
1.6
0.0
8.6
5-0
4.0
3-o
1.8
o.o
162
45-7
18.6
6-3
1.2
0.0
166
29-3
13-1
3-7
I.O
0.0
1 66
33-6
17.7
6-9
i-4
o.o
162
114
69
32
5-5
0.9
1 66
117
64
25
9
4
167
117
66
30
6-5
i-4
(Water nuclei) 2
3
I
( 6
(Ions) i
(Water nuclei) 2
3
4
6
(Ions) i
(Water nuclei) 2
3
4
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.
5.
o.i2S=.r'.
wxio- 3
(exh.).
nx io- 3 .
Calculated
nx io~ 3 .
The same, with ions from X-rays. Bar. 76.1; temp. 21 C. Ions, ^ = 24 cm.;
dp 3 =22.g cm.; [^ = 22.4 cm.; dp 3 /p = o.^oi. Water nuclei, dp'= 18.5 cm.;
^3=17. 7 cm.; [ 2 ]=i7.o cm.; d/> 3 //>=o. 233.
7-
8.
9-
10.
ii.
12. '
\ dons} i
O IO2
50
4
30
19
102
54
4i
30
17
gy 124
63
46
33
23
13
o
g' 123
66
49
38
27
17
g' 128
66
47
35
26
17
128
7i
50
39
29
18
o
12. 2
6.0
4-8
3-6
2-3
o.o
12.2
6-5
4-9
3-6
2.0
14.9
7 .6
5-5
4.0
2.8
1.6
o.o
14.8
7-9
5-9
4.6
3-2
2.0
15-4
7-9
5-6
4-2
3-i
2.0
15.4
8.5
6.0
4-7
3-5
2.O
O.O
475
57
29
13
3-2
o.o
475
74
30
13
2.2
813
H5
44
17.6
5-7
1.9
o.o
813
128
53
26
8.5
2.2
IIOO
128
4 6
20
8.0
2. 2
IIOO
162
57
28
11.7
2.8
o.o
475
350
221
122
47
18
475
350
228
128
49
813
607
415
245
112
16
2
813
607
419
263
140
37
IIOO
823
568
348
174
50
IIOO
823
580
366
199
72
26
(Water nuclei) 2
3
4
5
6
i
2
3
4
5
(Ions) i
(Water nuclei) . ... 2
3
4
5
6
7
(Ions) i
(Water nuclei) 2
3
4
6
(Ions) i
(Water nuclei) 2
3
4
5
6
dons) . i
(Water nuclei) . 2
3
4
5
6
7
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.
109
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, D = 4o, 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.I25=/.
wXio- 3 .
Calculated
nXio- 3 .
Bar. 76.0 cm.; temp. 20 C. For vapor nuclei, ^ = 33.1 cm.; ^3=31.3 cm.;
[#/? 2 ] = 30.8 cm.; ^3/^ = 0.412. For water nuclei, dp'=i8.$ cm.; <5/> 3 =i7-7
cm.; [dp 2 ]=i 7 .o; dp,/p = 0.233.
(Vapor nuclei) . i
V 1 17
14.0
'905
905
(Water nuclei) ... 2
j i
so
9.6
234
674
3
6 7
8.0
135
482
4
52
6.2
66
333
i . <
5
39
4-7
27.7
214
6
28
3-4
10.9
116
7
19
2-3
3-3
39
8
10
I . 2
0-3
13
(Vapor nuclei) i
y 116
p cor 72
13-9
8.6
'905
1 66
905
673
(Water nuclei) 2
3
r^ ^- /
r 61
7-3
103
473
4
50
6.0
57
319
2.
5
37
4-4
23-7
20 1
6
26
3- 1
8
103
7
20
2.4
3-7
26
i 8
IO
1.2
0-3
6
Bar. 76. i cm.; temp. 21 C. For vapor nuclei, ^3=28.3 cm.; d/> 3 //>= i -233- For
water nuclei, dp s /p o. 37 2.
(Vapor nuclei) i
6.8
5-2
8.2
6.2
172
66
172
120
(Water nuclei) 2
3
4.0
4.8
29
77
3-
4
2.7
3-2
9.1
42
5
i-7
2.0
2. I
12
6
0.0
O.O
0.0
4
4-
(Vapor nuclei) . . . . i
7-i
5-i
4-3
8.5
6.1
5-2
191
61
35
191
134
85
(Water nuclei) .... 2
3
4
3-3
4.0
17-7
49
5
2-5
3-0
6.9
22
1 Water nuclei removed by exhaustion, but not the vapor nuclei.
110 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. ^
ZO 40
60 80
100
1ZO 140
FIG. 35. Relative difference of nucleation (n f 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/s 2 ,^), 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' n **ndf- l &- l TL
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 (w 1 + w 2 )/2, very roughly,
I00)000 vapor nuclei ions, < x '^
= 50,000 vapor nuclei ions, { x = ' 2
= 10,000 vapor nuclei ions, I x = ' ^
results which are too irregular for further comparison.
A simple term like (n f n)/n is preferable in other respects, and in
order to put the larger and more certain data on the diagram, (n' n)/n
may be constructed in terms of i /n. If it were 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 io 6 /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
Computed
n' X io- 3 .
IO 6 /M.
(-,*.
xXio*.
x, x', x", etc.
d'Xio 5 .
4-
162
162
6
....
....
38
46
114
22
2.0
40
0.40
57
19
69
54
3-8
52
.68
80
6
32
159
5 *
59
7i
no
i
6
830
4-5
69
i . i
190
5-
1 66
166
6
o
37
29
117
34
3-o
25
0.25
67
13
64
76
3-9
45
.80
89
4
25
267
5-7
53
75
133
i
IO
IOOO
8-5
80
2-7
200
6.
1 66
167
6
37
34
117
30
2.4
29
o. 29
64
18
66
56
2.7
51
.90
80
7
30
145
3-3
61
.89
107
i
6
690
3-6
68
9i
1 80
7-
475
475
2
o
....
26
57
350
17
5 J
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
5 1
.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
1 60
9-
810
813
i
21
j j e
607
9
4-3
19
o. 19
4 2
44
415
23
8.4
48
58
58
18
245
57
12.5
52
65
8O
6
112
175
18.5
47
71
114
10.
810
813
i
....
22
128
607
8
3-7
21
0.21
41
53
419
19
6-9
51
.62
54
26
263
38
9.1
56
.76
70
8
140
118
15-4
50
.61
IOO
n.
IIOO
IIOO
i
21
128
823
8
5-4
16
o. 16
4 1
46
568
22
11.4
43
5 1
57
,_/
20
8
348
174
50
125
16.4
21
49
46
*8i
76
103
12.
IIOO
IIOO
I
O
21
162
823
6
4-1
20
o. 20
38
57
28
12
580
366
199
17
36
85
9-2
12. I
16.0
4 6
53
49
77
76
53
68
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'Xio- 3 .
I0 6 /W.
(n'-n)/n.
*Xio 2 .
x, x', x", etc.
dXio 5 .
i.
905
905
j
0.0
23
234
674
4
i-9
35
0-35
33
135
482
7
2.6
53
.80
40
66
333
15
4.0
58
7i
52
28
214
36
6-7
60
65
68
ii
116
92
9-5
-73
94
3-3
39
300
ii
.90
140
2.
905
905
i
o.o
23
166
673
6
3-o
25
25
37
103
473
10
3-6
47
.88
44
57
319
18
4.6
56
.82
53
24
201
42
7.8
59
.67
73
8
103
125
ii. 9
65
103
4
26
270
....
....
i-7
134
i
3-
172
172
6
0.0
....
....
39
66
120
15
0.8
55
0-55
52
29
77
34
i-7
62
.69
67
9
42
no
3-6
60
58
100
2
12
450
4.8
66
.82
160
4-
191
IQI
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 n t be the initial nucleation)
= n. 0.0029
\J . *~ n ~ f jO
.
5-3
5
.290
38
> .0021
4-7
10
.290
27
.
4-7
10
.290
27
1
.
3-8
20
.290
15-1
\ -033
....
.2
3-7
20
.292
13-9
j
. 2
. 2
3-7
3-3
2O
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
1 2O
.292
. 290
4.6
0.9
.0150
. I
1.6
1 2O
. 290
0.9
....
....
. 2
6-7
O
. 292
79
....
....
. 2
6.8
.292
82
II Air 2
22 . I
I Q
2QO
I 7
.1
* V
i-7
....
. ^^^/
.290
* /
1.2
....
20.7
r'
....
.272
0.2
20-4
r'
....
.268
0. I
....
*wr cor. *Radium removed. Corona glimpsed at fip= 20.4.
These data are given in fig. 40,* which also contains the observed
values of i fn and the corresponding computed values oii/nifb o. 0014.
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
n=o.29 6=0.0029
34
36
41
or a mean value 6 = 0.0033, ^ the l as ^ 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, o . 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 = bn 2 ) 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 dn'/dt = bn 2 + 2 bnn' + bn' 2
so that both dn/dt and dn'/dt are larger than bn 2 and bn' 2 . If n = n' ,
2dn/dt = 4bn 2 or dn/dt = 2bn 2
If but one-third of all the ions, 3^, are captured, dn/dl = g bn 2 ; etc.
Hence if but i/m of all the ions are captured, the coefficient of decay
4-0 30
60 70
FIG. 40. (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.
being as found should be about m times too large as compared with the
true values. This does not explain, however, why the coefficient b
increases when / 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
20
30
40
SO
60
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 nis 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 t increases.
If we combine the first observation with the fourth, etc., in series i,
# = 0.27, 6 = 0.0038, 0.0041, 0.0057, - OI 34 or a mean value of 6 =
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.
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. dp/p = o. 268 to o . 272 ; distances 40 and 250 cm.
8p t .
s.
t.
wXio- 3 .
Successive
b.
Mean
6.
cm.
cm.
sec.
I. Radium
20.7
6.4
o
66
....
....
.6
.6
6-3
5-o
o
5
63
30
j 0.0036
0.0045
4
.6
5-0
4-4
5
10
30
21.4
j -0031
5
5
4.2
3-6
10
20
19-5
12. I
.0042
5
5
3-4
3-i
20
30
IO.O
7-4
.0044
5
5
3-i
2-3
30
60
7-4
3-o
.0066
5
2-3
60
3-o
> 0180
4
i-5
120
0.7
.6
i-5
120
0.7
Air
6
o
o.o
Radium at 325 cm.
.6
r
O. 2
Bar. 76. 2 cm.; temp. 24.0 C.; dp/p = 0.254-0. 256.
II..
IQ.4-
3.0
o
6.1
4
3-2
7-5
\ 0.0206
O.O2I
5
2-5
5
3-9
/
5
3
2.6
1.7
5
10
4.1
i . i
j .1770
3
1.7
IO
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 6 decreases as the exhaustion increases
and finally approaches 6 = o . ooi 4, etc. The experiments of the following
tables show that 6 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 = 40 cm. Bar. 76 . 3 cm. ; temp.
24.oC. ; 3=22.3; dp 3 /p = 0.292. Above fog limit of air. dp' = 23. 8 cm.
5.
s.
/.
Exhausted
wXio- 3 .
wXio~ 3 .
6.
cm.
j'ec.
i Radium
l i ^
42
o
1 f 20.0
fj O
>3-6
*
4-3
o
\2I.5
. ...
2 3-9
4-7
o
2 J2J.3
2 4-o
3-o
3-i
3-i
3-o
4.8
3-6
3-7
3-7
3-6
o
5
5
10
10
128.9
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-i
20
7-9
10. I
1
2.4
2.9
20
6-3
8.1
2. 2
2.6
30
4.6
5-9
f .0041
2. I
2-5
30
4.1
5-2
1.8
2. 2
60
2.8
3-6
j
1.8
2. 2
60
2.8
3-6
Air
1.6
I
I 7
* * "
A /
1 Subsequent.
2 Initial.
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 n .
FIG. 44. Decay of ionization in fog chamber in lapse of seconds for different initial
ionization.
RESIDUAL WATER NUCLEI.
I2 7
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 vjv = i . 2 5 . 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 (dp 3 /p near
the fog limit); or to decay of ions in the lapse of time (exhaustion t
seconds after removing the radium from the fog chamber), or due to
TABLE 53. Decay of weak ionization. Radium at = 40 cm. Bar. 76.9 cm.; temp.
i8.oC.; dp 3 =2i.ocm.\ d/>3//>=o.273. Practically below fog limit of air. # = 250
cm. Exhaustion i . 25 =v^v.
S.
0.125 = ^.
t.
Exhausted
wXio~ 3 .
Corrected
wXio- 3 .
b.
sec.
2. Radium
-2 j
3- 7
o
13.2
I (i6 s)
29
3-5
* o
ii. i
KI3-9)
....
28
3-4
o
10.2
1 (l2.8)
25
23
25
3-o
2.8
3-o
5
5
10
6-5
6^5
8.1
6.4
8.2
0.0043
I 043
25
3-o
10
6.5
8.2
3
22
2.6
20
4-7
5-8
35
22
2.6
20
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
1.4
1.8
13
i.5
60
0.8
i .0
The same; stronger radiation. Radium at D = o from walls.
?
45
46
5-4
5-5
O
o
38.3
41.0
'(47.9)
'(51-3)
1
o
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
II . I
13-9
J
29
3-5
IO
II . I
13-9
25
3-o
20
6. 4
8.0
24
2-9
20
6.0
7-5
25
3-o
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 dp 3 /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)/n 2 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 io s w = 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 + bn 2
where a is the number generated per second by the radiation, en the
number independently absorbed per second, and bn 2 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 + bn 2
or
n n
where the nucleation n and n Q occurs at the times t and t Q , respectively.
If 6 = 0,
if c = o, the equation reverts to the preceding case, where dn/dt = bn 2 .
Hence when c becomes appreciable,
_ dn/dt c
- = -f-o
n 2 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
b 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 io 6 (c/n = 3 X io~ 8 ) ; but it will rapidly become so as n approaches
the order of io 4 (c/n = $X io~ 6 ), which again is closely verified by the
above data.
Finally, if the decay bn 2 is temporarily ignored and if the ions are
supposed to be absorbed with a velocity K at the walls of the cylindrical
fog chamber of length / and radius r,
I . 2nr . K . n = l . -xr 2 . en or K = cr/2
if = 3 . 5X10 ~ 2 , r = 6 cm. , K = o . i cm/sec. , which is not an unreasonable
datum. It is not improbable, however, that absorption occurs within
the fog chamber in view of the presence of water nuclei. Finally, if the
ends of the fog chamber be taken,
quite apart from the effect of internal partitions. Hence K estimated
at o . i cm. /sec. is an upper limit.
Again, if dn/dt = a + bn 2 + cn, the conditions of equilibrium are
modified and become (since dn/dt = o)
a = cn + bn 2
where a measures the intensity of radiation. It no longer varies with n 2 .
Thus
c
The complicated relation of n and a was not suspected in my earlier
work, where distance effects due to X-rays were observed.
130 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
77. The absorption of phosphorus nuclei.* The method of the pre-
ceding paragraph applied to the data obtained in the given paper with
phosphorus nuclei leads to striking results. It shows the possibility of
computing nucleation by passing a current of highly ionized air through
tubes of known length and section into the steam-jet apparatus there
developed. In these experiments, made a long time ago, the value of the
absorption velocity K was found to be 0.3 cm. per second, with the
condition that decay by the mutual destruction of phosphorus nuclei is
negligible. The equations here are
n = n e- aKx/rv
where v is the velocity of the air current bearing phosphorus nuclei
and flowing through a tube of radius r, and where n and n are the
nucleations at the ends of the tube of length x.
If V and V are the volumes of air in liters per minute of lengths
x and o, discharging equal numbers of nuclei per second into the steam
jet,
K = 2.6$ (V/rx)ln(V/V )
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 + n 2
or
n(e 2K(x -^ /rv (2K + K^rn ) K'rn,} = 2 JKn Q
where K' is the decay coefficient; or since v = iooo V/6o7:r 2
n
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,
V \ / V v \ n o
If V = V corresponds to %' = o (or the absence of the tube)
s Kr*/ a .6 S v/L +
\ n o
The equation therefore reduces to
i+Rrn
whence
* 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
54. Initial phosphorus nucleation, n , from steam-jet measurements (Smith-
sonian Contrib. No. 1309, pp. 34-36, 1901). Assumed 6=io~ 8 ; = 0.0356; b/2c=
1 4 X i o- 8 = # . V in liters per minute . n = ^ I jkfx/^6sV ^7 ~ I )
X.
V.
io- 6 w .
x com-
puted.
X.
V.
io- 6 w .
x com-
puted.
I. Absorption pipe gray rubber. 2 r
0.64 cm.; ^0 = 0.75.
V. Absorption pipe 'brown rubber.
2^ = 0.35 cm.; F = 6.
cm.
o
125
295
455
o
0.7
3-i
4-7
6.5
0.8
3-3
3-6
4.6
1 20
291
555
cm.
o
50
100
150
2OO
250
300
O
0.7
1-5
1.9
2-3
2.8
3-i
3-5
0.6
7-i
6.4
6.6
7-8
7-7
8-4
II. Same. = 0.75.
cm.
o
85
125
295
455
0-5
2. I
2.8
5-2
6. 9
1-9
2-7
4-4
5-3
49
97
360
624
VI. Absorption pipe lead. 27 = 0.63
cm.; V = o.6.
cm.
o
IOO
200
300
400
o
0.5
2-3
4-2
4.6
4-7
0.8
3-0
5-9
4.6
3-4
III. Absorption pipe brown rubber.
2^=0.35 cm.; F = o.6.
cm.
100
150
200
250
300
350
0-5
i-3
i-7
2. 2
2.6
3-3
4.2
"4.6
4-7
5-9
6.4
9.0
13.0
VII. Same.
cm.
o
34
68
IOO
200
3 00
0.5
1.2
2.O
2.6
3-8
4-3
0.6
i!6
3-2
4.1
4.6
3-9
I
IV. Absorption pipe glass. 2^=0.29
to 0.32 cm.; F = o.8.
VIII. Absorption pipe lead. 2^=3.2
cm.; F = o.7.
cm.
50
100
150
0.8
1.2
i-4
1-9
0.8
2-5
2. I
3-7
cm.
50
IOO
150
0.7
1.4
i-7
2.O
"4.*
4.1
4.4
132 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
for K' and K, and these are taken from section 79, where b = K = io Q
and ^7 = ^ = 0.0356, 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 V is very difficult to obtain closer than V = o.$ 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
V found in the experiment. Thus if V = o .& had been taken instead
of y o = o.6 the following values would have resulted:
jyj ( V 1.3 1.7 2.2 2.6 3.3 4.2 liters per minute.
\ io 8 w = 2.0 2.4 3.6 4.0 6.0 8.8
y f V= 1,5 1.9 2.3 2.8 3.1 2.5 liters per minute.
\ io e w = 4-o 4-o 4.0 5.2 5.2 6.4
These are much nearer the other values, showing that the great diffi-
culty of finding V , 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 n 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 = n V , it is therefore possible to
pass at once to the nucleations by writing C = n Q V OJ or
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.; 0^ = 22.9 cm.
Radium I-IV.
Cor- Successive
~ Successive
Cor- .!.
Time.
S.
s' = recte
o.i25 nX
d
Time.
5.
s' = recte
o.i25 nX
d
io- 3
io- 3
5 sec.
20 sec.
5 sec.
20 sec.
g'o 73
8.8 478
20
33
4.0 23
g'o 73
8.8 ^78
....
25
29
3.5 16 i. io
1.98
5
6.1 81 1.26
....
25
35
4.2 27
....
5
52
6.2 87
....
25
33
4.0 23
....
10
46
5-5 58 1.32
....
30
29
3-5 16 2.66
2.02
10
44
5-3 5i
30
30
3.6 17
....
15
35
4.2 27 3.44
....
60
21
2-5 5-5 4-i
3-30
I e;
77
A A 7O
60
21
2 > S S
A o
2O
o /
35
T- T" O ....
4.2 27 0.86
1.72
o
71
8.5 '165
2 2.2 5
II. X-rays. Z?=ioo. dp/p = o.^oo. Bar. 75.6cm.; temp. 27 C.
Cor-
Succes-
Cor-
Succes-
Time.
5.
.$' = 0. 125.
rected
sive
Time.
5.
S' = 0.125.
rected
sive
n X io- 3 .
&Xio 6 .
n X io- 3
6Xio'.
we 89
10.7
3 32i
1.50
40
25
3-0
8.9
2.40
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
88
10.6
....
20
36
4-3
28.1
5
58
7-0
119
30
30
3.6
16.9
5-23
5
54
6-5
95
30
30
3-6
16.9
III. X-rays. # = 50. dp/p = o.2gg. Bar. 76.0 cm.; temp. 25 C.
Cor-
&Xio 6
Cor-
6Xio
Time.
5.
S'=O. 125.
rected
succes-
Time.
5.
S f = O. 125.
rected
succes-
Xio-.
sive.
wXio- 3 .
sive.
w r 91
10.9
337
1.17
40
28
3-4
H
o
90
10.8
.
40
27
3-2
ii
....
IO
49
5-9
69
1.76
50
23
2.8
7-5
....
10
48
5.8
66
50
2 4
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
o
w r 86
10.3
288
....
30
30
3-6
17
....
Corrected for expansion, 231, 231, 215. 2 Mean. 3 If corrected for expansions, 414, 385, 407.
RESIDUAL WATER NUCLEI.
55 Continued.
135
IV. X-rays. 0=15. dp/p = o. 299. Bar. 76.ocm.; temp. 27 C.
Cor- &Xio 6
Cor- b X io e
Time.
5. s'=o.i2S. rected succes-
Time. S. s' = 0.128. rected succes-
wXio~ 3 . sive.
wXio- 3 . sive.
ybm 13.4 625 1.38
20 36 4.3 28
10
49 5-9 69
20 36 4.3 28
10
47 5.6 60 2.03
o g' 116 14.0 750
V. X-rays. #=15 cm. />//> = o. 297. Bar. 76. 4 cm.; temp. 26 C.
Time.
5.
S'=O.I2S.
Corrected
nXio- 3 .
Time.
S.
*'=O.I2S.
Corrected
wXio- 3 .
gy 124
14.9
620
50
26
3-i
10
10
54
6-5
93
50
28
3-4
H
10
49
5-9
68
30
3i
3-7
18
20
4i
4-9
40
30
34
4.1
24
20
35
4.2
26
10
5i
6.1
78
30
29
3-5
15
5
w o 70
8.4
200
3-
32
3-8
19
5
70
8.4
200
40
27
3-2
ii
gy 133
16.0
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 t Q directly are as follows:
TABLE 56. 1/- i/n Q =(i/n + 6/c
Series.
t-t .
io 3 6.
c.
io*b/c.
Temper-
ature.
Pressure.
seconds.
'-{
o, 15; 15, 30
5, 15; 20, 30
0.00239
.00286
-0.0177
.0196
-0.135
- .146
[ -
75-3
H. |
0, 20J 20, 40
10, 30; 30, 50
.00082
.00088
+ .0448
.0315
- .0183
.0281
I >
75-6
m. j
o, 20; 20, 40
10, 30; 30, 50
.00061
.00056
.0411
.0399
.0149
.0140
I -
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,
136 CONDENSATION OF VAPOR AS INDUCED BY 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 series 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 n are no better as a whole than will be the
case if the first set of constants of series II, for instance, are used.
soo
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
*Townsend, McClung and Langevin find b= 1. 1 X io~ 6 about, using electrical methods.
See Rutherford's Radioactivity, pp. 41, 42, 1905.
RESIDUAL WATER NUCLEI.
137
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 b is less than
io~ 8 and c greater than 0.035. If 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 6= io~ 6 , 0=0.0356.
rf'-
n given in thousands per cm 3 .
Series.
/.
io~ 3 Xw
observed.
io~ 3 Xw
computed.
Series.
t.
io- 3 Xw
observed.
io~ 3 Xw
computed.
i
24.4
24.4
2
310
310
5
17.2
18.3
5
107
107
10
17.2
14.2
10
55
60
15
13-7
ii. i
20
29
28
20
9-i
8.9
30
17
16
30
5-5
5-6
40
9
IO
60
3-6
1.8
50
7
6
2
o
ii. 5
ii. 5
3
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
1.4
i.i
50
8
6
3
39-6
39-7
4
625
625
5
28.5
28.1
10
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
178
178
2O
33
3i
5
84
82
30
17
17
10
54
50
40
ii
n
15
28
34
50
'12
7
20
25
25
30
21
17
25
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
T I
'38
CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS.
where r t / . If c is very small the exponential may be expanded,
whence
and if c = o, n (nfn i)/6r, as above. In these equations the value of
b is also given in terms of n and n/n and the time T, in a way already
specified, or
i/ I/MO (? i)/n
Suppose now that dn/dt = bn 2 for the true nucleation and that
N=A+Bn as the result of systematic errors of standardization. Then
dN/dt~b'N*+c'N+d', an equation broader in form than the one
( dnldt = cn + bn 2 ) accepted; and d f vanishes if A is very small; c'
vanishes with A. Hence the possible introduction of c through the
method of standardization is not excluded, however improbable, since
the equation is conditioned by the occurrence of A.
60
FIG. 49. Decay of ionization in fog chamber in lapse of seconds
observed and computed.
80. Conclusion. If the rate of decay of ionized nuclei be written
bn?, the coefficient b as found by the fog chamber increases as n decreases
and may reach tenfold the order of the usual electrical value b = io~ 6 .
The endeavor to explain this by supposing that but i /m of all the ions
are caught and dn/dt = mbn, is not satisfactory.
RESIDUAL WATER NUCLEI. 139
It makes no difference how the small efficient nucleation is produced,
whether by weak radiation, or by decay (time loss), from a larger nuclea-
tion, or by small exhaustion catching but few nuclei.
The data of the fog chamber may be explained by postulating the
absorption coefficient c so that if a be the number generated per second,
dnfdt =a+cn + bn?
In such a case, if b is io~ 6 the order of the corresponding decay of ions as
found by condenser, and if c is of the order of 3 . 5 X io~ 2 , the results of
the fog chamber are closely reproduced for all values of nucleation.
A similar theory may possibly be extended to include the absorption
of phosphorus nuclei, carried by an air current through thin tubes of
different lengths and section (absorption tubes).
Finally, it is improbable, though not impossible, that the constants
c may be introduced by a systematic error in the standardization of the
coronas of cloudy condensation. To test this it will be necessary to
devise some means by which the dust-free air in the fog chamber may
be homogeneously nucleated during the experiments for standardiza-
tion, so that coronas obtained may be without any distortion whatever.
Such experiments, however, require considerable labor and the present
work may therefore be terminated at this point of progress.
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