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