EXCHANGE 
 
"University of Cbtcaoo 
 
 OX THE MOTION OF A SPHERE OF Oil 
 
 THROUGH CARBON DIOXIDE AND AN 
 
 EXACT DETERMINATION OF THE 
 
 COEFFICIENT OF VISCOSITY 
 
 OF THAT GAS BY THE 
 
 OIL DORP METHOD 
 
 LEO JOSEPH LASSALLK 
 
 A DISSERTATION 
 
 SUBMITTED TO THE FACULTY OF THE OGDEN GRADUATE SCHOOL OF SCIENCE 
 
 IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY, 
 
 DEPARTMENT OF PHYSICS 
 
 CHICAC.O 
 1917 
 
tlbe Tllnlversitg of Cbtcago 
 
 ON THE MOTION OF A SPHERE OF OIL 
 
 THROUGH CARBON DIOXIDE AND AN 
 
 EXACT DETERMINATION OF THE 
 
 COEFFICIENT OF VISCOSITY 
 
 OF THAT GAS BY THE 
 
 OIL DORP METHOD 
 
 BY 
 
 LEO JOSEPH LASSALLE 
 
 A DISSERTATION 
 
 SUBMITTED TO THE FACULTY OF THE OGDEN GRADUATE SCHOOL OF SCIENCE 
 
 IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY, 
 
 DEPARTMENT OF PHYSICS 
 
 CHICAGO 
 1917 
 
of, 
 
 ON THE MOTION OF A SPHERE OF OIL THROUGH CAR- 
 BON DIOXIDE AND A DETERMINATION OF THE 
 COEFFICIENT OF VISCOSITY OF THAT 
 GAS BY THE OIL DROP METHOD. 
 
 458684 
 
[Reprinted Jrom the PHYSICAL REVIEW, N.S.. Vol. XVII, No. 3, March, 1921.] 
 
 ON THE MOTION OF A SPHERE OF OIL THROUGH CAR- 
 BON DIOXIDE AND A DETERMINATION OF THE 
 COEFFICIENT OF VISCOSITY OF THAT 
 GAS BY THE OIL DROP METHOD. 
 
 BY LEO JOSEPH LASSALLE. 
 
 SYNOPSIS. 
 
 i I. Coefficient of Viscosity of CO z by the Oil-drop Method. The value of e being 
 known, through work in air, to an accuracy of about .1 per cent., the oil-drop method 
 as developed by Millikan has been used in COz for the determination of the coefficient 
 of vicsosity of that gas with the result at 23 C. 77 = 1.490 X io~ 4 . 
 
 II. Coefficient of Slip between CO?, and Oil. The value of the constant A in 
 Millikan's equation e\ = e(i + AZ/o) 3/2 is found in COa to be 0.8249 as against 
 Millikan's value in air 0.864. 
 
 III. Variability of the Constant A for Values of I/a Greater than .5. Precisely as 
 in Millikan's work in air, A was found to be constant only up to I/a = .5, beyond 
 which it kept increasing as far as it was followed, viz., up to I/a = 12. 
 
 INTRODUCTION. 
 
 THE behavior of oil drops falling in air has been reported upon by R. 
 A. Millikan. 1 Every precaution possible was taken to assure the 
 highest degree of accuracy. The value of e obtained was shown to be 
 accurate to within 0.2 of one per cent. The law of fall for oil drops in 
 hydrogen was investigated by R. A. Millikan, W. H. Barber, and Y. 
 Ishida. 2 The same precautions as those taken for air were observed. 
 
 The work here described was undertaken at the suggestion of Dr. 
 Millikan in order to find the correction factor to Stoke 's law for carbon 
 dioxide, and the coefficient of viscosity of that gas by a new method. 
 
 The value of e? lz is directly proportional to the coefficient of viscosity, 
 77, of the gas used. As is shown later, this relationship furnishes an 
 elegant method of determining 77 for any gas, and is used in this paper 
 to obtain the viscosity coefficient for CO 2 at 23 C. 
 
 The apparatus used was the same one used by R. A. Millikan. 3 The 
 same precautions were taken to give as high a degree of accuracy as 
 
 1 "On the Elementary Electrical Charge and The Avagadro Constant," PHYSICAL REVIEW, 
 N.S., Vol. II., No. 2, Aug., 1913, p. 109. 
 
 2 "The Law of Fall of a Droplet Through Hydrogen," PHYSICAL REVIEW, Series 2, 5, 
 - P- 334- 
 
 PHYS. REV., N.S., Vol. II., No. 2, Aug., 1913, p. 109. 
 
MOTION OF A SPHERE OF OIL. 355 
 
 possible. All of the time observations were taken with a Gaertner 
 recording chronograph. This instrument records time to one one- 
 hundredth of a second. It was adjusted so as never to be in error by 
 more than two hundred ths of a second per minute. 
 
 The following method described by Langmuir was used in generating 
 the CO 2 . Using a Kipp generator, CaCO 3 + 2HNO 3 = CO 2 + Ca(NO 3 ) 2 
 + H 2 O + HNO 3 vapor + H 2 O vapor. The gas is bubbled through 
 NaHCO 3 , which takes up acid vapors but no CO 2 ; then it passes through 
 P 2 O 5 tubes which take up all H 2 O vapor. 
 
 The HNO 3 was a 50 per cent, pure H 2 O solution through which com- 
 mercial CO 2 had been bubbled for 5 hours before being put into the Kipp 
 generator. The CaCO 3 (marble) was broken and boiled 4 hours in a 
 very dilute solution of HNO 3 . The vessels into which the gas was intro- 
 duced were evacuated to a pressure below 0.5 mm. before they were filled. 
 They were then pumped down again to the same low pressure and 
 refilled with CO 2 . This process was repeated three times before any 
 observations were taken, thus assuring that not more than one part of 
 air in (i.soo) 3 parts of CO 2 remained in the vessels. 
 
 For a complete discussion of the apparatus used and the precautions 
 taken to assure accuracy in the determinations of the constants that 
 enter into the following results see paper by R. A. Millikan. 1 
 
 PART I. 
 
 Determination of Coefficient of Viscosity of COz- 
 
 Oil droplets were obtained for observation by aspirating oil with CO 2 
 gas under pressure. They were held for a sufficient length of time to 
 observe the time of fall under gravity (/) on an average of eighteen times. 
 The average number of changes of charge obtained for each drop was 
 seven for the first thirty-six drops, which are the ones used in the deter- 
 mination of the coefficient of viscosity and the correction factors "b" 
 and "A." 
 
 The results of the observations were such as to leave no uncertainty 
 as to the greatest common divisor of [(i/tg) -f (i ///)], which will be 
 represented hereafter by [(!//) + (iA/)]o, and which is the variable 
 factor upon which the value of (ei 2/3 /i?) and (a) are dependent. 
 
 It is significant that these thirty-six drops represent every drop 
 observed where P.D. was constant to as much as 0.4 of one per cent, and 
 where as many as three changes of charge were obtained. In the equation 
 
 (. + .)(.)"' 
 
 1 R. A. Millikan, PHYS. REV., N.S., Vol. II., No. 2, Aug., 1913, pp. 109-143; also Phil. 
 Mag., XXXIV., p. 13, 1917- 
 
356 LEO JOSEPH LASSALLE. 
 
 771 is the coefficient of viscosity of CO2 at 23 C., g the acceleration due 
 to gravity, <r the density of the oil, p the density of the CO 2 , v\ the speed 
 of descent of the drop under gravity and v z the speed of ascent under 
 the action of the electrical field of strength F. 
 
 If we now allow e\ to be the greatest common divisor of all the various 
 values of e n found on a drop during the observations upon it, and if we let 
 
 _D_ 
 
 _D_ 
 
 Vz ~ t f ' 
 and 
 
 d ' 
 
 where D is the distance the drop falls in time t a and the distance it rises 
 in time t f , and d is the distance between the two parallel, horizontal 
 condenser plates, between which a difference of potential in volts, repre- 
 sented by P.D., is maintained by means of storage cells which do not 
 change more than four parts in a thousand during a series of observations 
 on a given drop, then equation (i) may be written in the form 
 
 9 
 
 where [(i/t a ) + (i///)] is the greatest common divisor of [(i/t a ) + 
 for the given drop. 
 
 Equation (2) may be written 
 
 
 This gives a simple method of calculating 
 
 a, the radius of the falling drop, is calculated by means of the expression 
 
 77! (P.D.) 2 / 3 
 
 where 
 
 ,1/3' 
 
 C = I -1 
 
 ( N 
 
 ' ' f 
 
 which may be written, 
 
 The pressure of the gas p is observed directly. 
 
VOL. XVII. 
 No. 3. 
 
 MOTION OF A SPHERE OF OIL. 
 
 357 
 
 Table I. gives the values of the factors which enter into the deter- 
 mination of ei 2/3 /?7i and a, as well as into the values of e\ zl3 , e\, and e 213 * 
 The last three values can only be obtained after T;I and b have been 
 calculated. 
 
 For the present let us assume that the table does not contain i 2/3 , 
 e\, nor e 213 , and plot ei 2/3 /rji against i/pa. Curve I shows this relationship. 
 
 340 600 
 
 Fig. 1. 
 
 It is a straight line which crosses the ei 2/3 /*?i axis at 41.00 X io~ 4 . 
 If we write 
 
 2/3 _ 
 
 then 
 
 = 
 
 pa 
 
 It is evident that, for i/pa = o, 
 
 .,2/3 
 
 7 1 
 
 We are justified in saying that the value of the elementary electrical 
 charge on an oil drop is independent of whether it be in CC>2 or in any 
 other gas, say air. Since the value of e 213 in air is known to be 61.085 
 X io~ 8 E. S. units, with a probable error of less than o.i of one per cent., 1 
 then at i/pa = o, e^ 3 = e 2 ' 3 = 61.085 X io~ 8 ; 
 
 .'. = 41.00 X io~ 4 
 
 1 This is the value obtained by reducing the number given by R. A. Millikan in Phil. Mag., 
 XXXIV., p. 13, by .07 per cent, to allow for the change in the value of the coefficient viscosity 
 of air from .0001824 to .00018227. 
 
LEO JOSEPH LASSALLE. 
 
 gves 
 
 61.085 X io- 8 
 
 ill = - 7 = 1.490 X io~ 4 , 
 
 41.00 X io~ 4 
 
 which, because all the calculations were reduced to 23 C., gives the 
 value of the coefficient of viscosity at 23 C. 
 
 Wherever the temperature differed from 23 C. during an observation 
 the correction factor to be applied to the value of 171 was introduced into 
 the calculation of (0i 2/3 /T7i). Sutherland's equation was used and the 
 variation of log 771 with temperature was obtained by plotting log 171 
 against temperature. With the exception of drops 5 and 15, which 
 differ by about i C., the variation from 23 C. was always less than 
 0.5 C. 
 
 By the oil drop method, then, the value of the coefficient of viscosity 
 of CO 2 at 23 C. is found to be 
 
 l?C0jat23-(7 = 1-490 X I0~ 4 . 
 
 The accuracy of this result is dependent upon the accuracy with 
 which the value of e 2/3 is known and the accuracy with which the inter- 
 cept on the ei 2/3 /T7i axis for CO 2 is known. 
 
 e 2/3 is known with an accuracy of about o.i of one per cent. The ei 2/3 /7ji 
 intercept is known with a probable error of about 0.5 of one per cent. 
 Therefore, the value of 771 given by these observations should be accurate 
 to about 0.5 of one per cent. 
 
 Therefore 
 
 *7co 2 at23'C = (1490 0.0080) X io~ 4 . 
 
 Breitenbach 1 obtained 
 
 at 15o(7 =1457 X I0~ 4 . 
 
 Applying the Sutherland equation to his value there results 
 
 *?C0 2 at23oC = 1494 X IO- 4 . 
 
 If we assume that this investigator's value is too high for CO 2 in the 
 same ratio that his value for air is too high, we get 
 
 1786 
 i?co 2 at23.c = (1494 X iQ" 4 ) = J 474 X io- 4 , 
 
 a value I per cent, lower than the one obtained in this paper. 
 
 Ernst Thomson, 2 using a vibrating disc, obtains a value of ij for CO 2 
 which is 0.0000004 higher than Breitenbach's. However, the main 
 object of his investigation was to find the relationship between the 77 for 
 
 1 Breitenbach, Ann. d. Phys., 5, 1901. 
 
 *"Ueber die innere Aeibung von Gasgemischen," Inaugural Dissertation, der Konigl. 
 Christian-Albrechts Univ. zu Kiel. 
 
MOTION OF A SPHERE OF OIL. 359 
 
 two gases and the 77 for various mixtures of these two gases. He does 
 not claim any high degree of accuracy for his value of the coefficient of 
 viscosity of CO2. 
 
 P. Phillips 1 gives a value of 77 which reduced to 23 C. by Sutherland's 
 equation, becomes 
 
 *7CO,at23C = 1-494 X I0~ 4 . 
 
 He used the A. O. Rankin device, 2 which is a capillary tube method. 
 The object of his investigation was to determine the variation of 77 with 
 pressure, going to pressures of eighty atmospheres. No high degree of 
 accuracy is claimed for the determination of the 77 at atmospheric pres- 
 sure. The important point sought after was to obtain relative values 
 as pressure varied. 
 
 If, however, we take the mean of the values obtained by Breitenbach, 
 Thomsen and Phillips, a value of 77 C 2at2 3<>c = 1-489 X io~ 4 is obtained. 
 This value is different by less than o.i of one per cent, from the one here 
 obtained. 
 
 PART II. 
 
 The A and b Correction Terms in CO 2. 
 
 Table I. gives the values of ei z ' 3 /r]i corresponding to the various values 
 of I / pa. ei 213 is obtained by multiplying ei 2l3 /iji by the value of 771 as 
 found in part I. 
 
 Fig. 2 gives the result of plotting e\- lz against i/pa. 
 
 If, now, we write 
 
 / T \ 
 
 (7) 
 
 and let y = e^ l3 \ y = e 213 , and x = (i/pa), we have y = y + byox. By 
 differentiation, then, the above becomes 
 
 / dy \ Slope of (y, x) curve 
 
 b = ( ~, ~j~ y ] == ~~ . ~~ . (8) 
 
 \ dx ) ^-intercept 
 
 This gives a simple method of determining the correction factor &. 3 
 The last column in Table I. gives the values of e 213 calculated by sub- 
 stituting in (7) and solving. The values of e follow directly from those 
 of e 213 . It will be noticed that no value of e 213 varies from 61.085 by as 
 much as 0.5 of one per cent. 
 
 The value of b, obtained by substituting in (8) is 
 
 _ Slope of y, x curve _ (75-37 61.085) 
 y-intercept 600 X 61.085 
 
 1 P. Phillips, Roy. Soc. Proc., Ser. A, 87. pp. 48-61. 
 
 s Roy. Soc. Proc., 1910, A, Vol. 83, p. 265. 
 
 ' R. A. Millikan, PHYS. REV., II., p. 118, 1913, and XXXII., p. 381, 1911. 
 
360 
 
 LEO JOSEPH LASSALLE. 
 
 (SECOND 
 [SERIES. 
 
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VOL. XVII.1 
 No. 3. J 
 
 MOTION OF A SPHERE OF OIL. 
 
 x ,_;,_; o *-< -< *-< o' 
 
 M 
 
 X 
 
 >o >o 
 c 
 
 o" 
 
 o 
 
 M 
 
 X 
 
 c 
 
 I 
 
 oooooooo 
 
 O O\ ' 
 O i 
 
 i 
 
 o 
 X 
 
 o ^2 o o o o o 
 o o o o o o o 
 o'oo'oo'ooo 
 
 i 
 
 4 
 
 3 
 
 Q 
 
 t 
 
LEO JOSEPH LASSALLE. 
 
 [SECOND 
 
 [SERIES. 
 
 or 
 
 b = 0.0003898 
 (see Fig. 2). 
 
 It should be noticed that the value of b is independent of any theory 
 and is determined by the use of values which are directly measurable. 
 If, however, it is desired to write (7) in the form 
 
 ,2/3 _ 
 
 (9) 
 
 then A can be calculated in the same way that b was, provided the values 
 of I/a are known. 
 
 Using 77 = o.35O2ww/C, where the Boltzmann value of K is used so 
 
 76 
 
 TS 
 
 74 
 
 73 
 
 7* 
 
 fl 
 
 70 
 
 69 
 
 6! 
 
 66 
 
 62] 
 
 rtrf 
 
 ^ 
 
 50 60 90 
 
 300 360 420 480 
 
 509 
 
 Fig. 2. 
 
 as to give an A that can be compared with that for air obtained by R. A. 
 Millikan in the paper previously referred to, the values of I [a can be 
 calculated. 
 
 From equations (7) and (9) it is evident that 
 
 '--= 
 
 a pa 
 
 (10) 
 
 At a constant temperature i/pl is a constant. Therefore, A = bB, 
 which means that the (ei 273 , ijpa) curve becomes the (ei 2/3 , //a) curve 
 simply by changing the scale of the abscissae. 
 
 By calculating for a given drop and substituting in equation (10) the 
 value of A/b = B is obtained. This is checked by making the calcu- 
 
VOL. XVII 
 No. 3. 
 
 MOTION OF A SPHERE OF OIL. 
 
 363 
 
 ation for several drops. In this way B was found to be equal to 2116. 
 This gives for CO 
 
 A = 0.8249. 
 
 The value obtained by R. A. Millikan in his work in air was A = .864. 
 The difference would seem to be slightly more than the experimental 
 error involved in the determination of the slope of the line from which A 
 is obtained. This error should scarcely exceed two or three per cent. 
 There is then here a somewhat uncertain indication that the coefficient 
 of slip between CO 2 and oil is a trifle less than that between air and oil. 
 
 TABLE II. 
 
 No. 
 
 Temp. 
 
 P. D. 
 
 Volts. 
 
 (Sec.) 
 
 X (eV)- 
 
 n 
 
 aXlO 5 
 Cms. 
 
 / Cms. 
 Hg. 
 
 i 
 
 a ' 
 
 -*" 
 
 35 
 
 22.70 
 
 3245.0 
 
 53.833 0.014186 3-9 
 
 10.63 
 
 16.70 
 
 631.6 
 
 0.2985 76.19 
 
 36 23.04 
 
 2604.8 
 
 38.036 0.00971 3-13 
 
 12.58 
 
 12.02 
 
 661.3 
 
 0.3125 
 
 77.01 
 
 37 23.15 
 
 2583.0 
 
 22.63 
 
 0.00771 ; 8-19 
 
 16.11 
 
 8.160 
 
 760.83 
 
 0.3595 
 
 79.33 
 
 38 23.15 
 
 2589.5 
 
 27.67 
 
 0.00920 5-13 
 
 14.22 
 
 7.638 
 
 921.09 
 
 0.4352 
 
 82.94 
 
 39 22.90 
 
 1288.5 
 
 9.32 
 
 0.00274 67-168 
 
 24.24 
 
 4.210 
 
 980.14 
 
 0.4632 
 
 84.63 
 
 40 
 
 22.87 
 
 1288.4 
 
 14.83 
 
 0.003817 18-66 
 
 18.59 
 
 4.588 
 
 1172.5 
 
 0.5540 
 
 90.38 
 
 41 
 
 23.38 
 
 1938.6 
 
 24.02 
 
 0.00735 7-13 
 
 14.57 
 
 5.566 
 
 1233.3 
 
 0.5828 
 
 91.05 
 
 42 
 
 22.85 
 
 1286.5 
 
 20.81 
 
 0.00460 8-56 
 
 15.60 
 
 5.279 
 
 1214.6 
 
 0.5739 
 
 91.50 
 
 43 
 
 22.87 
 
 1286.0 
 
 26.67 
 
 0.00560 | 7-87 
 
 13.45 
 
 5.365 
 
 1386.1 
 
 0.6550 
 
 96.06 
 
 44 
 
 22.90 
 
 1288.2 
 
 20.36 
 
 0.00514 
 
 10-44 
 
 15.15 
 
 4.410 
 
 1497.1 
 
 0.7074 
 
 99.18 
 
 45 
 
 23.35 
 
 1933.3 
 
 38.55 
 
 0.01073 
 
 3-12 
 
 10.97 
 
 5.910 
 
 1542.7 
 
 0.7290 
 
 100.05 
 
 46 
 
 22.86 
 
 1288.8 
 
 19.20 
 
 0.00522 
 
 11-35 
 
 15.37 
 
 4.110 
 
 1583.1 
 
 0.7480 
 
 102.14 
 
 47 
 
 22.80 
 
 650.3 
 
 7.01 
 
 0.00169 
 
 86-137 
 
 24.94 
 
 2.450 
 
 1636.3 
 
 0.7732 
 
 106.2 
 
 48 
 
 22.85 
 
 648.5 
 
 16.91 
 
 0.00298 
 
 26-99 
 
 15.37 
 
 3.356 
 
 1938.5 
 
 0.9160 
 
 115.9 
 
 49 
 
 22.74 
 
 1289.5 
 
 27.39 
 
 0.00772 
 
 5-33 
 
 11.99 
 
 3.860 
 
 2161.6 
 
 1.021 
 
 117.8 
 
 50 
 
 22.79 
 
 651.4 
 
 10.19 
 
 0.00254 
 
 29-153 
 
 19.22 
 
 2.290 
 
 2271.5 
 
 ,1.073 
 
 123.0 
 
 51 
 
 22.90 
 
 653.5 
 
 9.58 
 
 0.00267 
 
 38-129 
 
 19.32 
 
 2.055 
 
 2518.7 
 
 1.190 
 
 129.5 
 
 52 
 
 23.20 
 
 92.70 
 
 9.90 
 
 0.000391 
 
 240-376 
 
 18.91 
 
 1.970 
 
 2684.7 
 
 1.269 
 
 131.0 
 
 53 
 
 22.83 
 
 649.5 
 
 23.23 
 
 0.00530 
 
 12-60 
 
 11.42 
 
 2.638 
 
 3319.6 
 
 1.569 
 
 152.9 
 
 54 
 
 22.95 
 
 656.7 
 
 16.06 
 
 0.00550 
 
 12-44 
 
 12.80 
 
 1.990 
 
 3925.1 
 
 1.855 
 
 176.0 
 
 55 
 
 22.79 
 
 651.1 
 
 42.68 
 
 0.01510 
 
 2-6 
 
 6.58 
 
 2.390 
 
 6356.7 
 
 3.004 
 
 250.4 
 
 56 
 
 23.55 
 
 649.8 
 
 9.96 
 
 0.00809 
 
 12-31 
 
 13.15 
 
 1.060 
 
 7171.5 
 
 3.389 
 
 269.3 
 
 57 
 
 22.08 
 
 156.0 
 
 31.26 
 
 0.00364 
 
 26-77 
 
 7.29 
 
 1.840 
 
 7457.8 
 
 3.524 
 
 278.4 
 
 58 
 
 23.14 
 
 155.72 
 
 13.45 
 
 0.00275 
 
 37-159 
 
 10.59 
 
 1.100 
 
 8582.6 
 
 4.056 
 
 307.2 
 
 59 
 
 22.83 
 
 192.50 
 
 7.18 
 
 0.00117 122-225 
 
 14.60 
 
 0.798 
 
 8584.2 
 
 4.056 
 
 302.7 
 
 60 
 
 22.90 
 
 155.21 
 
 6.87 
 
 0.00241 j 64-122 
 
 13.84 
 
 0.719 
 
 10051. 
 
 4.750 
 
 352.2 
 
 61 
 
 24.46 
 
 157.00 
 
 28.32 
 
 0.00507 1 3-85 
 
 6.76 
 
 1.450 
 
 10205. 
 
 4.822 
 
 359.9 
 
 62 
 
 23.22 
 
 156.8 
 
 13.23 
 
 0.00469 17-27 
 
 8.94 
 
 0.736 
 
 12076. 
 
 5.706 
 
 438.8 
 
 63 
 
 22.82 
 
 652.2 
 
 82.18 
 
 0.05502 1-2 
 
 3.44 
 
 2.211 
 
 13147. 
 
 6.212 
 
 476.1 
 
 64 
 
 22.86 
 
 156.72 
 
 13.03 
 
 0.00571 14-18 
 
 8.41 
 
 0.841 
 
 14142. 
 
 6.683 
 
 502.7 
 
 65 
 
 22.80 
 
 158.22 
 
 36.08 
 
 0.01945 3-6 
 
 3.99 
 
 1.112 
 
 22524. 
 
 10.64 
 
 805.2 
 
 66 
 
 23.02 
 
 92.56 
 
 9.87 
 
 0.00708 14-27 
 
 7.21 
 
 0.540 
 
 25702. 
 
 12.14 
 
 904.4 
 
 67 
 
 22.93 
 
 89.97 
 
 23.59 
 
 0.01103 
 
 2-8 
 
 4.60 
 
 0.824 
 
 26552. 
 
 12.55 
 
 926.4 
 
LEO JOSEPH LASSALLE. 
 
 PART III. 
 
 [SECOND 
 
 [SERIES. 
 
 Limits to the Validity of Millikan's Equation in CO 2. 
 
 Observations were taken on drops at as large values of I/a as practicable 
 with the method of obtaining drops that was used throughout these 
 observations. It was found very difficult to get drops at pressure below 
 one cm. of Hg. A more direct method of blowing the drops and one 
 which will introduce less gas into the system is desirable in order to go 
 to low pressures. 
 
 At low pressures it is not possible to have such high potential differ- 
 ences; also it is not possible to observe on drops of the same size as 
 those used at pressures above, say 2 cm. These two factors tend to 
 counterbalance each other as far as the difficulty of observing on drops 
 with a small number of charges is concerned. If the number is not 
 small the greatest common divisor of the series of speeds begins to be 
 uncertain. However, no drop was used in these calculations where 
 there was doubt as to this greatest common divisor. 
 
 Table II. gives the values of the various factors entering into the 
 
 goo /oao /zco MOD 1600 /goo -?ooo ,2400 Z400 600 
 
 Fig. 3. 
 
 determinations of e^ 13 , i/pa and I/a for drops where the values of i/pa 
 are greater than 600. 
 
 Fig- 3 gives the relationship between e^ 13 and if pa, which is also that 
 between e x 2 / 3 and I/a. It gives this relationship from i/pa = 600 to 
 i/pa = 2,500. It will be seen that from 600 to about 1,100 the slope is 
 the same as that for i/pa = o to i/pa = 600. But at about the value 
 of 1,100 the slope clearly begins to change. This behavior is quite like 
 that found by R. A. Millikan in his work with air. He found (Pnvs. 
 
VOL. XVII. 
 No. 3. 
 
 MOTION OF A SPHERE OF OIL. 
 
 365 
 
 REV., II., p. 138) that the linear relation between ei w and i/pa began 
 to break down at about i/pa = 650, which corresponds to a value of I/a 
 of about .5. Here the break comes at about i/pa = 1,100 which will 
 be seen from Table II. to also correspond to a value of I /a = .5. 
 
 J9foo S3SOO 
 
 Fig. 4. 
 
 Fig. 4 shows the graph of the relations contained in Table II. in the 
 range I/pa = 2,500 up to if pa = 26,500, i.e., in the range I/a = I to 
 
 I/a = 12. 
 
 SUMMARY. 
 
 I. Using the oil-drop method, the coefficient of viscosity, ij, of CO 2 at 
 23 C. was found to be 1.490 X io~ 4 . 
 
 II. The correction factors b and A as given in the equations 
 
 2/3 _ 
 
 and 
 
 were determined for CO 2 and found to be 
 
 b = 0.0003898, 
 A = 0.8249. 
 
 Applying the correction term to the various drops, 36 in number, 
 values of e 213 were obtained, no one of which varies from 61.085 X io~ 8 
 by as much as 0.5 of one per cent. 
 
366 LEO JOSEPH LASSALLE. 
 
 III. The relationship between ei 2/3 and I/pa was found for values up 
 to I / pa = 26,500. The value of A = 0.8249 holds until I/a = 0.50, 
 approximately. The slope of the curve then increases. 
 
 The values of I/a for CO%, at which the change in slope begins is the 
 same as that found by Millikan in the case of air. 
 
 It gives me pleasure to acknowledge the cheerful and able assistance 
 of Dr. Y. Ishida and Mr. B. L. Steele. I am especially indebted to 
 Dr. R. A. Millikan, who suggested the problem and who advised me 
 throughout the course of the investigation. 
 
 RYERSON PHYSICAL LABORATORY, 
 
 UNIVERSITY OF CHICAGO, 
 
 August 10, 1917. 
 
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