446 



SCIENCE 



[N. S. Vol. XXXII. No. 822 



studied tkrougiiout a period of 47 consecutive 

 days. The three drops which have been es- 

 cluded all yielded values of e^ from two to four 

 per cent, too low to fall upon a smooth e^v, 

 curve like that shown in Fig. 1, which is the 

 graph of the results contained in table XII. 

 It is probable that these three drops corre- 

 sponded not to single drops, but to two drops 

 stuck together. Since we have never in all 

 our study observed a drop which gave a value 

 of e^ appreciably above the curve of Fig. 1, 



Negative drop No. 32 

 Distance between cross hairs = 1.003 cm. 

 Temperature =23.2" C. 



7=8577 



i^= 28.70 

 F^8573 



= 2.462 



J'= 15.72 



F=8568 



F=59.1 

 F= 8565 

 i^=6C.O 

 F=8563 



1^=81.5 

 7=8561 



^"=20.0 

 7=8555 



G (sec.) J" (sec.) 



M2 



— 8.7"! 



— 8.3 I 123 622.40 



— I 8.5 J 

 Changed without radium. 



:„X10i<i eiXlOio 



111 



558.78 



Change forced with radium. 

 !.44 15.7 - 

 !.48 15.7 

 15.7 

 15.7 

 15.8 . 



Change forced with radium. 

 59.11 

 2.50 59.1 ; 



F 2.45 



59.: 

 59.81 

 60.2 J 



100 503.42 



100 503.22 



5.032 



99 498.12 5.031 



Change forced with radium. 



— I 81.0 1 



— I 82.1; 



Change forced with radium. 

 2.44 I - - - • ■ 

 2.50 20.1 !- 11081 543.41 | 5.032 

 2.42 



Mean ej (weighted) = 5.033 



i"s mean = 2.452. M's mean (? = 2.467. 



Differences 



543.41 — 498.12 = 45.29 

 503.23 — 498.12= 5.11 

 558.78 — 503.42 = 55.36 

 558.78 — 524.25 = 34.53 



9 = 5.032 

 1 = 5.11 

 11 = 5.035 



7 = 4.94 



Prob. error 

 .5 per cent. 



3.0 per cent. 

 .5 per cent. 



3.0 per cent. 



and since further a sphere must have a higher 

 rate of fall than a body of any other form 

 whatever having the same mass and density, 

 the hypothesis of binary drops to account for 

 an occasional low value of Cj is at least nat- 

 ural. After eliminating dust we found not 

 more than one drop in ten which was irregu- 

 lar. The drop shown in table I. is perhaps the 

 best illustration of the case under considera- 

 tion which we have observed. It yields a 

 value of gj, which is four per cent, too low to 

 fall on the curve of Fig. 1. This is as large a 

 departure from this curve as we have thus far 

 obtained. 



§ 6. The Correction of Stohes's Law. — The 

 procedure actually adopted for correcting 

 Stokes's law will be detailed elsewhere. The 

 end result is this. An equation of the follow- 

 ing form is made to replace Stokes's equa- 

 tion (2) : 



X = GiTfiav 1 1 + ^ — ) 



^2 ga'(g — p) 

 '■ 9 fi 



(5) 



(6) 



in which a is the radius of the drop, I the 

 mean free path of the gas molecule, and A an 

 undetermined constant which we obtain from 

 our observations. It turns out that A is iden- 

 tical to within the limits of observational 

 error (not more than 1 or 2 per cent.) with the 

 value deduced by Cunningham" from the 

 kinetic theory considerations, provided the 

 /of his formula' is made equal to zero. This 

 means that the value of A given by our obser- 

 vations is .815. The values of a in tables XH. 

 and XIII. are computed from (6), in which 

 a is now the only unknown. 



§ 7. The Absolute Value of e. — Using now 

 (6) instead of (4) to combine with (1) and 

 denoting by e the absolute value of the ele- 

 mentary charge and by e^, as heretofore, the 

 value of this charge as obtained from the use 

 of the usual form of Stokes's law, i. e., from 

 (4) there results at once 



('+-iy 



=«i" 



(7> 



Mean difference (weighted) =5.031. 



'Proc. Roy. Soc., 83, p. 360. 

 ' Cf. p. 361, I. 0. 



