620 Prof. T. H. Havelock on an Integral Equation 



Table IV. 



Gas. 



Viscosity in C.G.S. units xlO -4 



A in cm. 2 X 10" 13 . 



17°-0C. 



! U. 



100° oo. s o°-oc. 





Methane ... 



Sulphuretted 

 hydrogen 



Cyanogen ... 



1094 



} 1-251 



0995 



1-363 

 1-610 

 1-281 



1-035 ! 198 

 1-175 331 

 0-935 330 



0*772 

 0-773 

 1-21 



Our value of! the viscosity of methane at 0° C, viz., 

 1*035 x 10 -4 , is very close to the value 1'033 x 10 -4 found by 

 Vogel*. For sulphuretted hydrogen our value, viz , 1*175 

 X 10 -4 , has to be compared with 1*15 X 10~ 4 due to Graham 

 (Kaye and Laby's Tables). With reference to cyanogen the 

 value of 7} now obtained is identical with that previously 

 published [loc. cit.), but Sutherland's constant is 330 as 

 compared with 280, with the result that the mean collision 

 area is 1*21 x 10~ 15 cm. 2 instead of the less reliable value 

 1*31 x 10~ 15 cm. 2 It still remains true, however, that the 

 cyanogen molecule is of nearly the same dimensions as the 

 bromine molecule, their respective mean collision areas 

 being- 1*21 x 10~ 15 cm. 2 



Imperial College of Science 

 and Technology. 



July 22, 1921. 



LXXITI. The Solution of an Integral Equation occurring in 

 certain Problems of Viscous Fluid Motion. By T. H. 

 Havelock, F.R.S.f 



1. rTlHERE are a few well-known solutions of problems of 

 A viscous fluid motion in which a solid body starts 

 from rest and moves through the fluid under the action of 

 given forces : for example, the fall of a sphere under gravity 

 when the square of the fluid velocity is neglected, or the 

 corresponding simplified problem of the fall of n plane in 

 which this limitation does not arise. These problems lead 

 to integral equations which have been solved by an applica- 

 tion of Abel's theorem f. In these cases the fluid was 



* H. Vogel, Berlin Dissertation, 1914. 



f Communicated by the Author. 



% Bogg-io, Rend. d. Accad. d. Lincei, xvi. pp. 613, 730 (1907) ; Basset, 

 Quart, Journ. of Math. xli. p. 369 (1910) ; Ravleigh, Phil. Mag. xxi. 

 p. 697 (1911). 



