From the PuitosopHicaL Maa@azing, vol. xlii. November 1921, 
The Solution of an Integral Equation occurring in certain 
Problems of Viscous Fluid Motion. By T. H. HAvsLock, 
ERS. 
ik HERE are a few well-known solutions of problems of 
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 a 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 theoremt. In these cases the fluid was 
{ Boggio, Rend. d. Accad. d. Lince?, xvi. pp. 618, 730 (1907); Basset, 
Quart. Journ, of Math. sli, p. 369 (1910); Rayleigh, Phil. Mag. xxi. 
p. 697 (1911). 
176 
