71] 



TRANSLATION OF A CYLINDER. 



93 



The stream-lines are in each case the same for all confucal 

 elliptic forms of the cylinder, so that the formulae hold even when 

 the section reduces to the straight line joining the foci. In this 

 case (9) becomes 



A|T = vc e~ cos ?; (10), 



which would give the motion produced by an infinitely long 

 lamina of breadth 2c moving broadside on in an infinite mass of 



liquid. Since however this solution makes the velocity infinite at 

 the edges, it is subject to the practical limitation already indicated 

 in several instances*. 



* This investigation was given in the Quart. Journ. of Math., i. xiv. (1875). 

 Results equivalent to (8), (9) had however been obtained, in a different manner, by 

 Beltrami, &quot; Sui principii fondamentali dell idrodinamica razionale,&quot; Mem. dell 

 Accad. delle Scienze di Bologna, 1873, p. 394. 



