344 The Hon. J. W. Strutt on BessePs Functions. 



The first integral =7r/(l + i^)-. 



In forming the second^ we must remember that ii p^ and ^2 are 

 two different values of y;, 



f 



r 



'1 



*■ 

 Thus 



'27rrdr(b'—-~ when z = 

 ^ dz 



Jo p\hip)y p" 



Accordingly 



2 Kinetic Ener^rv =7r/'ln-^a)- + 167ra-2 -^> 



or 



2 Kinetic Energy _ / ,^ fi^ y 1 

 [Rate of Total Flow] '^ ~ ^^^ "^ 77(1+^/^)2 ^^• 



By calculation I find for the approximate value of 2-x> 



2 i =-0012822. 



In the application to the investigation which was the origin of 

 the problem here considered, 



•0012822 g^ 8 1 + fi^ -f .,\/.^ 



(1+i/.)^ +377 {i^if.y 



has to be made a minimum by variation of fi. 

 The minimum value comes out 



a=-8281. 



In the paper '' On Besonance'' (Phil, Trans. 1871) I had deter- 

 mined a='8282 by the consideration of a motion within the 

 cylinder satisfying the same boundary conditions as in the pre- 

 sent problem^, but not having a velocity-potential. The close 

 agreement of the results furnishes a confirmation of the methods 

 used on that occasion. 



