Purser — Apj)/ications of Bessel's Functions to PJu/^ics. 51 

 The constant terms corresponding to 5 = give 



i.e. A, + li\o%R = ^o + Yi ^ - Tl^'' 



^^^^ 2]^^^ = -^^' 



AVe have, then, 



£q may be taken = 0, and then 



A.Hog. = |-ri.l„g^.^-f). (70) 



Kinetic Energy of Motion. 



This -will be - ^ C^JI F</aS over upper surface, 4- \xi JJ YdS over orifice. 

 The former of these, remembering that V may be neglected when com- 

 pared with xi^ and R when compared with i?', becomes 



i06 71 il ) 



Simplifying, as above, and remembering that the two last terms 

 vanish, this becomes 



12 16/ 



Or, since UR'- = 2(R\ 

 xrR-R" -KXi} 



16/ • 12/^^ 



\\ u- rdr - rVr + 2 - B,MK, uR cos nl\ • 



(Jo 2 -iOo W ) 



