184 Lord Rayleigh on the Discharge of 



between the disks. From (9) 



^^Jt^^W^ + H^^sin^.JoJv/CW 2 /^-!).^}, 

 and 



(p) = H*/(W 2 /a 2 -l) . sin/3?. J o '(2-405). . (20) 



The latter equation gives the radial velocity at the 

 boundary. I£ SR denote the variable part o£ the radius 

 of the jet, 



• • • (21) 

 Again, if Sp be the variable part o£ the pressure at the axis 



where p is the average density in the jet and 8iv the variable 

 part o£ the component velocity parallel to z. Accordingly 



^ = -WHcosj8s; .'.... (22) 



P 7 



and 



SR _ J '(2-405) y/(Wy-l) 



Sp/p J3W 2 ' ' ' 



In (23) we may substitute for {3 its value, viz. 



2-405 a 



iV(W 2 -o' 



and for J '( 2*405) we have from the tables of BessePs 

 functions — 0"5191 ; so that 



H = -0-2158R(a-*-W-s). . . . (24) 



As was to be expected, the greatest swelling is to be found 

 where the pressure at the axis is least. 



A complete theory of the effects observed by Mach and 

 Emden would involve a calculation of the optical retardation 

 along every ray which traverses the jet. For the jet of 

 circular section this seems scarcely practicable ; but for the 

 jet in two dimensions the conditions are simpler and it may 

 be worth while briefly to consider this case. As before, we 



(23) 



