114 Mr Sharpe, On Liquid Jets. [Nov. 24, 



which will be true at both limits if 



. 7r . Sir . 5tt _ ... ox 



a, sin- + a, sm f-a K sin — = (1*3). 



1 p 3 p 5 p 



Identifying the second of (5) and the second of (8) we have 



c n + c n ' + r n = (14). 



From (6) the equation to AFGB is 



c ' 

 \<f x sin y + ±b 3 €~ 3x sin Sy + £<f" sin 5y + % -^ e mx sin W + % 



7 . 7r , 7 37r ., . 5tt Bit /1c . 



= 6.sui- +16, sin— +46. sin — + — (15). 



1 p 3 3 ^,55 ^ p 



Since J.« = 7r, we must have 



, . 7T 17 . 37T 17 . 57T (»— 1)2?7T / - „>. 



6, sm - + 46, sm — + 46. sin — = ^ '- ... (16). 



p p p p 



It has already been shewn that there is a sharp turn at F. 

 From (9) we have 



Q = 2 ^sin? + 2^f sin^+2^#-sin 5 ^...(17). 



^ 1 1T p 3 37T p 5 57T p 



, p . 7T COSW7T . . 3» . 37T COS 717T 



#„ = — 4 J.J - sm — x -2-g — t - 4J. S — sm - - x -^-5 — ? 



7T 



p p 2 n 2 — 1 3 7r ^> pn* — 9 



. . 5« . 57T COS 717T /1C ,. 



- 4<A, -^- x sm — x -^-2 — — (18). 



5 7T p pV-25 v y 



From (12) we have 



P . 7T 71 COS 727T , JO . 3*7T W COS W7T 



r = — 4a ■£- sm - x — »-= — =- — 4a„ — sm — x — 2-5 — ~ 

 71 * 7r p pn - 1 7r £> pn — 9 



. » 2 . 57T ?l COS W7T ,, AX 



-4a. *- sm — x , g a , (19). 



From (10) and (14) c n = - %r n - %q n \ , 9m 



c ' = _i r + i a f ^ u '" 



°« 2'n^ 2^/J 



When the above conditions are satisfied, the velocities on each side 

 of OB will be continuous. 



3. Equations (3), (13) are the only equations connecting the 6 

 quantities a 1} A v a s , A 8 , a B , A B , therefore so far 4 are independent. 

 Equations (11), (16), (17) serve to connect A with B and either 

 with ctj, A v &c. From (20) c n , c n ' are functions of n and a v A x , 

 &c. The 6 quantities * x , A x , &c. may any of them (consistently 

 with the above relations) be as small as we like, but none of them 



