Mr H. J. Sharpe, On Liquid Jets 



[Oct. 28, 



the only limitation we shall put upon the position of the orifice 

 H is that its ordinate must not exceed twice 01). 



x> 



3. Different analytical expressions, containing an arbitrary 

 number of arbitrary constants, will be assumed for the velocities 

 on either side of Oy, but it will be shewn that they can be so 

 chosen as to make the velocities on either side of Oy continuous, 

 and leave any required number of arbitrary constants to satisfy 

 conditions now to be given. It will be shewn that in all cases 

 the equation to BHG can be expressed in the form (putting, for 

 brevity, z for e*), 



y = a — c l z sin y — \ c. 2 z 2 sin 2y — &c. 

 and the velocities on the left of Oy in the form 



— -r = 1 + c t z cos y + c 2 z 2 cos 2y + &c. ; 



v 



-j = c x z sin y + c 2 z 2 sin 2y + &c, 



■(1), 



(2), 



where of course a. is the ultimate value of Cos'. We are concerned 

 only with the velocities at all points along HG, so that x and y 

 in (1) are the same as x and y in (2). As z is less than 1 we can 

 solve (1) so as to express y in a series of ascending powers of z. 

 We shall have therefore at every point of HG to the second order 

 of approximation 



y = a — c 1 z sin a + &c (3), 



A 



5 (u 2 + v 2 ) = 1 + 2CjZ cos a + &c. 



.(4). 



