1889.] 



Mr H. J. Sharpe, On Liquid Jets, <lx. 



rapidly nearly perfect. If the position of the orifice (subject 

 however to the limitation that the coefficient of contractoin must 

 be >^) be arbitrarily chosen, it will be seen that it can be so 

 chosen as to make the coincidence as close as may be desired. If 

 however, which seems the more correct course, it be chosen from 

 a consideration presently to be given (Art. 5) it is not easy, I 

 think, to say for certain whether the above-named coincidence 

 can be made as close as may be desired. It is an interesting ques- 

 tion which remains for solution. The motion is in two dimensions 

 and everywhere finite. The species of vessel for which solutions 

 are obtained may be described generally as a canal, whose sides 

 up to a certain point are straight and then turn off abruptly at 

 right angles into a curve towards an orifice, at the axis of the 

 canal, on each side of which the fluid motions are symmetrical*. 

 The jet ultimately approaches an asymptote parallel to its axis. 

 The ratio of the breadth of the vessel to the ultimate breadth 

 of the jet can be made anything we like, but we shall always 

 suppose it an even integer. 



2. Liquid is supposed to be flowing from right to left, roughly 

 speaking parallel to the axis of x, which is taken as the axis of 

 the vessel and jet. The stream-line AFBH is taken for the 

 boundary of the vessel. Fig. 1 may be taken as the type of the 



Fig. 1. 







general case. OE is always ir, and OB, OD submultiples of it. 

 In figures of which fig. 2 is a type B and D coincide. At present 



* It will be seen, however (Art. 6), by an obvious extension of the method, that 

 it is not confined to canals having this peculiarity, but is applicable also to canals 

 having flowing curvilinear boundaries. 



