178 Lord Rayleigh on the Discharge of 



Ify = l*408, this limiting velocity is 2*214 c Q . It is to be 

 observed, however, that in considering the rate of discharge 

 we are concerned with what the authors cited call the 

 " reduced velocity," that is the result of multiplying q by 

 the corresponding density p. Now p diminishes indefinitely 

 with p 9 so that the reduced velocity corresponding to an 

 evanescent p is zero. Hence if we identify p with the 

 pressure pi in the recipient vessel, we arrive at the im- 

 possible conclusion that the rate of discharge into a vacuum 

 is zero. From this our authors infer that the identification 

 cannot be made; and their experiments showed that from 

 p 1= =0 upwards to jt?] = '4^0 the rate of discharge is sensibly 

 constant. As pi still further increases, the discharge falls om, 

 slowly at first, afterwards with greater rapidity, until it 

 vanishes when the pressures become equal. 



The work of Saint- Venant and Wantzel was fully discussed 

 by Stokes in his Report on Hydrodynamics*. He remarks 

 " These experiments show that when the difference of pressure 

 in the first and second spaces is considerable, we can by no 

 means suppose that the mean pressure at the orifice is equal 

 to the pressure at a distance in the second space, nor even 

 that there exists a contracted vein, at which we may suppose 

 the pressure to be the same as at a distance." But notwith- 

 standing this the work of the French writers seems to have 

 remained very little known. It must have been unknown to 

 0. Reynolds when in 1885 he traversed much the same 

 ground |, adding, however, the important observation that 

 the maximum reduced velocity occurs when the actual 

 velocity coincides with that of sound under the conditions 

 then prevailing. When the actual velocity at the orifice 

 reaches this value, a further reduction of pressure in the 

 recipient vessel does not influence the rate of discharge, as 

 its effect cannot be propagated backwards against the stream. 

 If ry = 1*408, this argument suggests that the discharge reaches 

 a maximum when the pressure in the recipient vessel falls to 

 *527 p , and then remains constant. In tho somewhat later 

 work of Hugoniot J on the same subject there is indeed a 

 complimentary reference to Saint- Venant and Wantzel, but 

 the reader would hardly gather that they had insisted upon 

 the difference between the pressure in the jet at the orifice 

 and in the recipient vessel as the explanation of the im- 

 possible conclusion deducible from the contrary supposition. 



In the writings thus far alluded to there seems to be an 



* B. A. Report for 1846; Math, and Plrvs. Papers, vol. i. p. 176. 

 t Phil. Mag-, vol. xxi. p. 185 (1886). 

 X Ann. de CMm. t. ix. p. 383 (1886). 



