54 Canon Moseley on the steady Flow of a Liquid, 



apply tlie same method of investigation to them. The filament 

 of maximum velocity is the common axis of all the films. Assu- 

 ming the forms of the films to be given, equation (52) determines 

 in terms of the maximum velocity the velocity at any given distance 

 from that axis; equation (53) determines the discharge in terms 

 of the maximum velocity. Equations (5 4 a) and (54 Z>) deter- 

 mine the maximum velocity itself, and equation (55) the dis- 

 charge from a pipe of any given form and dimensions, the geo- 

 metrical forms of whose films are also given, as they are in the 

 case of circular pipes. 



Hitherto my inquiries have applied only to the case of closed 

 channels supplied from a reservoir, and my results have been 

 complicated by that arbitrary constant 7 which is dependent on 

 the oblique direction of the liquid on passing from the reservoir 

 into the channel. In open channels this difficulty disappears^ 

 and y assumes in every case the value unity. 



The discharge from an open channel being half that from a 

 closed channel of twice the dimensions, is determined at once 

 from the formulae I have given for the latter by the substitu- 

 tion {mutatis mutandis) of unity for 7. There remains, there- 

 fore, only the determination of the relation which exists 'between 

 the forms of the films and the internal form of the channel. In 

 the case of a closed circular channel this relation is one of iden- 

 tity. In the case of channels of other forms it approaches it in 

 greater or less degrees of accuracy. I have tested this degree 

 of accuracy in great numbers of the experiments of MM. Darcy 

 and Bazin, in respect of open rectangular and trapezoidal chan- 

 nels of great varieties of forms and dimensions and depths of 

 water. The results are stated in various Tables of the present 

 paper, and compared with the results of experiment. It is on 

 the faith of this comparison that I propose (in all those cases to 

 which my comparison has extended) the following formula as 

 representing sufficiently for alL practical purposes the discharge 

 from a stream of given section in terms of its velocity at its 

 mid surface — that is, its maximum velocity *. This formula is 

 independent of the inclination of the stream, or the roughness 

 or smoothness of the channel, both of which conditions are re- 

 presented in the maximum velocity. 



And now I have to acknowledge my obligations to the admi- 



* Editor's Note.— This formula is not actually specified in the paper. 

 There can, however, be no doubt that it is that given in equation {67), viz. 



«=|[-(i+'t^)-^]- 



212'- - X 

 where 12 = area of stream, 



X= wetted perimeter. 



