38 Canon Moseley on the steady Flow of a Liquid. 



/a 



Substituting in equation (53), 



■ «=.-^{'-(? -•)-}•■.■ ■ <"> 



This formula has this advantage in its application to Messrs. 

 Darcy and Bazin^s experiments, that the numerical values of ^ 

 and O have in every case been calculated by them. 



The discharge Q in tenns of the head of water h, and the length 

 of the pipe I. 



It may be shown, as in equation (4), that 



U,= ""-^Cv^rdr^ "^^(V^-yrrdr, 

 ff Jo 9 Jo 



since v—VQe'^^'^^, or, as in equation (25), 



also 



U3=*2R^;r^/(/^, + X,Y2)V, 



or, neglecting yitj as small compared with X^V'*^, 

 whence we obtain, as in equation (26), 



_._ ys^ w-^[%gYh-'^^ 



!^^^ S e^y^^ - 37^R - U + ^\IR 



%(7^)^ 



V = i^)^(2g)^^^ ^ (,,^^ 



But Y=VQ€-y'^^, 



Vev^R; (54B) 



* Editor's Note. — The form of the expression /ij+XiV^ is discussed in 

 a note at the end of this paper. 



