Canon Moseley on the steady Flow of a Liquid. 33 



Differentiating twice and dividing by dx dy^ 



Observing that J =0, and transposing, 



(dvy Cdv\_ wv^ w fh ] ' '\ 

 \dyJ \dxJ ^yi^gl ydxy J ' 



Let 



and 



©'^-+©'^=(«'"^-^)*^ 



but* 



.*. adding, 



transposing, 



Since the left-hand member of this equation is an exact differen- 

 tial, the right-hand must be one alsof. This condition is sa- 



(?) 



tisfied if <i ^ iyi\ ^^ ^ function of [y—w)-, but it may be any 

 function. 



* In the original MS. this expression has been inadvertently written 

 j — jc?a?+ {—\dy. I have corrected this error as far as it goes; it does not 



affect the form of equation (48). — W. R. Brov^^ne. 

 t This is the well-known method of Lagrange. 



Phil Mag, S. 4. Vol. 44. No. 290. July 1872. D 



