Canon Moseley on the steady Flow of a Liquid. 189 



Let , = i. Then integrating between the limits and r, and 

 assuming /j, not to be a function of r, 



i f v \ i /v 2 — tf 2 \£ wir 



.'•log,y-log,(^ r ;;,)=-- i 



■■• ©fey--?- » 





2w?V 



=6 M 



1 







.,2 



(10) 



+ K)->F 



In certain of the experiments of M. Darcy, the velocities of 

 films of water were determined at three different distances (r) 

 from the axes of pipes of diameters varying from 0*188 to 

 0*500 metre, under heads of water (h) varying from 0*202 to 

 13*427 metres, the values of v corresponding to which varied 

 from 1*18 to 16*56 metres. Throughout this range of experi- 

 ments the values of (—j were for the same values of r approxi- 

 mately the same. 



This will be seen by inspecting the following Table I., in the 



two central columns of which are given the values of the ratio 

 ( — j in respect of the first, second, and fourth films, as deter- 

 mined by the experiments of M. Darcy in pipes of different dia- 

 meters, and of different degrees of roughness internally, and 



under different heads of water. These values of f — ) are calcu- 



lated in respect of all the experiments of M. Darcy in which he 

 has determined the values of v and v ; and in all, the value of 

 that fraction is approximately the same for the same value of r. 



