﻿Canon Moseley on the Uniform Flow of a Liquid. 395 



of different films with velocities varying from the axis of the pipe to 

 its internal surface. The direction of the motions of the molecules 

 of such a liquid being known, and all in the same film moving with 

 the same velocity, which velocity is a function of the radius of the 

 film, and the law of the resistance of each film to the slipping over it 

 of the contiguous film being assumed to be known, as also the head 

 of water, it is possible to express mathematically 



(1st) the work done per unit of time by the force which gives mo- 

 tion to the liquid, and 



(2nd) the work per unit of time of the several resistances to which 

 the liquid in moving through the pipe is subjected, and 



(3rd) the work accumulated per unit of time in the liquid which 

 escapes — and thus to constitute an equation in which the dependent 

 variables are the radius of any given film, and the velocity of that 

 film. This equation being differentiated and the variables separated, 

 and the resulting differential equation being integrated, there is ob- 

 tained the formula _250r 



v = v e l > 



where v is the velocity of the film whose radius is r, and v that of 

 the central filament, and I the length of the pipe — the unit of length 

 being one metre, and of time one second. 



The method by which the author has arrived at this formula is 

 substantially the same as that which he before used in a paper read 

 before the Society on the " Mechanical Impossibility of the Descent 

 of Glaciers by their weight only," and which he believes to be a 

 method new to mechanical science. It was indeed to verify it in its 

 application to liquids that he undertook the investigations which he 

 now submits to the Society, which, however, he has pursued beyond 

 their original object. 



The recent experiments of MM. Darcy and Bazin* have supplied 

 him with the means of this verification. These experiments, made 

 with admirable skill and precision, on pipes upwards of 100 metres 

 in length, and varying in diameter from m, 0122 to m, 5, under 

 heads of water varying in height from m, 027 to 30 m, 714, include 

 (together with numerous experiments on the quantity of water which 

 flows per second from such pipes under different conditions) expe- 

 riments on the velocities of the films of water at different distances 

 from the axes of the pipes, made by means of an improved form and 

 adaptation of the well-known tube of Pitot. These last-mentioned 

 experiments afford the means of verifying the above-mentioned for- 

 mulae. With a view to this verification, the author has compared the 

 formula with sixty of the experiments of M. Darcy, and stated the 

 results in the first two Tables of his paper. 



The discharge per 1" from a pipe of a given radius may be cal- 

 culated from the above formula in terms of the velocity of the cen- 

 tral filament. This calculation the author has made, and compared 

 it with the results of eleven of M. Darcy's experiments. 



* Recherches Experimentales relatives au mouvement de l'Eau dans les 

 Tuyaux, par H. Darcy: Paris, 1857. Kecherches Hydrauliques, par MM. 

 Darcy et Bazin : Paris, 1865. 



