On Moseley's Theory of Steady Flow. Ill 



nels, at any rate, all modern experiment points* to the con- 

 clusion that the motion is essentially unsteady and that the 

 stream-line* interlace freely in all directions. Xext, hypothesis 

 Xo. 2 is contrary to the eyidence of Bazin's experiments. 

 In Bazin's work two diagrams are givenf of cross sections of 

 two rectangular iron pipes (flowing full) laid with two sides 

 horizontal, with velocity-nieasureinents made at many points 

 on several horizontal and several vertical lines thereof figured 

 thereon : now the contours of loci of points of equal velocity 

 traced thereon are all rounded (like ellipses); so that hypo- 

 thesis No. 2 disagrees with nature. 



From these hypotheses X 1 os. 1 to 5, the primary result is an 

 expression for the velocity at any point in a pipe flowing full ; 

 and thence follows, by a simple integration, an expression for 

 the discharge through the same. By help of Xo. 6 (which is 

 a result of pure experiment) this last result is extended so as 

 to give a formula for discharge in open channels. 



It will be seen that the results for pipes (flowing full) are 

 strictly dependent on the hypotheses Xos. 1 and 2 of steady 

 motion in parallel lines, and of the surfaces of equal velocity 

 being similar and similarly situate to the enclosing margin; 

 whilst the formula for discharge in open channels involves no 

 assumptions as to the actual motion therein, but depends only 

 on the correctness of the theory of the motion in pipes flowing 

 full together with the connecting link Xo. 6 (derived from 

 experiment). 



From the uncertainty of the assumptions, it is evident that 

 the only test of the correctness of the theory is the comparison 

 of numerical results therefrom with observation. 



The extensive small-scale experimental results % of MM. 

 Darcy and Bazin on pipes and open channels not exceeding 

 2 metres in width nor \ metre in depth were applied (in the 

 original essay) in numerical verification of the formulae quoted 

 — viz. for Velocity at any part of a circular pipe flowing full, 

 and for Discharge both in pipes flowing full and in open chan- 

 nels. The result was apparently satisfactory ; that is to say, 

 there was certainly a remarkable approximation on the whole 

 (with occasional very large discrepancies) between the expe- 

 rimental and theoretical results. A sound theory of flow of 



* See ' Koorkee Hydraulic Experiments,' vol. i. chap. vi. ; for a summary 

 of the evidence. 



t Recherches experimentales sur Vecoidement de Veau dans les canaux 

 decouverts, pi. xviii. 



X Recherches experimentales relatives au mouvement de Veau dans les 

 tuyaux, by H. Darcy. Paris, 1857. 



Recherches experimentales sur Vecoulement de Veau dans les canaux de- 

 couverts, by H. Darcy and H. Bazin. Paris, 1865. 



