Canon Moseley on the steady Fluiu of a Liquid. 193 



This formula may be proved independently as follows : — 2irrl 

 being the surface of a film whose radius is r, and /j, the resistance 

 per unit of surface to its being made to move over the film whose 

 radius is r + dr, ^irrlfju represents the whole resistance to its being 

 so moved. And since the distance it is moved over it in the unit 



of time is represented by — ( — ]dr, the whole work, per unit of 

 time, of that resistance is represented by 



Also, since h is the head of water and the vertical section of 

 the film which receives the constant pressure of this head of 

 water is represented by (27rrdr), the pressure constantly acting 

 to give motion to the film is [2irrdr)wh. But in the unit of 

 time this pressure acts through the distance v, because the film 

 moves through that distance. Therefore the work per unit of 

 time of the pressure which gives motion to the film is repre- 

 sented by 



fyrwhvrdr. 



Therefore, since the motion is uniform, by the principle of virtual 

 velocities, 



— 2irljj,r \-r) dr = Qirwlivrdr ; 



wh _ wi 

 fit fju 



, / v \ wir 



j 



P. 



In this investigation the accumulation of work in the liquid 

 which escapes per unit of time is neglected. It is so far ge- 

 nerally incorrect ; and therein lies the difference between the 

 values of v as determined by equations (10) and (12). It would 

 be absolutely true if, by the pressure of an additional head of 

 water, that in the horizontal pipe had been made to enter it 

 with the velocity with which it eventually leaves it, the pressure 

 of the head h only acting to overcome the resistances to its 

 motion through the horizontal pipe, and so to preserve in it the 

 work with which it entered it and with which it leaves it. Now 

 this was nearly the case in the experiments of M. Darcy, so 

 that equation (12), not absolutely true in the general case, is 

 approximately true in the special case of his experiments. Ey 



Phil Mag. S. 4. Vol, 42. No. 279. Sept. 1871. 



