44 Canon Moseley on the steady FIov: of a Liquid. 



pipe into two equal portions, acted upon by similar and equal 

 forces, and subjected to similar and equal conditions of motion. 

 If, therefore, we conceive the portion of the liquid above the 

 plane to be removed, and the same pressures to be exerted on 

 every point of the surface of the portion which remains as it 

 exerted, it is clear that the motion of the latter wdll remain un- 

 changed, as also the discharge of that portion, which, as the 

 discbarge of the whole was represented by Q, will be represented 

 by ^Q. But by the removal of the upper portion of the liquid, 

 the pressure on the different points on the surface of that which 

 reuiains will be changed ; for whereas before it cannot but have 

 been different at different distances from the axis, because the 

 velocities at such different distances were different^, now they 

 are the same, being everywhere equal to the pressure of the at- 

 mosphere. As the pressure is everywhere less where the velocity 

 is greater, it is evident that there will be a tendency in the liquid 

 on the surface to flow from the sides of the channel towards the 

 centre, and that thus the velocity of the surface-water at the 

 centre wull be diminished, and the water heaped up, drowning, 

 as it were, the point of greatest velocity in the section. 



This disturbance of the motion of the liquid will not be limited 

 to the surface ; there will result therefore a disturbance of the 

 films of equal velocity. The experiments of M]^I. Darcy and 

 Bazin afford evidence of this disturbance. In the first of the 

 accompanying figures the films of equal velocity are shown in 

 the pipe (sect. 0*8 metre by 0'5 metre) when closed and full, and 

 in the second when open and half full. (Plate I. figs. 1 & 2.) 



Notwithstanding this new disturbance of the velocities of the 

 different parts of the liquid, it is to be observed that the work 

 of its weight over a given space remains the same; so that if 

 there is no considerable change in the resistances, the discharge 

 of the half of the now opened pipe may be expected to be the 

 same as the discharge of that half was before. 



This was found by the experiments t to be the case. The 

 rectangular pipes above described, whose sections were respec- 

 tively 0'8 metre x 0"5 metre and 0*48 metre x 0"3 metre, had 

 their tops removed, and water was made to flow through them 

 so as just to half fill them. The following were the results : — 



* Phil. Mag. November 1871. equation (20). 

 t RechercTies Hydrauliques. pp. 176 &c. 



