Canon Moseley on the steady Flow of a Liquid. 351 



It is important to observe that the indeterrainateness of the 

 function 7 is due not to our ignorance of the conditions of the 

 motion of the liquid in the pipe, but of its antecedent motion in 

 the reservoir. Whenever the conditions of the latter shall be 

 expressed mathematically, 7 will be determined and the solution 

 of the problem will be complete. Meanwhile there is an im- 

 portant case in which the value of y is necessarily unity, and in 

 which the solution may be completed. It is that of an open in- 

 clined channel in which the liquid has attained a uniform depth 

 and a steady equable motion. Before it has reached the point 

 where this begins to be the case, the work U 1 has been already 

 communicated to it, and the work U 2 has been already done by a 

 pressure (that of the water in the reservoir) which no longer acts 

 upon it. For the rest of its motion, all the work U that has to 

 be done by its weight is the overcoming of the resistances to its 

 motion in the channel ; so that in equation (2) U x -f U 2 =0, and 

 U = U 3 + U 4 . I shall discuss this case in a subsequent and con- 

 cluding paper. 



The pressure on the liquid at any point in the pipe. 



By a well-known formula"* of the steady motion of a liquid, 

 neglecting the consideration of those resistances whose unit is, 

 in the case of a pipe, represented by /ll, 



where jOj represents the unit of pressure on any molecule of the 

 liquid whose velocity is ?>, p' that at the common surface of 

 the liquid and the atmosphere, z the depth of the molecule 

 below the surface, and w the weight of a cubic unit. Let this 

 equation be supposed to obtain as long as the water is in the re- 

 servoir but not in the pipe, and let the depth of the aperture be 



-. At the aperture it becomes 

 7 



*>.=/ + «>- -3 -v* (18) 



If p be taken to represent the unit of pressure at a point 

 whose distance from the entrance of the pipe is oc, and from its 

 axis r, and if a section be imagined perpendicular to the axis 

 through that point, the pressures on the liquid between it and 

 the entrance to the pipe will be in equilibrium. 



* Treatise on Hydrostatics, by the author of this paper, p. 14/. Cam- 

 bridge : 1830. 



