340 PHILOSOPHICAL TRANSACTIONS. [aNNO 1718. 



Case 2. — If the line of direction abcde, fig. 21, consist of several right lines 

 AB, BC, CD, EP, inclined to each other, the motion of the water will be the 

 same. For, the motion of the water, in the whole compound pipe abcde, 

 consists of the motions of the water in the several parts of it, ab, bc, cd, de, 

 added together. For water, flowing according to the right line ab, and chang- 

 ing that direction into another, by which it is carried according to the right 

 line BC, loses nothing of its motion : for fluids do not follow the same laws as 

 are observed in the motion of solids, when their direction is changed. Other- 

 wise the motion of a fluid, on changing its direction into another perpendicular 

 to the former direction, would be entirely stopped ; which experiment by no 

 means shows. Moreover, water running out at the hole of a vessel, whether it 

 be carried downwards, or according to the plane of the horizon, or straight 

 upwards, has the same velocity. But if at any time it should be found, either 

 by more subtile reasoning, or by experiment, that some diminution of the mo- 

 tion proceeds from the change of direction, regard is to be had to it. 



is 



If the line of direction ab, fig. 22, be a curve, it is to be referred to th 

 case ; for it may be conceived as consisting of numerous small right lines. 



Case 3. — If the pipe ab, fig. 23, be divided into several branches bc, bd, be, 

 of equal length, the motion of the water will be found in the same manner, 

 assuming for the line of direction the length abd, consisting of the length of 

 the principal pipe ab, and the length of any branch bd. For it is the same 

 thing, whether the water run from the principal pipe towards the branches, or 

 from the branches towards the principal pipe. But if the branches be unequal, 

 the motion of the water in each branch must be found out, taking for the line 

 of direction the length, consisting of the length of each branch and that of th^ 

 principal pipe. This is easily deduced from case 2. 



Case A. — If the equal branches, into which the pipe ab, fig. 24, is divided, 

 unite again into one pipe fg, to find the motion of the water, we must take 

 for the line of direction the whole length abdfg, consisting of the length of 

 the principal pipe ab, of any branch bdp, and of the united pipe fg. If the 

 branches be unequal, the motion of the water in each must be found, and the 

 sum of their motions added to the motion of the water in the united pipe. 

 This follows from case 2 and 3. 



Corol. 1 .-rHaving given the length of the pipe, and any section thereof; the 

 motion of the water will be in the ratio of the velocity, with which the water 

 runs through that section. 



Cor. 2. — Having given any section, and the velocity of the water running 

 through that section, the motion of the water will be as the length of the pipe. 



