3 



the pipe, totally regardless of all other circumstances whatsoever. 

 In other words, if the flow at one cross section of a pipe be ten 

 gallons a minute, it is ten gallons a minute at every cross section 

 of the pipe, and the velocity is therefore fixed absolutely if the 

 cross section be known. From this it follows further (as is well 

 known, and has been held to be well known and established 

 ever since the days of Toricelli, a period of some two hundred 

 and fifty years, neither is, or is conceived to be, any novel or 

 fresh doctrine, nor has been found to be in discordance with 

 the facts of experience) that given the head and velocity at any 

 one point in a tube filled with incompressible fluid flowing along 

 it, then both the head and velocity will be (except for friction) 

 fixed at every point along it by the cross sectional area, and 

 vice versd ; the head or pressure, and velocity, being indissolubly 

 connected together. It is furthermore assumed that when a 

 body moves in a circle, the centrifugal force is directly pro- 

 portional to the square of its circumferential velocity, and in- 

 versely proportional to the radius, and this doctrine is at least 

 as old as the days of Sir Isaac Newton, say two hundred years, 

 and the sun and moon, and the earth and the planets and the 

 comets, have been moving in accordance therewith since a time 

 that the memory of man runneth not to the contrary, neither 

 has this doctrine been ever found to be in discordance with the 

 facts of experience. 



The principal reasons why the known, acknowledged, ac- 

 cepted, acted upon, and practically successful theory of turbines 

 has not, so far as the author is aware, been applied in exactly 

 the same way to the case of screw propellers are these. The 

 first is, that the persons who had to make the calculations for, 

 and apply their results to, turbines, were not usually the same 

 as those who deal with propellers, and, when the true mechanical 

 theory of turbines was first brought out, the persons who did so 

 could not possibly have concerned themselves with screw pro- 

 pellers, the same not being then in use, or even perhaps invented. 

 The second is that in the case of turbines the work done by the 

 rotary force is the only matter of importance, and the end 



