9 



circle, a corresponding particle of water for which D is as much 

 lower than A, so that if gravity helps the one, it resists the other 

 to an equal extent, and this is true whatever the hydrostatic 

 pressure may happen to be, so that the equation just found is 

 equally true for all depths, and whether the axis of the screw is 

 horizontal, vertical, or inclined, provided that the general sur- 

 face of the ocean is undisturbed. 



In the case of a turbine, the general surface is not undisturbed 

 but may be thirty or forty feet higher at one side of the turbine 

 than at the other, the difference of level being in fact the source 

 of work done on the turbine by the water when employed as a 

 source of power, and vice versd in the case of a centrifugal pump r 



The equation just found is an important one, as it connects 

 together the circumferential speed of the water, rw ; the longi- 

 tudinal velocity, v ; the speed of the ship, K ; and the circum- 

 ferential speed of the screw, measured by its angular velocity £2 ; 

 and this equation, like the corresponding one for a turbine, is 

 the fundamental one governing these quantities, which is there- 

 fore one condition they must fulfil, irrespective of all other 

 circumstances. 



It appears at once that if a>=0, i.e. if the water have no 

 angular velocity imparted to it, v 2 — K 2 =0 and therefore v=K, 

 so that, as the thrust is proportional tov — K, there is no thrust. 

 That is, if the water be not made to revolve, there is no thrust. 

 Consequently any design of blade intended to prevent, or avoid, 

 rotary motion of the water, would, if successful in so doing, also 

 prevent any thrust being obtained, or any power being consumed, 

 except in friction. 



The next thing to be considered is the head or pressure, at 

 various points in the screw disc, the head being less as the 

 velocity is greater, by a law previously mentioned. Suppose 

 the head at a point, somewhere at a long distance from the screw, 

 in the tube ASA', where the velocity is K, to be H, then if the 

 the velocity at radius r, is called u, (u being now AD, the actual 

 velocity in the actual direction of motion of the water) then 

 2g{H—h 1 )=u 2 —K 2 and at r 2 similarly 

 2g{H-h 2 )=u*-K* 



