and is smaller than the former, though perhaps not much 

 smaller in some cases, and we have no direct means of calculating 

 it. It is manifest that all questions arising from proximity to 

 the ship's body, surface disturbance produced by the screw, 

 frictional and displacement resistance, and so forth, must be left 

 out of account in giving a theory of its action in any tolerably 

 simple form, just as similiar sources of loss are in making a 

 preliminary estimate of the horse power of an engine. The 

 screw will therefore hereinafter be treated as if the blades had 

 no thickness or surface friction, and as if it were sufficiently 

 deeply immersed to produce no surface disturbance. The effect 

 of the latter cause has been found, by experiment with screws 

 much more deeply immersed than is usual, to be practically in- 

 sensible, or at any rate trifling, so long as the screw does not 

 break the surface. 



The water has originally no rotary motion, and in the case of 

 screws fitted in the usual place, this applies, in all probability 

 even to water quite close to the screw ; whether or no, the 



ro) 



rotary impulse is — lbs. per lb. of water per second entering the 



screw at radius r, and acquiring a circumferential velocity r<a. 

 In the theory of turbines ro> is called vcosa, v being the velocity 

 of issue from the guide blades, and a their angle of inclination 



to the plane of the buckets ; — is therefore the pressure of the 



screw against the water at radius r, in lbs. per lb. of water per 

 second flowing through at that radius ; the screw itself moves 

 with velocity rQ at that radius, and the work done is therefore 



— Xr£l= lbs. per lb. per second, just as in a turbine the 



work done by the water is Vvcosa, V'm this case standing for 

 the circumferential velocity of the bucket wheel, or turbine 

 itself. See any treatise on turbines written (except by lunatics) 

 in the last fifty years, or thereabouts. In accordance with the 

 notation and principles known and applied to such matters 

 since the days of Des Cartes (some two hundred years) the 



