11 



Here again ft is an independent arbitrary constant, being the 

 screw's angular velocity, and consequently the same for every 

 point whatsoever, so that dividing across by it we get the 

 equation in the form 



, -v (wtanfl) 



-Jr^ <a)=ra> ll- V — ft— 



in which all the terms are of the dimensions of velocities. 



The stream lines of the screw converge towards it from the 

 ship, and diverge again behind it, consequently (except near the 

 boss) they must be, in the screw, approximately parallel to the 

 axis. This means that tan# is small, except near the boss. 

 The amount of thrust in practice is found to agree pretty well 

 with the amount of longitudinal slip, proportional to v—K 

 supposed uniform, consequently (except, as before near the boss, 

 where only small quantities of water, having but a slight in- 

 fluence on the result, are dealt with) v exceeds K, but, in practice 

 not much, and cannot therefore differ much at different radii, 



d 



—vtanv 

 dx 

 consequently ^ is small numerically if the stream lines 



if the screw be tolerably fair and not sharply curved in the 

 screw itself. It is likewise observable in practice, and agrees 

 with calculation, that the angular velocity of the water is, except 

 as before stated, near the boss, for the most part but a small 

 fraction of the angular velocity of the screw. It is also observable, 

 and agrees with calculation that in the outer tube of flow, the 

 curve ASA' at the screw is convex to the axis of the screw. 

 Consequently, for the most part of the screw disc, the equation 



d 



-r-vtand 

 or w dx 



- s Sr"*)-n> s -'— s — 



consists on its right hand side, of the difference of two terms, 

 both of which are small ; and therefore the result of that equation, 

 whatever the precise values they may have may be, must be 



approximately expressed by —~(r 2 (o)=0 which being integrated 



