It is much shorter to express the circumferential velocities 

 thus than to say, " let iVbe the revolutions per minute, and let 

 D be the diameter of any circle drawn on the screw disc ; then 

 the circumferential velocity of the screw at this place is 3"i4i6 

 ZWfeet per minute or 0-05236 AT) feet per second "; and then 

 afterwards be always dragging in this abominable 0-05236 every- 

 where. 



The circumferential velocity of the water is not actually the 

 same at all points on the circumference of the same circle ; but 

 hereafter to is understood to mean the average angular velocity 

 at any given radius. Neither is the circumferential velocity of 

 the water the same at different distances from the axis ; and it 

 is the purpose of this Note to point out by what rule this is 

 governed, approximately. Similarly for v, the longitudinal 

 velocity. This, in the ordinary theory of the propeller is 

 assumed to be uniform, or nearly uniform, over the whole screw 

 disc. In this Note this assumption is shown to be, for practical 

 purposes, correct, though not necessarily true absolutely. It is 

 furthermore assumed in this Note, that the ordinary mechanical 

 law, that a loose, or free body, when acted on by a force for a given 

 time, will have a quantity of motion generated in it proportional 

 to the force, and in the direction of that force, irrespective of 

 the previous direction of motion, or velocity, of the body, is true, 

 and that the application of this law, as commonly employed in 

 calculating the power developed by turbines and other engines 

 worked by the impulse of water, is correct, and justified by the 

 fact that in such engines the power calculated on comes out 

 right in practice. There is absolutely no novelty in the prin- 

 ciple, or its application. It is furthermore assumed that when 

 a liquid flows in a closed pipe or tube the head, or pressure of 

 the liquid, varies if the velocity of flow varies, in accordance 

 with the ordinary established law that the change in the head 

 is proportional to the difference of squares of velocities, from 

 point to point. It is furthermore assumed that an incompres- 

 sible liquid, flowing along a full pipe, will vary in velocity at 

 different places in accordance with the cross sectional area of 



