THE MOTION OF STEAM VESSELS. 321 



paddle increases as it deviates from the vertical, but that the effective horizontal 

 force also increases up to all angles within the limits ofjhe immersion of paddle-wheels. 

 It should be stated, however, that although an increased propelling power is ob- 

 tained from the vertical paddle upwards as far as these limits, it is not to be under- 

 stood that so great an angle is practically advantageous ; for the vertical resistance 

 becomes very great, and the shock on the engine by the paddles striking the water 

 at so great an angle is tremendous. 



Comparative efficiency of oblique and vertically acting Paddle-wheels. 



In order to make a comparison of the efficiency of different wheels, it is necessary 

 to estimate what part of the whole power of an engine is transmitted through them 

 upon the boat, and what part is actually lost. In oblique-acting paddles, a loss of 

 power is sustained in two ways : first, by the resolution of the power of the engine, 

 in which one part is referred to a vertical line, which is wholly inefficient as a pro- 

 pelling power; this part therefore is lost : and of the resolved horizontal force, another 

 part is lost by the motion of the wheel backwards in the water. This may perhaps 

 be best illustrated by the case of a locomotive engine. If the friction between the 

 wheel and the rail is such that the former does not slip, the motion of the carriage is 

 the same as that of the circumference of the wheel ; the whole power of the engine is 

 employed in propelling the carriage, and consequently there is no lost power. But 

 if the friction be not sufficient, the wheel will slip back some quantity, the same steam 

 will be consumed in a revolution of the wheel, but the carriage will not be advanced 

 as before, and there will therefore be a loss of power proportional to the skidding or 

 receding of the wheel. So in a steam vessel, all that the centre of pressure actually goes 

 back in the water, or all that its circumferential velocity exceeds that of the vessel (the 

 expense of steam being proportional to the former and the effect to the latter,) may be 

 esteemed lost power ; for although the nature of the medium requires some back 

 motion of the wheel to get up the necessary resistance, yet the less there is of this re- 

 trogradation, within the limits of practical convenience, the better ; because the less 

 power will thus be absorbed by the paddle and the more will be left to act upon the 

 vessel ; hence the superiority of one wheel or another will depend upon the quantity 

 of lost power it gives rise to, that wheel being of course to be preferred in which the 

 loss is the least. 



The lost power of an engine with the common wheel, or, which is better, the effective 

 part of the power, may be found as follows : First, reduce the variable tangential re- 

 sistance on the paddle to a mean constant resistance ; find also the mean resolved 

 horizontal resistance ; then if this mean resolved resistance be supposed to be applied 

 to the circumference of the wheel, the case will exactly resemble that of a locomotive 

 engine, and the part of this force which is to the whole as v to V, will be that part 

 which is employed in propelling the vessel, all the rest will be lost power. The general 

 expression for the tangential resistance on an oblique paddle has been shown to be 



