THE MOTION OP STEAM VESSELS. 323 



ber of paddles and tangential velocity should be equal to the power of the engine. 

 The depth of immersion not being given in every experiment, the exact angle at 

 which the paddles entered the water is not known ; but as the experiments were 

 generally made immediately after the engines were fitted, when the vessel had not 

 taken in her cargo of coals, the paddles were but slightly immersed. 



From the preceding data, and inquiries I have made, I am led to assume a dip of 

 three feet six inches, or the water level to be twelve inches above the top of the pad- 

 dle, as a mean for the first class, which will make the centre of pressure enter the 

 water at 44°. 



Then calling V = 4 and v = 3, which is nearly the mean ratio of the velocities of the 

 common wheel and vessel, I find the mean resistance of the paddle passing through 

 the whole arc to be to the resistance of the vertical one as 175 : 1. Now as the whole 

 circumference contains sixteen paddles, and the arc passed through is 88°, we may 

 consider three paddles and a half to be acting ; this will make the whole resistance to 

 the engine equal to 6-12 times that opposed by the vertical paddle, or the power of 

 the engine exerted on the vertical paddle = -163, the whole power being 1 ; while the 

 mean obtained from the experiments is -157. In the second class, the paddles, though 

 smaller, (being proportionably immersed,) may be considered to enter the water at 

 the same angle of inclination, so that the same mean resistance will result from it, 

 viz. 175. The number of paddles, however, being less in the small wheels, there 

 are not more than three of them effective, which gives the proportion of the power of 

 the engine exerted on the lower or vertical paddle -190 ; the mean obtained from the 

 experiments being -193. We are thus able in the common wheels to account for the 

 power of the engine, which not only proves quite satisfactorily the accuracy of the 

 principles adopted in the preceding calculations, but that the supposed lost power 

 from back-water is very trifling. 



We have in the above investigations considered the paddles to be in the direction 

 of the radii from the centre. It is necessary, however, to mention, that in some of 

 the wheels the radii of the paddles are made to proceed from a point on one side of 

 the centre, with a view of reducing the shock produced by the paddle striking the 

 water at too great an angle. But this deviation is not sufficient to make any sensible 

 difference in the amount of the resistance opposed to the engine ; for although it is 

 decreased at the commencement of its action by the angle being smaller, it is 

 increased after passing the centre, which resistance observes the same law until the 

 column of water above is less than that due to the square of the velocity. 



It now remains to account for the power of the engine in the new wheel, where we 

 have found the horizontal resistance to the paddle to be (V cos (p — vy. The power 

 of the engine necessary to overcome this resistance will be (V cos (p — v^ cos p, as will 

 be readily seen from the following resolutions. 



Referring again to figure 4, let G B represent the horizontal resistance or force on 

 the paddle : it is to be ascertained what force in the direction F B will overcome it. 

 Resolve G B into two forces H G, H B, one at right angles to^ and one in the direction 



