132 APPENDIX. 



conceive the object of so much secresy : it can hardly answer any useful end, whereas it 

 would be a certain benefit to the nation if the public were made acquainted with all facts 

 relating to steam navigation. We have ascertained the diameters of the following paddle 

 wheels, which differ from those given in Mr. Barlow's table : ' Messenger's,' 20 ft. ; ' Dee's,' 

 20 ft.; ' Rhadamanthus,' 'Salamander,' and 'Phoenix,' each 21 ft. ; ' Firefly's,' most probably 

 18 ft., and the depth of the floats of ' Medea's' wheels, 3 ft. 8 in. 



The power expended on the wheels of a steam vessel would be found much more readily 

 if we knew the position of the centre of pressure, but we are not aware of any direct method 

 of finding that point. 



By centre of pressure is understood a point on the surface of the paddle-board at such a 

 distance from the axis of the wheel, that if the whole surface of the board were concentrated 

 in that point, or in the horizontal line passing through it, the mean resistance would not be 

 affected by the change ; it does not however follow that the effective resistance would remain 

 unaltered, so that this point is only the centre of total pressure, and not of effective pressure ; 

 nor is it the centre of pressure of the float in any given position, but the mean for all the 

 positions taken by the float during its passage through the water, and should therefore, 

 strictly speaking, be called the mean centre of pressure ; but as it is already known as the 

 centre of pressure, we will retain this expression for the sake of brevity. The position of 

 this point being known, we can find the power in the following manner. 



Let y be the distance of the centre of pressure from the axis of the wheel, 8 the angle at 

 which it enters and leaves the water, a, b, p, n and m, the same as in the former calculations, 

 and /the depth of the float. The pressure on the float at any angle </> is equal to the product 

 of its area bf, by the square of its effective velocity and the weight of a cubic foot of water, 

 divided by 2 g. The effective velocity of the float is equal to 



irn r ,-, 



[y-pcos.0], 



2 2 ft y* 



so that the pressure is equal to ^ [y pcos. <] 2 , 



900 x 2 ff 



and the moment of the resistance to ^-^ ^- [yp cos. <f>]* y. 



^ \y\j\j x // 



The mean value of this expression is equal to the definite integral 



A 



f* , ,-,, 



If -** 



27000X2 

 which is 



which is slooox^l [2y 3 + ^ 2 ]a+[p 2 -4y 2 rf 



This multiplied by 2 m, and reduced to horse powers, becomes, 



(3) 



The first member of this equation being equal to the second member of the equation (1) 

 (page 126), it is evident that the sum of the terms between the brackets in the former, multi- 

 plied by 6/ must be equal to the sum of the terms between brackets in the latter, or, calling 

 S that sum in formula (1), and S" the sum in formula (3), we must have 



