THE MOTION OF STEAM VESSELS. 327 



the velocities V and v will be changed. Let the former become p V, and the latter 

 n V ; our equations are therefore 



(V — v^Y a : {p\ — n vf p\ a '. Y : m, 



(V •— vY a: {pY — nvy a: I -.n^, 



which reduced, give p =. n, and each equal to the v' m ; that is, the velocity of the 

 vessel will be increased in the ratio of the cube root of the powers expended. 



We see therefore that when an engine is not able to perform its whole duty, the 

 diameter of the wheel ought to be reduced, and not, as is usually done, the area 

 of the paddle ; for in the former case the velocity is increased in the ratio of the cube 

 roots of the number of strokes, while in the former it remains the same as when the 

 less power was developed. 



To find the change in the diameter required to produce this effect, we know the 

 circumferential velocities are as V : V ^ m, or as 1 : l/~7n\ we know also that these 

 velocities are as the number of strokes multiplied by the radii of the wheels ; putting 

 therefore r and r' for the two radii, the velocities are as r : m r', or r : w r' : 1 : ^m, 

 whence , r 



the required radius of paddle. 



In the case of the Salamander, from the great immersion of the paddles the engine 

 could only make fifteen strokes instead of twenty, its full duty. We may now find 

 what increase of speed would have been given to the vessel by reducing the wheel so 

 as to allow the engine to perform its whole duty. 



We have m = 1*25, whence r' = "8617 r, and w v = 1*077 ^ ; if therefore the dia- 

 meter of the wheel of the Salamander had been reduced in the ratio of 1 to '8617, the 

 speed of the vessel would have been increased in the ratio of 1 to 1*075 ; that is, by 

 reefing each paddle about fifteen inches, the speed of the vessel would have been in- 

 creased about two thirds of a mile, and at the same time the consumption of fuel 

 would be increased only in a very small degree, as has been demonstrated by the ex- 

 periments given in the preceding article. 



In these calculations I have assumed a similar action of the paddles with every 

 variation of diameter, which in reality is not strictly true, as every change of the 

 position of the floats will vary the angle at which the centre of pressure enters the 

 water. I find, however, in the greatest extent of reefing ever required^ this variation 

 to be so small, that it is not necessary to introduce it into the calculation. As far as 

 its effect extends it is favourable to the reefing, as thereby the obliquity of action is 

 diminished, and consequently the loss of power. 



Comparison of the Resistance of a Steam Vessel with that of a Plane Surface. 



The resistance of vessels being a subject which has of late much engaged the at- 

 tention of engineers, I have been induced to add the following comparison of the re- 



2 u2 



