ON THE GENERAL THEORY OF THE STEAM ENGINE. 197 



effective surface of resistance. Denote this surface by S', and the force of resistance in Its. 



will be - S' v 3 . Multiply by 60 v, the speed per minute, divide by 33000, and we obtain the 

 2 ff 



number of horses' power effectively developed on the vessel, h = . S' v 3 = <7r c S' v 3 . 



550 2 g 2000 



Hence, 



c , 2000 h , N 



o = . (). 



7TC V 3 



This expression will serve to calculate the surface of resistance in any experiment ; and by 

 substituting the preceding value of h for any particular wheel we shall express the necessary 

 relation between the velocities for a given vessel at a given immersion ; and this relation will, 

 in fact, express a constant ratio between the velocities. For the common wheel, for instance, 

 this relation is, 



7T C 



A'-2B' + B 



V IT 



V . 



and the ratio is determined by the positive root of quadratic equation, 



- .. 



v v 3 2 S 



EXAMPLES. Take the case of the 'Salamander' calculated by Mr. Mornay, at pages 127 

 and 135. The radius to the centre of pressure for the whole power is by Mr. Mornay 

 denoted by y, and, in page 135, is 9'3937 feet ; and that for the effective power is, page 138, 

 z = 9'355 feet ; also the paddles are 16 in number, depth 2 feet 6 inches, and breadth 8 feet 

 9 inches, making a surface of 350 square feet. 



1. COMMON WHEEL. 



For the calculation of the POWER OF THE ENGINE we have therefore a = 5, k = 9'3937, 

 speed of the engine re = 15 strokes per minute, speed of the vessel 8' 15 miles per hour, and 

 the surface of paddle on each wheel S = 350 square feet. Hence, 



log. n 



1-17609 

 0-97284 



const. 9-02003 

 30 



log. V 1-16896 



log. V 2 2-33792 



A 0-06588 



SV 



1000 



3-11683 



1308-7 



log. 8-15 0-91116 



99 



const. _ 0-16633 

 15 



0-71303 - 



log. v 1-07749 



V 1-16896 



log. VD 2-24645 



B 9-98945 



- - - 0-71303 



2-94893 



889-06 



log. S 

 , V 



2-54407 

 1-16896 



SV 

 1000 



0-71303 



log. v 2 2-15498 

 B' 9-92516 

 - - - 0-71303 



2-79317 



621-1 

 1308-7 



1929-8 

 1778-1 



Horse Power 151-7 



2 c 



