158 OF THE POWER OF STEAM, [SECT. iv. 



10 x EC 



D C : E C : : 10 : 



DC 



the effect at E, that at D being 10. If the centre of curvature C were nearer to 

 the side of the vessel, the effect at E would be less ; therefore the effect of the 

 pressure to produce motion is less than in a straight vessel, having the same base ; 

 and if the bases be the same, the space the pressure acts through will be as the 

 quantity of steam. Consequently, the quantities of steam being equal, the power 

 of rotary action will be less than that of rectilineal action. 



314. If a rectangular piston, D C, revolve round a centre C, then nearly 

 half the power of the steam will be lost. 



This rough inquiry will be sufficient to show that much is lost by attempting to 

 employ the rotary action of steam, besides the various other objections arising out 

 of the excess of friction, and the difficulties of executing the parts so as to act 

 properly, usually called practical difficulties. 



315. To conduct the inquiry so as to reduce the effect to more accurate cal- 

 culation, put 



a = D E, the diameter of the piston ; 



r = E C, the radius of the interior circle ; 



x = any variable portion of the diameter of the piston counted 



from E; 



y = the breadth of the piston, 

 and /= the force of the steam on an inch of area. 

 Then r + a = D C ; and, 



f 



r + a ' 



the force at the distance x from E ; and 



/y(r + x)d* 

 r + a 



is the differential of the pressure at that point ; and the space described being 

 2 r (r + x) we have 



2ff/y(r + x)~ dx 

 r + a 



for the differential of the power. 



When y is uniform and therefore constant, the integral is 



+ xY p. 



and making this expression nothing, when x o, that is, when the power is 

 nothing, it becomes 



