SECT. 1V .] AND PROPORTIONS OF ENGINES. 159 



_ 



3 (r + a) 



and when x = a, we have 



for the power of the steam acting in a rotary direction, the piston being the rect- 

 angle ay. 



316. If the piston D C revolve on an axis in the centre C, then r = o, and 



2 *-/y g2 the rotary power. 

 3 



But the space occupied by the steam is ir a (2 r + a) y, and its rectilineal power 

 is TT/ (2r + 0) y. Hence the rectilineal is to the rotary effect of the steam, as 



or as 



2r 2 + 3ra + a 2 :2 (r* + ra + % a*). 



When r = o, or the piston revolves on a centre, then the ratio becomes 3 : 2, 

 or one-third of the power is lost; the same conclusion resulting however the 

 steam acts. 



317. We have supposed the piston to be of parallel width, but in some 



schemes it has been made circular ; and in such a case the value of \ y is */ a x .1*. 

 Consequently, 



r a 



is the differential of the rotary power. Its integral, from x = o to .r = a, is 



* f *(* + **+ -ft**} 



2 J r + a 



the entire power. 



This is a little less than the effect of a rectangular piston. When the piston 

 revolves round an axis in its edge, the rectilineal power of a given quantity of 

 steam is to its rotary power as 3 - 2 : 2. In the rectangular one it was as 3 : 2. 

 Hence, we see there is no possibility of applying steam with the same advantage 

 in a rotary as in a rectilineal engine ; and, even to approximate to it, the radius 

 of the circle described must be great in comparison wtth the diameter of the 

 piston, and consequently difficult to execute. To employ any other than a circular 



