830 Transactions of the American Institute. 



Thus, if P represents the steam pressure on the piston, and O G 

 the length of stroke, B being the point of mid-stroke, POGH will, 



on this supposi- 

 tion, represent the 

 work done during 

 the stroke, and P 

 O B C the work- 

 done during the 

 first half stroke. 

 But if the recipro- 

 cating parts of the 

 engine are of such 

 a weight that the 

 whole force P O 

 is only sufficient to give to them 'the requisite initial accelera- 

 tion, then, by joining P B, it will be manifest, from what has 

 been already shown, that the entire work represented by the triangle 

 P O B will be absorbed by these moving parts, so that the work done 

 by the engine through the crank will be only that represented by the 

 triangle P B C ; and the steam force which reaches the crank at the 

 successive points M, 1ST, etc., wi-ll be proportional to the partial ordi- 

 nates L Q, K K, etc. 



In the second quarter revolution, however, the crank will not only 

 be acted, upon by the full pressure of the steam, but also by the living 

 force of the reciprocating parts of the engine ; and the work done 

 will be represented by the trapezoid CBYH; the forces at succes- 

 sive points, as Y, "W, of the stroke being proportional to D V, E X, etc. 

 It is obvious, therefore, that in working without cut-off, the inertia 

 of the reciprocating parts of the engine has the effect to diminish the 

 amount of work done during the first half stroke, and to increase it 

 during the second ; this disturbance of the distribution reaching, in 

 the case here presented, the large irregularity shown in the ratio 1 : 3. 

 It has the further bad effect of producing a final strain on the 

 crank double of that which the full pressure of the steam would pro- 

 duce, while the initial strain is reduced to zero. 



But this property which makes the heavy piston engine unfit to be 

 worked with a full head of steam throughout the stroke., is precisely 

 the property which is needed in using steam expansively. 



