[ 239 ] 



XXXVI. On thi Mechanical Action of Heat. jBy William John 

 Macquorn Rankine, C.E., F.R.SS. Lond. and Edinb. ^c. 

 [Concluded from p. 185.] 

 [With a Plate.] 

 On the Power and (Economy of Single-acting Expansive Steam- 

 engines, being a Supplement to the Fourth Section of a Paper 

 ' On the Mechanical Action of Heat^.' 



(34.) ^I^HE objects of this supplementary paper are twofold : 

 A first, to compare the results of the formulae and 

 tables relative to the power of the steam-engine, which have been 

 deduced from the dynamical theory of heat, with those of expe- 

 riments on the actual duty of a large Cornish engine at various 

 rates of expansion ; and secondly, to investigate and explain the 

 method of determining the rate of expansion, and, consequently, 

 the dimensions and proportions of a Cornish engine, which, 

 ^\'ith a given maximum pressure of steam in the cylinder at a 

 given velocity, shall perform a given amount of work at the least 

 possible pecuniary cost, taking into account the expense of fuel, 

 and the interest of the capital required for the construction of 

 the engine. 



This problem is solved with the aid of the tables already 

 printed, by drawing two straight lines on a diagram annexed to 

 this paper (Plate III.). 



The merit of first proposing the question of the oeconomy of 

 expansive engines in this definite shape belongs, I believe, to the 

 Artizan Club, who have offered premiums for its solution ; having 

 done so (to use then- own words) " with a view to enable those 

 who, from their position, cannot take part in the discussions of the 

 various scientific societies, to give the profession the benefit of 

 their studies and experience." The 5th of April is the latest 

 day fixed by them for receiving papers ; and as this communica- 

 tion cannot possibly be read to a meeting before the 7th of April, 

 nor published until some months afterwards, I trust I may feel 

 confident that it will not be considered as interfering with their 

 design. 



Formula applicable to the Cornish Engine. 

 (35.) The equations of motion of the steam-engine in this and 

 the original paper are the same in their general form with those 

 of M. de Pambour. The differences consist in the expressions 

 for the pressure and volume of steam, and for the mechanical 

 effect of its expansion ; the former of which were deduced from 

 a forrimla suggested by peculiar hypothetical views, and the 

 latter from the dynamical theory of heat. 



♦ Read to the Royal Society of Edinburgh, April 21, 1851. 



