Mr. W. J. M. Rankine on the Mechanical Action of Heat. 245 



Supposing one pound of the best Welsh coals to be capable 

 (as found by Mr. Wicksteed) of evaporating 9'493 lbs. of water 

 at the pressure in the boiler during the experiment F, then the 

 duty of a Cornish bushel, or 94 lbs. of such coals, in the cir- 

 cumstaaces of that experiment would be — 



By theory .... 88,288,000 ft. lbs. 

 By experiment . . . 90,801,000 ... 



Difference . . . + 2,513,000 ... 



(Economy of Single-acting Expansive Engines. 



(37.) By increasing the ratio of expansion in a Cornish engine, 

 the quantity of steam required to perform a given duty is dimi- 

 nished ; and the cost of fuel and of the boilers is lowered. But 

 at the same time, as the cylinders and every part of the engine 

 must be made larger to admit of a greater expansion, the cost of 

 the engine is increased. It thus becomes a problem of maxima 

 and minima to determine what ratio of expansion ought to be 

 adopted under given circumstances, in order that the sum of the 

 annual cost of fuel, and the interest of the capital employed in 

 construction, may be the least possible as compared with the 

 work done. 



That this problem may admit of a definite solution, the fol- 

 lowing five quantities must be given : — 



Pj, the initial pressure in the cylinder. 



F, the resistance not depending on the useful load. 



In, the amount of the length of the effective strokes made in 

 unity of time. 



h, the annual cost of producing unity of weight of steam in 

 unity of time, which consists of two parts ; the price of fuel, and 

 the interest of the cost of the boilers. 



k, the interest of the cost of the engine, per unit of area of 

 piston. 



Hence the annual expenditure to be taken into consideration, 



of steam, that when an elastic fluid expands without jjcrfonning work, by 

 rushing through a narrow orifice, so that all the power developed by the 

 expansion is exi, uded in agitating the particles of the fluid, and extin- 

 guished by their friction, then the heat produced by that friction partially 

 compensates for the heat which disappears during the expansion. Hence 

 in a Cornish engine, when the steam is wire-drawn so as to be at a lower 



Cressurc in the cylinder at the commencement of the stroke than in the 

 oiler, the friction of its particles causes its temj)crature, and therefore its 

 volume in the cylinder, to be greater than those corres])onding to satura- 

 tion at the given pressure, u])on which the calculations in the text are 

 founded ; and hence a somewliat less weight of steam than that computed 

 by the formulae nuifices to perform a given amoimt of work. 



