Mr. W. J. M. Rankine on the Mechanical Action of Heat. 247 



Through the point C, therefore, draw a straight hne CT, 

 touching the locus of Z ; then the ratio (63) is a maximum at 

 the point of contact T, and the abscissa at that point represents 

 the ratio of expansion required. 



Example. 



(38.) To exemplify this method^ let us take the following data. 



Greatest pressure in the cylinder P, = 20 lbs. per square inch, 

 = 2880 lbs. per square foot. 



The corresponding value of Vj is 20*248 cubic feet per pound 

 of steam. 



To obtain this initial pressure in the cylinder of a Cornish 

 engine, it wdl be necessary to have a pressure of about 50 lbs. 

 per square inch in the boiler. 



F, resistance not depending on the useful load =2 lbs. per 

 square inch, =288 lbs. per square foot, =y%Pi. 



In, amount of down strokes, = 4800 feet per horn- ; being the 

 average speed found to answer best in practice. 



To estimate h, the annual cost of producing one pound of 

 steam per hour, I shall suppose that the engine works 6000 

 hours per annum ; that the cost of fuel is one penny per 100 

 lbs. of steam* ; that the cost of boiler for each pound of steam 

 per hour is 0-016 ton, at £27, =£0-432; and that the interest 

 of capital is five per cent, per annum. Hence h is thus made up : — 



Fuel for 6000 lbs. of steam at 0-Olrf. . . £0-2500 

 Interest on £0-432, at 5 per cent. . . . 0-0216 



^ = £0-2716 



Estimating the cost of the engine at £250 per square foot of 

 piston, we find A = 5 per cent, per annum on £250 = £12-5, and 



'^=0-0217; ^=5-144. 

 a: a;Vi 



The line BOA, then, is to be drawn so that its ordinates are 



P, *- 10*' 



The point C is taken on this line, at -j-~- =5-144 divisions of 



the axis of abscissae to the left of OY. 



The tangent CT being drawn, is found to touch the locus of 

 Z at 2-800 divisions to the right of OY. 



Tlien .s = 2*800 is the ratio of expansion sought, corresponding 

 to the greatest oeconomy. 



• TliiB estimate is made on the supposition that coals, capable of pro- 

 ducing uinc times their weight of steam, are worth about 16*. 9rf. per ton. 



