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" those who, from their position, cannot take part in the discus- 

 " sions of the various scientific societies to give the profession the 

 " benefit of their studies and experience." As the author's paper 

 will not be published until some time after the date fixed by the 

 Artizan Club for receiving Essays, he expresses a confident belief 

 that it will not be considered as interfering with their design. 

 The problem in question is this ; given the following — 

 Pj, the initial pressure in the cylinder. 

 F, the resistance independent of the useful load. 

 I n, the amount of the length of the effective strokes in unity of 



time. 

 A, the annual cost of producing unity of weight of steam per 

 unit of time, which consists of two parts, cost of fuel and 

 interest of cost of boilers. 

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

 of piston. 

 It is required to determine the ratio of expansion s (and thence 

 the dimensions of the engine), such that the annual expense due to 

 interest and fuel 



hW + kA 



shall be a minimum as compared with the useful effect E. 

 This condition is fulfilled by making the ratio 



F 



hln + S 



a maximum. 



This problem is solved graphically, by drawing two straight lines 

 on a diagram, a copy of which is annexed to the paper on a scale 

 large enough for practical purposes. 



The following formulas serve to compute the dimensions of the 

 engine. 



Mean resistance of the useful load per square foot of piston : — 



R =— P,-F 



E 



Area of piston = A = :^— — 



