SECT, i.] THE STEAM ENGINE. 33 



model of the double acting engine, with a new mode of forming the valves ; and, 

 Prony says, from merely seeing the exterior of a double acting engine when at 

 work. 1 



1790. R. PRONY. 



41. M. Prony is the author of one of the most extensive of the French works 

 on the steam engine : it forms a part of his ' Architecture Hydraulique,' which 

 commences in the first volume, and occupies nearly the whole of the second. 



M. Prony begins with the properties of caloric, and the tables of Bettancourt on 

 the force of vapour ; and from the latter constructs an empirical formula for cal- 

 culating the force of vapour at different temperatures. These are not a little 

 complex, considering their want of conformity with experiment. He then proceeds 

 to the description of engines as then constructed, and their parts ; which are illus- 

 trated by plates having figures on a large scale. When he arrives at the parallel 

 motion, the nature of the curve described by the extremity of the piston rod is very 

 fully investigated, with tables to show its variation from a straight line for a given 

 range in the curve. It is followed by the proposal of a method for determining the 

 diameter of the steam cylinder, which is little better than telling the artist to guess 

 at it, and correct his guess by an intricate formula. The part on the steam engine 

 terminates with a calculation of the effect produced by a given quantity of fuel, 

 where the time of combustion is certainly erroneously introduced. 



The rest of the volume is occupied by an analytical investigation of empirical 

 formulae for the expansive forces of elastic fluids and vapours at different tem- 

 peratures ; which has been rendered wholly useless by later researches having 

 shown the experiments to be inaccurate. 



It is remarkable that Prony had not acquired a knowledge of the advantage of 

 steam acting expansively ; though, when his second volume appeared, it had been 

 fifteen years a contested discovery in England. Of his labours it may be said, that 

 they afford the strongest evidence that mere mathematical talent is not sufficient 

 for the promotion of mechanical science, otherwise the principles of the steam 

 engine would not have remained to be investigated. 



1795. JOHN BANKS. 



42. Mr. Banks, in a work on mills published in 1795, has treated of the 

 maximum of useful effect in atmospheric steam engines. He considers the space, 

 or length of the stroke, the given quantity ; in which his investigation differs from 



1 Archit. Hydraulique, vol. i. p. 574. 

 E 



