264 OUTLINES OF NATURAL PHILOSOPHY. 



356. If b be the length of the stroke of the pis- 

 ton, r the radius of the cylinder, and h the height 

 of the column of water which balances the pres- 

 sure of the atmosphere, K r* h is the moving force, 

 and its momentum is <x r* h x b. If the radius of 

 the piston of the pump worked by the beam be r' 9 

 d the depth of the water, and li the height to 

 which it is raised at one stroke, *r r d h' will be 

 the momentum of the resistance : then, in order 

 that the machine may work, r 2 bh> r' 2 d h'. 



To a complete theory of the steam engine, much 

 more is necessary than the knowledge, that r 2 b h 

 is greater than r' 2 d h' ; for the rate of working de- 

 pends on that excess, and must be determined as 

 in the problem, 186. The weight of the pump 

 rods must be included, and also the effect of fric- 

 tion. 



It is here supposed, that a perfect vacuum is produ- 

 ced in the cylinder by the jet of cold water. This, 

 however, is not the fact, for by the alternations of 

 the heat and cold to which the cylinder is exposed, 

 it can neither acquire the heat necessary to the full 

 elasticity of the steam, nor the cold necessary for 

 its complete condensation. On this account, the 

 effect of the machine falls much under the compu- 

 tation. 



357- When the cylinder is full of steam, if a 

 valve be opened, by which the steam is allowed to 



escape 



