SECT, iv.] AND PROPORTIONS OF ENGINES. 153 



to half the atmospheric pressure to the line passing over the pulley ; then the 

 elastic force of the steam being unbalanced, the piston would rise till that elastic 

 force would be half the atmospheric pressure, or till the piston would be at double 

 its former height. Now conceive the steam to be condensed, and the weight 

 removed from the pulley at the same instant, and the power of the descent, less 

 the power added to produce the ascent, will be one half more than by simply con- 

 densing steam of atmospheric elastic force ; and even this ratio may be increased 

 by adding the weight in portions to the line over the pulley, and diminishing the 

 elastic forces of the steam. This is the principle of the expansion engines of 

 Watt and Hornblower. 



300. It has been assumed that steam at least of atmospheric elastic force was 

 generated ; but this is not a necessary condition, for it frequently occurs that 

 engines work with steam of less elastic force. The same mode of illustration will 

 show whence this happens. Let half the pressure of the atmosphere on the piston 

 be balanced by a weight over a pulley. Then, on the application of heat, steam of 

 half the atmospheric elastic force would be generated, and raise the piston to 

 double ,the height that it would be raised by steam capable of supporting the 

 atmospheric pressure ; consequently, on its being condensed, the descending force 

 will be half the atmospheric pressure acting through double the height ; and the 

 steam produces the same effect as before. 



We shall have occasion to show the value of this principle in regulating the 

 power of atmospheric engines. 



301. In all these illustrations of the modes of obtaining power from steam, 

 I have taken the atmospheric pressure as one of the active forces ; in some cases 

 steam pressure is employed in practice, but the difference in employing this or 

 that kind of pressure is dependent on other circumstances than its force, such as 

 the rate of cooling and the like, and does not affect the relations of the forces of 

 steam acting with only small alterations of temperature. 



OF COMPUTING THE PoWER OF STEAM TO PRODUCE RECTILINEAR MOTION. 



302. If we suppose the force of steam in a cylinder to be equal to the mean 

 pressure of the atmosphere, we may easily compute the power of the steam of a 

 given quantity of water, as far as it possibly can be obtained by condensation, and 

 not acting expansively. Thus the space occupied by steam of 212 is 1711 times 

 the bulk of the water which produces it, (art. 120.) when it is capable of resisting 

 the mean pressure of the atmosphere, and that mean pressure is 2120 Ibs. on 

 a square foot; hence 1711 x 2120 = 3,627,320 Ibs. raised 1 foot by the 

 steam of a cubic foot of water. Or multiplying by the area of a circle whose 



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