426 Hydrodynamics. 



for the same weight at a lower temperature and less elastic. 

 But while the steam is raised to a higher temperature, it becomes 

 also more dense ; so that considerably more weight is necessary 

 to fill the same cylinder, than when its temperature is lower. 

 This second circumstance, therefore, requires in the same ma- 

 chine, a greater quantity of fuel, according as the temperature 

 of the steam is increased ; so that it only remains to ascertain 

 whether this increase of fuel is, or is not, compensated by a 

 corresponding increase of elastic force. Now this point is easi- 

 ly decided, if we reflect that the vapour of water and that of 

 other liquids, so long as they exist in a state of vapour, are sub- 

 ject to the same physical laws of compression and dilatation, as 

 the permanent gases. Accordingly, let w represent the weight 

 of a cubic inch of aqueous vapour, such as it would be, if it 

 were capable of being reduced to the temperature of melting 

 ice, and under a barometric pressure of 29,92 inches ;t and let 

 w' represent the weight of an equal volume of the same vapour, 

 as it would really exist at another temperature /, and with the 

 elastic force jP, equal or inferior to the maximum density be- 

 longing to this temperature. If we put t' =. t 32, or the 

 number of degrees distant from freezing, according to the laws 

 470. of the dilatation of the permanent gases, we shall have 



wF 

 a/ 



29,92 (1-H'. 0,00208) 



All the experiments of philosophers upon aqueous vapour, and 

 those of Despretz upon the vapour of several other liquids, 

 show that this formula is really applicable to them ; so that we 

 may safely employ it for the purpose under consideration. Now 

 calling c' the quantity of heat necessary to convert 1 5,5 grains 

 TroyJ of water, in a liquid state, at $2, into vapour, having the 

 temperature t 1 ; c' w f will be the absolute quantity of heat neces- 

 sary to form the weight a/ of such a vapour ; and consequently 

 if n be the number of cubic inches contained in the cylinder 

 to be filled, the whole quantity of heat necessary for this pur- 

 pose, will be 



c' n w F 



29,92(1 -|- t' . 0,00208) 



t Or, more accurately, 15,444 grains, or one gramme. 

 { Equal to 0,76 of a metre. 



