Saturated Steam expressed by a New Formula. 5 



In the year 1850, M. Clausius published a formula by means 

 of which the density of saturated steam may now be calculated. 

 This formula is given in the Philosophical Magazine for August 

 1851, at page 107. It contains two quantities which are super- 

 fluous, as they are not found in the new formula above given. 

 Nevertheless the results yielded by M. Clausius's formula for 

 volume, are nearly identical with the results of the new formula 

 for volume. M. Clausius deduced his formula from a theory of 

 the moving force of heat originating with M. Carnot in 1824, 

 and improved by M. Clapeyron in 1834. 



The formula of M. Clausius is an expression for the latent 

 heat of saturated steam relative to water (L), in terms of Joule's 

 mechanical equivalent for a unit of heat (J), absolute tempe- 

 rature (a + t), excess of volume of a unit weight of saturated 

 steam above volume of same weight of water (V—v), and the 



d? 



differential coefficient -j-. If v be omitted as insignificant and 



within the errors of observation, the formula of M. Clausius 

 may be written thus, 



d? 

 The value of -j- obtained from the new formula for pressure 



1+ -j . If this value be sub- 



stituted in the formula of Clausius, we shall have 



L=]( 8 -M)VxP«(l+g = }.«PV(l + -) ; 



i. e. y 



In the preceding equation the variables L and PV represent 

 ratios to constants L and P V . The actual latent heat is 

 represented by L x L , and the actual expansive force by 

 PV x P V . On substitution of these values in this equation, 

 we get 



L x L = j • *a PV x YoV p- n ; 

 or separating variables from constants, we have 



L i ««P.v opv 



J L n 



