286 PROFESSOR WILLIAM THOMSON ON THE 
57. If we suppose » and L to be known for any temperature, equation (32) 
enables us to determine the value of = for that temperature; and thence de- 
ducing a value of d7, we have 
ac ~~ dp . ; : : ‘ : (35) ; 
which shews the effect of pressure in altering the “ boiling point” if the mixed 
medium be a liquid and its vapour, or the melting point if it be a solid in contact 
with the same substance in the liquid state. This agrees with the conclusion 
arrived at by my elder brother in his Theoretical Investigation of the Effect of 
Pressure in Lowering the Freezing Point of Water.* His result, obtained by taking 
as the value for p, that derived from Table I. of my former paper for the tem- 
perature 0°, is that the freezing point is lowered by ‘0075° cent. by an additional 
atmosphere of pressure. Ciausius, with the other data the same, obtains -00733° 
as the lowering of temperature produced by the same additional pressure, which 
differs from my brother’s result only from having been calculated from a formula 
which implies the hypothetical expression J ; — ;for yu. It was by applying equa- 

‘ Sed: : : 
tion (33) to determine Pa! for the same case, that Cuausius arrived at the curious 
result regarding the latent heat of water under pressure, mentioned above (( 45). 
58. Lastly, it may be remarked that every quantity except h, which appears 
in equation (33), is known with tolerable accuracy for saturated steam through a 
wide range of temperature ; and we may therefore use this equation to find A, 
which has never yet been made an object of experimental research. Thus we 
have 
———_ — — |—_ 4+ ¢ 
Hey SAB hen dp (4 
eS SEEN sais, dt ) 
For the value of y the best data regarding the density of saturated steam 
that can be had must be taken. If for different temperatures we use the same 
values for the density of saturated steam (calculated according to the gaseous 
laws, and ReGNAvtt’s observed pressure from — taken as the density at 100°), 
the values obtained for the first term of the second member of the preceding 
equation are-the same as if we take the form 
Lp » f@l 
Rama eee, eb 
derived from (34), and use the values of » shewn in Table I. of my former paper. 
The values of —/ in the second column in the following table have been so calcu- 
* Transactions, Vol. xvi., Part y. His paper was republished, with some slight modifications, in 
the Cambridge and Dublin Mathematical Journal, New Series, Vol. V.i—Nov. 1850. 

