324 PROCEEDINGS OF THE AMERICAN ACADEMY 



The value C^^ A4 is larger than the solid specific heats at constant 

 pressure for the same interval (Table III.), and hence a fortiori larger 

 than the corresponding solid specific heats at constant volume, which 

 are as yet indeterminable. § 9. 



With this result, a direct computation based on equation (9) above 

 may be compared. Integrating betvreen 22° and 38° (Table VI.), — 

 i. e. betveeen the specific volumes 1.02860 and 1.04167, — the expan- 

 sion energy is found to be 2.56 to 2.42 g. cal., according as the mo- 

 lecular force at the beginning or the end of the interval is inserted. 

 The total energy imparted within this interval is .506 X 16- Hence 

 the purely thermal energy per degree between 22° and 38° has the 

 mean value of .35, or about two thirds the specific heat at constant 

 pressure. 



Compared with the preceding datum, .44, this result is considerably 

 too small ; i. e. the expansion energy applied is about twice as large 

 as its true value. I might point this out as an indication of the diffi- 

 culty encountered in deducing internal pressure from the curvature 

 of the isothermals (§ 11) ; but the true nature of the discrepancy is 

 an error in principle, since the change of internal pressure with tem- 

 perature must be radically different when the body is kept at constant 

 external pressure in one case, and at constant volume in the other. 

 Hence I do not regard the present result as conflicting with § 12. 



15. Melting Point and Pressure. — The data of Tables I. and H. 

 suflfice for a preliminary computation of this value. Using the nota- 

 tion of Clausius (Warmetheorie, Chap. VII,, § 2), Table I. shows that 

 at T = 50° (melting point, nearly), a — r = .0763. From Table II. 

 the mean value (0°-50°) of r' is 24.7, the minimum value 23, and 

 the maximum 27. Hence, if pressures be expressed in atmospheres 

 instead of dynes per sq. cm., the mean relation of melting point to 

 pressure is d T/ dp = .024 ; or, more clearly, 



.025 >dTldp > .022, 



where the upper limit is probably more nearly correct. This value 

 lies well within the margin of data (.020 to .036) thus far in hand, 

 and found with wax, paraffine, spermaceti, and naphthalene. From 

 a perusal of my work on the continuity of solid and liquid,* it appears 

 clearly, however, that a more accurate value of o? Tdp is obtainable 

 from direct experiment, from which a value for latent heat may 

 then be computed by inverting the thermodynamic ecjuation. 



* Am. Journal, Vol. XLII. p. 144, 1891. 



