306 The Fusion Constants of Igneous Rock. 



temperatures are 24 and 16 respectively. The coincidence of 

 results in both of the independent constructions (Tables II L 

 IV.) is in a measure accidental. 



15. The Relation of Melting-point to Pressure. — The first and 

 second laws of thermodynamics leid to the equivalent of 

 James Thomson's fusion equation, which in the notation of 

 Clausius* is dT/dp=T(c—T)/~Ejr r ; where T is the absolute 

 melting-point, a — r the difference of specific volumes solid 

 and liquid at T, / the latent heat of fusion, and E Joule's 

 equivalent. 



Combining the present. Series I. of thermal measurements 

 with the former Series III. of volume measurements, I ob- 

 tain at 1200°, since T=1470°, a- t = -0394/2'72 (where 2'72. 

 is the density of the solid magma at zero), and r' = 24. 



(?) =-° 21 ; 



\<Wl200 



and at 1100°, since T= L370 3 , a— r= 0385/2*72, and ^ = 16, 



WAioo 

 Similarly, combining the present (heat) Series II. with the 

 former (volume) Series IV., at 1200°, since <r— r = , 0352/2 , 72, 

 and / = 24, 



(?) - 019 ; 



and at ,"1100°, since <r-T = -0341/2"72, and /=16, 



(?) =-<^. 



\dphw 



Hence the probable silicate value f of dT/dp falls within the 

 margin ('020 to *036) of corresponding data for organic sub- 

 stances (wax, spermaceti, paraffin, naphthalene, thymol). I 

 may, therefore, justifiably infer that the relation of melting- 

 point to pressure in case of the normal type of fusion is 

 nearly constant irrespective of the substance operated on, and 

 in spite of the enormous differences of thermal expansibility 

 and (probably) of compressibility. And in the measure ill 

 which this is nearly true on passing from the carbon com- 

 pounds to the thoroughly different silicon compounds, is it 



* Warmetheorie, i. p. 172 (1876). 



t For reasons to be stated elsewhere, m =«-|--O25i> (where m is the 

 melting-point in °C. at the pressure p atmospheres) will be assumed in 

 making geological application of the above data. 



