738 



dv, = — {d.v, + dy,, + dz,) (24) 



while furtlier tlie well known relations: 



hold for the liquid phase. 



On introduction of (12), {2^), and (25) we get from (28). 



iv, 



(26) 



->i,) dT = dp ( ] + — [(Xx— p) d.v, + I 



+ ( J'y-i^) '(y.'/ + (^c -/') c/^. + Tc^i/^ + ^^dz, -I- Ay.6-y]'* 

 We can now put: 



V. -n. = Y - ■' ' ^'^^ 



Tn this we can call the "heat of melting" r, by which that (juantity 

 of heat is to be understood which must be added to convei-t the 

 unity of mass from the solid to the liquid phase, without the con- 

 dition of the two phases changing for the rest. We then get: 



d2' = ^ f- - i) dp + -^ [{K.-P) d.v, + (yy-p) dyy + I 



-f {Z,-p) dz, + Y-d,j, + Z^dz., + Ay.cyj ) 



When the only deformative force is the hydrostatic pressure, we 

 "et the known formula of Thomson and Clausius, since then the 

 following eipuitions generally hold : 



' Ax- -jt> = U Yy-p = Z,—j>=zOï 



K = Z, — ^y — ^ 



(29) 



7' / 1 1 

 dT=^{ ]dp (30) 



If on the other hand dp = 0. we get : 



dT=: — [{X,-p) d.v, -f {r,~p) Jny + {Z,-p) dz, -f 



r.Q, \ . (31) 



-j- Y~dy~ + Z:,dzjc + Xydxy] 

 Since the form between square brackets, provided with the negative 

 sign, represents the work performed in the deformative forces, with 

 the exception of the pressure p, a deformation will bring about a 

 lowering of the freezing point, when this work is positive. 



5. We shall now assume that the initial stale (for which we put 

 «'■j) y<ii 2:, ?/:, 2a, '^'y equal to zei-o) is to be considered as without 



