THERMODYNAMIC THEORY. 231 



whatever be the values of specific heat and conductivity. An effect of such 

 magnitude, produced by radio-activity or otherwise, is not to be lightly 

 assumed. It is perhaps more likely that the effect of these agencies is 

 largely confined to the superficial strata. 



Another possible explanation of the discrepancy respecting the tem- 

 perature-gradient is that the assumed density laws may not properly repre- 

 sent the variation of density near the surface. For, independently of any 

 special hypothesis, it is plain that in descending from the surface the den- 

 sity would tend to increase on account of the increase of pressure, and to 

 decrease by virtue of the increase in temperature; which effect controls 

 depends on the values of elastic modulus, coefficient of expansion, and 

 thermal gradient. 



Let the density p through its dependence on p and 6 be thereby a func- 

 tion of the distance s below the surface. Then 



but since 



this may be written: 



^=^(gp-Kar) (170) 



With the values K = 4X10", a = 2X10~^ used above, which appear to be 

 well supported by observation, this would be positive or negative accord- 

 ing to whether the gradient is less than or more than 1° in 30 meters, or 

 just about the observed value. If the gradient were greater than this there 

 would be at first an actual decrease of density from the surface downward, 

 because of the preponderant effect of temperature over pressure; if less 

 there would be an immediate increase in density such as is ihiplied in the 

 formulas (25) and (74). In the intermediate case, where Ka-jr = gp, as ap- 

 pears to be nearly realized at the present time, the density-curve would have 

 a horizontal tangent at the surface-point. It would be useful if a family of 

 such density-curves could be found, expressible in tractable analytic form, 

 and satisfying the conditions named in connection with equation (92), so 

 that the effect of such a modification could be determined, through a review 

 of the preceding theory with the appropriate changes. 



For a discussion of the bearing of these results on geological theorjr 

 reference must be made to the papers of Professor Chamberlin, to whom 

 the writer is deeply indebted, not only for the opportunity of co-operation 

 in this work, but for suggestion and assistance freely given during repeated 

 conferences. 



