70 Arthur Holmes — -Radio-activity . 



We may now proceed to apply these formulae to different cases with 

 the data already provided. 



Case 2 : Acid Rock.— Here a = 52 x 10-7 and 9 = 700° C. This 

 eertainly does not reproduce the actual conditions, for d, the half- 

 value depth, is only reached at about 13 km., so that rock of basaltic 

 -composition would only be reached at a depth of 25 km. Again, the 

 value of k adopted for acid rocks is too high to carry down to such 

 depths, and the temperature obtained is insufficient. 



Case 3 : Basic Hock— (a) Here « = 2-1 x 10-7 and 6 = 1580° C. 

 if the temperature gradient 000032° C. per cm. be used in equation 6. 



(b) If, however, we use the gradient appropriate to basic rocks, 

 viz. 0-00048° C. per cm., then a becomes T4x 10 _ 7 and the maximum 

 temperature is 3560° C. 



(c) If now this result be applied to the sub-oceanic rocks it 

 becomes necessary to make, as before, a correction for the smaller 

 content of the radio-active elements under the oceans than that under 

 the continents. Taking these contents respectively as 1 : 2/3, then the 

 gradient due to radio-activity is only 0-00032° C. per cm., so that the 

 temperature is just what we obtained at first, 1580° C. Any remaining 

 part of the gradient would then, as already stated, be attributable to 

 some other source of heat, which would correspondingly increase the 

 temperature in depth. 



Case If : Average Rock.— {a) Here a = 4'0 X 10 -7 and 6 = 800° C. 

 when a temperature gradient of 0-00032° C. per cm. is used. 



(b) Using the more appropriate gradient of 0-00038° C. per cm., 

 the value of a is found to be 3-4 X 10-7 and 6 becomes 1200° C. 



The latter result is the most probable yet obtained and deserves 

 further attention. The average radio-thermal conditions for the earth 

 seem to lie between case 1 for the continents (temp. 1000° C.) and 

 case 3(a) or 3(c) for the oceans (temp. 1580° C.). Case 4 (b) thus 

 fairly represents the temperature requirements. At a depth of 

 50 km. the temperature would be 1100° C. (equation 9) according 

 to the average conditions of case 4 (b). At the same depth the 

 temperature under the oceans, case 3 (c), would be 1400° C, and 

 under the continents, case 1, 900° C. Case 4 (b) may therefore be 

 accepted as a fair representation of the earth's average conditions, 

 stated in a way suitable for mathematical treatment. The data on 

 which it is based are as follows : — 



k, thermal conductivity . . = 0-005 C.G.S. units. 



ddjdx, temperature gradient . = 00038° C. per cm. 



A, total heat production per 



c.cm. at the surface . =26-9 X 10 _14 calories per sec. 



It must be carefully noticed that these data do not represent the 

 facts at any actual place. They are simply an attempt to express the 

 facts of rock distribution, both superficially and in depth, in a single 

 average capable of being treated exponentially. I have tried various 

 other more direct methods, but without success. The problems which 

 await solution cannot be attacked except by an indirect method such 

 as the above, which has the conspicuous advantage of giving results 

 in harmony with volcanic phenomena. 



