738 DEPARTMENT OF THE INTERIOR 



2 GEORGE V., A. 1912 



magma ; c = the temperature of the wall-rock assumed as initially uniform ; and 

 u = the required temperature. We have : 



x 



2Vd 



2 f ~/3 2 



u=b + (c-l) — r/ e dfi. 



o 



x 

 For values of — — t^.- which are less than 2-6 the value of the integral can be 



readily found from the table of the probability integral which appears in 

 standard text-books on the Method of Least Squares. For the higher values of 



x 

 ~ — the value of the integral can, in many cases, be computed by developing 



<& VKt 



it into a series. Kelvin's value for K is peculiarly favourable for such computa- 

 tion and the corresponding units have been used by the writer in the calculations. 

 Let & = 2200° F. (about 1200° C); c = 400° F. (about 200° 0.); t = l, 4, 16, 

 and 100 years ; and let x have the different values shown in the left-hand column 

 of the following table (XL VII). The corresponding temperatures are shown in 

 the other columns. 



Table XL VII. — Showing values of u when K = 400 and 





r 







"\ 



X 



t = 1 year. 



t = 4 years. 



t = 16 years. 



t = 100 years. 



0' 



2200° F. 



2200° F. 



2200° F. 



2200° F. 



10' 



1703 



1947 



2074 





20' 



1263 



1703 



1947 





40' 



683 



1263 



1703 





80' 



408-5 



683 



1263 





100' 



ca.400 



537 



1078 



1703 



160' 



400 



408-5 



683 





200' 



400 



ca.400 



537 



1263 



320' 



400 



400 



408-5 





400' 400 400 ca.400 683 



The table shows that, at the end of the first year, the temperature of the 

 rock is but slightly affected by the magmatic heat at a point 80 feet from the 

 contact, and that the temperature gradient for the 80-foot shell then averages 

 nearly 23° F. per foot. At the end of four years the temperature is but slightly 

 affected at a point 160 feet from the contact and the temperature-gradient is 

 about 11° F. per foot. 



But k cannot be nearly so great as 400 in the case before us. We have seen 

 that k decreases rapidly with rise of temperature in rock. The experiments of 

 Weber, Bartoli, Roberts- Austen and Riicker, and Barus show that the specific 

 beat of rock averages about -180 at 20° C. and increases regularly with rise of 

 temperature, so that at 1103° O. the specific heat averages about -280.* It 



* For references see J. H. L. Vogt, Christiania Videnskabs-Selskabets Skrifter, I. 

 math.-naturv. Klasse, No. 1, 1904, p. 40. 



