24 Ji. A. Daly — Mechanics of Igneous Intrusi 



ion. 



Least Squares. For higher values of -= the value of the 



2 V «t 

 integral can, in many cases, "be computed by developing it into 

 a series. Kelvin's value for k is peculiarly favorable for such 

 computation and the corresponding units have been used by 

 the writer in the calculations. 



Let b = 2200° F. (about 1200° C.) ; c = 400° F. (about 200° 

 C.) ; t ~ 1, 4, 16, and 100 years; and let x have the different 

 values shown in the left-hand column of the following table 

 (I) The corresponding temperatures are shown in the other 

 columns. 



Table I. —Showing values of u when a = 400 and 



X 



t = 1 year. 



t = 4 years. 



t = 16 years. 



t = 100 ye; 



0' 



2200° F. 



2200° F. 



2200° F. 



2200° i 



10' 



1703 



1947 



2074 





20' 



1263 



T703 



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 temper- 

 ature 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 tempera- 

 ture-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 It decreases rapidly with rise of tempera- 

 ture in rock. The experiments of Weber, Bartoli, Roberts- 

 Austen and Rucker, and Barus show that the specific heat of 

 rock averages about "180 at 20° C. and increases regularly with 

 rise of temperature, so that at 1100° C. the specific heat averages 

 about '280.* It follows that thermal diffusivity in rock decreases 

 with rising temperature even faster than the conductivity 

 decreases. At 1100° C, k may, indeed, be only 



/•180 293 1-000 \ 



V280 1373 -973 / 



141 



or less than one-seventh, of the diffusivity at 20° C. For rock 

 heated to 1000° or 1200° C. k is, thus, probably not much more 

 than 60 in the Kelvin system of units. 



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

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



