JR. A. Daly — Mechanics of Igneous Intrusion. _ 23 



"Weber has found that 7c for gneiss at 0° C. is 0*000578 and 

 at 100° C. O000I16, showing a very great lowering with increase 

 of temperature.* In fact, through the interval 0°-100° C, 7c 

 seems to vary about inversely as the absolute temperature. f 

 If this law should hold to 1100° C. the conductivity of average 

 rock at 1100° falls to about 0*001 — nearly the value for water, 

 which is famous as a poor conductor. 



In the present connection the thermal diffusivity (V) of rock, 

 rather than its conductivity, is of first importance. If s = 

 specific heat and d = density, we have 



. A 

 s.d 



For rock at room temperature (20° C.) Kelvin assumed 400 as 

 the value of k when the unit of length is a foot, the unit of 

 time a year, and the unit of temperature one degree Fahrenheit. 

 This value is close to that which represents the average of the 

 determinations made for different rocks at room temperatures, 

 during the years since Kelvin wrote his famous essay.;); 



If k be assumed as 400 at all temperatures up to 1300° C, 

 it is possible to calculate the temperature gradient in the wall- 

 rock of a molten batholith at the end of specified periods of 

 time. For practical purposes the surface of contact may be 

 regarded as infinite ; let it further be considered as plane. 

 Under these conditions the following Fourier equation furnishes 

 the datum for calculating the temperature at a point a? feet 

 from the contact at the end of t years. § In the equation & = the 

 temperature of the magma ; c = the temperature of the wall- 

 rock assumed as initially uniform ; and u = the required tem- 

 perature. We have : — 



/ 



S Kt 



b + (c-b) -=- / e~' 3 ' 2 d/3. 



For values of — "—= which are less than 2*6 the value of the 

 2 \7 K t 



integral can be readily found from the table of the probability 



integral which appears in standard text-books on the Method of 



* Values taken from Landolt-Bornstein Phys.-Chemische Tabellen. Forbes 

 and Hall have proved analogous relations for iron and for magnesium oxide ; 

 cf. J. D. Forbes. Trans. Roy. Soc. Edinburgh, xxiv, p. 105, 1867, and E. H. 

 Hall and others. Proc. Amer. Acad. Arts and Sciences, xlii, p. 597, 1907. 



fCf. P. G. Tait, Eecent Advances in Phvsical Science, 2d ed., London, 

 p. 270, 1876. 



f Trans, Soy. Soc. Edinburgh, 1882. 



?! Cf. W. E. Byerly's Elementarv Treatise on Fourier's Series, Boston, 1893, 

 p. 86. 



