510 Prof. John Milne— On the Form of Volcanos. 



heat flows through rocks is a subject of which we have little or no 

 personal experience, and about which we cannot therefore form any 

 prima facie opinion. 



To give some idea of what actually must take place, the case of 

 an infinite mass of rock heated from a plane surface of constant 

 temperature has been taken as the simplest case for which calcula- 

 tions can be made. The temperature of the plane is taken at 2000° 

 Fahr. ; and the time during which conduction has taken place at 

 2000 years, the object being to find the temperature at various 

 distances from the hot plane in the surrounding rock. We might 

 consider the hot surface to be spherical or a vertical cylinder, but 

 the simple case of a plane surface kept constantly at a high tempera- 

 ture is easier to calculate, and at the same time sufficiently illustrates 

 my idea. 



If the isothermal surfaces are parallel planes, and x is measured 

 at right angles to these planes, then an element of rock of unit area 

 and thickness dx, if it is at a temperature v at the time t, receives 

 heat when increasing in temperature dv ; — 



CD. dv. dx in the time dt, where CD. is the capacity for heat of 

 the rock. 



But through one face it receives heat by conduction in the time 

 dt, and through the other face it loses by conduction, and the dif- 

 ference is — 



_ d 2 v . 7 

 K.-j-o dx. dt. 



dx~ 



K being the conductivity, and hence — 



CD. -rr dx=K -r-y dx 



dv K. d 2 v 

 dt = 7UJ.~dx 2 



The initial conditions are that where x=0, the temperature v is 

 constant ; when t=0, then v=0 everywhere except where sc=0, and 

 the above equation leads under these circumstances to the result — - 



dx JTTkt. 



This equation cannot be integrated in finite terms, but the follow- 

 dv 

 hag table of values for — — has been calculated; t being 2000 



years, K as equal to 400 in Foot, Year, Fahrenheit units, 1 and V Q 



the temperature of the melted rocks which fill the plane fissure, 

 being at least 2000° Fahr. 



1 For this value I am indebted to the experiments of Professors Perry and Ayrton, 

 " On the Conductivity of Stone," Phil. Mag. 1878. 



