CORRELATION OF ISOGEOTHERMAL SURFACES 43 
subject to the condition 
dv 
k— = h(v — 4) (2) 
On 
which represents the loss of heat from the surface of the earth at any point on 
the plain or mountain slope. 
In these equations, y=temperature at point x, 2; v.=temperature of air 
in contact with the surface of the ground at the given point; w=number of 
calories of heat generated per second per cubic centimeter by radioactive 
processes; k =coefficient of thermal conductivity of the rocks; h =coefficient 
of emissivity ; 7 =numerical magnitude measured inward along the normal to 
the surface of the ground. 
Now let us put, also, »=annual mean temperature of soil just beneath 
the plain surface of the ground; a=temperature gradient beneath the plain; 
a’ =temperature gradient in the air along the mountain slope. 
61 = (a — a’) /a 
C2 = (2 = Do) /a 
(3) 
H=elevation of top of hill referred to level of plain; b=half-breadth of hill 
at elevation # nearly one-half the height of the hill; d=distance from apex 
of hill to point on contour at elevation k above the plain. (See Fig. 9). 
B = w/2k(a — a’) 
h (1+ Bh) 
= ae (4) 
H (1+ 6H) 
The quantity 8 is dependent on radioactivity. Eq. (4) is an arbitrary as- 
sumption introduced for convenience in handling the equations. 

Fig. 9. Transverse section of imaginary hill or mountain. 
Without going through the necessary steps of integration of Eqs. (1) and 
(2) and the subsequent transformation of the integrals in order to take into 
account the cross-section of the mountain, we write at once the equation to 
the contour of the transverse section, 
(g¢+ H+ 4d) 
2(1 oe Bz) + Hd(i ae ate Gab ay ae = 0 (5) 
187 
