Compression, during Cooling of a Solid Earth. 147 



through 0°, and contracted in the vertical dimension only, 



... Z ' = ^\l + W)dz; 



= z+m*0dz, 



• /y>' 



dh 

 dz 



= 2z^yddz, neglecting E' 



Diagram of temperature-curve, adapted from Sir W. Thomson's paper. 



a ° jt 



7000°^ 



N the depth below the surface = x. N P the excess of temperature 

 above the temperature of the surface —v. Q the excess of the melt- 

 ing temperature above that of the surface = V. P n the temperature 

 through which matter at the depth x has cooled = 6. O a = a. 



Let x be the depth of the layer under consideration from 

 the surface at 0. Then, using Sir W. Thomson's notation, 

 we shall have 



&=Y-v, 

 or i r* x x2 



e=Y--\ e-a*dx; 



V 



V being the temperature of solidification, and b = j — — ; and 



a a depth, which may be determined at once (without know- 

 ing the conductivity or the time of cooling) by means of the 



dv 2V* -Jl 

 formula ~r — — ^=e <#, from the temperature-rate near the 

 ax a j^/rjr 



