228 SEE— TEMPERATURE, SECULAR COOLING [April 20, 



40 miles, or about one tenth of that found for the 1000 milHon year 

 period. The short period thus gives rapid rise of temperature near 

 the surface, while the long periods give slow augmentation of tem- 

 perature extending to great depths. All the Fourier curves, those 

 for the rate of increase as well as for the temperature, become asymp- 

 totic to certain lines, as shown in the diagrams. 



We have already considered how to pass from these Fourier 

 solutions to a double solution which will take account of the increase 

 of temperature downward at the initial epoch. This method of 

 superposed or multiple solutions may be applied to all cases, but it 

 has not seemed worth while to consider any case except that with a 

 period of 10 million years and a surface temperature of 2000°. 

 Whether we use the pure Fourier solution, or the compound produced 

 by superposing two solutions of different period, it appears that the 

 actual temperature increases at a nearly uniform rate for a depth of 

 more than 40 miles, after which it is probable that the approximate 

 elliptical law holds true to the center of the planet. 



The temperature ellipse is not imagined to extend into the cooled 

 crust, but to begin at the lower boundary of this layer. As we have 

 treated of a superposition of two solutions of different periods, so 

 also we might have compounded three, four or more solutions, with 

 as many independent periods, which would enable us to represent any 

 steady and continuous law of temperature within the earth. If this 

 procedure is justifiable, it will follow that the uniform rise of tem- 

 perature is nearly maintained for at least a tenth of the radius. 

 Under the circumstances it is not to be hoped that any deviation from 

 the uniform rate of increase near the surface will ever be discovered 

 from experimental measurements of underground temperature. And 

 observations indicating unequal rates at various depths are to be 

 explained by the unequal conductivity of the different layers of the 

 crust, and by fissures filled with hot lava during earthquakes of past 

 geological ages. 



From Fig. D, in the diagram, we see the principle of the multiple 

 solution illustrated. The difference between the middle and lower 

 curve is the effect of an additional 10 million years. This depression 

 with changed sign should therefore be added to the simple Fourier 

 solution to give the temperature curve under the hypothesis that 



