Proceedings of the American Philosophical Society Held At Philadelphia for Promoting Useful Knowledge 46
Proceedings of the American Philosophical Society Held At Philadelphia for Promoting Useful Knowledge 46
American Philosophical Society
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. . F*, one may approximate the true curve asymptotically near the surface, and carry the determination to any desired depth. In our present numerical work we have thought it sufficient to take Tj i= 10 million years, and F' = F' = 2000®. By carrying this process far enough we may obtain a multiple solution which is almost absolutely rigorous, and it will include all the effects of rising tem- perature beneath the surface as well as the uniform temperature embraced in the original solution of F...ourier. The principal difficulty in extending the method to the propagation of heat at great depths is the uncertainty respecting the original law of temperature within the earth, before encrustation began. But it appears clearly and un- mistakably that the true curve of temperature is much steeper than that resulting from the simple Fourier solution. At greater depths the steepness increases more and more, till it finally takes the form of the arc of an ellipse, as already pointed out. The curve is thus con- cave near the surface, and convex at great depths, so that it has a point of flexure, probably at no very great depth, but the exact loca- tion cannot be determined.
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