We have thus demonstrated that the temperature of the stratum C cannot be the same as that of B. We have also demonstrated that it cannot be colder than B. We must therefore believe that C is hotter than B. This proves that the stratum immediately beneath that stratum to which the observations have extended must be hotter than it. Thus, though the stratum below the bottom of the hole lies beyond the reach of our actual observation, we have, nevertheless, been able to learn something with regard to its temperature. Having established this much, we can continue the same argument further; indeed, it would seem that we can continue it indefinitely, so long as there is a succession of such strata. Underneath the stratum C must lie another stratum D. But we have shown that C must be hotter than B, and precisely the same argument that has proved this will prove that D is hotter than C. Underneath D comes the stratum E, and again the same argument will apply. Inasmuch as D is hotter than C, it follows that E must be hotter than D. These three strata, C, D, and E, are all beyond the reach of the thermometer, we know nothing of their temperatures by direct observation; but none the less is the argument, which we are following strictly, applicable. Thus we obtain the important result that in the crust of the earth the temperature must be always greater, the greater the depth beneath the surface. We have seen that the rate of increase of temperature with the depth is about 80° for the first mile, and we deem it probable that the rate of increase may be maintained at about the same for the second mile. But we do not suppose that the rate of increase mile after mile will remain the same at extremely great depths. It may perhaps be presumed that there must be some increase of temperature all the way to the earth’s centre; but the rate of increase per mile may change as the centre is approached. The point of importance for our present argument is, that the temperature of the earth must increase with the depth, though the rate of increase is quite unknown to us at depths greatly beyond those which the thermometer has reached. It is easy to see that the conditions prevailing in the earth’s interior might greatly modify any conclusion we should draw from observations near the surface. Our argument has been based on the laws of heat, as we find them existing in matter on the surface of the earth submitted to such ranges of different physical conditions as can be dealt with in our laboratories; but at such excessively high temperatures as may exist in the earth’s interior the properties of matter may be widely different from the properties of matter as known to us within the temperatures that we are able to produce and control. The enormous pressure to which matter in the interior of the earth must be subjected should also be mentioned in this connection. It is wholly impossible to produce pressures by any