* 108. In 1849 James Thomson made a very remarkable application of Carnot’s reasoning, the first of a series of such applications which have since done immense service in the extension of almost every branch of physics. He showed in fact that, because water expands in the act of freezing, _the melting point of ice must be lowered by pressure_. Sir W. Thomson in the same year verified this deduction, to its numerical details, by direct experiment. Trifling as the predicted and measured effect appears (one degree centigrade for each 2000 lbs. additional pressure per square inch), there can now be no doubt that it goes at least very far to explain the varied effects of the extraordinary plasticity of glacier-ice so beautifully made out by the direct measurements of Forbes. * 109. We have said that Carnot unfortunately based his reasoning on the assumed materiality (and therefore indestructibility) of heat. It therefore became a question of great importance to find how properly to adapt his methods to the true theory. James Thomson’s verified prediction had already given a correct and absolutely new physical result from Carnot’s principles. How then must we get rid of his false assumption? Clausius attempted this in 1850, but his method is based solely upon the observed fact that in general heat tends from hotter to colder bodies. This we know is not always the case, for a fine wire may be made red-hot by the current from a thermo-electric battery (of a sufficient number of pairs) where ice and boiling water alone are used to cool and heat the alternate junctions. Here heat certainly passes from colder bodies to a hotter one. Clausius, no doubt, several years later, extended his original statement, so as to make it stand thus:—Heat cannot _of itself_ pass from a colder to a hotter body. We do not consider even this sufficiently obvious for an axiom, were it certainly true, but, as will be seen presently, it is not. In fact the so-called axiom is constantly being violated, though on a very small scale, in every mass of gas. * 110. It was Sir W. Thomson[40] who (in 1851) first correctly adapted Carnot’s magnificently original methods to the true theory of heat; and it is especially noteworthy to remark how, even at that early time, he saw the full danger of attempting to lay down anything too definite on the subject. The following is the axiom he gives:— ‘_It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects._’ But he appends the following guarded note:— ‘If this axiom be denied for all temperatures, it would have to be admitted that a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or, in reality, from the whole material world.’ The full importance of this will appear presently.