Our readers are no doubt familiar with a method which Euclid frequently adopts in proving his propositions. Starting with the supposition that they are not true, and reasoning upon this hypothesis, he comes to an absurd conclusion--hence he concludes that they are true. Now, we may adopt a method somewhat similar with regard to our principle, only instead of supposing it untrue, let us suppose it true. It may then be shown that, if it be true, under certain test conditions we ought to obtain certain results--for instance, if we increase the pressure, we ought to lower the freezing point of water. Well, we make the experiment, and find that, in point of fact, the freezing point of water is lowered by increasing the pressure, and we have thus derived an argument in favour of the conservation of energy. 119. Or again, if the laws of energy are true, it may be shown that, whenever a substance contracts when heated, it will become colder instead of hotter by compression. Now, we know that ice-cold water, or water just a little above its freezing point, contracts instead of expanding up to 4° C.; and Sir William Thomson has found, by experiment, that water at this temperature is cooled instead of heated by sudden compression. India-rubber is another instance of this relation between these two properties, for if we stretch a string of india-rubber it gets hotter instead of colder, that is to say, its temperature rises by extension, and gets lower by contraction; and again, if we heat the string, we find that it contracts in length instead of expanding like other substances as its temperature increases. 120. Numberless instances occur in which we are enabled to predict what will happen by assuming the truth of the laws of energy; in other words, these laws are proved to be true in all cases where we can put them to the test of rigorous experiment, and probably we can have no better proof than this of the truth of such a principle. We shall therefore proceed upon the assumption that the conservation of energy holds true in all cases, and give our readers a list of the various transmutations of this subtle agent as it goes backwards and forwards from one abode to another, making, meanwhile, sundry remarks that may tend, we trust, to convince our readers of the truth of our assumption. CHAPTER IV. _TRANSMUTATIONS OF ENERGY._ _Energy of Visible Motion._