The evidence which tells us that the molecules of a given substance are alike, is only approximate. The theory leaves room for certain small deviations, and consequently if there are any conditions at work in the nature of the ether, which render it impossible for other forms of matter than those we know of to exist, the great probability is, that when by any process we contrive to sift molecules of one kind from molecules of another, these very conditions at once bring them back and restore to us a mass of gas consisting of molecules, whose average type is a normal one.
Now, I want to consider a speculation of an entirely different character. A remark was made about thirty years ago, by Sir William Thompson, upon the nature of certain problems in the deduction of heat. These problems had been solved by Fourier, many years before, in a beautiful treatise. The theory was, that if you knew the degree of warmth of a body, then you could find what would happen to it afterward, you would find how the body would gradually cool. Suppose you put the end of a poker in the fire and make it red hot, that end is very much hotter than the other end, and if you take it out and let it cool, you will find that heat is traveling from the hot end to the cool end, and the amount of this traveling and the temperature at either end of the poker can be calculated with great accuracy. That comes out of Fourier's theory. Now, suppose you try to go backward, in time, and take the poker at any instant when it is about half cool, and say, "This equation—does it give me the means of finding out what was happening to it before this time, in so far as that state of things has been produced by cooling?" You will find the equation will give you an account of the state of the poker before the time when it came into your hands, with great accuracy up to a certain point, but beyond that point it refuses to give you any more information, and it begins to talk nonsense. It is in the nature of a problem of the conduction of heat, that it allows you to trace the forward history of it to any extent you like; but it will not allow you to trace the history of it backward, beyond a certain point. There is another case in which a similar thing happens. There is an experiment in the excellent manual, "The Boy's Own Book," which tells you that if you put some beer into a glass half full, and put some paper on it, and then pour in water carefully, and draw the paper out without disturbing the two liquids, the water will rest on the beer. The problem, then, is to drink the beer without drinking the water, and it is accomplished by means of a straw. Let us suppose these two resting on each other, we shall find that they begin to mix, and it is possible to write down the equation, which is exactly of the same form as the equation for the conduction of heat, and it would tell you how much water should have gone at any given time after the mixture began. So that, given the water and the beer half mixed, you could trace forward, the process of mixing, and measure it with accuracy,
