THE FIRST AND THE LAST CATASTROPHE. 281 



The evidence which tells us that the molecules of a given sub- 

 stance 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 char- 

 acter. 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 be- 

 fore, 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 tem- 

 perature at either end of the poker can be calculated with great ac- 

 curacy. That comes out of Fourier's theory. Now, sujipose 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 cer- 

 tain point, but beyond that point it refuses to give you any more in- 

 formation, 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 for- 

 ward 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 experi- 

 ment 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, 



