and give a perfect account of it; but if you attempt to trace that back you will have a point where the equation will stop, and will begin to talk nonsense. That is the point where you took away the paper, and allowed the mixing to begin. If we apply that same consideration to the case of the poker, and try to trace back its history, you will find that the point where the equation begins to talk nonsense is the point where you took it out of the fire. The mathematical theory supposes that the process of conduction of heat has gone on in a quiet manner, according to certain defined laws, and that if at any time there was a catastrophe, one not included in the laws of the conduction of heat, then the equation could give you no account of it. There is another thing which is of the same kind. That is the transmission of fluid friction. If you take your tea in your cup, and stir it round with a spoon, it won't go on circulating round forever, but comes to a stop; and the reason is, that there is a certain friction of the liquid against the sides of the cup; and of the different parts of the liquid with one another. Now, the friction of the different parts of a liquid or a gas is precisely a matter of mixing. The particles which are going fast, and are in the middle, not having been stopped by the side, get mixed, and the particles at the side going slow, get mixed with the particles in the middle. This process of mixing can be calculated, and it leads to an equation of exactly the same sort as that which applies to the conduction of heat. We have, therefore, in these problems, a natural process which consists in mixing things together, and this always has the property that you can go on mixing them forever, without coming to any thing impossible; but if you attempt to trace the history of the thing backward, you must always come to a state which could not have been produced by mixing, namely, a state of complete separation.
Now, upon this remark of Sir W. Thompson's, which you will find further expressed in Mr. Balfour Stewart's book on the "Conservation of Energy," a most singular doctrine has been founded. These writers have been speaking of a particular problem, on which they were employed at the moment. Sir W. Thompson was speaking of the deduction of heat, and he said this heat-problem leads you back to a state which could not have been produced by the conduction of heat. And so Prof. Clerk Maxwell, speaking of the same problem, and also of the diffusion of gases, said there was evidence of a limit in past time to the existing order of things, when something else than mixing took place. But a most eminent man, who has done a great deal of service to mankind, Prof. Stanley Jevons, in his very admirable book, "The Principles of Science," which is simply marvellous for the number of examples illustrating logical principles which he has drawn from all kinds of regions of science, and for the small number of mistakes that occur in it, takes this remark of Sir W. Thompson's, and takes out two very important words, and puts in two other very
