1. The Kinetic Theory of Matter rests essentially upon two closely related hypotheses; the first—that of the molecular structure of matter, the second—the hypothesis that heat is a manifestation of molecular motion.

The first of these hypotheses belongs to the domain of chemistry; indeed it forms the basis of modern chemical science. It is believed not only that all matter is composed of a great number of molecules, but also that all molecules of the same chemical substance are exactly similar as regards size, mass, etc. If this were not so, it would be possible to separate the molecules of different types by chemical processes of fractionisation, whereas Dalton found that the successively separated fractions of a substance were exactly similar. It is true that very modern research has thrown some doubt on whether the molecules of a substance are all as exactly identical as they were once thought to be, but it is also true that the hypothesis of exact similarity of molecules is now, as a broad truth, unassailable, and forms a suitable and convenient working hypothesis for the Theory of Matter.

The second hypothesis, the identification of heat with molecular motion, is that with which the Kinetic Theory of Matter is especially concerned. This hypothesis was for long regarded as pure conjecture, incapable of direct proof, and probable just in proportion to the number of phenomena which could be explained by its help.

74. Two methods of obtaining the Law of Distribution of molecular velocities have now been given and also a comparison between them. These two methods have been limited to the consideration of molecules which may be treated as elastic spheres, exerting no forces on one another except when in actual collision. There is a more general way of treating the question, which permits of the molecules being dynamical systems of the most general type, capable of any kind of internal motion and exerting upon one another any forces we please. This method will be explained in the present chapter.

With a view to obtaining results which will be required later in the development of the subject, we shall not limit the discussion of the present chapter to the problem referred to above; we shall consider the “Statistical Mechanics” of a perfectly general dynamical system, not in the least limited to consisting of a gas. The special applications of the present chapter will be to a gas, while in later chapters we shall have occasion to apply the results to more general systems.

Degrees of Freedom.

75. The total number of independent quantities which need to be known before the configuration and position of any dynamical or other system can be fully known, is called the number of degrees of freedom of the system.

For some time there had been a growing wish on the part of my parents to live in the country. Their health made London undesirable in many ways and they both preferred the freedom and quiet of a country life. They decided to buy a country-house, but out of prudence resolved upon not going beyond a moderate price, and as they also wished to be near London, there was a weary search before they found anything at all suitable. In her little diary under the date July 22nd, 1842, I find the entry, “Went to Down,” and this, I think, must have been her first sight of her future home. It was bought for them by Dr Darwin for about £2,200, and the purchase was quickly completed, for they moved in on September the 14th.

Down was then ten miles from a station and the whole neighbourhood was intensely rural and quiet, though only sixteen miles from London Bridge. To the south there were miles of copse, now cultivated as fruit grounds. A charm, which would be slight in the eyes of most people, had a good deal to do with the purchase. My father was delighted with the varied hedges and many flowers of a chalk district. This, and despair at getting anything pleasanter for the money they were prepared to give, decided the matter. But we have always been sorry that a prettier bit of the south of England was not found.

In 1860 my poor mother's thoughts and time were engrossed with the care of me in a long illness, lasting with relapses from May 1860 till Midsummer 1861. In July I was well enough to be moved to Hartfield, “the kindly hospital for all who are sick or sorry” as Fanny Allen calls it. But I soon had a bad relapse and gave her as much anxiety as ever.

Poor Etty will long be an invalid, but we are now too happy even at that poor prospect. Your letter has amused us all extremely, and was read with roars of laughter. Etty has not yet heard it; but you cannot think what a pleasure your letters are to her; they amuse and cheer her so nicely. I shall copy your account of dialogue before the Bishop and send it to Hooker and Huxley. I daresay I will send some queries to your friend the cook. You may tell the gardener that I have seen an ant's nest in a tree, but it is rare….

The Review by the Bishop of Oxford and Owen in last Quarterly is worth looking at. I am splendidly quizzed by a quotation from the Anti-Jacobin. The naturalists are fighting about the Origin in N. America even more than here, as I see by the printed reports.

363. In Chapters VIII and IX we developed a purely mathematical theory, which was found to lead to an explanation of the phenomena of viscosity, conduction of heat and diffusion of gases. This theory, although mathematically perfect, did not go far towards revealing the physical mechanism underlying the phenomena.

There is another method of treating these problems, in which we follow as closely as possible the physical processes which result in the phenomena. This method we now proceed to examine. It does not lead to results possessing the same mathematical exactness as the former method: its importance lies rather in its disclosure of the physical mechanism at work. Briefly, the three phenomena under consideration are regarded as transport phenomena—viscosity is a transport of momentum, conduction of heat is a transport of energy, and diffusion is a transport of mass. The mechanism of transport is provided by the free path; a molecule describing a free path of length λ is in effect transporting certain amounts of momentum, energy and mass through a distance λ. If the gas were in a steady state each such transport would be exactly balanced by an equal and opposite transport in the reverse direction, and the net transport would always be nil. But if the gas is not in a steady state there will always be an unbalanced residue, and this want of balance results in the phenomena we wish to study.

The Great Exhibition of 1851 made more stir than this generation, who are used to exhibitions and world-fairs, every year or so, can imagine.

Fanny Allen writes:

……The day I came here, Fanny, Hensleigh, and Erasmus Darwin took me to the Grand Exhibition in Hyde Park, and it certainly is the most beautiful thing I ever saw. We were two hours there and yet I did not see the 10,000th part of what is to be seen, not even the grand avenue entirely. The great diamond was the only thing that I should say was a “failure,” as old Wishaw would have said. I expected to see a diamond 10 times the size…….

Mrs Sydney is affectionate and kind as it is possible to be. She gives me all her husband's papers and correspondence to look over and read, and gives me the drawingroom to read, write, and to receive my company, if I should have any; and at 2 or half-past we take our dowager drive, and we read and work in the evening. We have seen no one.

In April, 1843 John Allen, the brother so beloved by all his sisters, died. Emma and Fanny Allen now left Cresselly, which Seymour, John's eldest son inherited, and joined Jessie Sismondi and Harriet Surtees at their house in Tenby. Emma Allen writes:

Tenby, May 4th [1843].

The Memorial Statue of my father was to be unveiled on the 9th June, 1885, at the Natural History Museum. My mother did not attend the ceremony, although she had had some thoughts of going, for she wrote, “I should like very much to be present but I should prefer avoiding all greetings and acquaintances.”

My dear Sara,

I came on Friday, having spent two days at 31, Queen Anne St.

One of the mornings I went to see the statue. The situation is unique and I liked the attitude, but I do not think it is a strong likeness. George has been with Mr Boehm to have a cast of his hand taken as a sort of guide to altering the hands; but I believe if he attempted to make them as small as they really were, they would look out of proportion with the size of the figure. I also perceived the defect in the eyes that you attempted to get altered. However I never expected to be satisfied with the likeness, and the general look of dignity and repose is of more consequence.

It was a dismal black day on my arrival [at Down], but I was glad to wander about alone before the others came. On Saturday it was pretty and bright and the garden very gay, and everything in great order.

In February, 1872, my father and mother took a house in Devonshire Street for a month. This was chiefly planned for my sake. I was much out of health and my husband and I stayed there with them and thus my mother could take care of me. My marriage separated me very little from her. We were constantly up and down to Down, and they shared their London visits between our house and Erasmus Darwin's in Queen Anne Street.

My dearest Aunt Fanny,

You are alone again to-day and so I will write, though I have little enough to tell you. We have had a few charming days, as one often has in April, but our flowers don't behave like yours, and we have little out but forget-me-nots and wallflowers. Eliz. went down to her Tower yesterday. Her neighbours are all wanting to nibble at her land, but strange to say she declines to sell for the sake of her heirs, and a little for the sake of the village too, as Mr Sales would be sure to build some more ugly houses if he got the land. Leonard is bringing a young man from Chatham to-day with the assurance that we shall hate him. Frank is also bringing a friend, a Mr Crawley, of Monmouthshire, who is very nice. But I don't feel at ease in the company of young men and feel out of my element.

My dear Emma,

I should be grateful for anything that brought me one of your sweet letters, and I most gratefully thank you for your affection which has prompted you to send me a souvenir, and though I have no need of one with regard to you, yet I am sure it will perform its pleasant office of putting me in mind of you, whenever I sit down to write, or indeed whenever I look at it. I trust the colds and coughs of your children are now quite gone, and that all is as usual in your happy home, where nothing is wanting but health to Charles…. Your anecdote of Willie is charming—so much love and patience with Georgy. Such a character in the eldest child, ensures all the rest being good. You deserve to be a happy father and mother, and you have a fair promise. You are very right, no child can spoil another by kindness. Men and women have great power in spoiling, as I perceived last week when I was at—.

I hope Mrs — does not bother her daughter to accept of M. Milnes. He is not worthy of her. Have you seen his life of Keats? T. Macaulay says he never knew what religion he was of till he read this book. He expects to find an altar to Jupiter somewhere in his house. We are near the end of Macaulay's History, and it is very entertaining reading. I do not see the ‘new views’ which they talk of in this history.