After my father's death his children agreed that the following letter should be sent to Mr Anthony Rich.

My dear Mr Rich,

Since my father's death my brothers and sisters and I have been thinking much over your generous intention of leaving your property to my father, and, as we understood, to us as his heirs. We wish to tell you how truly grateful we feel to you for this emphatic recognition of his services to science and the world. It deeply gratified him, and we never shall forget this. I gather that it was your intention that his death should make no difference in the disposition of your property, but we want you to be assured that we feel that a new state of things has arisen, and one of which you could not calculate the effect until it actually came. No one as long as they live can help acquiring new interests, and it is impossible for you to foresee what may happen in the years I hope you may still have to live.

We, therefore, earnestly beg you to remember that if you should see fit to alter the disposition of your property, we shall never feel that we owe you any less gratitude for your generous intentions towards our dear father; and we ask you to keep this letter, in order that you may always bear in mind that this is our most deliberate request.

432. In the last three chapters we have considered the free path phenomena of viscosity, conduction of heat and diffusion, and have found for the three corresponding coefficients formulae involving in every case the quantity σ, the diameter of the molecule of the gas in question. Thus we have three phenomena from which the molecular diameter may be calculated.

The values of σ which can be deduced from the phenomenon of viscosity have already been calculated and exhibited in the table on p. 288. A similar set of values can be deduced from the observed values of the coefficient of conduction of heat given on p. 301. To do this, it is necessary to make some definite assumption as to the transfer of internal molecular energy, and the assumption which has been made is that already explained in § 403. Finally, it is possible to obtain a third set from the coefficients of diffusion given in the tables on pp. 323, 324, although the procedure here is rather more complicated than in the two former cases. In these tables we have thirteen observations from which to determine the eight molecular diameters involved. A leastsquare solution would be laborious, and of little real value since obviously some of the values given for D12 have a much greater observational value than others. The following simple plan has therefore been followed.

The values of the molecular diameters of the three gases hydrogen, oxygen and air have been determined solely from the first three entries in the first table. The value of σ for nitrogen can then be obtained from the fourth entry.

35. In the last chapter it was twice found convenient to represent the three velocity coordinates u, v, w of a molecule, by a point in space of which the coordinates referred to three rectangular axes were u, v, w. The principle involved is a useful one, capable of almost indefinite extension, and will be largely used both in the present chapter and elsewhere in the book.

The space of nature possesses three dimensions, but just as it is open for us to represent any two coordinates in an imaginary space of only two dimensions, so in the same way we may represent any four coordinates in an imaginary space of four dimensions. Similarly if a dynamical system is specified by any number n of coordinates, we can represent these coordinates in a space of n dimensions, and the various points in this space will correspond to the various configurations of the dynamical system.

In the present chapter, we attempt to find the law of distribution of velocities by a method which consists essentially in regarding the whole gas as a single dynamical system, and in representing its coordinates in a single imaginary space of the appropriate number of dimensions.

Let us suppose that the gas consists of a great number N of exactly similar molecules, enclosed in a vessel of volume Ω.

My father's one surviving sister, Caroline, the wife of Josiah Wedgwood, of Leith Hill Place, died on January 5, 1888.

She had not been well early in the year, but in March had recovered and wrote to me at Cannes, where I had gone for my health:

March 11th, 1888.

Sismondi was now seriously ill and Jessie's life was full of sadness and anxiety. Her deafness interfered with her enjoyment of society, and she, as well as Sismondi, was miserable at the revolution which broke out in Geneva. Finding he could neither guide nor stem it, he was planning to leave Geneva and return to Peseta, when death ended his sufferings in June, 1842.

…Public events have come nearer me and disturbed me more than ever they did before. The storm is passed, but no one yet can tell the ravages it will have made. The Constituante continues its sittings daily, but Sismondi has given up attending them and I imagine will be dismissed if he does not dismiss himself. The Radicals are now attacking the national Church, and the Methodists and Catholics unite with them, so that there is little hope but that it will fall with the Constitution, and the Academy after that, in short everything of the old Geneva will be effaced from the earth. There are no concerts, balls, or soirées among the Genevoises, one meets no one in the streets or shops. It is exactly as if half the town were dead and the other half in mourning. The evil they have done me individually, and after all one's patriotism, humanity, general good, &c, is nothing in comparison, is to up-root me from hence, and send me to Pescia, and I shudder to think how unhappy it will make me.

My primary aim in the first edition of this book was to develop the Theory of Gases upon as exact a mathematical basis as possible. This aim has not been forgotten in the preparation of a second edition, but has been combined with an attempt to make as much of the book as possible intelligible to the non-mathematical reader. I have adopted the plan, partially followed in the first edition, of dividing the book to a large extent into mathematical and physical chapters. The reader whose interest is mainly on the physical side will, it is hoped, get an intelligible account of the present state of the subject by reading the physical chapters I, VI, VII and XI to XVIII, and regarding the more mathematical chapters simply as material for reference. Apart from this, something is, I think, gained by clearing the ground by a full mathematical treatment before any physical discussion is attempted.

Since the first edition of this book appeared the position of the Kinetic Theory has been to some extent revolutionised by the growth and developments of the Quantum Theory, and it has been by no means easy to decide what exact amount of prominence ought to be given to the Quantum Theory in the arrangement of the book. The plan finally adopted has been to confine the Quantum Theory to the last chapter; the difficulties arising out of the classical treatment have been allowed to emerge in the earlier chapters, but have been left unsolved.

My mother's only living sister Elizabeth, who it will be remembered left London and came to Down in 1868, had had a serious illness in the autumn of 1879. From this she never entirely recovered, and died on November 7th, 1880, at the age of 87. Her little bent figure had been a familiar sight as she came into the drawing-room leaning on her stick and followed by her dog Tony. The first question would always be, “Where is Emma?” My mother would then put by whatever she was doing in order to go to her. This was sometimes difficult, but she never let any sense of hurry appear and was always ready to give her a warm and equable welcome. She shared in all her interests and made constant attempts to protect her from the beggars and impostors who beset her to the end of her life. This devotion and care never failed in the twelve years aunt Elizabeth lived at Down.

I think that we none of us felt intimate or quite at ease with our aunt. There was a curious film of reserve, even with my sister Bessy, who was most faithful and regular in reading to her and doing all she could to make her life happier and less monotonous.

During the last year of my mother's life her health was better than it had been for some years. Her letters show how full of energy, vigour, and enjoyment she was, and her power of living in the lives of those she cared for made her really enjoy their pleasures at secondhand, and kept many avenues to life open that are often closed to the old. It was difficult to remember that she would be eighty-eight on May 2nd of this year.

From about 1892 she put down in her diary all the letters she wrote, almost daily to one or other of her children and many to her friends; but besides these it is characteristic to note the number where the object of writing was to give pleasure or help, perhaps to an old servant or to an invalid, or to someone whose life was bare of enjoyment.

Jan. 15th, 1896.