28o 



NATURE 



\Feb. 7, 1878 



probability "of the occurrence within a given time of a 

 given amount of deviation from the most probable distri- 

 bution of a finite number of molecules of two different 

 kinds in a vessel, and has given a numerical example of a 

 particular case of the diffusion of gases. 



The same method might be extended to the diffusion 

 of heat by conduction, and the diffusion of motion by 

 internal friction, which are also processes by which energy 

 is dissipated in consequence of the motions and encounters 

 of the molecules of the system. 



The tendency of these motions and encounters is in 

 general towards a definite state, in which there is an 

 equilibrium of exchanges of the molecules and their 

 momenta and energies between the, different parts of the 

 system. 



If we restrict our attention to any one molecule of the 

 system, we shall find its motion changing at every 

 encounter in a most irregular manner. 



If we go on to consider a finite number of molecules, 

 even if the system to which they belong contains an 

 infinite number, the average properties of this group, 

 though subject to smaller variations than those of a single 

 molecule, are still every now and then deviating very 

 considerably from the theoretical mean of the whole 

 system, because the molecules which form the group 

 do not submit their procedure as individuals to the laws 

 which prescribe the behaviour of the average or mean 

 molecule. 



Hence the second law of thermodynamics is continually 

 being violated, and that to a considerable extent, in any 

 sufficiently small group of molecules belonging to a real 

 body. As the number of molecules in the group is in- 

 creased, the deviations from the mean of the whole 

 become smaller and less frequent ; and when the number 

 is increased till the group includes a sensible portion of 

 the body, the probability of a measurable variation from 

 the mean occurring in a finite number of years becomes 

 so small that it may be regarded as practically an impos- 

 sibility. 



This calculation belongs of course to molecular theory 

 and not to pure thermodynamics, but it shows that we 

 have reason for believing the truth of the second law to 

 be of the nature of a strong probability, which, though it 

 falls short of certainty by less than any assignable 

 quantity, is not an absolute certainty. 



Several attempts have been made to deduce the second 

 law from purely dynamical principles, such as Hamilton's 

 principle, and without the introduction of any element of 

 probability. If we are right in what has been said above, 

 no deduction of this kind, however apparently satis- 

 factory, can be a sufficient explanation of the second law. 

 Indeed some of them have already indicated their un- 

 soundness by leading to determinations of physical 

 quantities which have no existence, such as the periodic 

 time of the alternations of the volume of particular gases.^ 



J, Clerk Maxwell 



OUR BOOK SHELF 



Heroes of North African Discovery. By N. D'Anvers. 



(London : Marcus Ward and Co., 1877.) 

 Mr. D'Anvers has here made an interesting rhum^ of 



' Szily, Phil. Ma^., October, 1876; Clauslus, Pogs:- Ann., cxlii., p. 433; 

 Pozs:- Ann., cxlvL, p. 585, May, 1872 ; J. J. Miiller, Pog^r- Ann., clii., p. 

 I' 5' 



the work of the principal travellers who have made 

 Africa known to the world. He briefly dismisses the 

 earlier explorers, the bulk of the volume being devoted to 

 those of the eighteenth and nineteenth centuries. Mr. 

 D'Anvers has evidently read his authorities carefully, 

 and gives a clear account of his heroes' adventures, and 

 of the main results achieved. The book is evidently 

 meant for young readers, and to them both the text and 

 the numerous illustrations will prove attractive. But all 

 who wish to have a fair knowledge of what has been 

 hitherto achieved in the field of African discovery should 

 read this interesting and instructive volume. The author 

 prefixes a list of the authorities he has consulted, and 

 promises another volume on South Africa, in which the 

 results obtained by Mr. Stanley will be embodied. 



Manual of Agriculture ; including the Application 

 thereto of Chemistry, Geology, Botany, Animal 

 Physiology, and Meteorology . By Richard Henderson. 



This is a reprint of one of the Highland Agricultural 

 Society's prize essays. It forms a very marked exception 

 from the thoroughly practical essays which are usually 

 published by that society, so much so indeed, that it is a 

 source of regret that a society which has done so much to 

 improve agricultural education, should have in any way 

 stamped the present work with its approval and authority. 



The work is divided into seven chapters, of which five 

 are devoted to some notices of chemistry, geology, botany, 

 animal physiology, and meteorology, and the seventh 

 alone treats upon the application of these sciences to 

 agricultural practice, which is the professed subject of the 

 work. 



A few extracts from the first six chapters will given an 

 idea of the character of this part of the work. The second 

 chapter deals with chemistr>', and is largely made up of 

 comments upon eighteen elements, the descriptions being 

 remarkably similar to those given by Roscoe in his 

 " Lessons." It is fair to say that the author occasionally 

 introduces original remarks, as, for instance, in saying 

 that " carbon forms about fifty per cent, of the residue of 

 plant-life when the latter is charred, and access of atmo- 

 spheric air or oxygen prevented, for oxidised carbon 

 escapes as a gas." Prof. Roscoe fares rather badly at the 

 hands of our author, since he in another place says, 

 " Roscoe gives the following graphic formula as the 

 average composition of blood," and he^ appends the 

 average percentage composition. 



We are told again that at the sea- level the pressure of 

 the air " can support a column of mercury thirty inches 

 high in a tube in vac7w." Concernmg fogs and mists, 

 " they result from the radiation of heat from land and 

 water, taking with it aqueous vapour, which becomes 

 visible upon encountering cooler air. Similarly rain is 

 produced when heated volumes of air are deprived of their 

 heat, through the fall of condensed vapour, which assumes, 

 according to the temperature it encounters, the form of 

 hail, rain, or snow." 



LETTERS TO THE EDITOR 



[The Editor does not hold hitnself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts . 

 No notice is taken of anonymotis communications. 



[ 7 he Editor urgently requests correspondents to keep their letters as 

 short as possible. The pressure on his space is so great that it 

 is impossible otherivise to ensure the appearance even of com- 

 muuications containing interesting and novel f cuts ^ 



Sun-Spots and Terrestrial Magnetism 



Mr. B. G. Jenkins, in his letter to Nature, vol. xvii. p. 260, 

 says, " I have ventured to state my belief that we are now passing 

 through a long minimum period, one very similar to that which 

 occurred at the close of last century." It was the chief object of 



