Jan. lo, 1878] 



NATURE iq 



199 



voyage of circumnavigation, you found Gallia to be com- 

 posed—a substance to which your geological attainments 

 did not suffice to assign a name.* 



" The professor took the cube, and, on attaching it to the 

 book of the steel yard, found that its apparent weight 

 was one kilogramme, and four hundred and thirty 

 grammes. 



" ' Here it is, gentlemen ; one kilogramme, four hundred 

 and thirty grammes. Multiply by seven ; the product is, 

 as nearly as possible, ten kilogrammes. What, therefore, 

 is our conclusion ? Why, that the density of Gallia is 

 just about double the density of the earth ; which we 

 know is only five kilogrammes to a cubic decimetre. 

 Had it not been for this greater density, the attraction of 

 Gallia would only have been one-fitteenth instead of one- 

 seventh of the terrestrial attraction.' 



" The professor could not refrain from exhibiting his 

 gratification that, however inferior in volume, in density, 

 at least, his comet had the advantage over the earth." 



We have given this long extract to show the pleasant 

 way in which, in this latest form of French light literature, 

 amusement is combined with instruction. It would not 

 be fair to the book to say more of the plot or of the 

 dhtoiieinent. 



We have dwelt especially upon Jules Verne's latest 

 book, but equal praise must be given him for all those we 

 have named. A boy, for instance, who had read how the 

 frozen island in the " Fur Country" was kept together by 

 Dr. Black's device, would at once understand the rationale 

 of Pictet's and Cailletet's recent splendid work, to say 

 nothing of the physical geography he would have gradually 

 absorbed in following the strange adventures recounted in 

 that volume. 



We are glad to have such books to recommend for 

 boys' and girls' reading. Many young people, we are sure, 

 will be set thirsting for more soHd information. 



OUR BOOK SHELF 



The Geometry of Compasses ; or, Problems Resolved by the 

 mere Description 0/ Circles, and " the Use of Coloured 

 Diagrams and Symbols^ By Oliver Byrne. (London : 

 Crosby Lockwood and Co., 1877.) 



This is only our old friend," La Geometriadel Compasso 

 di Lorenzo Mascheroni" (Paris, 1797), decked out in the 

 manner we have indicated in the quoted portion of the 

 title. The order of sequence has been departed from, 

 but this is not a material point. The constructions are 

 the same and the proofs the same with, we believe, one 

 exception, in which case we give the preference for 

 simphcity to Mr. Byrne. 



There are twenty problems, which are in most cases 

 given in duplicate, first construction and figure in colours, 

 then proof and unadorned figure on the next two pages. 



The merits and nature of Mascheroni's work are well 

 known ; hence the present work, for reasons given above, 

 is good. But we cannot call this Mr. Byrne's book. 

 Problem XX., which is the last, is an elegant construction 

 for dividing the circumference into seven equal parts by 

 plane geometry. But for this the compiler is indebted 

 to an able mathematician, Dr. Matthew Collins. The 

 book is very neatly and correctly got up, and for frontis- 

 piece has a hand with a pair of compasses transferring a 

 given length. 



Proceedings of the American Philosophical Society. 

 VoL xvi., No. 99. January to May, 1877. 



Prof. Cope has several noteworthy papers in this part : 

 one, on the Batrachia of the coal-measures of Ohio, de- 

 scribes the new genus, Ichthycanthus, and the newspeties of 



Leptophractus and Tuditanus. He also describes remains 

 of a Dinosaurian from the trias of Utah ; the humerus is 

 one of the longest, and distally the most contracted 

 known in the group. These remains are the first dis- 

 covered fossils in the triassic beds of the Rocky Moun- 

 tain regions. Another valuable paper is on the brain of 

 Coryphodon. One of the longest contributions will be 

 much esteemed by geologists, viz., Mr. Ashburner's mea- 

 sured section of the palaeozoic rocks of Central Pennsyl- 

 vania (Huntingdon County), a section extending vertically 

 through 18,394 feet. A very valuable series of physio- 

 logical experiments is recorded in a paper by F. L. 

 Haynes, on the asserted antagonism between nicotin and 

 strychnia. Philology is well represented by a paper on 

 the Timucua language, by Mr. A. S. Gatschet ; this lan- 

 guage, formerly spoken in Florida, appears to be the oldest 

 within the American Union of which writings of some 

 extent are preserved. 



LETTERS TO THE EDITOR 



[The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undet-take to return, 

 or to correspond with the writers of rejected manuscripts. 

 No notice is taken of anonymous communications. 



The Editor urgently requests correspondents to keep their letters as 

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

 is impossible otherwise to ensure the app arance even of com- 

 munications containing interesting and novel facts.} 



The Radiometer and its Lessons 



With reference to the controversy between Mr. Stoney and 

 Mr, Osborne Reynolds about the laws of the conduction of heat 

 in gases, it seems desirable to call the latter gentleman's attention 

 to the fact that neither Clausius' nor CJerk Maxwell's investiga- 

 tions, as published in the Philosophical Magazine, affect the 

 controversy between them. 



The latter, in his papers in the Philosophical Magazine, vol. 

 xxxv., lays particular stress upon the fact that he supposes the' 

 motions of the molecules to be uniformly distributed in every 

 direction. He says, however, on page 188 : " When one gas is 

 diffusing into another, or when heat is being conducted through a 

 gas, the distribution of velocities will be different in the positive 

 and negative directions instead of being symmetrical, as in the 

 case we have considered." From this theory of the uniform 

 distribution of velocities he deduces the formula (29), (31), and 

 {32), as he numbers them, and to which he subsequently refers. 

 On page 214 he gets an equation (143) which represents the 

 translerence of heat through the medium, and says : " The 

 second term contains quantities of four dimensions ia ^ 97 ^, whose 

 value ivill depend upon the distribution cf velocity among the 

 molecules, //"the distribution of velocity is that which we have 

 proved to exist when the system has no external forces acting on 

 it, and when it has arrived at its final state we shall have by 

 equations (29), (31), (32) ..." certain results from which he 

 deduces his equation for the conduction of heat in gases. 



When he says ' ' has arrived at its final state " it is evident from 

 his reference to the equations that he means the state of a gas in 

 which neither diffusion nor conduction of heat nor currents of 

 any kind are going on. It will thus be seen that his final result 

 is only a first approximation and could not possibly be expected 

 to hold within distances comparable with the mean length of the 

 path of a molecule between two encounters. 



Clausius in his paper as translated in the Philosophical 

 Magazine for June, 1862, does suppose a distribution of velocity 

 among the molecules of such a kind that the velocity and number 

 of molecules moving in the positive and negative directions is 

 different, but assumes the mean between them to be the same as 

 the number moving in a direction normal to the direction of the 

 transference of heat. This is evident from the fact that what he 

 practically does is to assume that the number of molecules moving 

 in a direction making an angle Q with the direction of transference 

 of heat can be expressed by a formula of the form — 



« = «o (I + tfCOS fl), 

 for he neglects ^ throughout his investigation* In this form it 



is evident that n^ is the] number when Q = -and is the mean of 



2 

 the values «i s= «,(i + ^) and >^ = w^ (i - e), which represent 

 the numbers going towards and from the points of high tempera- 



