192 



NATURE 



\_yune 20, 1878 



FOURIER'S ''-ANALYTICAL THEORY OF 

 HEAT'' 



The Analytical Theory of Heat. J. Fourier. Translated 

 by A. Freeman. (University Press, Cambridge, 1878.) 



THERE cannot be two opinions as to the value and 

 importance of the Theorie de la Chaleur. It has 

 been called "an exquisite mathematical poem," not once 

 but many times, independently, by mathematicians of 

 different schools. Many of the very greatest of modern 

 mathematicians regard it, justly, as the key which first 

 opened to them the treasure-house of mathematical 

 physics. 



It is still the text-book of Heat Conduction, and there 

 seems little present prospect of its being superseded, 

 though it is already more than half a century old. It 

 contains the first satisfactory definition of Conductivity, 

 the first statement of the dimensions of various physical 

 -quantities, and the invaluable expression for periodic quan- 

 tities in terms of harmonics. Many important problems of 

 heat conduction are completely solved, and the results are 

 given so as to be immediately applicable in practice, as 

 for instance to the cooling of spheres (including the 

 secular cooling of the earth) the propagation of periodic 

 changes of temperature into the crust of the earth, &c. 



But the heat equations are of the same form as those 

 in certain other branches of physics. Here they are 

 solved once for all, and form a store from which all may 

 freely help themselves. Thus, a very minute fragment 

 of the work sufficed, by its application to electric currents, 

 to render the name of Ohm famous. More important 

 portions have been applied to Diffusion, to Signalling 

 through Submarine Cables, and to various other im- 

 portant questions. 



With all its transcendent excellences this great work 

 had two faults at first, and of late it had acquired a third, 

 (i.) It was a little prolix. Like Ampere's great work, 

 . and some others of that wonderfully fertile period, it was 

 made up as a sort of patchwork of memoirs sent to the 

 French Institute. Each memoir was, as it were, com- 

 plete in itself : and the putting together into one work, 

 without judicious paring down, necessarily involved a 

 good deal of repetition. 



(2.) It was so full of printers' blunders and mere slips 

 of the pen that it must have been very carelessly revised. 

 (3.) It had become very scarce, and consequently 

 expensive. 



The Syndics of the Pitt Press deserve great credit for 

 reproducing the book : — and the printers have done their 

 share of the work well. Still, the result can hardly be 

 , called satisfactory. For this there are many reasons. 



(i.) We think it was a great mistake to translate the 

 book into English. The poetry, except so far as it was in 

 the formulae, is gone ; and the prolixity, which was toler- 

 able in the original, is painful in the translation. The text 

 should have been considerably compressed in translation, 

 or else simply reproduced in French. Every one who 

 has any right to read Fourier reads French, or at least 

 ought to be able to do so. Again, though Conducibilite 

 and Conductibilite are good French, Conductibility (being 

 altogether erroneous) has hitherto been confined to the 

 jowest class of English books. Conducibility, which 

 Mr. Freeman most commonly employs, is not an English 



word at all ; ^ and, even if it were, could not possibly 

 mean Conducting power, or Conductivity. 



(2.) We have compared at least one whole chapter 

 with our own annotated copy of the original. Roughly 

 speaking, only about 50 per cent, of the misprints in the 

 original have been corrected. The others, some very 

 misleading, are reproduced. The worst of those we have 

 noticed are at 



pp. 124 [Eq". {a)\ 134, 189, 226. 



In p. 181 an erroneous reference is reproduced, and in 

 order to make it fit the text the reference mark is shifted 

 from the general equation (really referred to) to a mere 

 particular example. 



(3.) The translator has added a few notes, some by the 

 late Leslie Ellis. But they are very fragmentary. Surely 

 more than a single sentence might have been devoted to 

 the experimental results of Forbes [and Angstrom] ; 

 Stokes and Duhamel ought to have been mentioned with 

 reference to conduction in non-isotropic solids — and 

 Thomson's proof that Fourier's solution of the problem 

 of the cooling sphere is complete deserves much more 

 than the mere casual mention it has received. 



OUR BOOK SHELF 



Anthropology. By Dr. Paul Topinard, with a Preface 

 by Prof. Paul Broca, translated by Dr. R. Bartley. 

 (London : Chapman and Hall, 1878.) 



This volume forms another of the Library of Contem- 

 porary Science, and it purports to elucidate a science 

 which is well described by Paul Broca as being one of 

 vast dimensions and one in process of rapid develop- 

 ment, as well as one which has hitherto not received 

 sufficient attention. The masters of the science en- 

 gaged in original research naturally shrink from the 

 labour of writing a handbook of a popular charac- 

 ter : and it fell to Dr. Topinard's lot to make the 

 attempt — in which attempt he seems pretty fairly to 

 have succeeded. This work falls into three sections : 

 the first treats of the physical characters of man, and 

 of his place in nature. The chief human anatomical 

 peculiarities are briefly alluded to, with a somewhat need- 

 less — to our mind — reiteration of the assertion that the 

 organisation of anthropoids is a counterpart of that of 

 man, and differs widely from that of the other Simian 

 groups. The second section treats of the races of man- 

 kind ; and here we have a great many important and 

 interesting facts marshalled in fair order before us. A 

 few more woodcuts would have been an improvement to 

 this portion. In the concluding section the origin of 

 man is discussed ; and the author passes in array the 

 monogenestic theory of Quatrefages, the polygenestic 

 theory of L. Agassiz, the transformation theory of 

 Lamarck, and the natural selection theory of Darwin, 

 and works out in detail the application of each to man 

 and his genealogy. The translation, which is generally 

 good, might, however, in places be improved, and it is 

 sometimes a little confused. 



I On reference to Richardson we find one instance of the use of the word, 

 by (Bishop ?) Wilkins. We freely give Mr. Freeman any benefit which he 

 can extract from the following passage : — 



" Duties deriving their obligation from their conducibility to the promoting 

 of ends. " 



It may interest readers of Nature to be told that, in looklne; for the word 

 in the Supplement to the Imperial Dictionary, we found the followingextra- 

 ordinary statement (illustrated by a diagram) about Conjugate Foci :— " when 

 rays, falling upon a lens, are so refracted as to converge and meet in a point, 

 either nearer the lens than the principal focus, or farther from it, the point 

 in which they meet, and the principal focus, are called, with respect to each 

 ether. Conjugate Foci." 



