382 



NA TURE 



[FeBRUARV 22, 1894 



pointed out can exist as an irrotational one without 

 reaction in MacCullagh's medium. This same observa- 

 tion of course applies to Dr. Boltzmann's analysis, the 

 difference being that vortex rings would be rings of 

 magnetic current instead of electric current, and atoms 

 would act like electric diads instead of elementary 

 magnets. The existence of unclosed lines of electric ; 

 vector, however, seems to make this simple interpretation 

 of Dr. Boltzmann's analysis impossible, and as we cannot t 

 in general substitute whirl for flow in fluid motion, the 

 vortex ring analysis could not be applied if Dr. Boltz- 1 

 mann's electric vector were interpreted as a whirl ; and 

 hence Mr. Larmors investigation seems confined to the . 

 interpretation he has given. 



Having assumed that the medium is such as to react j 

 elastically against curl of the tonus (t), and his funda- 

 mental equations thus being — 



(I), E = f ; (3), T=K/8 7r.E2 

 (2), H = curlT ; (4), V=i//2 . H- 



he proceeds to deduce the equation corresponding to (2), 

 namely, (5)KE = curl H by applying Hamilton's principle 

 to T- V in a way which isvAell known. He now remarks 

 that in accordance with his dynamical principles KE 

 is rate of change of momentum, and he adds to curl H any 

 external impressed forces, which he divides into two 

 classes : (i) those due to reversible causes, such as electro- 

 motive of contact, chemical action, &:c. (F) ; and (2) those 

 due to irreversible causes, such as ohmic resistance, &c., 

 which are proportional to the electric vector, and thus 

 obtains this equation in the form 



KE = curl H-47rC (E + F) 



It would thus seem as if the electric conduction current 

 were a differert thing from a changing electric displace- 

 ment, though both depending on curl H. This arises from 

 the difficulty noticed above, and seems to require careful 

 consideration. By judicious theories as to the function 

 of the matter in stopping the continual acceleration with- 

 out uncurling the H,the difficulty can be surmounted. 

 In order to get over all the difficulties of discontinuities 

 at the surfaces of bodies. Dr. Boltzmann assumes that 

 the properties of the ether vary rapidly but continuously 

 in passing across a surface, so that he can assume that 

 these equations apply everywhere. 



Depending on his dynamical basis, Dr. Boltzmann has 

 obtained the following dimensions for electromagnetic 

 quantities, which, of course, differ entirely from both the 

 electric and magnetic systems of units — 



[E] - [LT-i], [K] = [ML-3] 



[HI = [ML-iT-2]* [m] = [M-iLT--] 



After a short discussion as to the possibility of found- 

 ing the science upon a purely analytical basis, by assuming 

 equations and showing that they lead to true results, 

 which is the basis of Hertz's method, and a short criticism 

 of this method as applied by Hertz, Dr. Boltzmann pro- 

 ceeds to show how the old equations of action at a dis- 

 tance and von Helmholtz's work are connected with 

 Maxwell's view of the subject. His treatment of super- 

 ficial effects by means of a rapid variation of structure 

 of the ether at the surface of solids, seems essentially the 



* This is misprinted in the text, but right in the table of formulse at the 

 end of the book. 



same as Mr. O. Heaviside has advocated in opposition 

 to von Helmholtz's double electric layers. All this 

 analytical method is, of course, necessary and interesting 

 in what may be called a transition work, one that con- 

 cerns those who have been brought up under one school 

 of thought and are entering another ; a sort of epistle to 

 the Hebrews, a college between youth and manhood. 

 It concerns the past rather than the future, towards which 

 we should press, forgetting those things that are behind. 



Although Dr. Boltzmann has left out all embellish- 

 ments, he has had pity on his readers. There are 

 necessarily included in a transition work of this kind 

 innumerable formulae, of which 168 are frequently 

 referred to, and these he has collected into two folding 

 sheets, each of five folds, at the end of his work. This 

 is most considerate. Books dealing with many formulas 

 might well follow suit, although it certainly is a little 

 terrifying to have 168 formulae presented as the outcome 

 of the book in a way that necessarily attracts the atten- 

 tion of anyone who thinks of reading it. Those who are 

 frightened by this should, however, recollect that the 

 whole subject of electromagnetism depends on only four 

 very simple equations. Dr. Boltzmann would have 

 much simplified his work if he had adopted any 

 vector symbolism. 



It is to be hoped that this part of Dr. Boltzmann's 

 work, as well as the former part, will soon be translated, 

 and so made easily accessible to English students. The 

 work of a great master, the product of a great mind, 

 helps all men who can understand it. 



THE STORY OF THE SUN. 

 The Story of the Sun. By Sir Robert Ball, LL.D. 

 (London : Cassell and Co., 1893.) 



THERE is no more interesting chapter in science than 

 that which deals with our great central luminary. 

 Its story has been gradually gaining in interest since the 

 first application of the telescope to its study by Galileo, 

 and since the advent of the spectroscope our knowledge 

 of solar phenomena has advanced by leaps and bounds. 

 At the present time the scrutiny of the sun is more minute 

 and continuous than ever, and the constant acquisition 

 of fresh information sufficiently explains the need for 

 additional works on the subject, or for new editions of 

 old ones. 



The author of the book before us does not approacfi 

 the subject as a practical investigator in this branch of 

 astronomy, and his efforts are therefore chiefly intended 

 for the delectation of that class of readers for which he 

 chiefly caters. The first thing that strikes one on glancing 

 through the pages of the book is the great variety of the 

 matter which it contains, and one begins to wonder if he 

 has mistaken the title of the volume. It is not too much 

 to say that nearly every department of astronomical 

 inquiry is touched upon more or less ; from the deter- 

 mination of the polar flattening of the earth to the photo- 

 graphy of minor planets and the appearances of nebute. 

 Though the author never seems at a loss to give reasons 

 for the introduction of matter apparently not at first sight 

 connected with the subject in hand, his reasons frequently 

 appear to be nothing more than excuses for fiUmg so 

 many pages. For example, we fail to see the necessity 



NO. T269, VOL. 49] 



