26 



NA TURE 



[May 12, 1881 



will be spreading themselves over tlie length and breadth, 

 or the height and depth, of Switzerland. Many of these 

 will be naturalists more or less acquainted with the Alpine 

 insect fauna. To those who have already made its inti- 

 mate acqutiintance and are competent to distinguish the 

 majority of the species in the field, this work will prove 

 invaluable for consultation on the spot ; to those who 

 leave the determination of their materials until arriving 

 home it will add interest to a not otherwise always enjoy- 

 able occupation: 



In these latter remarks we have endeavoured to make 

 it attractive to the numerous naturalists who are more or 

 less amateurs. But its claims for careful study by those 

 who are working at geographical distribution as a special 

 branch of science, and at the philosophical speculations 

 that such studies give rise to, are indisputable, and cannot 

 be neglected. R. McLachlan 



WORKS OF JAMES MACCULLAGH 



The Collected Works of James MacCiillagh. Edited by 



Professors Jellett and Haughton. Dublin University 



Press Series. (Dublin : Hodges, Figgis, and Co. ; 



London : Longmans, Green, and Co., 1880.) 



THE admirable practice of building a monument to 

 departed men of science from the original works 

 they have left behind them is steadily gaining ground, 

 and is now indeed almost the rule. The collected works 

 of Green, Rankine, Wheatstone, Cavendish, Graham, 

 and Clifford have been comparatively recently published ; 

 those of Maxwell are being edited. 



When the papers republished have been written many 

 years the judgment of editors must be severely exercised ; 

 the temptation to point out the relation of the work of the 

 original author to subsequent discovery is great, but the 

 difficulty of deciding how much to add is greater. The 

 late Prof. Maxwell in his edition of Cavendish added 

 much of his own, thereby increasing manyfold the value 

 and interest of the book, and at the same time more 

 clearly exhibiting the penetration and genius of Caven- 

 dish. In the volume before us little of annotation and 

 nothing of criticism is added, the work is left to speak for 

 itself. 



Nearly two-thirds of the book is occupied by the first 

 part, containing the papers on Physical Optics. These 

 are twenty-three in number. The first four deal with the 

 geometrical treatment of Fresnel's theory of biaxal 

 cryst lis. Unfortunately MacCullagh failed to perceive, 

 or at least to point out clearly, the remarkable experiment 

 of conical refraction, so soon after predicted by Hamilton 

 and verified experimentally by Lloyd. 



The method of the si.xth paper, on the ".Laws of Re- 

 flection from Metals," is characteristic, as we find a 

 somewhat similar treatment of the theory of transmission 

 of light in qu irtz and to some extent in the dynamical 

 theory of double refraction. There is no pretence to a 

 firm f jundition on mechanical principles. A formula is 

 assu ned, the physical meaning of which is not apparent 

 and the deductions from that formula are interpreted. 

 Fre nel's formulaefor the intensities of the reflected and re- 

 fracied rays in the case of an ordinary transparent medium 

 are taken as a starting point. It is further assumed with- 

 out attempt at physical interpretation that the velocity of 



propagation of waves in a metal is ;«(cosx 4- n'- i sin^). 

 The real value of the method may perhaps be best shown 

 by trying to interpret this apparently unmeaning assump- 

 tion. Passing over the difficulties in Fresnel's method of 

 interpreting n - i as extended by MacCullagh, we have 

 on the assumption of the paper — 



C= A sin 71 {a: — tm (cos x -|- n' — I sin y^, 

 or which is equivalent — 



f = ^ sin n \x (cos x — ^' - i sin x) - mi\ 



= ^[cos V— I « sin XA'+ ^' — I sin V— i n sin x ^'j 



X sin « [a- cos X — Mt\ 



= A e~ "^'"^ •'' sin nir cos x — "'f]. 



The physical meaning of this equation is obvious, it 

 clearly means absorption in the metallic medium. Mac- 

 Cullagh's theory of metallic reflection would bear the same 

 relation to a theory resting upon the fact of absorption in 

 the metal that Fresnel's theory of total internal reflection 

 does to Green's. 



In the seventh paper, " On the Laws of the Double 

 Refraction of Quartz," we find the same method of treat- 

 ment. Without any reason of a mechanical nature two 

 equations of motion are assumed, viz. : — 



— 4 



dr-' ^ d. 



dS 



dt- d2- 



+ C 



dH\ 

 ds^ 



and the integrals of these are shown to express experi- 

 mental facts. Subsequently Maxwell has obtained for 

 magnetic rotatory polarisation the equations — 



{d%_ 



dS 



dt- dz- dz'dt 





d-^r, 



(^ dH 



dz^d't 



It is interesting to remark that each system is strictly 

 appropriate to the case to which it is applied. MacCul- 

 lagh' s equations do not apply to magnetic rotation of the 

 plane of polarisation, for there the direction of rotation is 

 reversed if the ray be reversed. On the other hand 

 Maxwell's equations are not to be appHed to a solution of 

 sugar or to quartz. The distinction has been overlooked 

 by Verdet, who treats both sets of equations as appropriate 

 empirical formulae for magnetic rotation ; it is perhaps not 

 surprising that Maxwell's fitted those facts the best. 



MacCuUagh's fame as a physical optician rests mainly 

 upon the well-known paper entitled " An Essay towards 

 a Dynamical Theory of Crystalline Reflexion and Re- 

 fraction." This is the fourteenth paper of the series. Its 

 position, in relation to the theories of Green and Cauchy, 

 has been very ably examined by Prof. Stokes (British 

 Association Report, 1862). But the appearance of Max- 

 well's theory of the transmission of light leaves room for 

 a reconsideration of Stokes's criticism. The real point of 

 MacCuUagh's position may be shoftly stated. In order 

 to obtain his differential equations he must ascertain the 

 form of the function V which expresses the work done in 

 causing a given deformation of the medium which 

 transmits radiation. His reasoning is obscure, but it 

 virtually amounts to this. Let 1 1; f be the displacement 

 at the point xy s of the medium, and suppose a plane 



