CHAP. V., 6.] 



OPTICS. MACCULLAGH M. CAUCHY. 



121 



we are indebted for several interesting experimental 

 papers on optics, for an able and impartial review 

 of the progress of the science, 1 and for an excellent 

 elementary treatise on the Wave Theory, which forms 

 by far the best popular introduction to the subject. 

 (553.) Closely associated in his pursuits, as in personal 

 accul- friendship, with Sir W. R. Hamilton and Dr Lloyd, 

 was JAMES MACCULLAGH, a native of Tyrone, born in 

 1809, and who died prematurely and unhappily Oc- 

 tober 24, 184?. 2 His first paper was communicated 

 to the Royal Irish Academy at the age of 21. It 

 was one of the earliest original contributions of this 

 country to the development of the theory of Fresnel. 

 The construction of the wave surface in biaxal crys- 

 tals was simplified and improved ; and in 1835 a 

 second paper appeared, in which geometrical construc- 

 tions of great elegance were employed for the farther 

 investigation of the subject. Mr Maccullagh next at- 

 tacked the theory of the undulations of ether in quartz 

 crystals, to which he gave a mathematical expression 

 (see art. 512). In 1838 he published a paper on the 

 laws of crystalline reflection, in which he adopted 

 certain hypotheses, such as that the vibrations of the 

 ethereal particles, in the case of polarized light, are 

 parallel to the plane of polarization (contrary to Fres- 

 nel's opinion), and that the density of ether is the same 

 in all media. In a subsequent memoir on the dyna- 

 mical theory of reflection and refraction, he arrived 

 at similar results with fewer physical assumptions, 

 and by a more purely mathematical treatment of the 

 subject. Subsequent researches, presently to be men- 

 tioned, have diminished the value of these theoretical 

 investigations. 



(554.) Numerous mathematicians of eminence at home 

 ^ and abroad entered upon the same arduous enquiry, 

 bratory To attempt to deduce from the hypothetical constitu- 

 tion, tion of a very rare highly-elastic medium, together 

 with the known dynamic laws, the various complicated 

 facts of optics, was a problem whose difficulty was only 

 equalled by its indefinite character. For how little 

 do we know of the molecular constitution of such 

 fluids as air and water ] How much less then of a 

 fluid (if wemay so term it) almost infinitely rarer, and 

 incapable of being inclosed, measured, or weighed ? 

 The bare possibility of transversal undulations was 

 long contested by very able mathematicians ; and con- 

 ceding it, the mutual influence of such an ether and 

 the particles of gross matter (as shown by reflection 

 and refraction) must, it would seem, for ever remain 

 problematical. Yet, however gratuitous or even er- 

 roneoxis our reasonings about such ultimate questions 

 may be, there is no doubt a real benefit in obtaining 



from them at least a mathematical congruity with ob- 

 served facts. The progress of science shows that 

 there is a practical usefulness in this step. On the 

 other hand, we must not be discouraged to find 

 that there are so many handles to the matter, that 

 even the most profound thinkers may conceive that 

 they have reached the proposed end by different and 

 incongruous routes. Besides the mathematicians 

 whom I have mentioned, many others were in the 

 field ; for the result of tremors propagated through 

 elastic media of different kinds is an enquiry of ex- 

 cessive generality, and forms a part of many branches 

 of science besides optics. MM. Cauchy, Navier, 

 Poisson, Coriolis, Green, Kelland, and Neumann are 

 amongst those who attacked the problem. For a series 

 of years memoirs rose fast and thick on this favourite 

 battle-field ; and even a skilful mathematician might 

 find it no small penance to discuss the merits of the 

 various hypotheses and the solidity of the respective 

 deductions which were proposed. 



It must be owned that a great part of this vast C 555 -) 

 mathematical toil has been without immediate result i n g n 

 in optics. It is by comparing the conclusions ar- tics. 

 rived at by authorities of seemingly equal weight, that 

 we learn the difference between a stable physical in- 

 duction and a clever mathematical hypothesis. Mac- 

 cullagh, for instance, maintains the vibrations of ether 

 to be parallel to the plane of polarization ; Fresnel 

 and M. Cauchy 3 that they are perpendicular. The 

 first mathematician considered that the vibrations are 

 wholly transversal, the last believes that the normal 

 vibrations have also their share in affecting the 

 phenomena, whilst Poisson denies that transversal 

 vibrations can be propagated to a sensible distance. 

 Maccullagh finds that, to account for metallic reflec- 

 tion, the indices of refraction of mercury and silver 

 are 15-0 and 35-0, whilst Cauchy makes them but 

 1*77 and 0*34. One theorist assumes that the 

 density of ether is the same in all bodies, another 

 that it is greatest in a vacuum, and others pre- 

 cisely the reverse ; one that vibration is not accom- 

 panied by change of density, another that it is ; 4 

 and so on in almost endless variety. A matured 

 opinion can only be formed after the results of the 

 various assumptions, and their congruity with facts, 

 have been more thoroughly worked out. Already 

 two of Maccullagh's essential postulates have lost 

 much of their plausibility ; that respecting the di- 

 rection of the vibrations in polarized light has been 

 probably decided by Professor Stokes in favour of 

 Fresnel's opposite view, by an admirably devised ex- 

 periment on the effect of diffraction on polarized 



1 British Association Reports for 1834. 



2 It is unnecessary to suppress the fact that Mr Maccullagh died by his own hand, under the pressure of a fit of despondency, 

 brought on (it is believed) by over-work ; a fate happily extremely rare amongst students of exact science. I say it is needless 

 to suppress the fact, because it infers no blame. Mr Maccullagh was an amiable, pious, and exemplary man. Irresponsible in- 

 sanity was, of course, the cause. 



3 This is M. Cauchy's last view ; for some years he adopted the opposite one, which he then surrendered with great frankness. 



4 If, however, the vibrations were wholly transversal, it seems to be admitted that they would not affect the density of the medium. 



