(553.) 
Maccul- 
lagh. 
(554.) 
Mechanical 
theories of 
vibratory 
motion. 
Cnap. V., § 6.] 
we are indebted for several interesting experimental 
papers on optics, for an able and impartial review 
of the progress of the science,’ and for an excellent 
elementary treatise on the Wave Theory, which forms 
by far the best popular introduction to the subject, 
Closely associated in his pursuits, as in personal 
friendship, with Sir W. R. Hamilton and Dr Lloyd, 
was James Maccu.acu, a native of Tyrone, born in 
1809, and who died prematurely and unhappily Oc- 
tober 24, 1847.2. 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, 
Numerous mathematicians of eminence at home 
and abroad entered upon the same arduous enquiry. 
To attempt to deduce from the hypothetical constitu- 
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- 
roneous our reasonings about such ultimate questions 
may be, there is no doubt a real benefit in obtaining 
OPTICS.—MACCULLAGH—M. CAUCHY. 
919 
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 
mathematical toil has been without immediate result ; 
in optics. 
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* 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 
177 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 ;* 
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 ont, 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. 
* 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 stud 
to suppress the fact, because it infers no blame. Mr Muccullagh was an amiable, pious, and exemplary man. 
sanity was, of course, the cause. 
ts of exact I say it is needless 
Irresponsible in- 
% This is M. Cauchy’s last view ; for some years he adopted the opposite one, which he then surrendered with great frankness. 
“If, however, the vibrations were wholly transversal, it seems to be admitted that they would not affect the density of the medium. 
(555.) 
heir bear- 
- “ : ing on op- 
It is by comparing the conclusions ar- tics. 
