some of our physical theories, and to illustrate the subject of 
this ‘discourse by a few digres-ions suggested by the historical 
development. 
As a first example I chose the progress of the undulatory 
theory of light. There is no other branch of physics in which 
the power of mathematics has been more successfully shown, 
nor is there one which shows the relations of experimental to 
mathematical physics ina truer light. At first we had experi- 
inental facts ahead of theoretical explanatiors ; then we had the 
undulatory theory, which placed theory in advance of experi- 
ment; and now again a reversal has taken place, and un- 
explained experiments will remain unexplained until we shall be 
able to form more definite ideas of the relations between matter 
and the luminiferous ether. 
Huyghens first worked out scientifically the hypothesis that 
light consisted of the undulations of an all-pervading medium. 
But as those who adopted the rival theory professed to explain 
equally well all phenomena which were then generally known, 
the scientific world preferred to walk in Newton’s footsteps, and 
to reject what they believed to be the complicated and unneces- 
sary assumption of an universal medium. The corpuscular 
theory could easily explain the ordinary laws of reflection and 
refraction. Its attempts to explain the colours of thin plates 
and the fringes of shadows were less successful, but experi- 
“mental investigations of these phenomena were not sufficiently 
advanced to bring these facts prominently into view, nor had 
their true explanation as yet been given. It was only when 
mathematical analysis was applied to the undulatory theory that 
its enormous advantages were discovered. Neither of the men 
to whom we owe the greatest advance which has yet been made 
in the science of light was a professed mathematician. Young 
was a medical man, Fresnel was an engineer; nor was the 
subject, when these men took it up, in a state which would have 
attracted a mathematician, Conceptions distinctly physical had 
to be formed, and assumptions not quite satisfactory had to be 
made. Their chief claim to our gratitude rests, not so wuch on 
the mathematical treaument they have given, as on the fact that 
they left the subject in a state sufficiently advanced to allow 
mathematicians, even without special physical proclivities, to 
take it up, extend it, and establish its foundations more firmly 
than otherwise they could have dene. 
The different manners in which Young and Fresnel set to 
work to prove to the scientific world the truth of their favourite 
hypothesis, and the corresponding difference in their success is 
especially interesting for the purpose which we had in view. 
Both men had considerable mathematical ability, and of the 
two, Young perhaps had the greater inclination towards pure 
mathematics, yet he avoided wherever he could the use of 
niathematical symbols, and disdained to bring forward experi- 
mental verification for what he considered sufficiently clear 
without. It is to Young that we owe most of the physical 
conceptions wLich have secured a final success for the undulatory 
theory of light. He was the fir-t to explain the principle of inter- 
ference both of sound and of light, and he was the first to bring 
forward the idea of transverse vibrations of the undulations of 
light. The most diverse phenomena were explained by him, 
bnt their easy ex, lanstion was a sufficient proof to him of the 
theory he was defending, and he dd not trouble to verify his 
conclu ioas by extensive numerical calculations, It thus hap- 
pened, that although Young was first in the field in furni hing 
the true explanation of complicated phenomena, Fresnel, apply- 
ing mathematical analysis to a mucd greater extent, had a much 
more potent influence in turning the scale of public opinion in 
favour of their common theory. 
Thovgh Fresnel’s first memoir was published fourteen years 
after Young had established the principle of interference, 
Young’s writings had remained unnoticed by bim as well as by 
the scientific world in general, and Fresnel was surprised and 
irritated to hear that nother had been in the field before him, 
But everyone mu t agree that the chief share in securing the 
final triumph of the wave theory belongs to Fresnel, nor can 
there be any doubt that this is due to the mathematical calcula- 
tions which he applied to cases easily verified by experiment. 
For there is a great fascination in a table with one column 
headed “calculates,” another headed ‘‘ observed,” and a third 
giving the differences with the decime] point as much to the left 
as possible, And it is right that such tables should play an im- 
portant part in the history of science, for whatever the ultimate 
t ‘* For my part it is my pride and pleasure. so far as I am able, to super- 
sede the necessty of experiments.’’— Peacock's ** Life of Young,” p. 477 
Abstract of letter by Yc ung. 
“NATURE 
| Fed, 2 3.1 8s: 
fate of a jartially accepted theory, the one slid legacy which 
it will leave bel ind after its death is the array of numbers for 
which in its successful stage it has given a sufficiently correct 
account. ; 
Fresnel invented different pieces of apraratus to test Young’s 
simple supposi'ion, independently made by him, that waves may 
te.made mutually to destroy one another by addition, the crest 
of one wave being su, erposed on the hollow of another. It is 
necessary that the waves should originally be derived from a 
single source of light, yet they must seem to diverge from two 
different points. The necessary experimental conditions were 
fulfilled by the ingenious device of reflecting the light from two 
mirrors slightly inclined to each other. ‘Ihe light diverging 
from the two images of one source was allowed to cross, and 
bands alternately luminous and dark were measured at the places 
where the waves overlapped. A ronu:h micrometer of his own 
con-truction served to measure the intervals between the bands 
at various distances from the mirror, and Fresnel succeeded in 
obtaining sufficient data to test his theory. It cannot be my 
purpose to follow Fresnel and to describe all the various devices 
which he invented to confirm his views, and to estab'i h the true 
theory of diffraction. ‘Though he succeeded in making a convert 
of Arago, the greate:t ruthorities then living, and the most 
influential men in scientific matters, both Laplace and Poisson 
disdained to consider the theory. The ma’hematical basis on 
which the theory re:ted seemed to them to be weak and in«uffi- 
cient. No deubt they were right ; for many assumptions made 
hy Fresnel were daring, and only justified by the results of 
further more careful investigations ; some of his assumptions even 
were inaccurate, It wes only when they henomena of polari:ation 
and double refraction were explained that Laplace acknowledged 
the great power of the undulatory theory, and with a remarkable 
inconsistency publicly stated his admiration for Fresnel’s work, 
after a paper which is more unsati-factory from a mathematical 
point of view than anything else written by Fresnel. The oppo- 
sition to the undulatory theory cffered by the strictly mathemati- 
cal school no doubt prevent d its rapid acceptance by the general 
body of scientific men, Fut it is doubtful whether its final success 
was delayed. On the contrary, Fresnel was spurred on to greater 
exertions, and the excitement caused by the violent views taken 
by the opposed pariies rendered the question a burning cne, 
which it was necessary to settle definitely. The impartial obser- 
vers had, at the time of which we are speaking, ore strong argu- 
ment for suspending the’r judgment. One great class of pheno- 
mena, now known under the title of phenomena of polarisation, 
| were unexplained as yet, and it seemed d: ubtful to them whether 
the undulatory theory could successfully overcome the difficulty. 
Then, as before, it was Young who first gave the physical ex- 
planation, while it was reserved for Fresnel again to show how 
the explanation was sufficient to account numerically for all the 
observed facts, 
Those who first started the idea of lumincus undulations 
founded their belief in great part on the analogy between the 
phenomena of light and those of sound. In a wave of sound 
each particle moves in the direc’ion in which the waves are pro- 
pagated, and it was natural to make the ‘ame supposition for the 
waves of light. Yet the n ass of unexp!ained facts forced Young 
to consider the alternative case of waves in which the motion is 
in a plane at right angles to the direction of propagation. The 
waves of water in which such a meticn partly takes place may 
have given to Young the first idea of a supposition which, 2s he 
showed, could account fer many apparently singular phenomena. 
But his want of taste for calculations as well as for experi- 
mental verification prevented him from reaping the full fruits of 
his fertile ideas. Fresnel tells us that when he first conceived 
independently the idea of transverse vibrations he considered 
the supposition so contrary to received ideas on the nature of 
vibrations of ela-tic fluids, that he hesitated to adopt it, and he 
adds: ‘‘Mr. Young, more bold in his conjectures and less con- 
fiding in the views of geometers, publi hed it before me, theugh 
he perhaps thought it after ne.” Put when ence the question 
was raised, Fresnel applied to it the patient skill which, either 
by strict mathematical deductions or by happy guesses and 
assumptions surmounted all difficulties. The phenomena of 
double refraction and their connection with polarisation were 
now explained, and all the varied phencmena of light seewed 
naturally to follow from the simple suppositicn of waves of 
transverse vibrations. Such a svecessful application of n athe- 
matical calculations to the investigation of physical phenomena 
had not been heard of since the time of Newton, and could not 
| failin the end to produce its due effect. The supporters of 
