188 FRESNEL. 
Huyghens in favour of his fellow countryman Snell be 
accepted, we must give up the pretence of writing the 
history of science. 
A mathematical law has more importance than an 
ordinary discovery, for it is itself a source of discoveries. 
From it simple analytical transformations point out to 
observers a multitude of results more or less hidden, of 
which they would with difficulty have become aware ; 
but such results cannot be accepted without ‘reservation, 
so long as the truth of the primary law rests solely on 
measurements. It is necessary for science that this law 
should acquire that character of demonstration which 
mere experiments alone, however precise, cannot confer, 
by being traceable upwards to the first principles of 
matter. 
Descartes then attempted to establish his law of re- 
fraction by considerations purely mathematical ; perhaps 
it was thus also that he discovered it? Fermat com- 
bated the demonstration of his rival, and replaced it by 
a method more rigorous, but which had the serious fault 
Vossius states that, among others, the contents of Snell’s MS. were 
shown to Descartes. 
That philosopher, however, in a manner very usual with him, com- 
mences treating the subject on entirely original grounds; and, in the 
course of a purely theoretical speculation deduces the same law of 
refraction as a consequence of his a priori principles (Dioptrica, 1687, 
ch. ii. § 9), without making the slightest allusion to Snell. Hence 
the discovery of the law has been assigned to him, especially by 
French writers. It is to be observed, however, that he in no way at- 
tempts to found his deduction on any comparison of experimental 
results. Thus, even admitting that Descartes is entitled to the estab- 
lishment of the law as a theoretical deduction, he clearly has no claim 
to the experimental verification of it, which is by far the most material 
point; and the more so as his theory is based on the assumption, now 
proved to be false, that light is accelerated in passing through the 
denser medium.— Translator. 
