OF NATURAL PHILOSOPHY. 33 



previous trial, and all opinion was against it. But 

 when put to the test of experiment in a great variety 

 of new and ingenious methods, it was found to be 

 fully verified ; and to complete the evidence, the sub- 

 stances on whose imperfect examination the first 

 erroneous conclusion was founded, having been 

 lately subjected to a fresh and more scrupulous 

 examination, the result has shown the insufficiency 

 of the former measurements, and proved in perfect 

 accordance with the newly discovered laws. Now 

 it will be observed in this case, first, that, so far from 

 the principles assumed by M. Fresnel being at all 

 obvious, they are extremely remote from ordinary 

 observation ; and, secondly, that the chain of rea- 

 soning by which they are brought to the test is one 

 of such length and complexity, and the purely ma- 

 thematical difficulty of their application so great, that 

 no mere good common sense, no general tact or or- 

 dinary practical reasoning, would afford the slightest 

 chance of threading iheir mazes. Cases like this 

 are the triumph of theories. They show at once 

 how large a part pure reason has to perform in our 

 examination of nature, and how implicit our reliance 

 ought to be on that powerful and methodical system 

 of rules and processes which constitute the modern 

 mathematical analysis, in all the more difficult ap- 

 plications of exact calculation to her phenomena. 



(24.) To take an instance more within ordinary ap- 

 prehension. An eminent living geometer had proved 

 by calculations, founded on strict optical principles, 

 that in the centre of the shadow of a small circular 

 plate of metal, exposed in a dark room to a beam of 

 light emanating from a very small brilliant point t 

 D 



