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titled to assume henceforth a very high rank among the principles 

 of physical optics. 



The method which Mr. Mac Cullagh has adopted may he said 

 to he in general the method of mathematical induction, as distin- 

 guished from dynamical deduction. He has not sought to deduce, 

 from any pre-supposed attractions or repulsions, and arrangements 

 of the molecules of the ether, any conclusions respecting the vibra- 

 tions in the interior or at the boundaries of a medium, as necessary 

 consequences of those dynamical principles or assumptions. But 

 he has sought to gather from phenomena a system of mathematical 

 laws by which those phenomena might be expressed and grouped 

 together, be conceived in connexion with each other, and receive 

 an inductive unity. He has sought to arrive at laws which might 

 bear somewhat the same relation to the optical observations already 

 made, as the laws of Kepler did to the astronomical observations of 

 his predecessor Tycho Brahe, without seeking yet to deduce these 

 laws, as Newton did the laws of Kepler, from any higher and 

 dynamic principle. And though, no doubt, it is to such deduction 

 that science must continually tend ; and though, in optics, some 

 progress has been actually made, by Cauchy and by others, to a 

 dynamical theory of light, as a system of vibrations regulated by 

 forces of attraction and repulsion ; yet it may well be judged a 

 matter of congratulation when minds are found endowed with 

 talents so high as those which Mr. Mac Cullagh possesses, and 

 willing to apply them to the preparatory but important task of dis- 

 covering, from the phenomena themselves, the mathematical laws 

 which connect and represent those phenomena, and are in a manner 

 intermediate between facts and principles, between appearances and 

 causes. 



It was thus, that, in a former paper, Mr. Mac Cullagh proposed, 

 as mathematical expressions for the phenomena of Quartz, a system 

 of dhTerential equations, which are indeed simple in themselves, 

 and seem to agree well with observation, but have not yet been 

 shewn to be consistent with dynamic views. And in that later 

 memoir for which the present prize is awarded, he has, in like 

 manner, adopted some hypotheses, and rejected others, without 

 apparently regarding whether and how far it may seem possible 



