REFRACTIVE POWER. 139 



" To apply thus, without any limitation on its general- 

 ity, calculation to phenomena ; to deduce, from a single 

 consideration of a very general kind, all the solutions 

 which before were only obtained from particular consid- 

 erations, is truly to write a treatise on analytical optics, 

 which, concentrating the whole science in a single point 

 of view, cannot but contribute to the extension of its do- 



main.' 



The Academy decided (which is the highest degree of 

 approbation it can bestow) that the memoir of Mains 

 should be printed in the Recueil des Savants Etrangers* 



MEMOIR OX THE REFRACTIYE POWER OF OPAQUE 



BODIES. 



On the 16th November, 1807, Malus presented to the 

 Academy a memoir in which he treats a point of optics 

 of great importance, a question, in fact, involving no less 



* Malus' s analytical theory contained in his Traite d' Optique, is pre- 

 fixed to his prize memoir on Double Refraction, Paris, 1810. 



The ordinary deviations by reflexion or refraction which rays un- 

 dergo on impinging on given surfaces, may be investigated in all the 

 simpler cases by means of elementary geometrical constructions, lead- 

 ing to the theory of foci, caustics, &c. But more general investiga- 

 tions of the same kind have been pursued by considering the .algebraic 

 equations of rays undergoing such deviations. This higher generaliza- 

 tion leads to, and includes, the same results. An excellent discussion 

 of the subject treated in this point of view will be found in Dr. Lloyd's 

 Treatise on Light, and Vision. It is a still higher generalization of this 

 kind which was followed out by Malus. The reader who is desirous 

 of seeing a condensed abstract of the leading mathematical principles 

 involved, is referred to a brief but luminous summary drawn up by 

 the Rev. A. Neate, M. A., and inserted in Professor Powell's Elemen- 

 tary Treatise on Optics, p. 71, Oxford, 1833. But the entire subject 

 has been treated by a far higher analysis with extreme generality, and 

 by a new and powerful principle of his own, by Sir W. R. Hamilton, 

 in his essay on the Theory of Systems of Rays. Mem. of R. Irish Acad- 

 emy, vols. xv. and xvi., and Supplement, vol. xviii. Translator. 



