INTENSITY OF REFLECTED AND REFRACTED LIGHT. 395 



is due. This last investigation was reserved for M. Cauchy, who managed it with 

 great skill, in his Exerdces de Matliematiques, vol. iii. p. 188, and vol. iv. p. 129. 

 In the fifth volume, M. Cauchy applied his results to the theory of light ; but his 

 success was not complete at first, owing to the circumstance that he had recourse 

 to the method of expansion so universally adopted in physical investigations. In 

 subsequent publications, however, M. Cauchy has solved the difficult problem of 

 obtaining a relation between the velocity of transmission and the length of the 

 wave. This very important result, which removed from the undulatory theory 

 almost the only obstacle to its being entitled to the designation of a irwe physical 

 theory, appeared in 1830. Since that time M. Cauchy has pubUshed various me- 

 moirs on the reflexion of light, and on other points of the theory, in one of which 

 he has determined the law of force by which the particles act on one another to 

 be that of the inverse fourth power of the distance. 



In a memoir of my own ( Transactions of the Cambridge Philosophical Society, 

 vol. vi. p. ] 53), another law is arrived at, viz. that of the inverse square of the 

 distance. This conclusion, agreeing as it does with the great law of gravitation, 

 and necessary, moreover, as it appears to be, from the very condition of attrac- 

 tion, I have retained in all my subsequent investigations. One important corol- 

 lary from it will be found in page 180 of the same memou-, viz. that the vibra- 

 tions are altogether transversal to the direction of a nave. This conclusion Pro- 

 fessor Lloyd has also obtained from Cauchy's law of the inverse fourth power. 

 His paper was read to the Royal Irish Academy. It would be too wide a field to 

 enter on the discoveries of Sir William Hamilton. Copious information on the 

 subject, together with a translation of M. Cauchy's most important memoir, will 

 be found in the pages of the Philosophical Magazine. 



Nor is the arrangement and action of force thus assumed less in consistence 

 with statical than with dynamical truths. The great problem of cohesion, as 

 connected with expansion, &c., appeared to defy a law of force such as that of 

 the inverse square, until M. Mossotti, by a most skilful application of analysis, 

 removed the most glaring difficulties. The same subject has been commenced 

 by myself in the Transactions of the Camhndge Philosophical Society, vol. vii., in 

 which I have deduced results which demonstrate the possibility, or at least aiford 

 argument for the probability, of the universality of the law of universal gravita- 

 tion. This, therefore, is the present state of the molecular theory : it coincides 

 with the great law of attraction, and is the extreme limit to that law ; it accounts 

 for the complicated phenomena of light, which defy more simple investigation, 

 at the same time that it requires the introduction of no modification into those 

 processes which are adequate to effect their purposes without its aid ; it demon- 

 strates the necessity of a circumstance which had previously been only suspected 

 to exist, the perfect transversality of vibration ; and, lastly, it promises an insight 

 into the perplexing phenomena of absorption. Having thus pointed out the na- 



