Theory of Systems of Rays. By W. R. Hamilton, Professor of 

 Astronomy in the University of Dublin. 



Read Dec. 3, 1824.* 



INTRODUCTION, 



J. HOSE who have hitherto written upon the properties of Systems 

 of Rays, have confined themselves for the most part to the conside- 

 ration of those particular systems, which are produced by ordinary 

 reflexion and refraction at plane surfaces and at surfaces of revo- 

 lution. Mains, indeed, in his Traite D'Optique, has considered 

 the subject in a more general manner, and has made some valuable 

 remarks upom systems of rays, disposed in any manner in space, 

 or issuing from any given surface according to any given law ; but 

 besides that those remarks are far from exhausting the subject. 

 Mains appears to me to have committed some important errors, in 

 the application of his theory to the systems produced by combina- 

 tions of mirrors and lenses. And with the exception of this author, 

 I am not aware that any one has hitherto sought to investigate, in 

 all their generality, the properties of optical systems ; much less to 

 establish principles respecting systems of rays in general, which 

 shall be applicable not only to the theory of light, but also to that 

 of sound and of heat. To establish such principles, and to inves- 

 tigate such properties is the aim of the following essay. I hope 

 that mathematicians will find its results and reasonings interesting, 

 and that they will pardon any defects which they may perceive in 

 the execution of so abstract and extensive a design. 



Observatory, 

 June 1827. 



* Since tliis paper was first read before the Academy, various delays have occurred, which 

 postponed the printing until the present time. I have availed myself of these delays, to add 

 some developments and applications of my Theory, which would, I thought, be useful. 



