SQd THIRD REPORT — 1833. 



pressure preserves the same proportion to the pressing power 

 as far as the pressure of 65 atmospheres, and probably much 

 further ; but how far, I have not hitherto been able to try, my 

 apparatus not having resisted a greater pressure. 



" I have thus given you a short abstract of my researches into 

 the compressibility of water. They may be considered as a 

 continuation of those of Canton. I should feel much flattered 

 if they should obtain the approbation of the philosophers of the 

 country where the first good experiments upon the subject have 

 been made." 



On some Results of the View of a Characteristic Function in 

 Optics, ^y William R. Hamilton, M.R.I. A., Royal As- 

 tronomer of Ireland. 



The author gave a statement of some optical results, deduced 

 from the view which he had explained in the preceding year at 

 Oxford. 



His general method, for the study of optical systems, consists 

 in expressing the properties of any optical combination by the 

 form of ONE CHARACTERISTIC FUNCTION, One Central or radical 

 relation. In order to investigate the properties of the systems 

 of rays, produced by any object-glass, or atmosphere, or other 

 optical instrument, or combination of surfaces and media, ordi- 

 nary or extraordinary, he has proposed, as a fundamental pro- 

 blem, to express for any such combination, the laws of depend- 

 ence of the final and initial directions of a linear path of light 

 on the final and initial positions or points, and on the colour. 

 And the solution which he has offered for this fundamental pro- 

 blem consists, 1st, in reducing by uniform methods (analogous 

 to the methods of discussing the equation of a curve or surface,) 

 these several laws of dependence (of the four extreme angles of 

 direction of a curved or polygon ray on the six extreme coordi- 

 nates and on the colour,) to that one laic, different for different 

 combinations, according to which his one characteristic function 

 depends on the same seven variables. And 2ndly, in establish- 

 ing uniform processes for the research of the form of this func- 

 tion, namely, the action or time bf propagation of the light, for 

 any proposed combination. 



For example, in the case of a single plane mirror, supposed to 

 coincide with the plane of ,r y, we may propose to determine the 

 laws of the two extreme directions of the hnear path by which 

 light goes to an eye {x y %) from an object {x^ y' z'), or (ex- 

 pressing the same thing more fully,) to determine the final co- 

 sines a /3 y, and the initial cosines «' /3' y', of the inclinations of 



