Royal Irish Academy. 381 



December 1839 (Proceedings, vol. i. p. 374*). This was followed 

 soon after by a general Theory of Total Reflexion (Proceedings, vol. 

 ii. p. 96f)» founded on the same principles. The latter theory, form- 

 ing a new department of physical optics, and involving the solution 

 of questions not previously attempted, was analytically complete when 

 it was communicated to the Academy in May 1841 ; but its geome- 

 trical development has since required my attention from time to time, 

 and has not yet been brought to that degree of simplicity of which 

 it appears to be susceptible (see Proceedings, vol. ii. p. 174). Indeed 

 I have found that, in this instance, the geometrical laws of the phe- 

 nomena are by no means obvious interpretations of the equations re- 

 sulting from the analytical solution of the problem ; and in endea- 

 vouring to verify such supposed laws I have often been led to alge- 

 braical calculations of so complicated a nature that it has been im- 

 practicable to bring them to any conclusion, and I have been obliged, 

 from mere weariness, to abandon them altogether. On returning, 

 however, to the investigation, after perhaps a long interval of time, 

 I have usually perceived some mode of eluding the calculations, or 

 of directly deducing the geometrical law ; and when the theory comes 

 to be published in its final form, no trace of these difficulties will 

 probably appear. 



From the causes above mentioned, combined with frequent absence 

 from Dublin, the researches which I had entered upon, respecting 

 the action of metals upon light, have been hitherto interrupted ; and 

 as it may still be some time before they are resumed, I venture, in 

 the meanwhile, to submit to the Academy the results already spoken 

 of, which were obtained on the first trial of the instrument, and which 

 afford the best data that can yet be had for comparison with theory. 



The results, it must be confessed, are those of very rough experi- 

 ments, made one evening (about the month of July 1837) in com- 

 pany with Mr. Grubb, before I had received the instrument from his 

 hands, and merely with the view of showing him, when it was finish- 

 ed, the kind of phenomena that I proposed to observe with it, and 

 the mode of observing them. But the instrument was so far supe- 

 rior (in workmanship at least) to any apparatus previously employed 

 for this sort of experiments, that it was impossible, without great 

 negligence in using it, not to obtain measures of considerable accu- 

 racy. I did not, however, at the time, set much value on these mea- 

 sures, because I expected shortly to possess a series of observations 

 made with every possible precaution ; but having chanced to preserve 

 the paper on which they were noted down, I was tempted, a few days 

 ago, to try how far they agreed with my formulae ; and the agree- 

 ment turns out to be so close, that I think myself justified in publish- 

 ing them. Besides, it will be curious hereafter to compare them 

 with more careful measurements. 



Before we proceed, however, to the details of the experiments, it 

 may be well to give the formulae in a state fitted for immediate ap- 

 plication. The light incident on the metal being polarized in a cer- 

 tain plane, let a denote the azimuth of this plane, or the angle which 

 * Phil. Mag. S. 3. vol. xvi. p. 229; vol. xxi. p. 228.— Edit. 

 f lb. vol. xxiii. p. 137. — Edit. 



