[ 28* ] 



XL VII. On the undulatory Time of Passage of Light through 

 a Prism. By William K. Hamilton, Esq. Andrews 9 Pro- 

 fessor of Astronomy in the University of Dublin, and Royal 

 Astronomer of Ireland*. 



C INCE I communicated my little paper, On the Effect of 

 ^ Aberration in prismatic Interference, (p. 191.) I have seen 

 Professor Airy's remarks on Mr. Potter's experiment; in which 

 it is suggested, that the observed central points, which tended 

 towards the thickness of the prism, were not the points of si- 

 multaneous arrival of two homogeneous streams. From the 

 well-known experience and skill of Professor Airy as an ob- 

 server, I think it likely that he has assigned the true physical 

 explanation of Mr. Potter's instructive experiment; though 

 I wish that this experiment were repeated, with careful micro- 

 metrical measures. But I continue to think the mathema- 

 tical correction just, which I proposed in my recent paper. 

 In that paper, I took Mr. Potter's own account of his experi- 

 ment ; namely, that he had found, in the plane perpendicular 

 to the edge, a tendency towards the thickness, and from a cer- 

 tain intermedial line, in the locus of the points of simultaneous 

 arrival of two near homogeneous streams : and I endeavoured 

 to show, that according to the undulatory theory, this locus 

 ought, during a considerable range, to tend in this direction 

 and not in the opposite ; — a mathematical result, which was 

 contrary to Mr. Potter's conclusion. It is, I hope, unneces- 

 sary to repeat the expression of my sincere respect for the 

 gentleman from whom I have found myself obliged to differ 

 on this mathematical question. But as I only stated, in my 

 former paper, a correction of Mr. Potter's formula for the dif- 

 ference of times of arrival of two homogeneous streams, arising 

 from the prismatic aberration of figure, and showed the in- 

 fluence of this aberrational correction on the course of the 

 sought locus, without showing how I obtained the correction 

 itself, — it may be useful to give here an outline of the method 

 which I employ, for the treatment of this, and of other similar 

 questions ; referring, for more full details, to the recent and 

 forthcoming volumes of the Transactions of the Royal Irish 

 Academy. 



Let light be supposed to go, in a bent path A BCD, from 

 an initial point A to a final point D, through any prism or- 

 dinary or extraordinary, undergoing a first refraction at the 

 point of entrance B, and a second refraction at the point of 

 emergence C, the prism being placed in vacuo, and its angle 

 being small or large ; let the position of the final point D be 

 marked by three rectangular coordinates x,y, z, of which the 



* Communicated by the Author. 



