192 Prof. Hamilton on the Effect 



Mr. Potter believes it to be a mathematical consequence o* 

 the undulatory theory of light, that when rays, in a plane per- 

 pendicular to the edge of a prism of glass, diverge from a 

 luminous point in vacuo, and emerge from the prism after re- 

 fraction, into a vacuum again, the locus of the points simul- 

 taneously attained by the emergent light is a circle; — either 

 rigorously, or at least with an accuracy sufficient for the in- 

 vestigation of the positions of the central points of interference 

 of two emergent streams of homogeneous light, which had set 

 out together from two near luminous origins, namely, from 

 the images of a luminous point formed by two plane mirrors 

 inclined at a small angle to each other : — from which he con- 

 cludes that these central points of interference, in the given 

 plane perpendicular to the edge, are situated on a certain hy- 

 perbola, tending towards the angle of the prism, whereas he 

 found by experiment a tendency from that angle. I find, how- 

 ever, that in consequence of the prismatic aberration (which 

 is greater than the aberration of a lens), the section of an emer- 

 gent wave differs sensibly from the circular form, and the time 

 of arrival of the light at any proposed point of interference re- 

 quires a sensible correction ; by allowing for which I find, as 

 the locus of the points of central interference in the plane 

 perpendicular to the edge, a curve not hyperbolic, and not 

 tending towards but from the angle of the prism: so that the 

 phenomenon observed by Mr. Potter is a consequence of the 

 undulatory theory. 



To simplify the question I shall suppose, with him, that the 

 line joining the two near luminous origins is perpendicularly bi- 

 sected by a line which, if considered as an incident ray, would 

 undergo the minimum of deviation, and would emerge in a 

 certain direction, which I shall take, as he does, for the axis 

 of .r; supposing also, with hiin, that this emergent line passes 

 through, or very near the edge, and measuring the positive 

 ordinates y towards the thickness of the prism, while the po- 

 sitive abscissae x are measured from the incident towards the 

 emergent light. The problem is then to find, at least ap- 

 proximately, the equation in x, y, of the locus of points of 

 central interference, or of simultaneous arrival of the light from 

 the two luminous origins, with the undulatory law of velocity; 

 and, in particular, to examine whether this locus tends to or 

 from the angle of the prism, by examining whether the ordi- 

 nate y decreases or mcreases, while the abscissa x increases 

 from its value at the prism. 



Denoting, as Mr. Potter does, the coordinates of the pris- 

 matic focus or image corresponding to one luminous origin, 

 by the values x = m a, y =? a, 



