of Aberration in prismatic Interference. 19S 



ami those of the prismatic image of the other luminous origin 

 by x = 0, y = — a, 



in which a is half the interval between the two near luminous 

 origins, and m is a positive number depending on the angle 

 and index of the prism. Mr. Potter finds for the difference of 

 times of arrival of the two streams of emergent light at any 

 point x,y, not far from the axis of x, the expression 



A/x*+(y + a.y — s/ \x—maf-\-(y—af —ma... (I) 



and equating this expression to zero, he finds for the locus of 

 the points of central interference, the equation of a common 

 hyperbola, which may be put under the following approximate 

 form, 



*=tt : & 



If then this analysis were sufficient, it would show, as Mr. 

 Potter has concluded, that^ decreases, and that the locus tends 

 towards the angle of the prism ; whereas the experiment showed 

 a contrary tendency. 



But I find, that on account of the prismatic aberration, the 

 expression (1) for the difference of times of arrival, requires 

 this correction, namely, 



na ^ _ ,^^-ay m 



in which / is a positive quantity, namely, the length of the 

 path traversed by the light in arriving at the edge of the 

 prism ; and after allowing for this correction (3), the equation 

 of the sought locus, of the points of central interference, gives 

 the following approximate expression for the ordinate y, 



ma* ma* I , MS 



y=^~ ?**: ^ 



the second term being introduced by aberration, but being 

 of the same order as the first. And taking account of this 

 new term in the expression af the ordinate, we have, by dif- 

 ferentiation, ^ 



dy ma? ma 2 1 ma* (21— x) . 



dr ~ ~ TF + TP~ * Tx 1 " ' " l } 

 so that while x increases from its value I at the prism to the 



value 2/, the ordinate y increases from to , , and the 



curve tends towards the thickness of the prism, as it was found 

 Third Series. Vol. 2. No. 9. March 1833. 2 C 



