Interference Phenomena in a new Ref Tactometer. 237 



above-described instrument do not exist) ; and though the 

 solution is not perhaps adapted to the general problem, it 

 accounts satisfactorily for all the phenomena observed in the 

 special case. Let m x m 2 (fig. 2) be two plane mirrors 



Fia:. 2. 



-4- 



whose intersection is projected at 0, and whose mutual incli- 

 nation is <f). The illumination at any point P (not neces- 

 sarily in the plane of the figure) will depend on the mean dif- 

 ference of phase of all the pairs of rays starting from the 

 source and reaching P, after reflection from the mirrors — a 

 pair of rays signifying two rays which have started from the 

 same point of the source. 



If the area of the luminous surface is sufficiently large, the 

 illumination at P will be independent of the distance, form, or 

 position of the surface. Suppose, therefore, that the luminous 

 surface coincides with the surface m x . Its image in m x 

 will also coincide with m x ; and its image in m 2 will be a 

 plane surface symmetrical with Om L with respect to Om 2 ; 

 and for every point p of the first image, there is a correspond- 

 ing point p' of the second, symmetrically placed and in the 

 same phase of vibration. Suppressing, now, the source of light 

 and the mirrors, and replacing them by the images, the effect 

 on any point P is unaltered. Consider now a pair of points 

 p, p'. Let 3 be the angle formed by the line joining P and p 

 (or p') with the normal to the surface, S and $ being both 

 supposed small, 



A = Pj/ — Pp =pp f . cos •&. 



The difference between this value of A and the true value is 

 2Pp . sin 2 ^-, where ty is the angle subtended by pp 1 at P. 

 If S is a small quantity, ^ is a small quantity of the second 



