as applied to Micro metric Observations. 447 



centres remaining unaffected. We may suppose case (2) to 

 occur whenever the centre of either rectangle lies outside the 

 other, i. e. whenever v , — v>b\/2k, u / — u>b\/2h,u' — u being 

 the horizontal distance between J l and J 2 . 



(3) Almost complete superposition of the visible rectangles. 

 The fringes of high intensity are now affected. These are 

 destroyed or weakened whenever a is an odd multiple of 

 b\/4:(v f — v), provided that the intensity of one source be not 

 small compared with that of the other. 



Case (3) may be taken to occur when v' — v <b\/2k and 

 u' ' — u< b\/2h. 



The smallest value of a for which the fringes disappear is 

 b\/i(v f -v). 



If v r —v be very small, this may give a large value of a. 



Now a double star ceases to be resolved by a telescope of 

 aperture 2r if (v' — v)/b<\/2r, and when this relation holds 

 the smallest value of a for which the fringes disappear is not 

 less than r/2, which is the greatest separation of the slits 

 which can conveniently be used. Hence the method ceases 

 to be available precisely at the moment when it is most 

 needed. 



(4) Mr. Michelson, in the paper quoted above, noticed this 

 difficulty, and described an apparatus by means of which the 

 effective aperture of the telescope could be indefinitely 

 increased. He has not shown, however, that the expression 

 for the disturbance remains of the same form, to the order of 

 approximation taken, and he has made no attempt to work 

 out the results when the slit is taken of finite width, as it 

 should be. 



In his paper Mr. Michelson describes two kinds of appa- 

 ratus. I shall confine my attention to the second one, as 

 being somewhat more symmetrical. 



So far as I can gather from Mr. Michelson's description, 

 the instrument consists primarily of a system of three mirrors 

 a, b, c and two strips of glass e, d (fig. 4). The mirrors a and 

 b are parallel, and c, d, e are parallel. Light from a point P 

 in one slit is reflected at Q and R by the mirrors a and b, is 

 refracted through the strip e, and finally emerges parallel to 

 its original direction as T U. Light from a point P' in the 

 other slit is refracted through the strip d, and reflected at S' 

 and T' by the strips e and c. 



I may notice in passing that the strip e should be half 

 silvered, but not at the back, for if the ray S' T is allowed to 

 penetrate inside the strip and emerge after two refractions 

 and one reflexion, not only is a change of phase introduced, 

 owing to the path in the glass, which complicates the analysis, 



