THE AID OF THE ACHROMATIC FRINGES. 9 



If r is the length of the lever c, figure i , and Ax the displacement of the pin e 



(2) rA0 = A* 

 Hence 



(3) A* = (r cos *'/&)AJV 



The apparatus is more sensitive as r is smaller and b is larger. In the 

 instrument used (adapted from an earlier apparatus), 



r=ucm. 6 = 10 cm. i = 45 



so that 



(4) A* = o.778AAf 



But the main condition of sensitiveness is contained in the size of the 

 fringes, and these may be made indefinitely large by suitable rotation of the 

 mirrors M and M', for instance, in like direction on a horizontal axis (local 

 coincidence of rays on M'}. Since 



in case of the passage of n fringes, equation (3) becomes 



(5) &x = nr\/2b 



so that the limiting sensitiveness (w= i) would be (with the above data) 



(6) Ax=i 



for a single fringe, a few tenths of which may be registered with certainty. 

 When the achromatic fringes are used it is, however, usually more convenient 

 to standardize the ocular plate micrometer in the telescope directly by aid of 

 the screw micrometer s, at M', figure i. If the ocular plate is divided in tenth 

 millimeters along a centimeter of length and the fringes are of moderate size, 

 one may estimate that about 40 scale-parts correspond to AA/"=icT 3 cm., so 

 that a single scale-part of displacement of the achromatics is equivalent to 

 A A r = 2 5 X i o~ 6 cm . , while a few tenths of a scale-part may here also be estimated . 

 If the apparatus (fig. 3) is to be used as a spherometer, the ordinary method 

 of measuring from a plate of glass is at once available. If r is the radius of 

 the circle of the tripod and Ax the height of the central foot, we obtain, as 

 usual, for the radius R required 



(7) R = 



This method gives good results for lenses of all curvatures, however strong, 

 as the tests below indicate. But it is not necessary to use the plate to obtain 

 a fiducial reading, provided the system Gr carrying the lens g is on good right 

 and left slides. For in figure 4, let 6 be the angle between the plane of the 

 tripod and the slides, and let three readings of AN be taken for three preferably 

 equidistant points, /, c, v, of the lens, by sliding Gg over equal distances, r. 

 Let the reading be 



(8) y=N y' = N+rtan6+AN 



