﻿the Micro- Azimometer. 399 



of T only ; and it appears that, whatever value be assigned 

 to T, the most favourable relation between a and /3 is given 

 by 



/8V=1+ V3. 



When this relation is duly satisfied (7) reduces to 



27r 2nir ' 4 + 1/3 tnw 



xO-65. . . (7 a) 



31. As an example, suppose that a/27r = l/40 (the diameter 

 of the wire being thus 19/20 of the width of the central 

 bright band), and that n = 20, which implies that a 10 per cent, 

 difference of brightness between the right-hand and left- 

 hand "residual strips" could not escape detection. In this 

 case Sa/27r= 1/1230 ; or, in words, the greatest error which 

 the eye could tolerate in the setting of the wire would 

 amount to only 1/I2o0 of the width of the central band. 

 The conjectures on which this estimate is based appear 

 hardly extravagant, if we suppose the most brilliant obtain- 

 able source of homogeneous light to be used ; and there 

 seems to be at least a reasonable prospect that the results 

 given in Table I. could thus be surpassed (indeed these 

 probably do not represent the limit of sensitiveness attainable 

 with intense white light). On the simple diffraction theory 

 which has served for the calculations in this paper, the 

 ultimate sensitiveness realizable with a given mirror, and 

 with a light-source of given wave-length, should increase 

 indefinitely with the intrinsic brightness, to the fourth root of 

 which it should be proportional. 



32. Given the intrinsic brightness of the source of illumi- 

 nation and the dimensions of the (rectangular) reflecting 

 surface, it is easily shown that, within limits, the greatest 

 attainable angular sensitiveness is independent of the focal 

 length of the object-glass employed. For if, following a 

 change in /', we make a proportional change in the width cf 

 the slit and the diameter of the wire, and an inversely pro- 

 portional change in the equivalent focal length of the 

 cylindrical eyepiece, the diffraction pattern, partially eclipsed 

 by the wire, will be seen on the same lateral scale as before, 

 and with the same brightness at every point. The only 

 change observable in the field will be a reduction of the 

 apparent height of the pattern as the focal length / is 

 increased. It is only when the apparent height has been 

 thus reduced below a certain limit that the sensitiveness will 



