Interference Methods to Astronomical Measurements. 

 Differentiating with respect to 7, 



17 



dy 



dl 

 dy 



sin 2 -(7-</>) 



co t_( 7 _^) 



a 



?(7-+) 



Substituting «£=- (7— $), we have finally 



a o 



*^ 7r/«o (v-«/ 2 ) v VZa o/ V a o ' v 7 



fit ry 



Integrating this for different values of — and — , we 

 obtain the curve shown in fig. 9, which can be expressed 

 very closely indeed for < - < 1 by the simple formula 



(D.-K-'CGP.- 1 ]) • • • < 26> 



where 



f ~ ) is the ordinate to the dotted curve, 



( — ) „ „ full curve for any given value of— . 



> a oA a o 



The results of some observations by this method on the 

 size of a slit and of circular openings of varying diameters, 

 gave, in the case of the slit, errors varying from one to fifteen 

 per cent.', the average error being about eight per cent. ; and 

 in the case of circular openings errors of from three to twenty- 

 five per cent., the average error being about twelve per cent. 

 The accuracy of both this and the preceding method would 

 undoubtedly be increased by taking the mean of a number of 

 observations. 



Of the two methods, the first is by far the most accurate; 

 but even the second gives results which are from eight to ten 

 times as accurate as those which can be obtained by using 

 the telescope directly. 



The apparatus by which the observations in the preceding 

 tables were made is shown in Plate II. fig. 1. The objective 

 of the telescope (a very fine four-inch glass, for the use of 

 which I am indebted to the Worcester Polytechnic Institute) 

 was fitted with a pair of adjustable slits, whose distance apart 

 could be regulated by a right-and-left-hand screw geared to 



Phil Mag. S. 5. Vol. 30. No. 182. July 1890. C 



)#. 



(25) 



