i82 SCIENCE PROGRESS 



latter restriction may be removed, and widths up to one-third 

 of the distance between the centres utiUsed provided that the 

 formula a = 1*22 \/d is modified thus : 



a =.-22 ^{.+0-765(1)'} 



where a is the width of each opening and d the distance between 

 their centres. 



It is possible that the results obtained may be inaccurate 

 owing to the supposition having been made that the object 

 is of uniform brightness. It is more probable that the bright- 

 ness falls off towards the limb as in the case of the Sun. The 

 correction, corresponding to any proposed law of illumination, 

 is easily deduced and is not, in general, very large. 



(2) If the object consists of two circular objects whose 

 distance apart is at least several times the diameter of either, 

 then, if the slits be placed at right angles to the line joining 

 their centres, the fringes will disappear when the angle (a) 

 subtended by the two stars is given by a = \/2d, it being 

 supposed that the two stars are of equal brightness. If not, 

 and provided the disparity in brightness is not too great, a 

 minimum visibility will be found to correspond to the separa- 

 tion of the slits given by this equation. If, then, for a given 

 double star the position and distance apart of the slits for 

 which the fringes disappear be determined, the position angle 

 and angular separation of the components can be at once 

 obtained. Since the greatest separation of the slits is the full 

 aperture of the telescope (D), the angular separations of all 

 double stars which are not less than | X/D can be determined. 

 It was shown above that, by the ordinary method of observa- 

 tion, the least angular separation measurable was 1*22 VD, so 

 that the interference method at least doubles the theoretical 

 resolving power of the telescope, a matter of supreme impor- 

 tance which, for this type of observation, is equivalent to in- 

 creasing the aperture of the 100-inch to over 200 inches. 

 Using this method, with the 100-inch telescope, the separation 

 of double stars which are as close as o"-02 can be determined. 

 The method also possesses several very important advantages 

 when compared with the ordinary methods of double-star 

 observation — viz., both distance and position angle are deter- 

 mined with the same order of accuracy, whatever the separa- 

 tion, and for the successful application of the method, very 

 good observing conditions are not necessary. 



The results obtained in the case of Capella (Hale, Nature, 

 105, 268, 1920) may be mentioned. Capella was known, from 

 spectroscopic observations, to be a binary, but had never been 

 visually separated, though examined with the largest refractors. 



