460 On certain Diffraction Fringes. 



In either of these cases, if we rotate the slits about the axis 

 of the telescope, without altering a, then if the source is 

 elliptic, p and nr will vary, and the visibility of the fringes 

 will vary. 



Now suppose for a given position of the slits we vary a 

 until the visibility = for that position, and then rotate the 

 slits and note the different inclinations for which it vanishes. 



It will certainty vanish once again before a complete half- 

 turn has been made, namely, when the slits make an angle 

 with the direction of either axis of the ellipse equal to that 

 which they made at first, but on the other side of the axis. 



It may vanish more than once, but since the inclinations 

 for which it vanishes are symmetrical with regard to the 

 axes of the ellipse, there will usually be no difficulty in deter- 

 mining the directions of the axes. 



Their lengths can then be determined by two observations 

 of the disappearance of the fringes, one for each of the two 

 positions of the slits which are perpendicular to an axis. 



It must, however, be noticed that the accuracy of this 

 method for measuring ellipticity decreases with the size of 

 the source, inasmuch as the quantity which causes the altera- 

 tion in the fringes is the difference, not the ratio of the semi- 

 axes. 



To get some idea of the sensitiveness of the method, let us 

 estimate roughly the amount of ellipticity which could be 

 detected in a disk of angular semi-diameter 10 7 ', taking the 

 mean wave-length of light "5 X 10 -4 cms. 



The visibility vanishes when sin = 0, and will be 



quite sensible when sin , " = -^, say. Hence in order that 



we may be able to note a sensible difference of visibility in 

 the fringes, we must have 



£(*?)-;- le^; 



or 



P1—P2 _ 1_ JL 

 b "2 10 6 

 if a be a little above 4 cms. 



.*. difference of angular semi-axes ='01 (semi-diameter) 

 g.p.j or the amount of ellipticity which can be detected =*01. 



I have taken sin— - — - = as giving zero visibility, because 

 this example will clearly fall under case (a). 



