as applied to Micrometric Observations. 457 



-r, ( 4:7rav 



±1 = | cos iidv over the image 



47rav <#sr 6\ T (\iratz\ 



w 



The visibility is therefore 



7 /47rttOT\ / /A7ravr\ 



2,h {-i^-)/\~bir)> 



and vanishes whenever 



J.^-O. 



Hence we see that, for an elliptic source, if p = length of semi- 

 diameter perpendicular to the slits, -57 = length of perpendicular 

 on the tangent parallel to the slits, then the fringes disappear 



when sin =0, if the angular dimensions are of order 



ja r as indicated above, and when J : I )~0, when the 



angular dimensions are less than — - T . 



In the first case p is the quantity which determines the 

 disappearance of the fringes, in the second case w: and 

 further, we see that the validity of the formulae is entirely 

 dependent on the length and breadth of the slit, neither of 

 which is considered by Mr. Michelson. 



We may notice that the best results are obtained, in the 

 first case when h is large, in the second case when h is small. 



7. It remains to consider the intermediate case (c). This 

 does not perhaps present so much interest as the other two ; 

 the first will generally correspond to the case of a planet, the 

 second to that of a star, in astronomical observations. 



In dealing with case (c) we shall suppose the ano-ular 

 dimensions to be small, with regard to \/k 9 but not with 

 regard to \/h. We may then write 



\ «L_ 1 **l_1 cos * **«(*+*) , , 



1 *2irk{q + v) JTrh(p + u) t cos fa <V» 



I b\ bX ) 



. Jlirhu 



32A«A 8 ff 



IW 



I l b\ /- ±ira(q + v)\ 1 _ 



