as applied to Micro metric Observations. 459 



Hence: 



1 = 



bW 



j 2r -l r-l /4w7*\ T /47TO^\ 



bX l^ i / 47raOT / r(2r-l) 2* 



i (*— 1)1 



32A 2 OT.- 2 



6 2 X 2 



TT J_ 9 ^^ ™d ;■ I V 6\ / J\JW 



iV + Zcos __ ^ x ti } 1"^^" frl(2f— 1) 



Denote by 12 the total area of the image and by e the ratio 



/ 47r/^\ 2 //87T«'5T\ 



Then the visibility 

 2H 1 



T /47ra'sr\ e T /47ra«r\ 

 K 47m*7 i °\Jjr) 6 J VfaT7 + 



6\ 



i 



+<-«>" ^£r><-F) + ---| 



The series for the visibility is absolutely convergent, 

 because J n +i(®)/Jn{®) decreases numerically without limit 

 as n increases without limit. 



The roots of the equation 



/&7ra'&\ e T / liravrX / .. e r ~ l T /Aira'ST\ 



(-Mr)-6 J <-«r) + -- + <- 1 )'" l r-r(2^r) J {^r) + ---= 



give the values of a for which the visibility vanishes. 



Notice, however, that e contains d and the length of the 

 slit, so that the values obtained for a will be functions of 

 the horizontal diameter and of the length of the slit. 



8. Besides enabling us to determine the angular distance 

 of two point-sources and the radius of an extended source, 

 Mr. Michelson's method allows us to detect and measure the 

 ellipticity of a luminous disk. 



Keferringto the formulae for cases (a) and (b), the visibility 

 vanishes when 



sin , " = in case (a), 



OA> 



and when 



ji ' \ = in case (b). 



