Interference Methods to Astronomical Measurements. 15 

 Writing this in the form 



sm — 



7 + 



5) 



= + 



lb-l) 



we see that when — <1 the two sides of the equation have 

 opposite signs, because 



IT ( cc\ it { a\ 



*(*-*) <,r< ^(r+s); 



and we have 



7r/ «\ . 7T/ a\ 



Sill 



« V 7 2/ a l 7 ^ 



Expanding and solving for 7 we find 



, 777 a . 7ra 

 7 tan — = : tan^- 5 . . 



which gives the condition for a minimum when 



0<-<l, 2<-<3,...2m<-<2m + l 



(21) 



(22) 



"0 



a 



«o 



When 1 < — < 2, the si cm of the two sides is the same, 

 and we have 



. it r a\ . it ( a\ 



and solving for 7 as before we find 



. 7T7 . TTCl 



tan — - tan ■= — 



u 2u 



(23) 



which gives the conditions for a minimum for 



1 < - < 2, 3 < - < 4 ... 2m - 1 < - < 2m. 



