DISCUSSION OP THE DOUBLE-IMAGE MICROMETEK MEASURES. 47 



Let s, S, be the semi-diameters of Venus and of the SUN respectively ex- 



pressed in revolutions of the micrometer-screw. 

 r, R, the tabular semi-diameters in seconds of arc. 

 2m, the micrometer measure in revolutions of the screw. 

 A, the tabular distance of centers. 

 p, the value of one revolution of the screw. 



x r , x", the distance between the limbs that are nearly in contact, in 

 revolutions and seconds of arc respectively. 



Then when the center of Venus is without the SUN, and 2m is the measure 

 of the obtuse cusps : 



a* = 8 + * - (S* - m 2 )* - (s 2 - m 2 )* 

 s is determined by observation ; S = " with sufficient accuracy, 



r r 



D = - -T- - 



" S S 



II 'II Of ,f . X T r~. 



x + o x =. x r . p = -- 1 8 r 



5* ft yf <\ 

 or f> x st ST. 



S 



The true distance of centers is 



A + SA=rE + 8E + r-f8r- (x" + S x") 



whence the final equation' 



= R + r - (A + x") - I A + & B + (1 - f) I r 



where A is the sum of the corrections to the tabular parallax, B.A., and 

 N.P.D. each multiplied by the proper factor for its effect on the distance of 

 centers. 



For the measures of acute cusps (near internal contact) the equation is 



= E_r-(A- x") - 8 A + 8 R - (1 - j ) 8 r 

 and for measures of near limbs (after internal contact) 



= E-r-(A + x") - 8 A + 8 R - (1 + f ) 8 r 



With the 6-inch instrument we have, from the first series of measures of 

 the diameter of Venus 



s 3 r -5i7, 



and from the second series 



* = 3 r '4go. 



