32 



PROCEEDINGS OF THE AMERICAN ACADEMY 



due to the differential refraction ^^f will be eliminated if we combine 

 the observations over x^ and x.^ with corresponding observations over 



these lines extended below the line a:^. 



Designating the times of 



transit for Venus north of x^ by t\, t'^, t'^, and t'^, we shall have ; 



For Venus South. 



D 



D = V- cos 8 [(r, — rj sin {i -\- - 



5 cos 6 (tj — T^) cos i 



) + 



(ji — ^s) sin (i 



D 



15 cos S (r^ — T3) cos i 

 For Venus North. 



D = -V- cos 8 (r., — T,) sin ( « + 3-= ^^ , , 



^ L^ ^ 1^ \ ' 15 cos 5 (r'i 



^ 



15 cos 8 (r'4 — r'g) cos i 



)] + ^rf 



D 



(t^ — T3) sin ^ i 



, — r'j) cos i 



)]--B. 



) + 



Combining these equations, we shall still have, for any case except 

 where 'A^ is due to an error in the assumed value of ^, an equation of 

 the form : 



i) = 15 cos 8 (tj — Tj) sin i 



Two ruled plates were prepared for the observation of Dec. 6, 

 one for the East Equatorial and one for the West Equatorial. They 

 consist of one horizontal line, two vertical lines, and a series of lines 

 having the inclinations 10°, 20°, 30°, 40°, 45°, and the inclinations 

 135°, 140°, 150°, 1G0°, and 170°, respectively, to the horizontal line. 

 These lines were all extended below the line x^, giving the angles 

 225°, 230°, 240°, 250°, 260°, and the angles 315°, 320°, 330°, 340°, 

 and 350°. 



In general, a complete series of observations consists of 10 transits 

 over each of the inclined lines, and 20 transits over the vertical lines, 

 both for Venus south and for Venus north of the horizontal line. 



The results for Dec. 6, arranged in the order of the times of obser- 

 vation are as follows. 



TABLE IV. — East Equatorial. 



