BY A. B. BIGGS. 



81 



an enormous number of observations, of which I have taken 

 the means in convenient groups, with the means of the dates. 



I estimated the period separately both from the apparent 

 curve and the real orbit. First, from the apparent curve. I 

 start from its greatest elongation, the date of which I make to 

 be 1818. Kepler's 2nd law of planetary motion is : — that " the 

 Radius Vector describes equal spaces in equal times," and this 

 applies equally to the real and the apparent curve. The whole 

 area of the apparent curve is 165 "75 square seconds. Taking 

 the maximum elongation in 1818 as a starting point, we have 

 the sector between that and my last position (1887'4G) to be 

 described, in order to complete a revolution. The sector 

 measures 29"9 square seconds. Deducting this from the whole 

 ellipse, we have 135.8 square seconds traversed in 69'46 years. 

 The proportion will give 15"3 years to complete the curve, 

 making the whole period 69'46 + 15"3 = 84"76 years. 



In the same way, from the real orbit, I deduce a period of 

 84*85 years. 



I have not, so far, complicated the problem by allowing for 

 precession, by which the meridian (the standard of reference) 

 has a minute progressive shifting of its position. I reckon this 

 would make a difference of about a year, shortening the period. 



An analysis of the diagram yields the following results : — 



A2oparent Curve. 





Position of Node 



.. 25° 



„ „ Apsides 



.. 75°— 255° 



Apse from Node 



.. 50° 



Semi axis major of apparent ellipse . 



17'' 



„ „ minor ^ „ „ 



.. z"-i 



Maximum elongation 



..23''-25 t 1818 



Apparent periastron passage 



.. l''-7 t. 1878-2 



Period 



.. 84'76 years. 



Beal Orhit. 







I>7\ Doherck's Elements, 1879 



Node (position) 25° ... 



... 



... 25-14 



Apsides „ 75°-255° 







Apse from Node 50° ... 



... 



... 45°-58 



Semi axis major 18" "6 ... 



... 



... 18''-45 



Eccentricity , '543 ... 



... 



... -5332 



Inclination of plane of^ 







Orbit from line of sight ]■ 19° ... 



... 



... 79°-24 



(= angle VAX) j 







Periastron passage 1875"6 ... 



... 



... 1875-12 



Period (diminished byl oo-^ 

 precession) J 



... 



... 88 556 years. 



(I have appended Dr. Doberck's elements for comparison.) 



F 



