110 



SOME METHODS OF COMPUTING THE RATIO OF 



(103) When the angle (v" — v) is used (93) instead of the chord, f/ 



may be thus found, B. [5995] (30), (31), and (86): 

 (IW) (r-{-r"){l — q') = 2\/7r"cos.f'; 



(ia5)in which /' = ^ K-f), 9' =(7^ [{^y^'^" + i^r-y/7'f]. 



When y' and g' have been found from (98), g and g" are derived 



from g' by the equations, 

 (106) sin. ^= V'l ^ . sin. g' and sin. g"= ^l fi^ sin.^'; 



or in the case of (98) being satisfied by the hyperbolic values, 



sin./ 



(107) tan. A = V- !i2^ tan. h' and tan, 



^ ' r sin./' 



h" V :l and >^^ '^^^ tan. A', 



r r" sin. /' 



B. [5995] (70), [5997] (6), &c., which, used in (102), by chang- 

 ing the accents, will give y and y" and thence I^ = ^ ^, and 

 ^ ?r fr, which are to be used in (50), (52), or (54). When 

 these equations cannot be employed (60), two independent values, 

 q and q", are to be found from the assumed value of g (91 a) ; when 

 this is correct, (98) wUl give the observed values of t and t", or z'. 



V. The following example will serve as an illustration of the 

 preceding propositions. The positions employed are those of 

 Halley's comet in October, 1836, computed from an ephemeris, 

 and corrected for aberration, but affected by parallax (46), (47), 

 as seen from a point on the earth's surface in North lat. 42° 23', 

 and Ion. ^V. 4" 44" 



Gr. M. S. T. 



1336, Oct. 4.50000 

 " 14.50000 

 "2a50000 



Sun's > Sun's ) Suq's i Sun's 



Tabular Parallax Tabular Parallax 



AR. ' in AR. ' Dec. in Dec. 



190 03 11.5| —5.9 — 4 22 04.4 

 199 19 24.2 —5.9 — 8 10 21 

 207 47 11.41 —6.0 —11 26 17.9 



— 5.6 



— 5.4 



— S.2 



Tabular 



Value of 



R. 



0.99W521 

 0.9966131 

 0.9941330 



Cor. of K 



for 

 Parallax. 



Comet's AR. 



Comet's Dec. 



+ 135 a 107 27 33.0 J +45 32 15 9 

 + 155 «' 233 57 21.1 1 3' + 33 20 33.8 

 + 172 I »"236 09 20.7-3"- 06 59.8 



To find the angles 8, 8', and S", we have 



COS. d = sin. sin. -j-cos. cos. 6 cos. (O — «)• 



To find C (57) 



cot. w = cot. (o" — o) (522-^ sec. («" — «) — l) , C = a-\-w. 



For computing the known terms in (57) they may be a little 



