1891. ] Orbit of the Comes of Sirius. Ae 
The negative value of sin ) shows us that } is 
in the third quadrant ee aa ee A ae 
— ¢ (8 cos Q — a Sin Q) cost 
2 sin » 
= 0°71014n 0°30103 
9°38980 9°9711627 
0°09994” 0°27219n 
0:27219% 
OOO 7a cn ne Bi ie is s = '6726- 
eae 
sini Seah (1 — &) = [9°73848] 
0:71014 
9°73848 
COMIGCe ee ree a nein a —= 9°368- 
V.—DETERMINATION OF PeERI-ASTRON PaAssaGE AND PERIODIC 
TIME. 
The Peri-astron date and Periodic Time are computed from the: 
following formulae : 
(1) tan py = cos? tan (6 + A) 
——__—_— 
2) tan gu = 4/7 
€ 
Ae 
: tan 59 
(3) «— «sin u = nt 
The first formula gives the relation between the true orbit and its- 
projection on the plane of the background of the heavens. 
The second and third formulz are the usual formule for elliptical 
motion in these expressions : 
~ = Angular distance from node. 
2 = Inclination of orbit. 
9 = True anomaly. 
» — Longitude, or distance, of the Peri-astron from node. 
uw —= Eccentric anomaly. 
s == Eccentricity of orbit. 
nm == Mean annual motion. 
¢ — Time from Peri-astron date. 
By the aid of these formule the position angles given in Table I. 
are reduced to mean angular distances from Peri-astron. 
It is not necessary to reduce all the positions. Two sets a sfar 
