136 ON THE ORBITS OF THE ASTEROIDS. 
Themis. 
h = .0022 sin (0) + .0315 sin (1) — .0139 sin (2) + .1441 sin (147° 40' + 89".55 t) 
1 = .0022 cos (0) + .0315 cos (1) — .0139 cos (2) + .1441 cos (147° 40' + 89".55 t) 
p= M sin y + .0012 sin [1] — .0082 sin [2] — 0015 sin [7] + .0187 sin (318? 53’ — 89".55 2) 
q = M cos y + .0012 cos [1] — .0082 cos [2] — 0015 cos [7] + .0187 cos (318° 53’ — 89".55 t) 
Proserpina. 
h = .0019 sin (0) + .0277 sin (1) — .0155 sin (2) + .1115 sin (220° 23/ + 527.15 t) 
Z = .0019 cos (0) + .0277 cos (1) — .0155 cos (2) + .1115 cos (220° 23'-- 52”.15 £) 
p = M sin y + .0012 sin [1] —.0114 sin [2] -]-.0001 sin [5] —.0015 sin [7] + .0514 sin (31? 35’ — 52.15 t) 
q = M cos y + .0012 cos [1] —.0114 cos [2] + .0001 cos[5] —.0015cos[7] + .0514 cos (31? 35' — 59".15 t) 
Euterpe. (7) 
h = .0018 sin (0) + .0253 sin (1) — .0189 sin (2) — .0001 sin (4) + .0002 sin (5) + .0003 sin (6) 
+ .1772 sin (98° 2 + 38".02 t) 
| = .0018 cos (0) + .0253 cos (1) — .0189 cos (2) — .0001 cos (4) + .0002 cos (5) + .0003 cos (6) 
+ -1772 cos (98° 2 + 38".09 £) 
p — M sin y + .0013 sin [1] — .0181 sin [2] + .0001 sin [3] + .0003 sin [5] — .0015 sin [7] 
+ -0157 sin (110° 14’ — 38".09 t) 
q = M cos y + .0013 cos [1] — .0181 cos [2] + .0001 cos [3] + .0003 cos pis 0015 cos [7] 
+ .0157 cos (110° 14’ — 38”.02 i) | 
Bellona. (83) : 
h = .0020 sin (0) + .0286 sin (1) — .0148 sin (2) + .1665 sin (181° 37' + 591.13 2) 
1 = .0020 cos (0) + .0286 cos (1) — .0148 cos (2) + .1665 cos (131° 37’ + 59/.13 t) 
p = Msin y + .0012 sin [1] —.0102 sin [2]+-.0001 sin [5] —.0015 sin [7] +-.1517 sin (151° 11’—59”.132) 
q = Mcos y +-.0012 cos [1] —.0102 cos [2] +-.0001 cos [5]— .0015 cos E+ 1517 cos (151° 11—59".13 t) 
Amphitrite. 69 
h = .0019 sin (0) + .0269 sin (1) — .0162 sin (2) + .0001 sin (6) + -0603 sin (83° 44’ + 46”.97 t) 
| = .0019 cos (0) + .0269 cos (1) — .0162 cos (2) + .0001 cos (6) + .0603 cos (83° 41’ + 46”.97 o 
p= M sin y + .0012 sin [1] — .0128 sin [2] + .0001 sin [5] —.0015 sin [7] + .1088 sin 
(347° 59’ — 46".97 t) A i 
q = M cos y + .0012 cos [1] — .0128 cos [2] + .0001 cos [5] —.0015 cos [7] + .1088 cos 
(347° 59' — 47".97 1) 
Urania. (0) 
À — .0018 sin (0) E 0256 sin (1) — .0186 sin (2) — - 0001 sin (4) 4 0002 sin © E 0003 sin © 
+ -1005 sin (41° 26’ + 38.67 t) — 
. l = .0018 cos (0) + .0256 cos (1) — 0186 cos (2) — .0001 cos (4) 7 .0002 cos (5). ra -0003 cos (6) 
+ -1005 cos (41° 26’ + 38".67 t) 
p= M sin y + .0013 sin [1] — .0174 sin [2] + .0001 sin [3] + .0003 sin Ms .0015 sin [7] ; 
+ -0466 sin (295° 24’ — 38.67 1) ES uium 
(S Moos y + 0013 cos [1] — .0174 cos [2] + .0001 cos [3] T 0003 cos [5] — .0015 cos [7] 
+ .0466 cos (295° 24' — 38".67 t) : 
