132 : ON THE ORBITS OF THE ASTEROIDS. 
a X, Aa X3 X4 X5 X x, b 
2.65 | +.001220 | —.011432 |-+.000018 | +.000023 |-|-.000087 | +.000007 | —.001524 | 51.833 
2.70 | .001216 | .010886 | .000009 | .000018 | .000071 | .000005 | .001524| 54.619 
2,75 | .001212| .010413 |-+.000003 |. .000014 | .000059 | .000004 | .001524| 57.577 
2.80 | .001208 | .010002 |—.000001| .000011 | .000050 | .000003 | .001523| 60.724 
2.85 | .001204 | .009640 | .000003| .000008 | .000043 | .000002 | .001523| 64.074 
2.90 | .001201 | .009320 | .000006 | .000006 | .000037 | .000002 | .001523| 67.641 
2.95 | .001198 | .009036 | .000009 | .000004 | .000031| .000001| .001593| 71.450 
3.00 | .001196 | .008782 | .000012| .000002 | .000026 | .000001| .001592| 75.519 
3.05 | .001193 | .008555 | .000015 |-+.000001 | .000022 +.000001 | .001592| 79.875 
3.10 | .001191 | .008350 | .000019 |—.000001 | .000018 | .000000 | .001522| 84.543 
3.15 | .001189 | .008164 | .000023 | .000002 | .000015 | .000000 | .001521| 89.555 
3.20 | +.001187 | —.007996 | —.000027 | —.000004 |—.000013 | ..000000 |—.001521| 94.942 
The following are the values of 8, Bı, &c., y, 7, &c., and M, supposing the time to 
be reckoned from 1800, and the longitudes from the equinox of 1850.0. M — .027460. 
8 = 98 30 28 y. 106 50 18 
& = 26 32 23 n = 135 41 7 
fa = 127 17 9 ya = 126 42 20 
Bs = 86 27 45 | y = 28 20 25 
B. = 36 18 43 y. = 262 48 16 
Bs = 335 28 27 ys = 297 28 24 
fs = 315 11 1 y = 73 53 49 
B, = "14 214 o = 202 15 43 
If now, we put for brevity, 
(0) — 8 +gt : 
(1) = A+ at [1] = 7+ kt 
(2) = k+ gat [2] = n+ ht 
(7) = & + art [7] = +. + krt 
we shall have, for the elements A, l, p, and q of any asteroid in terms of the time, 
h= «sin (0) + a sin (1) + e sin (2)-+....4 & sin (7) + Asin (B 32) 
l = ecos (0) + 4 cos (1) + sz cos (2) + +... + & cos (7) + A cos (B+ 51) 
p= M sin y + » sin [1] + sin [2] +... -+ «sin [7] + K sin (C — bt) (12) 
q = M cos y + x, cos [1] + x cos [2] + .... + x; cos [7] + K cos (C — bt) 
A, B, x, and C being fixed by the values of h, l, p, and q at a given epoch. The 
quantities £, £ &c., %, %, &c., M, and b, are taken from Tables 1, 2, and 3, by entering 
with the mean distance of the asteroid as the argument. 
Let us now apply these data to those asteroids the elements of which are determined 
with sufficient accuracy, and the eccentricities and inclinations of which are sufficiently 
small. The latter class may be presumed to include all those for which each of these 
