ON THE ORBITS OF THE ASTEROIDS. 131 
We omit the terms dependent on M, in the values of J, because in the final result 
they will bring out kọ — M, as in the equation (9). 
n M, S . 
jag PE and to obtain the numerical values of 
these quantities we shall use the following values of g, g, &c., ky, hy, &c., which are 
deduced from the data given in the work of Le Verrier above referred to, and are par- 
tially corrected for the terms of third order. 
We shall now put e, = 
‘g = 2901 os 515 k= 0.0 k, = — 7.086 
gı = 3.808 g; = 17.153 k, = — 3.166 k; = —17.468 
g, = 22.828 gs = 17.863 k, = —96 568 ks = —18.568 
g = 5.299 g = 0.693 ky = — 4.795 k, = — 0.756 
We thus obtain the following values of £ and x for every .05 in the value of a be- 
. tween the limits of the mean distances of the asteroids. 
Tame l.— For Eccentricities and Perthelia. 
a € E, £a £3 Es Es Es $, 
2.20 |-L.001679 | +.024174 | —.023044 |+.000079 | —.000162 | +-.000352 | +.000597 | +-.000049 
2.25 | .001710 | .024567 | .021326 | .000064 | .000133 | .000269| .000448 | .000050 
2.30 | .001741 | .024960 | .019984 | .000052 | -000109 | .000209 | .000343 | .000051 
2.85 | .001772 | .025352 | .018913 | .000041 | .000089 | .000164 | .000262 | 000059 
2.40 | .001802 | .025743 | .018043 | .000033 | .000073 | .000131 | .000203 | .000053 
2.45 | .001832 | .026133 | .017329 | .000026 | .000060 | .000105 | .000159 | .000054 
9.50 | .001862 | .026593 | .016735 | .000020 | .000050 | .000085 | .000196 | .000055 
2.55 | .001893 | .026912 | .016237 | .000015 | .000041 | .000069 | .000100 | .000056 
2.60 | .001999 | .027299 | .015817 | .000011 | .000034 | .000056 | .000081 |  .000057 
2.65 | .001951 | .027685 | .015463 | .000007 | .000027 | .000046 | .000066 | .000058 
2.70 | .001980 | .028070 | .015162 | .000004 | .000022 | .000038 | .000054 | .000059 
2.75 | .002009 | .028454 | .014906 |+.000001 | .000017 | .000031| .000045 | .000060 
2.80 | .002038 | .028837 | .014688 |—.000001 | .000014 | .000026 | .000037 | .000061 
9.85 | .002067 | .029218 | .014502 | .000003 | .000011 | .000022 | .000030 | .000062 
2.90 | .002196 | .029598 | .014346 | .000004 | .000008 | .000018 | .000025 | .000063 
2.95 | .002225 | .029977 | .014214 | .000006 | .000006 | .000015 | .000021| .000064 
3.00 | .002153 | .030355 | .014104 | .000007 | .000004 | .000012 | .000017 | .000065 
3.05 | .002181 | .030732 | .014017 | .000008 |—.000002 | .000010 | .000014 | .000066 
3.10 | .002309 | .031107 | .013935 | .000009 | .000000 | .000008 | .000012 | .000067 
3.15 | .002237 | .031481 | .013875 | .000010 |-L.000001 | .000007 | .000010 | .000068 
3.90 |-L.002265 |-+.031854 |—.013831 | —.000011 | -+.000002 |-|-.000006 | +.000008 |-+-.000069 
Taste II.— For Inclinations and Nodes. Tate III. 
a ad EE ZE %3 X4 X5 
2.20 | +.001277 | —.028054 |--000185. | +.000122 -4.000616 |--.000165 —.001516| 32.815 
| 2.25 gea .023416 | 000150. T oin .000475 | .000110 | .001518| 34.488 
2.30 | .001961 | .020246 | 000123. | .000086 | .000373 | .000074  .001520| 36.256 
2.35 | .001254 | .017946 | 000101. | .000072 | .000296 | .000052 | .001522) 38.123 
2.40 | .001247 | .016200 | 000082. | .000060 | .000237 | .000037 | .001523) 40.097 
2.45 | .001941 | .014831 | 000065. | .000049 | .000191 | .000027 | .001523| 42.184 
2.50 | .001935 | .013729 | 000051. | .000040 | .000156 | .000020 .001524 44.394 
2.55 | .001930 | .012824 | 000039. | .000033 | .000129 | .000014| .001524| 46.732 
2.60 | -+.001225 | —.012070 |-1-000028.:|-1-.000028 |-+.000106 |-+-.000010 |—.001524| 49.209 
