(15) 
But this supposition is already very improbable @ priori. To arrive 
at certainty on this subject without an entirely new and prolix com- 
putation, I made use of the method of KLINKERFUES based on six 
angles of position. The ratio of the planes of triangles in the appa- 
rent orbit to those in the true orbit being always as cosi: 1 we have 
sin (gui) sin(vg—r5) __ sin (Og—O)) sin (0,—0,) 
sin (vz—v}) sin (vg—vg) sin (Og —O4) sin (Gg—O,) 
and two other similar equations in which the indices 4 and 5 are 
successively to be substituted for the index 3. For the epochs of the 
normal positions 2, 6, 10, 14, 17 and 20 the deviations of these 
normal positions were united with those of the two neighbouring ones 
according to the weights. We thus obtained : 
0,=76°.219 0,=59°.650 63 = 45°.476 
0, = 33°.573 6, —=13°.213 0; = 173°.079. 
The second members of the equations may be denoted by a, /? and y: 
c= 40481680 f=-+0.297904 y=-+ 0.120061 
I started successively from 4 hypotheses : 1° system II; 2° A M= + 1°; 
39 Au=+0°.03; 40 Ae= + 0.01, 
From the three anomalies deduced from these I computed : 
Ist hypothesis. 2ud hypothesis. 3d hypothesis. 4th hypothesis. 
ce +0.468089 +0.465082 + 0.464792 + 0.474842 
2 +0.294009 +0.290553 +0.290125 ~ + 0.304140 
Doden + 0117508 © 4. .0.116272 4 0.1851235 
from which the following equations ensued : 
— 0.003007 AM, — 0.008297 Aw + 0.006753 Ae == + 0.013591 
— 0.008456 AM, — 0.003884 Aw + 0.010131 Ae =-+ 0.003895 
— 0.002270 AM, — 0.003506 Aw + 0.015346 Ae = + 0.000283 
