i8o 
Mr. Ivory on a new Method of deducing 
circumstances abovementioned in which the problem becomes 
indeterminate when applied to the planets. We shall therefore 
proceed to analyze this case, which has already been noticed as 
forming a real distinction in the problem we are considering. 
Resume the three following equations which have already 
been investigated in No. 4, viz. 
<r'p cos. h + crp' cos. h' — (t"p° cos. cos. — n) = 
W (t + r) 
2 
-^] .R°cos. (e°— «) 
«r'p COS. i sin. h + crp cos. i sin. h' — <r''f cos. x° sin. [c°—n) = 
<r'p sin. i sin. h + o-p' sin. i sin. h' — o-"p° sin. = 0: 
and employing h° and 1° to denote the same things as in 
No. 5, let the following values found there, viz. 
■ cos. sin. (c° — = cos. i° sin. if 
sin. x° = sin. i° sin. h° 
be substituted in the two last of the equations above ; then 
these equations will become, 
o-'p cos. i sin. h + o"p' cos. i sin. h — cr''p° cos. i° sin. = 
sin. (.=-«) 
<r'p sin. i sin. h -|- <rp' sin. i sin. h — sin. sin. }f — 0: 
further let these two equations be added together, after being 
multiplied by cos. i and sin. i respectively; then we shall get 
o-'p sin. h + o-p' sin. Ji — o-''f cos. f sin. If = 
2 * (r^ ^ cos. I Sin. {^e n^. 
In the particular cases we are considering, either i = 2°; 
or 2 and 2° are both evanescent; in both which cases cos. f—i°) 
= 1. And if we attend to the analysis in No. 5, it will appear 
