note on Lambert’s theorem for elliptic motion. 
389 
472] 
Hence substituting for co, &>' their values in terms of %, we have 
Time 
AB!.. 
X - X - sin % + sin 
>> 
BA 1 
= 2tt - X + %' + sin x ~ sin 
» 
BA 2 
X-X~ sin X + sin 
BA 3 
= % “ %' - sin % + sin % ' } 
)) 
BA 4 
= x - x' - sin x + sin 
)) 
ba 5 
= 2 ?r - x + x' + sin % - sin x ■ 
and thence (restoring the omitted factor P -r- 2?r) 
Time AB 1 + Time BA X = P, 
„ ab. 2 - „ ba 2 = 0, 
„ AB 3 — „ BA 3 — 0, 
„ AB,~ „ BA, = 0, 
„ AB 5 + „ BAr, = P, 
which are the relations which in fact subsist between the times AB X and BA X &c.