Axis of 
332 
Proceedings of the Royal Society of Edinburgh. [Sess. 
§ 24. The case of e = 23° 27' and a = 18° evidently comes under I. 2, and 
the sequence is 
<£< 7 ° 4 ' 2 
7 ° 4 '<</>< 48 ° 33 ' 1 
48 ° 33 '<<£< 66 ° 33 ' 4 
66 ° 33 '<<£< 81 ° 7 
81 ° <</>< 84 ° 33 ' 10 
84 ° 33 '<<£ 15 
§ 25. The various cases and critical values can be represented graphi- 
cally, as follows. 
Fig. 3. 
There are nine critical values of a in terms of e. Considering e and a 
as both variable, these will be the equations of nine curves, the points of 
