56 



Scientific Proceedings, Royal Dublin Society. 



If we neglect the terms of the second degree in fyzs and <t, which 

 will be quite inappreciable, the equation A becomes 



t+ ** + %f- + 4 {^ - l) rf + 4 (4±?- lj ^ 



+ 2 



+ 2 

 + 4 



^- 2 + ^ 2 + 2( 0+ .)^- 2 



•WOT V OT OT 



2 /(<4 + ot) 2 <r 2 



•57 \ OT -5T 



(^, + OT) 2 Or 2 2 ( Q+ot) 2 a 2 | 



, <7 ($ +W)\ ((<A + ot) 2 (T 2 



\OT t«J / [■ 73 T3 vi- / 



> + OT 2 j (0 + OT j 2 <7 2 ' 



— i + 2 ~ - 



Z7 OTI OT 37 



(<*>+Q 2 <r 2 | 2 , . ( Q+ot) 2 <r 2 . )( ff + OT 



This, after some reduction, becomes 



= 0. 



«/ 4 + s 4 + 2#V + 4?V + 4%s 2 + 2 



■SJ OT 



3*.- 1-- 



H 



+ 2 



-2-1- 



[l-^i 



ZoJ 



s 2 + 4 r vi H_ 



or 



y+5 +'-i-= 



= 0. 



This is the equation of a circle, and represents the section of the 

 shadow-cone by the plane at right angles to its axis at the distance 

 of the moon. 



The effect of parallax is therefore to this degree of approxima- 

 tion imperceptible. 



