L4& OUTLINES OF NATURAL PHILOSOPHY.. 



S'M' is then = Va z 2 a z cos ft + a 2 = 



1 2 cos /3 -f i =5 2 a sin - = 2 a multi- 



plied into the sine of half the apparent inclination 

 of the moon's orbit. 



When s* = a* sin % or 5 = a sin there can be no 

 more than a contact of the moon and shade, 

 which will happen at the instant expressed by 



When s = a sin , sin /s = S - 9 and if sin -^^, there 



a a 



can be no eclipse, as sin ft = ; therefore, unless 



- be less than _-, there can be no eclipse. Now, 

 r a 



A* 



r = m + n + _ . _ nearly ; so that 



2 (m+w) 



A 



n + 



2 ( W + n) 



must be less than , otherwise there can be no 

 eclipse of the moon. 



It will serve as a limit, to consider whether - is 



m -f n 



less 



