PREDICTION OF SOLAR ECLIPSES. 



151 



dD -r% do • ht rr 7 / > / 



sin a -yffr + D cos a -j=-—n sin N—iJp k cos <p cos t 



dT 



dT 



=71 sin N' 



cos a -j7w— D sin a -£n=n cos N— fTp k' cos <p' sin <?' sin t 



)(19) 



—n cos N' 



we have from (18) 

 dD 



dT 



=n cos (<r—N') 



=n cos {<7—N)—k' IJp cos <p' {sin a cos t + cos a sin t sin d') = 0; 

 or cos (<r— N')— I 

 that is, a-iVW'(^) = 90 o or270 o (20) 



Substituting this value of <J in the fundamental equations of eclipses, 

 together with the condition that the sun is in the horizon, we get 



D sin (±90°+ N')= ±D cos N'=m sin M— Up sin v 

 D cos (±90 +N')=TD sin N'=m cos M—IIp cos 



"1 



v j 



.(21) 



where 



'hence 



x = m sin M j 

 y=m cos M i 



.(22) 



0= m cos {M— N')— Tip cos (v—N') ; 

 D = m sin {M—N')—IIp sin (v — N') ; 



therefore, pu t ti ng <p=v- N', we have 



cos <&=■%- cos (M-N') } 



Y Up 



D = m sin (M—N') — Up sin </> ) 

 There will be two values of </', since we may take sin <P with the 



•(23) 



