PREDICTION OF SOLAR ECLIPSES. 



153 



Substitute these values in (25) and putting 



1 



II 



1 

 7 



1 



m sin M=-jj— (a^-F-D cos N ) 



m cos M—-JTY (y ±D sinN ) 



I sin L = -fj— (x'+D c) 

 I cos L=-jj^ (7j ±D s) 



■ (26) 



we get, as usual, solving the equations for r, 



v— L = <p 

 sin (p=m sin (il/— L) 



cos <p m 



cos(M-L) 



T=T +z 



.(27) 



in which cos <p is to be taken positive or negative for the first or second 

 point, respectively. 



To find the latitude and longitude of these extreme points, take v=L 

 + <l> and proceed as before. 



12. To find the curve of central eclipse. 



This curve contains all those points of the surface of the earth 

 through which the axis of the cone of shadow passes. The condition 

 for the central eclipse is 



Then 



D=0. 



x=q = n COS (fxSill t 



y=q=n [(1 — c) sin cp x cos o—cos (f x sin d' cos t] 

 The following formulae will give the required places — 



■(28) 



