145 



—ft- = p sin z sin v 

 .J j = V sin z cos v 

 cos z 



• (10) 



PREDICTION OF SOLAR ECLIPSES. 



Further, putting 



£ v 



sin B 



cos B sin A 



cos B cos A — 



we have now the required solution 



cos <f 1 sin t=sin B 

 cos (f x cos t=cosB cos {A + o : ) 

 sin <fx = cos B sin (A + o x ) 

 tan<p=^^- L = t-T +e J 



where c is the equation of time. 



4. Visibility. — In order that the eclipse may be visible from a point 

 on the earth's surface, we must have z' less than 90° ; that is, cos z 

 must be positive, and therefore cos A and cos B must have the same sign. 

 Let us choose cos B to be always positive, then cos A is also, neces- 

 sarily, positive. In this way we can determine A and B without 

 ambiguity. 



For the first approximation, we must put (5) in the form 



.(ID 





for the penumbra. 

 „ ,, umbra. 



• (12) 



This value of D and the assumed value of a give £ and q from (4)rt. 

 Having found ç and '-?, the equation (10) and (11) will give the 

 required value of <p and L. 



The value of Oj and I in (8) may directly be taken from table 

 II. 



Table I gives the value of <f — <pi, <p\ being the argument. 



