144 



SHIN HIRAYAMA; 



x, y, and /7 be taken from the tables for the given time. Then the 

 co-ordinates, £, 1, of any place at which a contact may be observed at 

 the given time, must satisfy the condition (4) 



= x—u smo ) 



(4)« 



) = y — D cos a. J 



D sino=x—ç ) ç = x—D sin a 



\ or 

 D cose = y — r) ) rj. 



Let 



/=the hour angle of the sun 

 L=the east longitude of the place 



then we have 



t=T +L-e (6) 



Supposing a to be an arbitrary variable, what we want is to find out 

 <p and L from the equations (4), (3), (5) and (6). 



First, let us solve the equations (3) for <p' and t. 



Put 



psin<p'=(\-c)sin¥ x | 



p cos <p' = COS <f x j 



where 



_ 1 

 C ~ 299.15 - 



Then, 



£=/7 cos <p x sin t ; 



■q— Tl (1 — c) sin <p x cos o — 11 cos <p x sin d' cos t. 



Again, put 



(\—c)cosd'=lcosd 1 

 sin d'=l sin d x 

 then 



ç = n cosfysint 



■q=n I [sin (f x cos d x — cos <p x sin d x cos t\ 



