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SHIN HIRAYAMA 



positive or the negative sign, but that value of </> which would give D 

 greater than r+r' must be excluded. 



For the computation, first assume N' = N, and with the mean 

 value of p calculate v. This value of v will give a more accurate 

 value of N' from 



n sin (N'—N) = + h' lip sin o cos (v—N) ) 



(24) 



n cos (N'—N)= n—k' IJp sin d' sin (v—N) ) 



which can easily be derived from (3) and (19) 

 From N' we can derive v, which will give <p and t. 



10. To find the northern and southern limits of the eclipse. 

 This is fully treated in the work of Sawitsch. 



11. To find the extreme times between which the solution is possible. 

 It is evident that the first and last points of the curve are those 



for which cos z'=0. These points are also the first and last points 

 of the curve of maximum obscuration in the horizon, and therefore, the 

 limiting times are here the same as for that curve. If, however, we 

 wish to determine these limiting times independently, the following ap- 

 proximative process will give them, with all the precision necessary. 



N' ) 



[ (25) 



N' J 



Since cos z' = and o— iV = ±90 o , we get 



£= fjp sin v=x^fD cos N' 

 yj=flp cos v=y±D sin 



Let the required time be denoted by T=T +t, T being an assumed 



time near the middle of the eclipse ; 



let #o, y be the values of x and y for the time T , respectively, 

 x\ y' ,, ,, mean hourly changes of x and y, respectively, 

 c\ s ,, „ ,, ,, ,, ,, cos N' and sin N\ respectively. 



Then x = x + x'r ; cos N' = cos N + cr ; 



y=y +y'T ; sin N'=sin N +s'~. 



