146 



SHIN HIRAYAMA 



This was kindly computed by Mr. Matsuzaki of Tokyo astronomical 

 Observatory. 



5. Criterion of beginning or ending of the eclipse. 



The negative or positive value relatively to the time of the dif- 

 ferential co-efficient of the quantity D gives the criterion of beginning 

 or ending of the eclipse. 



clD . . „ da , t , 



-jjT sma + D cos a -—= r =x — c ; 



dD da , 



-^ cos a-D sid a-r^=y -y ; 



-— r== ( x '-£') sin a + {if- rf) cos a. 



Putting -^L=k'= 57 ] | 96 , log 7/=T,41797 ; we have 



ç ==k' Tip cos <p' cos t ; ■/]' — h' lip cos <p' sin o' sin t. 



Put x = n sin N ; cost =f cos F ; 



y' = ncos N ; sin d' sin t=f sin F ; 

 then, we have 



-jTjï=n cos (a — N) — k' IJp.f. cos <p'. sin{a + F). 



Except in the case where o — A r is nearly equal to 90°, the second 

 term is far less than the first. Hence -^- is negative or positive, that 

 is, the eclipse is beginning or ending, according as 



a~N>90 a but <270°, 

 or <7-A T <90° but >'270°. 



If <r—N is nearly equal to 90°, then compute -p^ by the strict formulae 

 above given. 



