150 SHIX HIRAYAMA; 



***** np _ D 



JJp — D , m n ,__ >T , 



r = — '■ cos è °- cos (M —N) 



n r n v u 



.(17) 



For the first approximation we take the mean value of p, x, and ij ', 

 for the assumed time near the conjunction. With the value of r, thus 

 found, we can repeat the calculation. 



8. Interior contacts. — When interior contacts exist, the rising and 

 setting limits form two distinct closed curves on the earth's suface. 

 Here, the value of sin <J> must he real, that is, Up — J) must be greater 

 than m sin (i)/ — ÎV). 



When interior contacts do not exist, the rising and setting limits 

 meet and form a single curve, extending throughout the whole eclipse. 

 The form of this curve may he compared to that of the figure 8 much 

 distorted. Here the value sin </> will become impossible, that is Up—D 

 is less than m sin (M —N). Hence 



when np — D > m sin (M —N), the rising and setting limits 



form two distinct curves ; 

 when rip — I) < m sin (M Q —N), the rising and setting limits 



form the figure of an 8 much 

 distorted. 

 {). To find the curve of maximum obscuration in the horizon. 

 The maximum of obscuration depends on the minimum value 

 of the apparent angular distance of the centres of the sun and the 

 moon. Since the measure of this angular distance differs very little 

 from the quantity D, we may consider the maximum of the eclipse as 

 the minimum time of D without sensible error. This condition is 



w=° ™ 



or puttin« 



