951 



50°, 91. The distance of the full moon to the perigee L — jr = v 

 thus decreases at each leap of 6 months by 180° -|- 25°,09, and at 

 eacli leap of 5 months by 180° + 50°,91. If the apparent ladii of 

 the moon and the sun be called ?• and r' , the lunar parallax /> (the 

 solar parallax may be neglected), tiie inclination of the lunar orbit 

 i, the radius of the earth's shadow is /? = |^ (p — r') and the latitude 

 of the moon / sin (P — 0°,4 sin V). The distance from the edge 

 of the shadow, where it is nearest to the moon, expressed in 

 12''is of the lunar equator, (this is always called the magnitude of 

 the eclipse in inches) is the quantity which determines the external 

 aspect and the duration of the eclipse. It is 



jR + r— i sin (P— 0°,4 sin v) 1 ,025 {p—r') -f r—i sin (P— 0°,4 sin v) 



m =: = 6 X 



7, r r 



p i 



As - = 3,67 and - = 20, whereas in the syzygies 

 r r 



1 1 r' 



— = — (1—0,065 cos v) and -=1,05 

 r r, r^ 



this gives, as 0°.4 cos P may always be replaced by 0°.4, 



. 6 X (4,76—1,05 ^0,065 cos v—2Q>\sin P( 1—0,065 cos v)^^'^sin v)] = 



6 X (3,71 4- 0,065 cos v— 20 sin P (1—0,065 cos r)-}- 0,1 4 si» v). 



If this quantity i« negative there is no eclipse; if it is smaller 

 than 12 the eclipse is partial ; if it is greater than 12 the eclipse 

 is total, and the totality lasts longer according as the number is 

 larger. Of course in these calculations only mean circumstances are 

 taken into consideration ; owing to the perturbations of the moon 

 and the eccentricity of the earth's orbit the actual course will deviate 

 somewhat from the mean. 



The results of our calculation are found in Table T; under "Aspect" 

 is given what an observer could note in the various eclipses. For 

 partial eclipses "upper" or "lower" is given according as the 

 N. or S. portion of the liioon remains uncovered; the same is also 

 given for total eclipses when the moon passes distinctly through the 

 upper or lower part of the shadow {m < 17), and therefore at the 

 beginning and end the N. or S. portion remains longer light; if the 

 moon disappears only for a short time in the shadow {m between 

 12 and 14), this is indicated by "short". It now appears that each 

 of the successive series has a different peculiar character in the 

 aspect of the successive eclipses. But in the 6^'' series the character 

 is exactly the same as that of the 1^' series, as P and v are almost 

 the same; similarly the 7^^ 8^'' and 9''' series will correspond in 

 character to the 2"^^ 3»^^ and 4^'\ This agreement is strengthened by 



