E C L 



*aine expression we substitute for c, P 4. p -f. -^ -f- , we have thi 



whole time of an eclipse, from the moon's first entering, till her finally 

 quitting the penumbra. 



6. Ecliptic limits. When the mean opposition is 12o. 3& distant from 

 the node, there can be no eclipse ; and when it is less than 9. distant 

 from it, there must be aa eclipse. Between these limits 120. SG' and 9. 

 the matter is uncertain, and must be decided by the calculation of the 

 true place of the moon. 



II. Eclipses of the Sun. 



1. -Let r, R be the radii of the moon and earth, the rest as before ; then 

 Jhe length of the moon's shadow 



__ N P^ 



-By means of this formula, we have 



Length of Moon'* 

 shadow, distance. 



Sun in apogee, moon in perigee ... 59.730 | 55.902 



San in perigee, moon in apogee 57.760 I 63.862 



Hence in the latter case, the moon's shadow never reaches the earth, 

 and the eclipse cannot any Avhcre be total. 



The moon's mean motion about the centre of the earth is 33' in an hour ; 

 and the shadow of the moon .'. traverses the surface of the earth, when 

 it falls on the surface perpendicularly, with a velocity of about 380 miles 

 in a minute. W T hen the shadow falls obliquely, its velocity appears 

 greater in the inverse ratio of the sine of the obliquity. 



The duration of a total eclipse ia any given place cannot exceed 1m. 



An annular eclipse may last 12?. 24*. 

 .2. The apparent f diameter of the moon's shadow = f ^ 1- __ . 



Hence when d D apparent J diameter =r o, or the vertex of the coni- 

 cal shadow just reaches the earth. When tf is less than D, the expres- 

 si-m is negative, ia ether words the shadow never reaches the earth. 



In a similar manner may the formulas for the penumbra of the earth 

 be transformed and adapted to the case of the moon. 



(jjj) The solar ecliptic.limits =' 17. 21'. 27". If the conjunction hap- 

 pens nearer to the node than this, t&ere may be an eclipse. If it be more 

 distant, there can be none. 

 .96 



