SECT. V. LUNAR ECLIPSES. 39 



the moon are occasioned by the earth intervening be- 

 tween the sun and moon when in opposition. As the 

 earth is opaque and nearly spherical, it throws a conical 

 shadow on the side of the moon opposite to the sun, the 

 axis of which passes through the centers of the sun and 

 earth (N. 109). The length of the shadow terminates 

 at the point where the apparent diameters (N. 110) 

 of the sun and earth would be the same. When the 

 moon is in opposition, and at her mean distance, the 

 diameter of the sun would be seen from her center 

 under an angle of 1918"-1. That of the earth would 

 appear under an angle of 6908"-3. So that the length 

 of the shadow is at least three times and a half greater 

 than the distance of the moon from the earth, and the 

 breadth of the shadow, where it is traversed by the 

 moon, is about eight-thirds of the lunar diameter. Hence 

 the moon would be eclipsed every time she is in oppo- 

 sition, were it not for the inclination of her orbit to the 

 plane of the ecliptic, in consequence of which the moon 

 when in opposition is either above or below the cone of 

 the earth's shadow, except when in or near her nodes. 

 Her position with regard to them occasions all the vari- 

 eties in the lunar eclipses. Every point of the moon's 

 surface successively loses the light of different parts of 

 the sun's disc before being eclipsed. Her brightness 

 therefore gradually diminishes before she plunges into 

 the earth's shadow. The breadth of the space occupied 

 by the penumbra (N. Ill) is equal to the apparent di- 

 ameter of the sun, as seen from the center of the moon. 

 The mean duration of a revolution of the sun, with re- 

 gard to the node of the lunar orbit, is to the duration of 

 a synodic revolution (N. 112) of the moon as 223 to 19. 

 So that, after a period of 223 lunar months, the sun and 

 moon would return to the same relative position with 

 regard to the node of the moon's orbit, and therefore 

 the eclipses would recur in the same order, were not 

 the periods altered by irregularities in the motions of 

 the sun and moon. In lunar eclipses, our atmosphere 

 bends the sun's rays which pass through it all round 

 into the cone of the earth's shadow. And as the hori- 

 zontal refraction (N. 113) or bending of the rays sur- 

 passes half the sum of the semidiameters of the sun 



