ECLIPSES. 



produced by the superposition, partial or total, of this disc on 

 that of the moon, and the circumstances and conditions which 

 determine such an eclipse are investigated upon the principles 

 already explained. 



41. By the solar tabtes, the apparent position of the centre of the 

 sun, from hour to hour, may be ascertained, and the position of 

 the centre of the section of the shadow may thence be inferred. 

 From the lunar tables, the position of the moon's centre being in 

 like manner determined, the distance between the centres of the 

 section of the shadow and the moon's disc can be ascertained. 



The magnitude of the eclipse is measured by the difference 

 between the sum of the semi-diameters and the distance between 

 the centres. 



42. That a lunar eclipse may take place, it is necessary that the 

 moon, when in opposition, should approach the ecliptic within a 

 distance less than the sum of the apparent semi-diameters of the 

 moon and the section of the shadow. 



When the distance from the node at opposition is greater than 

 5 44' 21", a total eclipse cannot, and when less than 3 54' 5", it 

 must, take place. Between these limits it may or may not occur, 

 according to the magnitude of the parallaxes and apparent 

 diameters. 



43. The duration of a total eclipse depends on the distance 

 over which the centre of the moon's disc moves relatively to the 

 shadow, while passing from the first to the last internal contact. 

 This may vary from 0, to twice the greatest possible distance of 

 the moon's centre from the centre of the shadow, at the moment 

 of internal contact. 



44. Long before the moon enters within the sides of the cone 

 of the shadow it enters the penumbra, and is partially deprived 

 of the sun's light, so as to render the illumination of its surface 

 sensibly more faint. When once it passes within the line a' p', 

 fig. 19, forming the external limit of the penumbra, it ceases to 

 receive light from that part of the sun which is near the limb b. 

 As it advances closer to a'f, the edge of the true shadow, more 

 and more of the solar rays are intercepted by the earth ; and 

 when it approaches the edge, it is only illuminated by a thin 

 crescent of the sun, visible from the moon over the edge of the 

 earth at a'. It might be thus inferred, that the obscuration of 

 the moon is so extremely gradual, that it would be impossible to 

 perceive the limitation of the shadow and penumbra. Neverthe- 

 less, such is the splendour of the solar light, that the thinnest 

 crescent of the sun, to which the part of the moon's surface near 

 the edge of the earth's shadow is exposed, produces a degree of 

 illumination which contrasts so strongly with the shadow as to 



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