SECT. V. ECLIPSES. 39 



inversely as the squares of the distance, were to revolve about an 

 axis as the earth does, it would assume the form of a spheroid 

 whose compression is ^ Since that is not the case, the earth 

 cannot be homogeneous, but must decrease in density from its 

 centre to its circumference. Thus the moon's eclipses show the 

 earth to be round ; and her inequalities not only determine the 

 form, but even the internal structure of our planet ; results of 

 analysis which could not have been anticipated. Similar ine- 

 qualities in the motions of Jupiter's satellites prove that his 

 mass is not homogeneous, and that his compression is ^. s . His 

 equatorial diameter exceeds his polar diameter by about 6000 miles. 

 The phases (N. 109) of the moon, which vary from a slender 

 silvery crescent soon after conjunction, to a complete circular disc 

 of light in opposition, decrease by the same degrees till the moon 

 is again enveloped in the morning beams of the sun. These 

 changes regulate the returns of the eclipses. Those of the sun 

 can only happen in conjunction, when the moon, coming between 

 the earth and the sun, intercepts his light. Those of the moon 

 are occasioned by the earth intervening between 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 centres 

 of the sun and earth (N. 110). The length of the shadow termi- 

 nates at the point where the apparent diameters (N. Ill) of the 

 sun and earth would be the same. When the moon is in oppo- 

 sition, and at her mean distance, the diameter of the sun would 

 be seen from her centre under an angle of 1918"'l. 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 opposition, 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 posi- 

 tion with regard to them occasions all the varieties in the lunar 

 eclipses. Every point of the moon's surface successively loses 

 the light of difierent parts of the sun's disc before being eclipsed. 

 Her brightness therefore gradually diminishes before she plunges 



