SECT. V.] LUNAK ECLIPSES. 45 



satellites prove that his mass is not homogeneous, and that 

 his compression is 73.5. His equatorial diameter exceeds his 

 polar diameter by about 6000 miles. 



The phases (K 108) 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 conjunc- 

 tion, 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. 109). The length of the shadow termi- 

 nates 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 centre under an angle of 1918"'!. 

 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 oppo- 

 sition, 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 varieties 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 



