Tlii APPENDIX. 



of the girdle will be brought everywhere into coincidence with 

 this; or would be, if the approximate coincidence originally ex- 

 isted. Then the ratios of E A, E B, and even those of the moon's 

 distance from the centre of gravity to them being all constant, the 

 angular velocity (inversely as the square of the radius vector) 

 will also be determined for all the same (and all the radii vectores 

 answering to the same ratio), each series on its own scale; and 

 this involves the very principle of the conservation of areas. 



CONFIRMATORY PHENOMENA. 

 Zodiacal Light: 



(1.) Lengthening into a narrow beam when the light is trans- 

 mitted through the sides of the girdle, as at New Moon, or at the 

 Full. 



(2.) Appearing bright, but short and broad at the quadratures. 



(3.) Exhibiting a bright spot or patch of light opposite to the 

 moon soon after the full where the longer axis of the oval termi- 

 nates on that side ; which bright spot rises from day to day, as 

 the moon moves on toward her last quarter. It has advanced 

 toward the top of the zodiacal illumination before the last quarter 

 comes. 



Observations of these phenomena have as yet been few ; but 

 Chaplain Jones's charts seem also to confirm them. 



Postscript. — The several parts of the girdle, as they revolve 

 with the moon, all describe ellipses similar to the moon's own 

 orbit ; but the outline form of the girdle itself (i. e. of its middle 

 line), does not differ much from a circle, except in the region near 

 the moon. 



Quoting the preceding table of dimensions, we have : — 



Moon's distance 



In Perigee 

 56.964 



Mean Dist. 

 60.2Y3 



In Apogee 

 63.583i 



E A, Int. dist. of Girdle 

 E B, Ext. dist. of Girdle 



48.309 

 56.790 



51.116 

 60.090 



53.9221 

 63.389 



At P and Q, where the moon's attraction is in the direction 

 of a tangent, the accumulation of material may be different from 

 that at places further around toward B, but with the moon's time 

 of revolution enforced, the distance E P (earth's central attrac- 

 tion fully operative) must be just a trifle less than the moon's 

 distance. 



Consulting the table, we find that is also true of E B. The feeble 

 action of the moon will insist upon a small deviation outward at 

 the sides. But from P, through B around to Q, the existing 

 distance of the moon from the earth's centre will be nearly pre- 

 served. But then even that requires a swelling out of the girdle 



(26) 



