APPENDIX. 



IX 



as the moon approaches the apogee, and a shrinking as she goes 



from there to the perigee ; 

 the different portions A, 

 B, &c., each fulfilling all 

 the conditions of rotation 

 in an ellipse similar (per- 

 turbation apart) to the 

 moon's orbit. 



The permanent distor- 

 tion of the girdle by the 

 moon's action is analogous 

 to, and yet different from, 

 an enormous tidal action ; 

 but with a tide in which 

 the variation of the attrac- 

 tive force in the inverse 

 ratio of the square of the 

 distance, and the variation 

 at different distances of the 

 centrifugal force of revolu- 

 tion have a very great in- 

 fluence. So A, the place 

 of what ought to be the flood tide, is the point nearest the earth ; 

 the stringent conditions of slow time of revolution and contest 

 of forces bringing about that negative tide-like result. 



The girdle form is not much troubled with the objection that 

 the earth's shadow ought to cut it in two at the direction of the 

 meridian at midnight. 



It will be perceived that the position of the point A is within 

 the limit assigned by Laplace to the region where the moon, in 

 ancient times, may have lost her atmosphere. The conditions of 

 revolution, &c. here give a centrifugal aid to the material, which 

 has to go too slow for its mere place, so that the nearest point 

 is for mean distance (60.2^3 — 51.116), i. e., 9.15t, or more than 

 one-seventh of the moon's distance within. 



M. Laplace has evidently made use of the ratio which would 

 make MA and A E as the square roots of the masses. 



It would be very curious certainly, if Saturn's rings, dusky and 

 bright, are preserved in place, because that planet has so many 

 satellites ; and our nebulous girdle be kept in place ju.st because 

 we have but one satellite: but even that is so much more than 

 belongs to our immediate neighbors. 



The earth is, indeed, the Saturn of the minor system interior 

 to Jupiter, in which system the asteroids and Mars correspond to 

 Uranus and Neptune of the major system; Earth is the Saturn 

 (with satellite, girdle and all) ; Venus is the Jupiter, and Mercury 

 (including material for more than one planet there) is the repre- 

 sentative of all the small planets on the greater planetary seal. 



(27) 



