260 The Rev. Samuel Haughton on the 



of the ellipticities in Tables I., II., III., we are led to infer that the action of 

 the Sun in elongating Jupiter, and so by internal friction causing his move- 

 ments of rotation and revolution to become equal, was much less powerful than 

 the corresponding action of Jupiter upon his satellites ; lience the physical cause 

 assigned by Laplace for this equality may be admitted in the case of Jupiter's 

 satellites. But this conclusion will not apply to the Earth. From Table I. it 

 appears, that the elongating action of the Earth upon the Moon is represented 

 by the fraction o^j.24 i while Table III. shows that the similar action of the 

 Sun upon the Earth is represented by the fraction g^.ggi • 



Before quitting this subject it may be useful to consider the various expla- 

 nations which might be offered to explain the difficulty which vmdoubtedly 

 exists in the case of the Earth and Moon. 



We are not at liberty to assume that the planets separated from the central 

 mass as annuli, and the satellites as nodules, which would give to the planets a 

 quicker rotation than to the satellites. In this case a ><p, and therefore e < 4e'; 

 hence the couche, on the friction of which the effect in question depends, would 

 be less for the planets, ceteris ]wrilms, than for the satellites. But this assump- 

 tion is not admissible, since the only annuli with which we are acquainted 

 in the solar system occur among the satellites. Neither are we at liberty to 

 assume greater friction among the particles of the satellites than of the planets, 

 for, according to the nebular hypothesis, they are probably composed of the same 

 materials. It is possible to explain the difficulty by assuming a sufficient amount 

 of contraction in the Moon. It is, in fact, easy to prove that the effect of the 

 Earth upon the Moon would be equal to that of the Sun upon the Earth and 

 Moon, supposed to extend as far as the orbit of the Moon, provided the Moon 

 extended to a distance represented by the equation 



8 a 



- = 24-322, or, - = ;i-07(5 : 



a ' ' a 



and this amount of contraction is physically possible, since it is less than the 

 distance from the Moon at which a particle would be equally attracted by 

 the Moon and Earth. But how are we to reconcile this amount of contraction 

 with the observed facts, without tacitly assuming that the internal friction of the 

 Moon, supposed fluid, was greater than that of the Earth ; an assumption which 

 is purely arbitrary, and made to explain the difficulty. 



