202 Rev. J. Cliallis on the Elliptlcities of the Planets. 

 lating now the ellipticities of Jupiter and Saturn by Clairaut's 

 Theorem, on the supposition that qc ^ ~«~> ^^ shall find 



for Jupiter-——, and for Saturn— — . The measurements of 

 ^ 13-1' 8-4- 



Professor Struve determine the ellipticity of Jupiter to be 



-— — -, and Herschel obtained—— for theellipticity of Saturn. 

 13-71 11 i J 



It must be observed that the above calculations take into 

 account only the first power of the ellipticity, and therefore 

 cannot be very accurate with respect to Jupiter and Saturn, 

 the ellipticities of which are not very small. We may, how- 

 ever, affirm that the ellipticity of Jupiter accords very well 

 with the theory we are considering. That of Saturn is consi- 

 derably less than what the theory gives. Herschel remarked 

 an anomaly in the shape of this planet, which, however, sub- 

 sequent observations have not yet confirmed; viz. that the 

 equatorial diameter was not so large as a diameter about mid- 

 way between the equatorial and the polar. It would seem, if 

 this be true, that some cause has operated to compress the 

 parts about the equator. The same cause would account for 

 an ellipticity less than what our theory requires. Possibly 

 the rings may have something to do with this. 



Venus, Mercury, and the Sun, in as much as they possess 

 no ellipticity discoverable by instruments, do not contradict 

 the theory. But Mars forms an exception. Its ellipticity is 



ascertained by observation to be ; whereas the ratio of the 



•' 16 



centrifugal foixe to gravity at its equator, which ratio differs 



little from the ellipticity that the theory gives, will be found 



to be -— 7, by taking "1386 for the ratio of its mass to that of 



the earth, •129'1' the ratio of the volumes, and 24*67 hours the 

 period of its rotation. The great ellipticity of this planet, 

 considering the time of its rotation and its small size, is re- 

 markable, and seems not to be in accordance with Clairaut's 

 Theorem, unless we suppose the gravity of the planet to di- 

 minish in passing from the equator to the pole. 



If the cause assigned in this theory be sufficient to account 

 for the increase of the density of a planet towards its centre, 

 then on the supposition that the nuclei of the planets are all 

 as to chemical composition homogeneous, and are similarly 

 constituted, though of different mean densities, the equation 



J c = - — ought to be nearly true for all, since it is nearly 



true 



