Original and Actual Fluidity of the Earth and Planets. 261 



There remains one real difference between the case of the planets and satel- 

 lites, which, so far as it operates, is a vera causa, and acts in the direction required. 

 The effect of the internal friction in destroying the increment of angular velo- 

 city must be greater in proportion as the mass of the planet or satellite is less; 

 as we observe small rivers more retarded by the friction of their bed than large 

 rivers. But it may be doubted whether this cause is sufficient to account for 

 the remarkable difference which exists between the planets and satellites. 



The conclusion which the foregoing calculations appear to warrant us in 

 drawing is the following : that the nebular hypothesis does not explain the 

 equality of the mean movements of revolution and rotation of the satellites, 

 although it cannot be said to be absolutely inconsistent with it. 



II. — Figure of the Earth and Planets. 



It is well known that on the hypothesis of the original fluidity of the planets, 

 it is necessary that the ellipticity of each planet should lie between two limits, 

 which are, respectively, five-fourths and one-half of the fraction which expresses 

 the ratio of centrifugal force to gravity at the surface of each planet;* the first 

 or major limit corresponding to the case of homogeneity, and the second or 

 minor limit corresponding to the case of infinite density at the centre. It is 

 possible to compare this theory with observation in the case of five planets and 

 the Moon. In the following Table, m denotes the ratio of centrifugal force to 

 gravity at the surface of each planet, gravity being expressed in feet, and cal- 

 culated from the formula 



P E^ 



in which G,g, denote gravity on the surface of the planet and Earth respectively; 



P, E, the masses of the planet and Earth ; i?, r, the radii of the Earth and planet. 



The centrifugal force at the equator of each planet is calculated from the ordinary 



formula 



r 



f- 4-^ J2» 



in which r is expressed in feet, and T, the time of rotation, in seconds. 



• Clairaut, Figure de la Terre, p. 294. 



2 m2 



