MARS AND HIS MOONS. 91 



rotation-period oi the primary becomes exactly the same as the orhital- 

 period of the satellite. When this condition is attained, the tides can 

 no longer retard the rotation-period of the planet. So far, therefore, 

 as the inner moon of Mars is concerned, it must long ago have ceased 

 to retard the rotation of the primary. For, the orbital-period of this 

 satellite being far shorter than the present rotation-period of Mars, its 

 tidal action would tend to accelerate instead of retarding the time of 

 rotation of the planet. So far as the outer moon is concerned, it is 

 evident that its tidal action must tend to retard the rotation-period 

 of Mars ; but, in consequence of its greater remoteness, the magni- 

 tude of its influence must be small compared with that of the inner 

 satellite. It is, therefore, difficult to conceive how the tidal influ- 

 ences of the moons of this planet can explain the anomalous fact 

 that its rotation-period is longer than the orbital-period of one of its 

 satellites. 



In connection with the idea of the rotation-period of Mars having, 

 at &0Tae former time, been much shorter than it is at present, it may 

 be noticed that the great compression or ellipticity of this planet is 

 totally inconsistent with its observed rotation-period.* 



In 1784 Sir William Herschel estimated the ellipticity of Mars at 

 ^. Schroter refused to admit this result ; he contended that, if the 

 ellipticity existed, it would not exceed -gV Bessel failed to discover 

 any appreciable ellipticity of Mars, even with the celebrated heliom- 

 eter of Konigsberg. On the other hand, Arago's measurements, ex- 

 ecuted at the Observatory of Paris, from 1811 down to 1847, all con- 

 firm the existence of an ellipticity in this planet of about ^*^. (" As- 

 tronomie Populaii-e," tome iv., p. 130. Paris, 1867.) More recent 

 observations give somewhat contradictory results. Professor Kaiser, 

 of Leyden, makes the ellipticity y-fr ; Main, of the Radcliffe Observa- 

 tory, deduced -^^ in 1862 ; and Dawes's measurements give negative 

 results. 



To show the discordance of these results with what may be deduced 

 from the theory of gravitation, it must be recollected that the ellip- 

 ticity of a rotating planet depends upon the ratio of the centrifugcd 

 force at its equator to the /brce of gravity at the same place. Thus, 

 to compare the earth and Mars — 



Let r and r' = equatorial radii of earth and Mars respectively. 

 " t ^ t' = time of rotation " " " " " 



" Q " Q' nr mass " " " " " 



" / " /' = centrifugal force at equator " " 



" <7 " g' z=L force of gravity " " " " " 



* The oblaleness or compression or ellipHciti/ of an oblate spheroid Is the difference of 

 its equatorial and polar radii, divided by its equatorial radius. Thus, if a and 6 are the 



equatorial and polar radii respectively, then ellipticity = -^. 



