igS PHILOSOPHICAL TRANSACTIONS. [aNNO 1758. 



which have satellites about them, not to be spherical but spheroidical, I thought 

 it worth while to enter upon the examination of such a problem. When the 

 primary planet is an exact globe, it is well known that the force by which the 

 revolving satellite is retained in its orbit, tends to the centre of the planet, and 

 varies in the inverse ratio of the square of the distance from it ; but when the 

 primary planet is of a spheroidical figure, the same rule then no longer holds : 

 the gravity of the satellite is no more directed to the centre of the planet, nor 

 does it vary in the proportion above-mentioned ; and if the plane of the satel- 

 lite's orbit be not the same with the plane of the planet's equator, the protu- 

 berant matter about the equator will by a constant effort of its attraction en- 

 deavour to make the two planes coincide. Hence the regularity of the satellite's 

 motion is necessarily disturbed, and though upon examination this effect is 

 found to be but small in the moon, the figure of the earth differing so little from 

 that of a sphere, yet in some cases it may be thought worth notice ; if not, it 

 will be at least a satisfaction to see that what is neglected can be of no conse- 

 quence. But however inconsiderable the change may be with regard to the 

 moon, it becomes very sensible in the motions of the satellites of Jupiter both 

 on account of their nearer distances to that planet when compared with its semi- 

 diameter, as also because the figure of Jupiter so far recedes from that of a 

 sphere. This is shown and exemplified in the 4th satellite; in which case indeed 

 the computation is more exact than it would be for the other satellites : for as 

 my first design was to examine only how far the moon's motion could be affected 

 by this cause, I suppose the satellite to revolve at a distance somewhat remote 

 from the primary planet, and the difference of the equatoreal diameter and the 

 axis of the planet not to be very considerable. There also arises this other ad- 

 vantage from the present theory, that it furnishes means to settle more accu- 

 rately the proportion of the different forces which disturb the celestial motions, 

 by assigning the particular share of influence which is to be ascribed to the 

 figure of the central bodies round which those motions are performed. 



I have added at the end a proposition concerning the diurnal motion of the 

 earth. This motion has been generally esteemed to be exactly uniform ; but as 

 there is a cause that must necessarily somewhat alter it, I was glad to examine 

 what that alteration could amount to. If we first suppose the globe of the 

 earth to be exactly spherical, revolving about its axis in a given time ; and after- 

 wards conceive that by the force of the sun or moon raising the waters, its figure 

 be changed into that of a spheroid, then according as the axis of revolution 

 becomes a different diameter of the spheroid, the velocity of the revolution must 

 increase or diminish : for since some parts of the terraqueous globe are removed 

 from the axis of revolution and others depressed towards it, and that in a dif- 

 ferent proportion as the sun or moon approaches to or recedes from the cujuator. 



