VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 1^ 



from the proportion of the lines ph and fg, the former being to the latter, as 

 the whole force of gravity at p, while the spheroid is at rest, to the force with 

 which a body descends at f, while it turns round its axis. 



3. From this last article it appears, that \ of the variation of gravity is occa- 

 sioned by the figure of the spheroid, and the remaining f by the centrifugal 

 force. And whereas the earth could not be of an oblate spheroidical figure, 

 unless it turned round its axis, nor could it turn round its axis, without put- 

 ting on that figure; therefore the diminution of gravity towards the equator, 

 known by the experiments with pendulums, prove both the rotation and oblate 

 spheroidical figure of the earth. 



A. The mean force of gravity on the surface, is to the centrifugal force at 

 any point f, as a rectangle under the radius and mean diameter, to a rectangle 

 under the co-sine of latitude, and 4- of the ditFerence of the longest and shortest 

 diameters. And at the equator, where the co-sine of latitude becomes equal 

 to the radius, the mean force of gravity is to the centrifugal force, as the mean 

 diameter to -f of the difference of the longest and shortest diameters. This ar- 

 ticle is found from the proportion of the lines fh and gh ; the former being to 

 the latter as the force of gravity to the centrifugal.force. 



5. The proportion of the diameters of the earth will be found in the following 

 manner: the moon revolves about the earth in 27'* 7*^ 43*", or in 39343 minutes: 

 and her mean distance is about b<^\ semidiameters of the earth, according to 

 La Hire's and Flamsteed's tables; but near 604- by Halley's tables. We shall 

 therefore take 60 for the mean distance, till it be better known; then according 

 to the nature of gravity, as the cube of the moon's distance is to the semidia- 

 meter of the earth, or as 216000 to unity, so is 1547870000, the square of 

 the periodic time of the moon, to 7^66, the squaje of the number of minutes 

 in which another moon would revolve about the earth at the distance of its 

 semidiameter. And as this last number is to 2062096, the square of 143(), the 

 number of minutes in a sydereal day, so is unity to 287-7 5 which would show 

 the proportion of the centrifugal force at the equator, to the mean force of 

 gravity, by corol. 2, prop. 4, lib. J, Princip. were it not for the action of the 

 sun on the moon. Therefore, by corol. 17, prop. 66, lib. 1, Princip. as the 

 square of the sydereal year is to the square of the periodic time of the moon, 

 that is, as 179 to unity, so is 287.7 to 1.6; which being added to 287.7 makes 

 289.3. And therefore, as unity to 289, neglecting the fraction, which is un- 

 certain, so is the centrifugal force at the equator to the mean force of gravity 

 on the surface. And thence, by article 4, as 28g to -f, so is the mean diameter 

 to the difference of the longest and shortest ; and therefore, as the axis is to 

 the equitorial diameter, so is 2307 to 2317, or in smaller numbers, as 231 to 



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