158 NEWTON S PRINCIPIA. 



fly off. Hence there is an accumulation of matter towards 

 the equator, which is raised, while the poles are depressed 

 and flattened, and the equatorial axis is longer than the 

 polar. By comparing the space through which heavy 

 bodies fall in a second in our latitudes with the centrifugal 

 force at the equator, he found that the gravity of bodies 

 there is diminished -g-J-g at least, or that the equatorial 

 axis is, at least, ^-J-g longer than the polar. But he con 

 sidered this estimate as below the truth, because it does 

 not make allowance for the effect produced on gravitation 

 by the increase of the distance at the equator from the 

 centre. Accordingly, by a skilful application of the 

 method of false position, he corrected this calculation, and 

 ultimately brought out the proportion to be that of 229 to 

 230, making the equatorial axis about 34J- miles longer 

 than the polar, the whole axis being about 7870 miles. 

 He also estimated the two axes of Jupiter to be as 11^ to 

 10, supposing the density of the body to be the same 

 throughout; but if it is greater towards the equator, our 

 author observed that the difference between the axes 

 might be decreased as low as 13 to 12, or even 14 to 13 ; 

 which agreed well enough with Cassini s observations in 

 those days, and still more nearly with Pound s. But 

 more accurate observation has since shown that the dif 

 ference is considerably less, the disproportion being not 

 more than that of 1074 to 1000 ; so that the planet must 

 be very for from homogeneous and its equatorial density 

 greatly exceed its polar. Thus, too, accurate measure 

 ments of a degree of latitude in the equatorial and polar 

 regions, and experiments on the force of gravity, 

 as tested by the length of the pendulum vibrating 

 seconds in those different parts of the globe, have led to 

 a similar inference respecting the Earth, its axis^being now 

 ascertained to bear the relation, not of 230 to 229, as 



