192 * MEASURING APPARATUS OF THE 



hemispheres consist of two parabolic conoids, the bases of which met at 

 the equator, where there w^as a ridge formed. 



Now, Navigators had gone over the equator, and they knew very well 

 that the line was a mathematical line — that their ship did not strike 

 against, or shew any manifest signs of such a ridge, and besides this, two 

 plumb lines placed on opposite sides of the equator, but near each other, 

 did not shew any sensible difference in their directions, nor did nature on 

 enquiry appear to vary from her usual course of doing nothing abruptly. 



Sir Isaac Newton was the first person w^ho gave any solution of this 

 question. In Prop. 19* Book 3d of the Principia, he demonstrates that a 

 homogenous body like the earth might, in consequence of its diurnal 

 motion, form itself into an ellipsoid of revolution, whose Polar axis was to 

 the diameter of the equator as 229 to 230. This solution was the effect 

 of the new arm, then, for the first time, brought to bear upon this disputed 

 point, for unless the law of the variation of gravity inversely as the square 

 of the distance had been previously discovered, no power of analysis ever 

 would have sufficed to elucidate it. 



But the demonstration was imperfect like almost all first attempts, 

 and some points were taken for granted which were not mathematically 

 true. Wet shall find some of these pointed out by M. Clairaut, one of 

 which is very important to the subject, and consists in the annunciation! 



* Propositio XIX. — Est igitur Diameter Terrae secundum aequatorem ad ipsius diametrum 

 per polos ut 230 ad 229 — Ideoque cum Terrae semidiameter mediocris juxta mensuram Picarti sit 

 Pedum Parisiensium I9615S00 seu miliarum 3923,16 (posito quod miliare sit mensura pedum 5000) 

 terra aitior erit ad sequatorem quam ad polos excessu pedum 85472 seu miliarum 17 J^, 



f II est aise de voir que ce theoreme est entierement contraire a ce que M. Newton a avance 

 dans la proposition XX. du troisieme Ilvre des Principes, P. 251, &c. PS. 50. 



^ Liber Tertius Prop. XX. Et propterea terra aliquanto aitior est sub sequatore quam pro 

 superiore calculo et densior ad centrum quam in fodinis prope superficiem. 



