“ that the board o f longitude in London propofed a prize o f five
“ thoufand pounds (or thirty-three thoufand three hundred and
“ thirty-three rix dollars, more or lefs) to whomfoever Ihould
“ conftrud new tables o f the moon, deduced from the principle
“ o f univerfal gravitation ; the errors o f which Ihould be within
the limits o f fifteen leconds, more or leis. But the rnoit icru-
“ pulous accuracy in the tables o f the moon would completely
“ fail o f its objed, lb long as the tables on the effeds o f the pa-
“ rallax are not proportionably exad. It was, among other mo-
“ tives, chiefly to remedy this defed, that the moft celebrated
focieties all over Europe, and particularly the royal academy o f
“ Paris, after the attention o f the learned had been called to this
objed by Huygens, confidered it as one o f the moil; facred duties
they could perform for the good o f humanity, to clear up
| this difficult point in mathematical cofmography. For this pur-
“ pofe meafurements o f degrees o f the meridian have been planned
I and executed at different times, and in different places ; which
“ when properly examined, in fail give a concurrent teftimony
“ that the earth is a ipheroid, oblate, or flattened towards the
“ poles;, but differ however in this,,that when you compare them
“ two and two, and fuppofe that the earth is generated by the
“ revolution o f an ellipfis round its ihort axis, you conftantly ob-
“ tain different values for the eccentricity o f the generating-
“ ellipfis. This is the true reafon why philofophers have fufpeded
“ that this furface, iff, is not a fpheroid, or other furface o f the
“ feCond order; 2 dly> that lt is not a figure that is the refult o f
“ revolutions;
*!• revolutions; 3dly, that its two hemifpheres on each fide o f the
“ equator are not alike. Aftronomers, neverthelefs, having ob-
“ ferved in the orbits o f the heavenly bodies a fort o f predilection
“ for lines o f the fecond order, and geometers having eftablilhed
“ on the moil incontellible evidence, that any fluid body whofe
“ furface is o f the lecond order, may remain in equilibrio, when
I the particles o f which it is compofed attrad in the reciprocal
w ratio o f the fquare o f the diftances, the learned have thought
“ that they were not warranted by reafons fufficiently ftrong to
u abandon the ellipticity o f the revolution ; having due regard to
“ the fmallnefs o f the errors in the executed meafurements which
“ might very well give occafion to all the diverfity o f the refults.
“ But to be convinced how cautious we ought to be before we
“ decide in matters o f this fort, let us recoiled the meafurements
i executed by Jean Dominique Caffini over the furface o f France,
“ which at firil fight feemed to prove that the earth, far from
I being oblate towards the poles, was rather a little raifed or
“ elevated. This refult, fo much the more ftriking, that it by
“ no means agreed either with the theory o f centrifugal force
“ advanced by Huygens, or with the principle o f univerfal gravi-
“ tation eftablilhed by Newton, having undergone a more rigor-
“ ous inveftigation by geometers, they foon perceived, that not
“ having perfectly feized the univerfality o f the prineiple, they
“ had confidered as contrary what was in fad one o f its moft
“ immediate confequences : and thus what they fuppofed was to
“ overthrow the firft foundation o f the lyftem o f attradion be-
3 C 2 “ came