Thus Sir Isaac Newton reasoned.  But at that time the English had but a very imperfect measure of our globe, and depended on the uncertain supposition of mariners, who computed a degree to contain but sixty English miles, whereas it consists in reality of near seventy.  As this false computation did not agree with the conclusions which Sir Isaac intended to draw from them, he laid aside this pursuit.  A half-learned philosopher, remarkable only for his vanity, would have made the measure of the earth agree, anyhow, with his system.  Sir Isaac, however, chose rather to quit the researches he was then engaged in.  But after Mr. Picard had measured the earth exactly, by tracing that meridian which redounds so much to the honour of the French, Sir Isaac Newton resumed his former reflections, and found his account in Mr. Picard’s calculation.

A circumstance which has always appeared wonderful to me, is that such sublime discoveries should have been made by the sole assistance of a quadrant and a little arithmetic.

The circumference of the earth is 123,249,600 feet.  This, among other things, is necessary to prove the system of attraction.

The instant we know the earth’s circumference, and the distance of the moon, we know that of the moon’s orbit, and the diameter of this orbit.  The moon performs its revolution in that orbit in twenty-seven days, seven hours, forty-three minutes.  It is demonstrated, that the moon in its mean motion makes an hundred and fourscore and seven thousand nine hundred and sixty feet (of Paris) in a minute.  It is likewise demonstrated, by a known theorem, that the central force which should make a body fall from the height of the moon, would make its velocity no more than fifteen Paris feet in a minute of time.  Now, if the law by which bodies gravitate and attract one another in an inverse ratio to the squares of the distances be true, if the same power acts according to that law throughout all nature, it is evident that as the earth is sixty semi-diameters distant from the moon, a heavy body must necessarily fall (on the earth) fifteen feet in the first second, and fifty-four thousand feet in the first minute.

Now a heavy body falls, in reality, fifteen feet in the first second, and goes in the first minute fifty-four thousand feet, which number is the square of sixty multiplied by fifteen.  Bodies, therefore, gravitate in an inverse ratio of the squares of the distances; consequently, what causes gravity on earth, and keeps the moon in its orbit, is one and the same power; it being demonstrated that the moon gravitates on the earth, which is the centre of its particular motion, it is demonstrated that the earth and the moon gravitate on the sun which is the centre of their annual motion.

The rest of the planets must be subject to this general law; and if this law exists, these planets must follow the laws which Kepler discovered.  All these laws, all these relations are indeed observed by the planets with the utmost exactness; therefore, the power of attraction causes all the planets to gravitate towards the sun, in like manner as the moon gravitates towards our globe.