S22

HISTORICAL VIEW OF THE

tops of the highest mountains ; it extends to the highestregion of the atmosphere: may it not reach as far asthe moon ? Again, within the short distances to whichobservation extends near the surface of the earth, thisforce does not diminish sensibly as we recede from theearth ; but may it not diminish at greater distances ? Ifso, according to what law ? Supposing it, as in somecases of the dynamical speculations in which he hadbeen engaged, to decrease as the square of the distancefrom the centre of the earth, it might be calculatedin what degree its intensity would be diminished at themoon, the moon’s distance being known. Indeed, thiscalculation might be carried a little farther, and theresult subjected to the test of observation. For the ac-tual intensity of gravity at the earth’s surface is esti-mated by the space through which a body falls in onesecond. By reducing this, in the ratio of the squares ofthe distances from the earth’s centre, we should havethe space through which the moon ought to fall towardsthe earth in one second, if not impeded by any othercause. But how tould this be ascertained, since suchan experiment cannot be tried upon the moon ? Newtonsaw that such an experiment is, in fact, constantly ex-hibited to us. The moon performs a revolution in anorbit whose dimensions had been ascertained by astro-nomers. Consequently, the velocity with which shemoves was known. But this velocity impressed uponsuch a body must, if nothing else interfered, carry it offin a straight line through space. The actual motion ofthe moon is in an orbit round the earth: and in anygiven portion, or arc, of that orbit, the quantity bywhich, at the end, for example, of one second, the moonhas deflected from the direction of the straight line,which is a tangent to the orbit at the commencement ofthat second, is known. This, then, is the space throughwhich, in one second, the moon is actually falling to-wards the earth.

Newton, then, in his calculation, had only to takethe distance of the moon from the centre of the earth,