第28章 ON ATTRACTION(2)

Having by these and several other arguments destroyed the Cartesian vortices,he despaired of ever being able to discover whether there is a secret principle in nature which,at the same time,is the cause of the motion of all celestial bodies,and that of gravity on the earth.But being retired in 1666,upon account of the Plague,to a solitude near Cambridge;as he was walking one day in his garden,and saw some fruits fall from a tree,he fell into a profound meditation on that gravity,the cause of which had so long been sought,but in vain,by all the philosophers,whilst the vulgar think there is nothing mysterious in it.He said to himself;that from what height soever in our hemisphere,those bodies might descend,their fall would certainly be in the progression discovered by Galileo;and the spaces they run through would be as the square of the times.Why may not this power which causes heavy bodies to descend,and is the same without any sensible diminution at the remotest distance from the centre of the earth,or on the summits of the highest mountains,why,said Sir Isaac,may not this power extend as high as the moon?And in case its influence reaches so far,is it not very probable that this power retains it in its orbit,and determines its motion?But in case the moon obeys this principle (whatever it be)may we not conclude very naturally that the rest of the planets are equally subject to it?In case this power exists (which besides is proved)it must increase in an inverse ratio of the squares of the distances.All,therefore,that remains is,to examine how far a heavy body,which should fall upon the earth from a moderate height,would go;and how far in the same time,a body which should fall from the orbit of the moon,would descend.To find this,nothing is wanted but the measure of the earth,and the distance of the moon from it.

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 123,249,600feet.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.

Finally,as in all bodies re-action is equal to action,it is certain that the earth gravitates also towards the moon;and that the sun gravitates towards both.That every one of the satellites of Saturn gravitates towards the other four,and the other four towards it;all five towards Saturn,and Saturn towards all.That it is the same with regard to Jupiter;and that all these globes are attracted by the sun,which is reciprocally attracted by them.