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THE EAETH.

independent of any separate consideration of what that weightmay be, or of the length of the rod, or of the twisting power ofthe wire ; provided that the joint effect of these three last-mentioned causes is snch as to make the rod, when set oscil-lating, perform its oscillations in a certain observed time.

In fact it is found that the proportion which the force inquestion must bear to the weight of the little balls, in orderto move them one inch from their original positions, musthe rather less than -^th of that weight, if, each oscillation ofthe rod in the instrument occupies one second of time.* More-over, it can also he proved, that, if the rod should oscillate in anyother number of seconds, the requisite force would he less in theproportion of the square of that number. If, for instance, theduration of an oscillation were 400 seconds, the requisite force tomove the small balls one inch would be nearly XF ^nr °f a aVthpart of their weight. And it is also a property of the apparatusin question, that the force required to move the balls any othernumber of inches would be almost exactly proportional to thatnumber. In order to move them six inches, very nearly sixtimes as great a force would be required as that which wouldmove them one inch ; the slight difference from an exactproportionality of the force being easily calculated and allowedfor.

If, therefore, we find that the large balls move the little onesa certain number of inches, then, without weighing these latter,or measuring and observing anything else except the time inwhich the rod oscillates (which we can do with very greataccuracy), we know exactly what proportion the attractionexercised by the big halls bears to the weight of the littleones.

Let us next see how this enables us to determine the weightof the Earth . It is a law' of the attraction of spheres upon

* The actual proportion varies slightly with the latitude of the place ofobservation. The accurate value of the denominator of the fraction mthe latitude of London is 39’139; and is the same, in any given locality, asthe number of inches in the length of an ordinary vertical pendulumthat will oscillate in a second. It is, therefore, always known with greatprecision.