Page:Popular Astronomy - Airy - 1881.djvu/278

264 we must have forces (for the same distances of displacement) four times as small; and so in proportion to the inverse square of the times of vibration. Thus if balls or anything else vibrate once in ten seconds, the dead pull sideways corresponding to an inch of displacement is $1⁄3913·9$ of their weight. So that in fact, all that we now want for our calculation, is the time of vibration of the suspended balls. This is very easily observed; and then on the principles already explained, there is no difficulty in computing the dead pull sideways corresponding to a sideways displacement of one inch; and then (by altering this in the proportion of the observed displacement, whatever it may be) the sideways dead pull or attraction corresponding to any observed displacement is readily found. The delicacy of this method of observing and computing the attraction of the large balls may be judged from this circumstance: that the whole attraction amounted to only about $1⁄20,000,000$ part of the weight of the small balls, and that the uncertainty in the measure of this very small quantity did not amount probably to $1⁄40$ or $1⁄50$ of the whole.

Then the next step was this: knowing the size of the large balls and their distances from the small balls in the experiment, and knowing also the size of the earth, and the distance of the small balls from the centre of the earth, we can calculate what would be the proportion of the attraction of the large balls on the small balls to the attraction of the earth on the small balls (that is the weight of the small balls), if the leaden balls had the same density as the mean density of the earth. It was found that this would produce a smaller attraction than that computed from the observations. Consequently the mean density of the earth is less than the density of lead in the