THE EARTH. 



4-59 



Let us suppose now that another plumb-line is suspended similarly on the 

 opposite side of the mountain, to m I : it is evident that the attraction of the 

 mountain will draw the plumb-line in this case in a direction opposite to that 

 in which it draws the former. Both plummets will be drawn toward the 

 mountain ; and if the string suspending one be made to point a little to the 

 eastward of the zenith, the string suspending the other will be made to point a 

 little to the westward of it. 



By due attention to this circumstance, we shall easily find the real deviation 

 of the, plumb-line from the zenith. Let the points in the heavens to which the 

 two plumb-lines are respectively directed be accurately observed : one of these 

 points will be as much to the eastward as the other will be westward of the 

 true zenith. If we take half the space between them, that will be the devia- 

 tion of the direction of the plumb-line from the zenith, or, in other words, it 

 will be the actual deviation of the plumb-line from the true vertical direction. 



We have then the amount of the deflection, and can therefore calculate the 

 proportion which the mass of the earth bears to the mass of the mountain. If, 

 then, we knew the mass of the mountain, we should necessarily know the mass 

 of the earth. 



The mountain on which Dr. Maskelyne tried this celebrated experiment 

 was Schehallien, in Wales. The geological structure of this mountain was 

 known, and the magnitude and nature of its stratification had been ascertained. 

 The weight, therefore, of the materials that composed it was easily calculated, 

 and thus the weight of the mountain obtained. 



By computing thence, by means of the experiments just described, the 

 weight of the earth, it was found to be about five times the weight of its own 

 bulk of water. 



The method adopted by Cavendish for solving this problem depended on a 

 different mechanical principle. It is well known that the vibrations of the 

 common pendulum, used as a measure of time in clocks, are produced by the 

 attraction of the globe of the earth on the matter composing the ball or disk. 

 If that attraction were greater, its vibration would be more rapid ; if it were 

 less, it would be slower ; in short, the rate of vibration of the pendulum is the 

 exponent of the energy of force by which it is moved. 



If we suppose, then, two globes, containing different quantities of attractive 

 matter, and near these globes two pendulums to be placed, each pendulum 

 being kept in a state of vibration by their attraction : by noting the rates 

 of vibration of these two pendulums, we should be enabled to compare the 

 relative quantities of matter in the two globes. In making this comparison, 

 however, there are several circumstances which should be attended to, which 

 need not be particularly adverted to here. Cavendish adopted this principle 

 as the basis of his method for determining the weight of the earth. He took 

 a large globe of metal, of known weight, and suspended near it in a horizontal 

 position a fine vertical needle, the point of suspension corresponding with its 

 centre of gravity. The effect of the earth's attraction was thus neutralized. Its 

 susceptibility of vibration in a horizontal plane depended upon the torsion of 

 the filament by which it was suspended. The ball of this pendulum was then 

 directed to the centre of the metallic globe, and the pendulum was put in vi- 

 bration near it, subject to the same mechanical condition as those by which a 

 common pendulum is affected near the surface of the earth. By observing the 

 rate of vibration of this horizontal pendulum, and comparing it with the rate of 

 vibration of the ordinary pendulum subject to the earth's attraction, Cavendish 

 was enabled to obtain the numerical proportion which the earth's attraction 

 bore to the attraction of the metallic globe which he used in his experiments. 

 Having computed thence the weight of the earth, he arrived at * conclusion 



