This may easily be verified experimentally. Let A and B be two bodies, whose weight is considerable, in comparison with that of the rod _a b_, which joins them. Let a fine silken string, with its ends attached to them, be hung upon a pin; and on the same pin let a plumb-line be suspended. In whatever position the bodies may be hung, it will be observed that the plumb-line will cross the rod _a b_ at the same point, and that point will divide the line _a b_ into parts _a_ C and _b_ C, which are in the proportion of the mass of B to the mass of A. (172.) The centre of gravity of three separate bodies is defined in the same manner as that of two, and may be found by first determining the centre of gravity of two; and then supposing their masses concentrated at that point, so as to form one body, and finding the centre of gravity of that and the third. In the same manner the centre of gravity of any number of bodies may be determined. (173.) If a plate of uniform thickness be bounded by straight edges, its centre of gravity may be found by dividing it into triangles by diagonal lines, as in _fig. 68._, and having determined by (154) the centres of gravity of the several triangles, the centre of gravity of the whole plate will be their common centre of gravity, found as above. (174.) Although the centre of gravity takes its name from the familiar properties which it has in reference to detached bodies of inconsiderable magnitude, placed on or near the surface of the earth, yet it possesses properties of a much more general and not less important nature. One of the most remarkable of these is, that the centre of gravity of any number of separate bodies is never affected by the mutual attraction, impact, or other influence which the bodies may transmit from one to another. This is a necessary consequence of the equality of action and reaction explained in Chapter IV. For if A and B, _fig. 67._, attract each other, and change their places to A′ and B′, the space a a′ will have to _b b′_ the same proportion as B has to A, and therefore by what has just been proved (171) the same proportion as _a_ C has to _b_ C. It follows, that the remainders _a′_ C and _b′_ C will be in the proportion of B to A, and that C will continue to be the centre of gravity of the bodies after they have approached by their mutual attraction. Suppose, for example, that A and B were 12lbs. and 8lbs. respectively, and that _a b_ were 40 feet. The point C must (171) divide _a b_ into two parts, in the proportion of 8 to 12, or of 2 to 3. Hence it is obvious that _a_ C will be 16 feet, and _b_ C 24 feet. Now, suppose that A and B attract each other, and that A approaches B through two feet. Then B must approach A through three feet. Their distances from C will now be 14 feet and 21 feet, which, being in the proportion of B to A, the point C will still be their centre of gravity.