CENTRE OF GRAVITY. 



237 



is often unsupported for a moment ; for the leg B is raised from the ground 

 before A comes to it, as is plain from observing the track of a horse's feet, the 

 mark of A being upon or before that of B. In the more rapid paces of all 

 animals the centre of gravity is at intervals unsupported. 



The feats of rope-dancers are experiments on the management of the centre 

 of gravity. The evolutions of the performer are found to be facilitated by 

 holding in his hand a heavy pole. His security in this case depends, not on 

 the centre of gravity of his body, but on that of his body and the pole taken 

 together. This point is near the centre of the pole, so that, in fact, he may be 

 said to hold in his hands the point on the position of which the facility of his 

 feats depends. Without the aid of the pole, the centre of gravity would be 

 within the trunk of the body, and its position could not be adapted to circum- 

 stances with the same ease and rapidity. 



The centre of gravity of a mass of fluid is that point which would have the 

 properties which have been proved to belong to the centre of gravity of a solid, 

 if the fluid were solidified without changing in any respect the quantity or ar- 

 rangement of its parts. 



The centre of gravity of two bodies separated from one another, is that point 

 which would possess the properties ascribed to the centre of gravity if the two 

 bodies were united by an inflexible line, the weight of which might be neglected. 

 To find this point mathematically is a very simple problem. Let A B, fig. 33, be 



Fig. 33. 



A! ... A. 



B' 



o-e 



the two bodies, and a and b their centres of gravity. Draw the right line a b, 

 and divide it at C, in such a manner that a C shall have the same proportion 

 to b C as the mass of the body B has to the mass of the body A. 



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. 



The centre of gravity of three separate bodies is defined in the same man- 

 ner 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. 



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. 

 34, and, having determined 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. 



