CHAMBERS'S INFORMATION FOR THE PEOPLE. 



The position of the centre of gravity in a tri- 

 angular-shaped body is not so obvious. It is thus 

 found. If ABC represent the surface of a thin 



triangular board, we 

 may suppose it com- 

 posed of a number 

 of small rods laid 

 side by side, the line 

 AB representing the 

 first, and the others 



A~~~ 5 is gradually diminish- 



Fig. 13. ing in length to the 



top. Now, the cen- 

 tre of gravity of the rod AB is in its middle point 

 D ; and if we join the points D and C, the line will 

 pass through the centres of gravity of all the other 

 rods ; because it is a property of a line drawn from 

 the top of a triangle to the middle of the opposite 

 side, to bisect or pass through the middle of all 

 lines in the triangle parallel to that side. The 

 centre of gravity of the whole, therefore, must lie 

 somewhere in the line CD. Again, by conceiving 

 the triangle made up of rods parallel to the side 

 CB, and drawing a line from A to the middle 

 point E, we see that the centre of gravity must, in 

 like manner, lie somewhere in the line AE. Now, 

 since it lies also in CD, it can lie only where the 

 two cross namely, at g. We have thus found the 

 centre of gravity of the surface, as it were ; and if 

 the board have any sensible thickness, its actual 

 centre of gravity will lie behind g, at the distance 

 of half the thickness. It is one of the properties 

 of the triangle, that the line Dg, determined as 

 above, is always one-third of the whole line DC ; 

 thus the centre of gravity of a triangle is readily 

 found. 



When two balls are connected by an inflexible 

 rod, they form but one body, and the common 

 centre of gravity is not situated in either, but 

 between them in the rod joining their centres. If 

 the balls are equal in mass, it will evidently be in 

 the middle of the rod ; but if they are unequal, 

 the point where they balance each other is found 

 to lie nearer to the larger mass. See MECHANICS. 

 The centre of gravity has always a tendency to 

 seek the lowest point, and this enables us readily 

 to find the centre of gravity of an irregular body. 

 For example, let a painter's pallet be suspended 

 from the thumb-hole, as 

 in the figure ; we know 

 that the centre of gravity 

 must be perpendicularly 

 below the point of suspen- 

 sion, and if we allow a 

 plumb-line or a straight 

 rod to hang down from 

 that point in front of the 

 pallet, and mark the line 

 under it, the centre of 

 gravity must be on that 

 line. Next, suspend the 

 Fig. 14. pallet from any other 



point, D, and apply the 



plummet as before, and another line is found also 

 containing the centre of gravity, which must there- 

 fore be where the lines cross. If a third line of 

 direction is tried, it will be found to pass through 

 the same point 



A perpendicular line from the centre of gravity, 

 which is called the line of direction, must fall 

 within the base of any object resting on the 



202 



ground, otherwise it will fall. A structure may 

 overhang its base within certain limits. In A 

 (fig. i s) the line of direction falls within the base, 



B 



Fig. 15. 



so that the centre is still supported, and would 

 have to rise before the body could tumble ; in B, 

 the centre is unsupported, and moves in a descend- 

 ing curve from the first. The instability here 

 arises from the height of the object, for the slope 

 and base are the same in both. 



This explains why vehicles when loaded high, 

 or made top-heavy, are so easily upset 



The Pendulum. 



Any heavy body, such as a ball, suspended by a 

 string or rod, so as to swing freely, constitutes a 

 pendulum. Swinging is no less an effect of gravity 

 than falling ; and from the importance of the pen- 

 dulum, as a measurer of time, the phenomenon 

 deserves attentive study. 



In the accompanying cut, a pendulum of the 

 most common construction is represented, sus- 

 pended at A. When the ball or bob, C, is drawn to 

 one side, as to D, gravity 

 urges it downwards, while 

 the tension of the rod draws 

 it towards A. The composi- 

 tion of the two forces makes 

 it describe a descending 

 curve to C. But the ball 

 does not stop here ; it goes D 

 on, by the law of inertia, in "*-..] 

 the ascending curve CD', 

 until gravity destroys its Fig. 16. 



acquired motion. If friction 



and the resistance of the air did not interfere, 

 the ball would reach the same elevation as it 

 started from. But these causes gradually render 

 the ascent less and less, and at last bring the 

 pendulum, when it has no maintaining power, to 

 a state of rest 



One sweep of a pendulum from D to D' is called 

 an oscillation. The most remarkable property of 

 the oscillations of the pendulum, and that on which 

 its use as a regulator of movement depends, is 

 that, whether long or short, they are all performed 

 in very nearly the same time. If we observe the 

 vibrations of any body set swinging, we find that, 

 though the arc it describes is continually diminish- 

 ing, there is no sensible shortening of the time in 

 which the single sweeps are accomplished. As 

 the journey becomes less, so does the velocity. 

 Galileo is said to have been the first that distinctly 

 noted and investigated this important fact. It is 

 easy to see, in a general way, that the wider the 

 sweep of the ball, the steeper is its descent at 

 the beginning ; and that the greater velocity thus 

 acquired must more or less compensate for the 

 longer journey ; but the mathematical proof that 



