288 



THE POPULAR EDUCATOB. 



. 4. Lastly, as is evident from d, e, f, in Fig. 35, when the 

 bodies incline to one side, the perpendicular from the centre of 

 gravity meets the base nearer to its circumference on that side ; 

 and, if the transverse force is applied in that direction, the 

 resultant tends more to fall outside the base ; that is, everything 

 else being the same, the stability is least when the upsetting 

 force acts in the direction in which the body leans. 



These are truths known to everybody from experience, but of 

 which here you see the "reason why," and, what is of no less 

 advantage, you obtain a rule by which you may measure the 

 amount of stability or instability in any case that may come 

 before yon. If you draw figures for bodies of different weights, 

 different bases, different transverse forces, and their heights of 



application, you 

 will by trial feel 

 your way, and 

 soon clearly 

 understand the 

 subject. 



But the cases 

 to which the 

 terms "sta- 

 bility" and "in- 

 stability " are 

 \ more commonly 

 ) applied, are 

 " those in which 

 there is only one 

 point of sup- 

 port, and the 

 slightest force 

 from without 

 causes disturb- 

 ance. In Fig. 36, as was shown in Lesson V. (page 152), tho 

 body supported at the point o is in equilibrium in the two 

 positions o A B and o c D. Now, the first of these is one of 

 stability, the second of instability. What do these terms 

 denote ? This : that if you pull the stable body out of its rest 

 into any other position to right or left, say o E F, back it will 

 return to A o B, as though by a free choice. In the disturbed 

 position o E F, the weight acting downwards at G pulls it back ; 

 it can descend, but not ascend. Try the same on the position 

 o c D ; the body, no longer supported from below, cannot re- 

 ascend ; down it will rush to the stable position; and, after 

 oscillating there for a few turns, come to rest. We see thus 

 that in stable equilibrium the centre of gravity is in the lowest 

 2>ossible position ; in unstable in the higliest. 



Now, take the same body attached to the post at its centre 

 of gravity, G, Fig. 37. How- 

 ever you turn it round, G is 

 supported, and the body rests. 

 The equilibrium, therefore, is 

 neither stable nor unstable. 

 It neither returns on disturb- 

 ance to the first position, nor 

 rushes away from it. This is 

 termed " neutral equilibrium ;" 

 the centre can neither ascend 

 nor descend. 



Now take the egg-shaped 



bodies, Fig. 38 ; that represented at b is stable, for the centre 

 of gravity, supported from below, is in the lowest possible 



position. Dis- 

 turb it into the 

 position a, this 

 centre ascends, 

 and the weight 

 pulling down- 

 wards brings 

 it back to b. 



C. - The body in 



the position c 

 is unstable. It 

 is in equili- 

 brium, but on 



disturbance rolls through the position c into the position b. In 

 this case also you see the centre, for stability, must be in its 

 lowest position ; for instability, in its highest. But perfectly 



Fig. 40. 



Fig. 38. 



Fig. 39. 



-U. 



round balls, such as in Fig. 27 (page 200), are neutral, their 



centres, as you roll them on the ground, can neither ascend nor 



descend. 



Take now the balls in a, Fig. 39, which represents a geological 



section of hills and valleys. Those on the tops of the hills are 



unstable, because their centres of gravity are in their highest 



positions. Disturb them, and 



down they roll into stable positions 



in the valleys, the lowest positions 



of these centres. But here now a 



new principle is brought to light. 



A body may admit of several 



positions of equilibrium, but an 



unstable is always between two 



stables, and a stable between two 



unstables. The ball in the valley 



has a ball perched on the hill on 



either side, and the ball on the 



hill has a ball in the valley on 



either side. 



Take another illustration. Let 



it be a convex body, like a sea-shore pebble, with one side, as 



in Fig. 39, b, flatter than the other. I showed yon in the last 



lesson that such a body should have as many positions of 



equilibrium on a plane as you can draw lines from its centre of 



gravity piercing its surface at right angles. Let such points 

 in this pebble be A, B, c, D, the first and 

 third more distant from the centre G than 

 the other two. If I now try to make it 

 rest on the ground at A, the centre being 

 higher than it would be if the body touched 

 the ground on either side of that point, it 

 will roll down to either B or D, which are 

 two stable positions. We thus learn that, 

 The Positions of Equilibrium of a con- 

 vex body, supported from below, are 

 alternately stable and unstable. 

 As a further illustration of the peculiarities of the centre of 



gravity, take an egg. Why does it generally rest with its 



pointed end downwards, as at d, Fig. 39, while an egg, as at c, 



turned in wood of tho same size and form, rests broad-end down ? 



Explain, also, the reason the prancing-horse toy, represented at 



Fig. 40, supported at the edge of a table, 



and having a wire attached to him, which 



carries a heavy ball at its other end, does 



not fall on the ground, but, when disturbed, 



rocks backwards and forwards. Also, how 



a rocking-horse is set rocking by the child 



on his back. The four-oared boat and 



crew in Fig. 41, supported by the point of a 



needle on the iron upright below, imitates 



a boat's motion at sea, rising, and plunging, 



and going round, if the oars are loaded at 



their ends; explain this. Also, how the 



harlequin, Fig. 42, is balanced on his 



pedestal, as he twirls round and bows, 



leaning forward and falling backward at 



the imminent peril of coming to the ground. Instances of this 



kind could be multiplied without end, but as much as our space 



allows has been said on the centre of gravity, which we shall 



now leave to apply the principles so far set forth to practice, 



commencing with the Mechanical Powers. 



ANSWERS TO QUESTIONS IN LESSON V. 



1. To prevent the perpendicular from his centre of gravity falling 

 outside his base as he springs on the fore-foot to advance. On coming 

 down to counterpoise the centre of gravity's falling forward. 



2. He draws his feet under the chair, in order to get a base over 

 which, by leaning forward, he brings his centre of gravity, and lifts 

 that centre upwards by his muscular strength. 



3. He leans to the opposite side in order to keep the common centre 

 of gravity of himself and bucket over the base of support. 



4. Else the perpendicular from his centre of gravity would meet the 

 ground in advance of his feet. 



5. Because the resultant of the forward motion, and the weight of 

 horse and rider acting at their common centre of gravity, is then more 

 apt to meet the ground outside the base of support of the horse's legs. 



6. Because in that case the perpendicular from the centre of gravity, 

 being lower do\ru, is less apt to meet the ground outside the base 

 when the road slopes to one side. 



Fig. 42. 



