_Mrs. B._ Caroline, what would be the effect, were the body supported in any other single point?

_Caroline._ The surrounding parts no longer balancing each other, the body, I suppose, would fall on the side at which the parts are heaviest.

_Mrs. B._ Infallibly; whenever the centre of gravity is unsupported, the body must fall. This sometimes happens with an overloaded wagon winding up a steep hill, one side of the road being more elevated than the other; let us suppose it to slope as is described in this figure, (plate 3. fig. 4.) we will say, that the centre of gravity of this loaded wagon is at the point A. Now your eye will tell you, that a wagon thus situated, will overset; and the reason is, that the centre of gravity A, is not supported; for if you draw a perpendicular line from it to the ground at C, it does not fall under the wagon within the wheels, and is therefore not supported by them.

_Caroline._ I understand that perfectly; but what is the meaning of the other point B?

_Mrs. B._ Let us, in imagination take off the upper part of the load; the centre of gravity will then change its situation, and descend to B, as that will now be the point about which the parts of the less heavily laden wagon will balance each other. Will the wagon now be upset?

_Caroline._ No, because a perpendicular line from that point falls within the wheels at D, and is supported by them; and when the centre of gravity is supported, the body will not fall.

_Emily._ Yet I should not much like to pa.s.s a wagon in that situation, for, as you see, the point D is but just within the left wheel; if the right wheel was raised, by merely pa.s.sing over a stone, the point D would be thrown on the outside of the left wheel, and the wagon would upset.

_Caroline._ A wagon, or any carriage whatever, will then be most firmly supported, when the centre of gravity falls exactly between the wheels; and that is the case in a level road.

_Mrs. B._ The centre of gravity of the human body, is a point somewhere in a line extending perpendicularly through the middle of it, and as long as we stand upright, this point is supported by the feet; if you lean on one side, you will find that you no longer stand firm. A rope-dancer performs all his feats of agility, by dexterously supporting his centre of gravity; whenever he finds that he is in danger of losing his balance, he shifts the heavy pole which he holds in his hands, in order to throw the weight towards the side that is deficient; and thus by changing the situation of the centre of gravity, he restores his equilibrium.

_Caroline._ When a stick is poised on the tip of the finger, is it not by supporting its centre of gravity?

_Mrs. B._ Yes; and it is because the centre of gravity is not supported, that spherical bodies roll down a slope. A sphere being perfectly round, can touch the slope but by a single point, and that point cannot be perpendicularly under the centre of gravity, and therefore cannot be supported, as you will perceive by examining this figure. (fig. 5. plate 3.)

_Emily._ So it appears: yet I have seen a cylinder of wood roll up a slope; how is that contrived?

_Mrs. B._ It is done by plugging or loading one side of the cylinder with lead, as at B, (fig. 5. plate 3.) the body being no longer of a uniform density, the centre of gravity is removed from the middle of the body to some point in or near the lead, as that substance is much heavier than wood; now you may observe that should this cylinder roll down the plane, as it is here situated, the centre of gravity must rise, which is impossible; the centre of gravity must always descend in moving, and will descend by the nearest and readiest means, which will be by forcing the cylinder up the slope, until the centre of gravity is supported, and then it stops.

_Caroline._ The centre of gravity, therefore, is not always in the middle of a body.

_Mrs. B._ No, that point we have called the centre of magnitude; when the body is of an uniform density, and of a regular form, as a cube, or sphere, the centres of gravity and of magnitude are in the same point; but when one part of the body is composed of heavier materials than another, the centre of gravity can no longer correspond with the centre of magnitude. Thus you see the centre of gravity of this cylinder plugged with lead, cannot be in the same spot as the centre of magnitude.

_Emily._ Bodies, therefore, consisting but of one kind of substance, as wood, stone, or lead, and whose densities are consequently uniform, must stand more firmly, and be more difficult to overset, than bodies composed of a variety of substances, of different densities, which may throw the centre of gravity on one side.

_Mrs. B._ That depends upon the situation of the materials; if those which are most dense, occupy the lower part, the stability will be increased, as the centre of gravity will be near the base. But there is another circ.u.mstance which more materially affects the firmness of their position, and that is their form. Bodies that have a narrow base are easily upset, for if they are a little inclined, their centre of gravity is no longer supported, as you may perceive in fig. 6.

_Caroline._ I have often observed with what difficulty a person carries a single pail of water; it is owing, I suppose, to the centre of gravity being thrown on one side; and the opposite arm is stretched out to endeavour to bring it back to its original situation; but a pail hanging to each arm is carried with less difficulty, because they balance each other, and the centre of gravity remains supported by the feet.

_Mrs. B._ Very well; I have but one more remark to make on the centre of gravity, which is, that when two bodies are fastened together by an inflexible rod, they are to be considered as forming but one body; if the two bodies be of equal weight, the centre of gravity will be in the middle of the line which unites them, (fig. 7.) but if one be heavier than the other, the centre of gravity will be proportionally nearer the heavy body than the light one. (fig. 8.) If you were to carry a rod or pole with an equal weight fastened at each end of it, you would hold it in the middle of the rod, in order that the weights should balance each other; whilst if the weights were unequal, you would hold it nearest the greater weight, to make them balance each other.

_Emily._ And in both cases we should support the centre of gravity; and if one weight be very considerably larger than the other, the centre of gravity will be thrown out of the rod into the heaviest weight. (fig.

9.)

_Mrs. B._ Undoubtedly.

Questions

1. (Pg. 46) If a body be struck by two equal forces in opposite directions, what will be the result?

2. (Pg. 46) What is fig. 5. plate 2. intended to represent?

3. (Pg. 47) How would the ball move, and how would you represent the direction of its motion?

4. (Pg. 47) What is supposed respecting the forces represented in fig.

6?

5. (Pg. 47) How would the body move if so impelled?

6. (Pg. 47) If the forces are unequal and not at right angles, how would the body move, as ill.u.s.trated by fig. 7?

7. (Pg. 47) How must a body be acted on, to produce motion in a curve, and what example is given?

8. (Pg. 48) When is a body said to revolve in a plane, and what is meant by the centre of motion?

9. (Pg. 48) What is intended by the axis of motion, and what are examples?

10. (Pg. 48) What is the middle point of a body called?

11. (Pg. 48) What is said of the axis of motion, whilst the body is revolving?

12. (Pg. 48) When a body revolves on an axis, do all its parts move with equal velocity?

13. (Pg. 49) How is this explained by fig. 1. plate 3?

14. (Pg. 49) What are the two forces called which cause a body to move in a curve; and what proportion do these two forces bear to each other when a body revolves round a centre?

15. (Pg. 49) If the centripetal force were destroyed, how would a body be carried by the centrifugal?

16. (Pg. 50) Explain what is meant by a _tangent_, as shown in fig. 2.

plate 3.

17. (Pg. 50) What forces impede a body thrown horizontally?

18. (Pg. 50) Give the reason why a body so projected, falls in a curve.

(fig. 3. plate 3.)

19. (Pg. 51) The curve in which it falls, is not a part of a true circle: what is it denominated?

20. (Pg. 51) What is the _centre of gravity_ defined to be?

21. (Pg. 51) What results from supporting, or not supporting the centre of gravity?

22. (Pg. 51) What is intended to be explained by fig. 4. plate 3?

23. (Pg. 51) What would be the effect of taking off the upper portion of the load?

24. (Pg. 52) When will a carriage stand most firmly?

25. (Pg. 52) What is said of the centre of gravity of the human body, and how does a rope dancer preserve his equilibrium?

26. (Pg. 52) Why cannot a sphere remain at rest on an inclined plane?