find, the rule holds in all cases, that the spaces described by bodies falling freely from a state of rest, increase as the SQUAKES of the times in

crease.

Charles. I think I shall not forget the rule. I will also show my cousin Henry how he may know the height to which his bow will carry. Father. The surest way of keeping what knowledge we have obtained, is by communicating it to our friends.

Charles. It is a very pleasant circumstance, indeed, that the giving away is the best method of keeping, for I am sure, the being able to oblige one's friends is a most delightful thing.

Father. I have but a word or two more upon the subject: since the whole spaces described increase as the squares of the times increase, so also the velocities of falling bodies increase in the same proportion; for you know that the velocity must be measured by the space passed through. Thus if a person travels six miles an hour, and another person travels twelve miles in the same time, the latter will go with double the velocity of the former: consequently the velocities of falling bodies increase as the squares of the times increase.

If now you compare the spaces described by falling bodies in the several moments of time taken separately, and in their order from the beginning of the fall, then they, and consequently their velocities also, are to one another as the

odd numbers, 1, 3, 5, 7, 9, 11, 13, &c. taken in their natural order, as you will observe by reflecting on the foregoing examples.

With this we conclude our present conversation.

CONVERSATION IX.

On the Centre of Gravity.

Father. We are now going to treat upon the Centre of Gravity, which is that point of a body in which its whole weight is as it were concentrated, and upon which if the body be freely suspended it will rest; and in all other positions it will endeavour to descend to the lowest place to which it can get.

Charles. All bodies then, of whatever shape, have a centre of gravity?

Father. They have: and if you conceive a line drawn from the centre of gravity of a body towards the centre of the earth, that line is called the line of direction, along which every body, not supported, endeavours to fall. If the line of direction fall within the base of any body,

MW

it will stand; but if it does not fall within th base, the body will fall.

If I place the piece of wood a (Plate 1. Fig 7.) on the edge of a table, and from a pin a a its centre of gravity be hung a little weight b the line of direction ab falls within the base, an therefore, though the wood leans, yet it stand secure. But if upon A, another piece of wood 1 be placed, it is evident that the centre of gravity of the whole will be now raised to c, at which point if a weight be hung, it will be found tha the line of direction falls out of the base, and therefore the body must fall.

Emma. I think I now see the reason of the advice which you gave me, when we were going across the Thames in a boat.

Father. I told you that if ever you were over. taken by a storm, or by a squall of wind while you were on the water, never to let your fears s get the better of you, as to make you rise from your seat, because by so doing you would elevate the centre of gravity, and thereby, as is evident by the last experiment, increase the danger: whereas, if all the persons in the vessel were, at the moment of danger, instantly to slip from their places on to the bottom, the risque would be exceedingly diminished, by bringing the centre of gravity much lower within the vessel. The same principle is applicable to those who may be in danger of being overturned in any carriage whatever.

Emma. Surely then, papa, those stages which load their tops with a dozen or more people, cannot be safe for the passengers.

Father. They are very unsafe, but they would be more so, were not the roads about the metropolis remarkably even and good: and, in general, it is only within twenty or thirty miles of London, or other great towns, that the tops of carriages are loaded to excess.

Charles. I understand then, that the nearer the centre of gravity is to the base of a body, the firmer it will stand.

:

Father. Certainly; and hence you learn the reason why conical bodies stand so sure on their bases, for the tops being small in comparison of the lower parts, the centre of gravity is thrown very low and if the cone be upright or perpendicular, the line of direction falls in the middle of the base, which is another fundamental property of steadiness in bodies. For the broader the base, and the nearer the line of direction is to the middle of it, the more firmly does a body stand: but if the line of direction fall near the edge, the body is easily overthrown.

Charles. Is that the reason why a ball is so easily rolled along a horizontal plane?

Father. It is; for in all spherical bodies, the base is but a point, consequently almost the smallest force is sufficient to remove the line of direction out of it. Hence it is evident, that heavy bodies situated on an inclined plane will, VOL. I.-E

while the line of direction falls within the slide down upon the plane: but they wi when that line falls without the base. The A (Plate 1. Fig. 8.) will slide down the DE, but the bodies B and c will roll dow

Emma. I have seen buildings lean very out of a straight line, why do they not f Father. It does not follow, because a b leans, that the centre of gravity does within the base. There is a high tower & a town in Italy, which leans fifteen fee the perpendicular; strangers tremble by it, still it is found by experiment t line of direction falls within the ba therefore it will stand while its materia together.

A wall at Bridgenorth, in Shropshire I have seen, stands in a similar situatio long as a line cb (Plate 11. Fig. 9.) let i the centre of gravity c of the building AB within the base CB, it will remain firm. the materials with which it is built go to

Charles. It must be of great use i cases to know the method of finding the of gravity in different kinds of bodies.

Father. There are many easy rules i with respect to all manageable bodies; mention one, which depends on the pr which the centre of gravity has, of alw deavouring to descend to the lowest poin If a body ▲ (Plate 11. Fig. 10.) be free