LECT ascent. ascent. Therefore, the velocity which a body acquires by falling, is sufficient to carry it up again to the same height from whence it fell: allowance being made for the resistance of the air, or other medium in which the body is moved. Thus, the body D in rolling down the inclined plane A B will acquire such a velocity by the time it arrives at B, as will carry it up the inclined plane B C, E D Center of gravity. direction. almost to C; and would carry it quite up to C, if the body and plane were perfectly smooth, and the air gave no resistance.-So, if a pendulum were put into motion in a space quite free of air, and all other resistance, and had no friction on the point of suspension, it would move for ever: for the velocity it had acquired in falling through the descending parts of the arc, would be still sufficient to carry it equally high in the ascending part thereof. The center of gravity is that point of a body in which the whole force of its gravity or weight is united. Therefore, whatever supports that point bears the weight of the whole body: and whilst it is supported, the body cannot fall; because all its parts are in a perfect equilibrium about that point. and line of An imaginary line drawn from the center of gravity of any body towards the center of the earth, is called the line of direction. In this line all heavy bodies descend, if not obstructed. Since the whole weight of a body is united in its In the above illustration, we have, for the sake of simplicity, sapposed that the body would pass through but one foot in the first second, this however, is not the fact, as any heavy body in that period of time, would have passed through about sixteen feet, and continue to increase in the same ratio. The rule therefore is to multiply the square of the time by sixteen, which will give the entire number of feet through which the body has fallen, center of gravity as that center ascends or descends, LECT I. we must look upon the whole body to do so too. But as it is contrary to the nature of heavy bodies to ascend of their own accord, or not to descend when they are permitted; we may be sure, that unless the center of gravity be supported, the whole body will tumble or fall." Hence it is, that bodies stand upon their bases when the line of direction falls within the base ; for in this case the body cannot be made to fall without first raising the center of gravity higher than it was before. Thus, the inclining H G body A D, whose center of gravity is E, stands firmly on its А, base DK, because the line of direction EF falls within the base. But if a weight, as I AGH, be laid apon the top of the body, E the center of gravity of the whole body and weight together is raised up to I; and then, as the line of direction ID falls with KI out the base at D, the center of gravity, I is F not supported and the whole body and weight tumble down together. Note 11. There are two apparent exceptions to the general law o. gravitation, which it may be proper to notice on the present occasion. One of these is well known, and is called the hanging tower of Pisathe other is a nearly similar building at Caerphilly in Glamorganshire. Of these two towers, the one leans twelve feet from the perpendicular and the other nearly fifteen, but as in both cases the center of gravity es within the base, no danger of their falling need be apprehended, whilst the materials retain their cohesive power. LECT. L Hence appears the absurdity of people's rising hastily in a coach or boat when it is likely to overset: for by Center of that means they raise the center of gravity so far as to gravity. endanger throwing it quite out of the base; and if they do, they overset the vehicle effectually. Whereas, had they clapped down to the bottom, they would have brought the line of direction, and consequently the center of gravity, further within the base, and by that means. might have saved themselves. The broader the base is, and the nearer the line of direction is to the middle or center of it, the more firmly does the body stand. On the contrary, the narrower the base, and the nearer the line of direction is to the side of it, the more easily may the body be overthrown a less change of position being sufficient to remove the line of direction out of the base in the latter case than in the former. And hence it is, that a sphere is so easily rolled upon a horizontal plane; and that it is so difficult, if not impossible, to make things which are sharp-pointed to stand upright on the point.-From what hath been said it plainly appears, that if the plane be inclined on which the heavy body is placed, the body will slide down upon the plane whilst the line of direction falls within the base; but it will tumble or roll down when that line falls without the base. Thus, the body A wi!! only slide down the inclined plane C D, whilst the body B rolls down upon it. When the line of direction falls within the base of our feet, we stand; and most firmly when it is in the middle: but when it is out of that base, we im mediately fall. And is not only pleasing, but even sur 12 prising, to reflect upon the various and unthought of LECT. I. methods and postures which we use to retain this position, or to recover it when it is lost. For this purpose we bend our body forward when we rise from a chair, or when we go up stairs : and for this purpose a man leans forward when he carries a burden on his back, and backward when he carries it on his breast; and to the right or left side as he carries it on the opposite side. A thousand more instances might be added." The quantity of matter in all bodies is in exact proportion to their weights, bulk for bulk. Therefore, heavy bodies are as much more dense or compact than light bodies of the same bulk, as they exceed them in weight. All bodies are full of pores, or spaces void of matter : All bodios and in gold, which is the heaviest of all known bodies, poroti there is perhaps a greater quantity of space than of matter. For the particles of heat and magnetism find an easy passage through the pores of gold ; and even water itself has been forced through them. Besides, if we consider how easily, the rays of light pass through so solid a body as glass, in all manner of directions, we shall find reason to believe that bodies are much more porous than is generally imagined. 13 Note 12. Rope dancers and tumblers maintain a species of tottering equilibrium by means of a long pole, which being rapidly shifted in any required direction, retains the center of gravity of the whole body within the toe. Note 13. Without attempting to assert, with a distinguished philosopher, that the whole of created nature may be compressed into the size of a nut-shell ; we may at least pause for a moment to examine the amazing porosity of some bodies, which would at first view appear perfectly dense and solid. Thus we find that glass, though of great specific gravity, is readily penetrated by the sun's rays, when conveyed to a focus by means of a burning glass; and the light of a candle may be seen through a thin leaf of gold. To further illustrate the matter, we may suppose a body to be so constructed as to have as much vacuity as matter, and as such, half the body vacuous. C LECT. All bodies are some way or other affected by heat; II. and all metallic bodies are expanded in length, breadth, The expan- and thickness thereby.-The proportion of the expansion of me- sion of several metals, according to the best experiments tals. The pyro meter I have been able to make with my pyrometer, is nearly thus Iron and steel as 3, copper 4 and a half, brass 5, tin 6, lead 7. An iron rod 3 feet long is about one 70th part of an inch longer in summer than in winter. The pyrometer here mentioned being (for aught I know) of a new construction, a description of it may perhaps be agreeable to the reader. AA is a flat piece of mahogany, in which are fixed If the particles of which the body is actually formed, be constructed in the same manner; then the vacuity will become three-fourths of the space occupied by the body. Carrying the supposition still further, we may suppose the last mentioned particles constructed in the same manner, the vacuity will then be seven-eighths; and if the series be carried forward to the tenth order of particles, the vacuity will exceed the matter one thousand and twenty-three times. A very obvious illustration of the effects of caloric in producing porosity is shewn in the formation of vesicular vapour or steam, which may be increased to many thousand times its original bulk, by an increase of temperature. |