the height at which a body would lose įth of its weight at the Earth's surface is .1543672 x 4000 = 617.4688 miles. The force of gravity does not vary in the same manner below the Earth's surface as above it; for, on the principle that every particle of matter possesses the property of attraction, mathematicians prove that, in descending from the surface towards the centre, gravity diminishes in the direct ratio in which the distance decreases. If, therefore, d denote the distance below the surface, and r, w, and was before, we shall have r:r-d :: w: w', and therefore (r-d)w w' = Consequently, when r, d, and w are given, w' becomes known; or if w, w', and r are given, d is easily found; for rw d= and consequently rw d=12 w The next aspect in which the action of gravity on terrestrial bodies should be considered, is when these are at liberty to obey its influence, and consequently to descend in the direction in which that influence is exerted. The motion which is thus produced is found to agree in all its circumstances with that which mathematical investigation proves ought to result from the action of a constant force. The spaces through which bodies fall are always proportional to the squares of the times of their descent: if these times be 1, 2, 3, 4, &c. seconds, for instance, the spaces described are as 1, 4, 9, 16, &c. The space is also the same, whatever may be the magnitude of the body, independently of the resistance which it experiences from the medium through which it moves; a circumstance which shows that the action of gravity is always proportional to the mass of matter, or the number of particles the body contains. In these descents also, the increments of velocity, and consequently the whole velocities, are found to be proportional to the times which the bodies have been in motion. Hence, when the space described, and the velocity acquired in any given unit of time, are ascertained, the space and velocity for any other time are easily determined, or the time corresponding to any other space or velocity found; and consequently all the circumstances and phenomena of bodies descending in perpendicular lines, or even down inclined planes, thence become known. It has been found at a falling body in the latitude of London, and independently of any resistance of the air, when urged by gravity, descends through 16 feet and an inch in the first second of its descent from rest, and acquires a velocity which would carry it through double that space, or 32 feet 2 inches, in the next second of time, if gravity ceased to act and the acquired velocity were uniformly continued during that period. For, as the velocities are proportional to the times, and the spaces as the squares of either, if any other time in seconds be denoted by t, the space by s, and the final velocity by v, and g=161 feet, we have 1":t:: g: gt=s, and 1:t:: 29 : 2gt=v; hence by finding the value of g and t in the last of these equations, and substituting them in the first, we shall have 22 s =gt = {tv = 4g By substituting the given numbers in these formulæ instead of their respective letters, the true résults in any particular question will be obtained. If, for example, it were required to find the space through which a heavy body would descend in 3 seconds, then s=gť=1615 *9=144 feet, the space required. And if the velocity at the end of the same time were required, by taking the second and third formulæ, we have {tv=gt, from which v=2gt=321 *3=96 feet, the velocity required. The time, either of describing a certain space or of acquiring a certain velocity may also be readily found: for if the time of falling through a space of 500 feet were required, we should have 500 5 =100 = 10 193 =5.57567 seconds, the time required. The time of acquiring any given velocity may likewise be readily found; for let it be required to ascertain the time in which a body would acquire a velocity of 300 feet per second; then since gť =jtv, 161 we have 2=32 193 300 1800 = 9:32642 seconds. The same law applies equally to the ascent as to the descent of bodies, but in a contrary sense, that which is accelerating force in the one case becoming retarding force in the other. Thus, if a body were projected with a certain velocity in a direction perpendicular to the surface of the Earth at the point of projection, its motion would be opposed to the action of gravity, and the whole of its velocity would be destroyed by this force in exactly the same time as that in which it would have been generated in descending freely from a state of rest; and the same space would be described in each case before the effect was produced. When a body is projected in any direction not perpendicular to the horizon, another kind of effect is produced by the action of gravity. In this case, it deflects the body from the line of its projectile motion, and causes it to describe a curve, concave towards the earth. Thus, when the action of gravity is considered as acting in parallel lines, and the resistance of the medium through which the body moves is not taken into the account, the curve which is described by the combined effects of these two motions. is a parabola, situated in the vertical plane passing through the centre of the earth and the line of its projectile motion. The effect of gravity upon a body thus projected is measured by the curvature of the line it describes, or the space through which it is caused to deviate in a given time from the line of its projectile motion, which constitutes the tangent to the first point of the curve. A slight acquaintance with the phenomena of the physical world furnishes us with numerous examples of all these effects; and amply proves that the power which imparts weight to bodies, oscillation to the pendulum, and stability to the ocean, which accelerates the descent of bodies in perpendicular lines, and deflects them when projected obliquely, is strictly analogous to that which regulates the motions of the planetary system. It was the effect of this power upon a projectile that constituted, in the mind of the great investigator of the laws of gravitation, the first link of that chain which not only binds the earth to the heavens, but mutually connects all the bodies in our system with each other. It was this effect which first caused bim to stretch his thoughts beyond the confines of this narrow sphere, and fix himself, as it were, in the centre of the solar system, there to contemplate the simplicity of the law which regulates, and admire the harmony of the motions which characterize, the revolutions of the celestial orbs. (To be continued.] The Naturalist's Diary For SEPTEMBER 1819. Her charms in part, as conscious of decay! SEPTEMBER is, generally, accounted the finest and most settled month in the year. The mornings and evenings are cool, but possess a delightful freshness, while the middle of the day is pleasantly warm and open. October also frequently partakes the character of its precursor. A morning's walk' at this season is replete with gratification to the admirer of Nature's beauties. What a magnificent phenomenon is every day exhibited in the rising of the Sun! yet how common is the observation, that indolence and the love of sleep prevent a great part of mankind from contemplating this beauteous wonder of the creation! What numbers are there, in high life especially, who prefer a few more hours of sleep to all the pleasures of a morning walk !-See some reflections ou this subject in our last volume, p. 234. Oh, busie folly! Why do I my braine Whate'er is earth in us to grow all soule? Rural scenery is now much enlivened by the variety of colours, some lively and beautiful, which are assumed, towards the end of the month, by the fading HABINGTON. |