The areas bounded by curves and their asymptotes, though indefinitely extended, have sometimes limits to which they may approach indefinitely near: and this happens in hyperbolas of all kinds, except the first or Apollonian, and in the logarithmic curve. But in the common hyperbola, and many other curves, the asymptotical area has no such limit, but is infinitely great. Solids, too, generated by hyperbolic areas, revolving about their asymptotes, have sometimes their limits; and sometimes they may be produced till they exceed and given solid. Also the surface of such solid, when supposed to be infinitely produced, is either finite or infinite, according as the area of the generating figure is finite or infinite. The way of discovering whether any proposed curves have asymptotes, and the manner of drawing them when they are inclined to the axis, may be easily derived from the method of tangents. ATMOSPHERE, that gaseous or aeriform fluid which every where invests the surface of the terraqueous globe; and partakes of all its motions, both annual and diurnal. We have already considered the mnechanical properties of this fluid, under the article A in ; and it therefore only remains to treat of it as forming one body, viz. its figure, pressure, altitude, &c. Figure of the Atmosphere.—As the atmosphere envelopes all parts of the surface of the earth, if both the one and the other were perfectly at rest, and were not endowed with a diurnal motion round their axis, the atmosphere would be exactly spherical, according to the universal laws of gravity; for the parts of the surface of a fluid in a state of rest, must be equally remote from its centre. But the earth and the ambient atmosphere are invested with a diurnal motion, which carries them round their common axis of rotation; and the different parts of both having a centrifugal force, the tendency of which is more considerable, and that of the centripetal force less, - *Arts are more remote from *and, consequently, the figure of the atmosphere must become that of an oblate spheroid, because the parts that correspond to the equator have a greater cemtrifugal force than the parts which correspond to the poles. Besides, the figure of the atmosphere must represent such a spheroid, in consequence of the sun striking the equatorial regions more directly than those about the poles': whence it follows, that the mass of air, or part of the atmosphere, about the polar regions, being less heated, cannot expand so much, nor reach so high ; nevertheless, as the same force which contributes to elevate air, diminishes the pressure on the surface of the earth, higher columns of it at or near the equator, all other circumstances being the same, will not be heavier than those of the lower belonging to the poles; but, on the contrary, without some compensation they would be lighter, in consequence of the diminished gravity of the upper strata. Weight or Pressure of the Atmos. phere.--Torricelli found that the pressure of the atmosphere sustains a column of quicksilver, of an equal base and 39 inches height; and as a cubical inch of quicksilver is found to weigh near half a pound avoirdupoise, therefore the whole 30 inches, or the weight of the atmosphere on every square inch, is nearly equal to 15sb. Again, it has been found that the pressure of the atmosphere balances, in the case of pumps, &c. a column of water of about 344 feet high; and, the cubical foot of water weighing just 1000 ounces, or 62.1b. 34 times 62}, or 215Slb. will be the weight of the column of water, or of the atmosphere on a base of a square foot; and, consequently, the i44ts, part of this, or 151b. is the weight of the atmosphere on a square inch ; the same as before. Hence the pressure of this ambient fluid on the whole surface of the earth. is equivalent to that of a globe of lead of 60 miles in diameter. And hence also it appears, that the pressure upon the human body must be very considerable; for. admitting the surface of a man’s body to be about 15 square feet, and the pressure about 25lb. on a square inch, he must sustain 32,400lb. or nearly 14, tons weight for his ordinary load. And it might be easily shown, that the difference in the weight of air sustained by our bodies in different states of the atmosphere, is often near a ton and a half. Height and Density of the Atmosphere.—The densities of the air decrease in geometrical progression, as the altitudes increase in arithmetical progression; and, therefore, if no other cause existed, it would follow that the atmosphere was of indefinite height. But this cannot be, in consequence of the other planetary bodies: our atmosphere, for instance, cannot extend beyond the common centre of attraction of the earth and moon; for if in the first instance we conceive it to surpass this limit, it is obvious, that as the earth revolves ou its axis, and thereby turns all its parts successively towards the moon, this body, in consequence of its superior attraction beyond that point, would draw that part of our atmosphere towards her own centre, and either leave a vacuum between the terrestrial and lunar atmospheres, or the limits of both would be the common centre of attraction of the two bodies. Another cause, viz. the centrifugal force, would also operate against an indefinitely extended atmosphere; for as this fluid partakes of the diurnal motion of the earth, it is obvious, that beyond that point where the centrifugal force is equal to the force of gravity, the fluid would be thrown off by the rotatory motion of the body, and the limits of the atmosphere terminated in that point. If the air was every where of the same uniform density as at the earth's surface, where its specific gravity to that of water is about as 3 to 2500; or where a cubic foot weighs 1} ounces, it would follow, that its altitude would be about 54 miles: for the whole atmospheric pressure is equal to about 33 or 34 feet of water; and the density of this latter fluid being about m and M the heights of the barometer, the former at the lower place and the latter at the top of the eminence, which are also as the densities of the air at those places, and therefore conversely to find the density of the air corresponding to any particular altitudes, we may change the formula into A = 10000 log. m. — 10000 log. M; whence A + 10000 log. M. 10000 From which formula is deduced the following table, which exhibits the comparative density of the air at the several corresponding heights, viz. Height in Miles. No. Times rarer. 0 - - - - - - - 1 3 - - - - - - 2 ; - - - - - - 4 14 - - - - - - 16 21 - - - - - - 64 28 - - - - - - 256 35 - - - - - 1024 42 - - - - - 4096 49 - - - - - - 16384 56 . . . . . . 65536 63 - - - - - - 26:14.4 70 - - - - - - 1048576 And by pursuing the calculation in this table, it might easily be shown, that a cubic inch of the air we breathe would be so much rarefied at the reight of 500 miles, that it would fill a sphere equal in diameter to the orbit of Saturn. With regard to the extent of the atmosphere, from the principles upon which our calculation is sounded it is indefinite; but it must of necessity have a certain limit. For one of the principal effects of the atmosphere being the refraction of light, the particles of which are the smallest of any we know of in mature, it is reasonable to fix the boundary of the atmosphere where it begins to have the effect of bending the rays of light. Now Kepler, and after him La Hire, computed the height of the sensible atmosphere from the duration of the twilight, and from the magnitude of the terrestrial shadow in lunar eclipses, and found that it was sufficiently dense at a height of between 40 and 50 miles, to reflect and intercept the light of the sun. So far, therefore, we may be certain that the atmosphere extends ; and at that altitude we may collect, from what has been already said, that the air is more than 10,000 times rarer than at the earth's surface; but how much farther it may be extended, is totally unknown. frefractive and Reflective Powers of the Atmosphere. — The atmosphere has a refractive power, which is the cause of various phe. momena. This power is ascertained by the production of twilight, and by many other facts and experiments. It has also a reflective power, and this power is the cause of objects being so uniformly enlightened on all sides. Were it not for this, the shadows of objects would be so dark, and their enlightened sides so very bright, that probably we should only be able to see those parts of them which were absolutely exposed to the sun’s rays, if indeed the extreme light in this case did not even render them too powerful for the delicacy of the optic nerve. Temperature of the Atmosphere.— The temperature of the atmosphere diminishes, as the distance from ille earth increases, though apparently in a less ratio. M. de Saussure found, that by ascending from Geneva to Chamouni, a height of 347 toises, Reaumer's thermometer fell 4° 2'; and that, on ascending from thence to the top of Mont Blanc, 1941 toises, it fell 20° 71: this gives 221 feet £nglish for a diminution of 1° of Fahremleit, in the first case, and 268 in the second. Nevertli.eless, from the accuracy which the rule for barometical measurement pos sesses, it may be inferred, that the heat, in degrees of the centigrade thermometer, is *( g - #) ,which seems to agree well with observa. tion. The mean temperature of the atmosphere in any parallel of latitude remains nearly constant, but it decreases from the equator to either pole; and if t be made to represent the mean temperature of any parallel of which the latitude is L, M the mean temperature in the latitude of 45°, and M + E the mean temperature at the equator; then is t = M + E. cos. 2. L.; whence the mean temperature in any latitude is readily ascertained. The mean temperature in latitude 45° is 58° = M, at the equator it-is 85°, whence 85°–58° = 27° = E ; therefore t = 58°-H 27° x cos. 2 L, which, when 2 L → 90, the cosine being negative, is less than 5S°. But if the place is at any height above the surface, then the iormula becomes t = M- |. + E. cos. 2 L; M and E being still the same as above, and H the height of the place in English feet. On ascending into the atmosphere, at a certain height in every latitude a point is found where it always freezes, or where it freezes more than it thaws, so that the mean tempcrature does not exceed 32°, and the curve joining or passing through all those points produced in a great measure by the same causes. ATOM, a particle of matter indivisible, on account of solidity, hardness, and impenetrability, which preclude all division, and leave no vacancy for the admission of any foreign force to separate or disunite its parts. - — 15577 =294, 27 – 58–32 and conseq. H = 7642+ 7.933. cos. 2 L. Which formula seems to agree very nearly with actual observation. See Playfair's “Outlines of Natural Phil.” p. 285; see also a different formula for expressing the line of perpetual congelation, Leslie, “Elements of Geometry,” 2d edition, p. 495. A1 Mosp H ERE of the Planets.Since the planets and their satellites are allowed to be bodies of a nature similar to the earth we inhabit, there are few who attempt to deny that the planets are surrounded with atmospheres analogous, in most respects, to that whose properties have been explaimed in the preceding articles. These atmospheres are flattened towards the poles, and protuberant at the equator. But this oblateness has its limits; and in the case where it is greatest, the ratio of the polar and equatorial diameter is as 2 to 3. The atmosphere cannot extend itself at the equator to a greater distance than to the place where the centrifugal force is exactly eqaal to the force of gravity. With regard to the sun, this point is remote from its centre to a distance measuring the radius of the orbit of a planet which would make its revolution in the same period as that luminary employs in its rotation. The solar atmosphere cannot, therefore, extend to the orbit of Mercury; and consequently it cannot produce the zodiacal light, which appears to extend even to the orbit of the earth. ATMOSPHERIC Tides, are certain periodical changes in the atmosphere, similar, in some re•rectoo those of the ocean, and ATOMICAL Philosophy, is, the doctrine of Atoms; a system which accounts for the origin and formation of things from the hypothesis, that atoms are endowed with: weight and motion. ATTRACTION, in Physics, a general term used to demote the cause, power, or principle, real or imaginary, by which all bodies mutually tend towards each other, and cohere, till separated by some other power. The laws, phenomena, &c. of attraction, form the chief subject of Newtonian philosophy, these being found to obtain in almost all the wonderful operations of nature. The principle of attraction, in the Newtonian sense of it, was first hinted at by Copermicus. Kepler calls gravity a corporeal and mutual affection between similar bodies, in order to their union. And he pronounced more positively, that no bodies whatever were absolutely light, but only relatively so; and, consequently, that all matter was subjected to the power and law of gravitation. The first who, in this country, adopted the notion of attraction, was Dr. Gilbert, in his book De Magnete; and the next was the celebrated Lord Bacon. In France it was received by Fermat and Roberval; and in Italy, by Galileo and Borelli. But till Newton appeared, this principle was very imperfectly defined and applied. Before Newton, no one had entertained such correct and clear notions of the doctrine of universal attraction as Dr. Hooke, who observes, that the hypothesis upon which he explains the system of the world is founded upon the three following principles: 1. That all the celestial bodies have not only an attraction or gravitation towards their proper centres, but that they mutually attract, each other within their sphere of activity. 2. That all bodies which have a simple and direct motion, continue to move in a right line, if some force, which operates without ceasing, does not constrain them to describe a circle, an ellipse, or some other more complicated curve. 3. That attraction is so much the more powerful, as the attracting bodies are nearer to each other. But Hooke was not able to solve the general problem relative to the law of attraction, which would occasion a body to describe an ellipse round another quiescent body placed in one of its foci ; this discovery being reserved for Newton. Attraction may be considered as it regards celestial bodies, terrestrial bodies, and the minuter particles of bodies. The first case is usually denoted by the word attraction, or universal gravitation, the second by gravitation, and the third by the words affinity, chemical attraction, or molecular attraction. Many philosophers are now of opinion, that it is the same force contemplated under different aspects, yet constantly subject to the same law. At a finite distance, all the bodies in nature are said to attract one another in the direct ratio of the masses, and the inverse ratio of the square of the distance. According to a law of Kepler, deduced from observation, the radii vectores of planets and comets describe about the sun areas proportional to the times; but this law can only have place so long as the force which incessantly deflects each of these bodies from the right line is constantiy directed towards a fixed point, which is the origin of the radii vectores. The tendency, therefore, of the planets and comets towards the sun, follows necessarily, from the proportionality of the areas described by the radii vectores to the times of description: this tendency is reciprocal. It is, in fact, a general law of nature, that action and re-action are equal and contrary : whence it results, that the planets and comets re-act upon the sun, and communicate to it a ten dency towards each of them. The satellites of Uranus tend towards Uranus, and Uranus towards his satellites: the satellites of Saturn tend towards Saturn, and Saturn towards them. The case is the same with regard to Jupiter and his satellites. The earth and moon tend likewise reciprocally the one towards the other. The proportionality of the areas described by the satellites to the times of description, concur with the equality of action and re-action, to render these assertions unequivocal. All the satellites have a tendency towards the sun ; for they are all animated by a regular motion about their respective planets, as if they had been immoveable; whence it results that the satellites are impelled with a motion common also to their planets; that is to say, that the same force by which the planets tend incessantly towards the sun, acts also upon the satellites, and that they are carried towards the sun with the same velocity as the planets. And since the satellites tend towards the sun, it follows that the sun tends towards them, because of the equality of action and re-action. Observations have convinced us that Saturn deviates a little from his path when he is near Jupiter; whence it follows, that Saturn and Jupiter tend reciprocally the one towards the other. It therefore appears, that all the heavenly bodies tend reciprocally towards one another: but this tendency, or rather the attractive force which occasions it, appertains not solely to their aggregate mass ; all their inoleculae partake of it, or contribute to it. If the sun acted exclusively upon the centre of the earth, without attracting each of its particles, the undulations of the ocean would be incornparably greater, and very different from those which are daily presented to our view. The tendency of the earth towards the sun is, therefore, the result of the sum of the attractions exerted upon all the moleculae, which consequently attract the sun in the ratio of their respective masses; |