and the pressure about 15lb. on feet, for the height of a uniform a square inch, he must sustain column; which is a little more 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.

than 5 miles. But the density decreases as the altitudes increase, the former in geometrical, and the latter in arithmetical progression. We have also, under the article ALTITUDE, shown that the general formula for ascertaining altitudes above the earth's surface, at the temperature of 31°, is A = 10000 X log. ; A being the altitude, and

m

M

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

Height and Density of the Atmos phere. 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 on its axis, and thereby turns all A+ 10000 log. M. its parts successively towards the 10000 moon, this body, in consequence From which formula is deduced of its superior attraction beyond the following table, which exhithat point, would draw that part bits the comparative density of the of our atmosphere towards her air at the several corresponding own centre, and either leave a va-heights, viz.

log. m.=

0

1

3.

2

7

4

14

16

21

64

28

256

35

1024

42

4096

cuum between the terrestrial and Height in Miles. No. Times rarer. 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.

63

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 height of 500 miles, that it would fill a sphere equal in diameter to the orbit of Saturn.

atmosphere, from the principles With regard to the extent of the founded it is indefinite; but it must upon which Our calculation is of necessity have a certain limit. For one of the principal effects of the atmosphere being the refrac tion of light, the particles of which are the smallest of any we know

of in nature, it is reasonable to fix sesses, it may be inferred, that the the boundary of the atmosphere decrease of heat for the greatest where it begins to have the effect heights which we can reach, is of bending the rays of light. Now not far from uniform; but that the Kepler, and after him La Hire, rate for any particular case must computed the height of the sensi- be determined by observation, ble atmosphere from the duration though the average in our climate of the twilight, and from the mag.may be stated at 1° for 270 feet of nitude of the terrestrial shadow in perpendicular ascent. lunar eclipses, and found that it Professor Leslie has given a was sufficiently dense at a height formula for determining the temof between 40 and 50 miles, to re-perature of any stratum of air flect and intercept the light of the when the height of the mercury So far, therefore, we may in the barometer is given. The be certain that the atmosphere ex- column of mercury at the lower of tends; and at that altitude we two stations being b, and at the may collect, from what has been upper B, and the diminution of already said, that the air is more heat, in degrees of the centigrade than 10,000 times rarer than at the b β earth's surface; but how much farther it may be extended, is totally unknown.

sun.

thermometer, is 2.5

seems to agree well with observa

Refractive and Reflective Powers tion. of the Atmosphere. -The atmoThe mean temperature of the sphere has a refractive power, atmosphere in any parallel of latiwhich is the cause of various phe-tude remains nearly constant, but nomena. This power is ascertain-it decreases from the equator to ed by the production of twilight, either pole; and if t be made to and by many other facts and ex-represent the mean temperature periments. It has also a reflective of any parallel of which the lati power, and this power is the cause tude is L, M the mean temperature of objects being so uniformly en- in the latitude of 45°, and M + E lightened on all sides. Were it the mean temperature at the equanot for this, the shadows of objects tor; then is 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.

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° 27° × cos. 2 L, which, when 2 L> 90, the cosine being negative, is less than 58°. But if the place is at any height

The temperature of the atmo-above the surface, then the forsphere diminishes, as the distance mula becomes from the earth increases, though apparently in a less ratio. M. de Saussure found, that by ascending

tM

H

+ E. cos. 2 L;

270

from Geneva to Chamouni, a M and E being still the same as height of 347 toises, Reaumer's above, and H the height of the thermometer fell 4° 2; and that, place in English feet. on ascending from thence to the top of Mont Blanc, 1941 toises, it fell 20° 7: this gives 221 feet English for a diminution of 1° of Fahrenheit, in the first case, and 268 in the second. Nevertheless, from the accuracy which the rule for barometical

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 temperature does not exceed 32°, and the curve joining measurement pos-or passing through all those points

is called the curve of perpetual produced in a great measure by congelation. The equation to which the same causes.

is found by making

E. cos. 2 L+ M-32

15577 =294, 2758-32 and conseq. H= 7642+7933. cos. 2 L. Which formula seems to agree very nearly with actual ob servation.

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.

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.

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.

in almost all the wonderful operations of nature.

The principle of attraction, in the Newtonian sense of it, was first hinted at by Copernicus. 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.

ATTRACTION, in Physics, a general term used to denote 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 ATMOSPHERE of the Planets.- chief subject of Newtonian philoSince the planets and their satel-sophy, these being found to obtain lites 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 explained 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 The first who, in this country, a greater distance than to the adopted the notion of attraction, place where the centrifugal force was Dr. Gilbert, in his book De is exactly equal to the force of Magnete; and the next was the gravity. With regard to the sun, celebrated Lord Bacon. In France this point is remote from its centre it was received by Fermat and to a distance measuring the radius Roberval; and in Italy, by Galileo of the orbit of a planet which and Borelli. But till Newton apwould make its revolution in the peared, this principle was very same period as that luminary em-imperfectly defined and applied. ploys 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.

Before Newton, no one had entertained such correct and clear notions of the doctrine of univer sal attraction as Dr. Hooke, who observes, that the hypothesis upon which he explains the system of the world is founded upon the ATMOSPHERIC Tides, are cer- three following principles: 1. That tain periodical changes in the all the celestial bodies have not atmosphere, similar, in some re-only an attraction or gravitation spects, to those of the ocean, and towards their proper centres, bat

that they mutually attract each sun, and communicate to it a ten other within their sphere of acti-dency towards each of them. vity. 2. That all bodies which The satellites of Uranus tend tohave a simple and direct motion, wards Uranus, and Uranus towards continue to move in a right line, his satellites: the satellites of Saif some force, which operates turn tend towards Saturn, and Sawithout ceasing, does not constrain turn towards them. The case is the them to describe à circle, an el-same with regard to Jupiter and lipse, or some other more compli- his satellites. The earth and moon cated curve. 3. That attraction is tend likewise reciprocally the one so much the more powerful, as the towards the other. The proporattracting bodies are nearer to tionality of the areas described by each other. But Hooke was not the satellites to the times of deable to solve the general problem scription, concur with the equality relative to the law of attraction, of action and re-action, to render which would occasion a body to these assertions unequivocal. describe an ellipse round another quiescent body placed in one of its foci; this discovery being re-all animated by a regular motion served for Newton.

All the satellites have a tendency towards the sun; for they are

about their respective planets, as Attraction may be considered as if they had been immoveable; it regards celestial bodies, terres- whence it results that the satellites trial bodies, and the minuter par- are impelled with a motion comticles of bodies. The first case is mon also to their planets; that is usually denoted by the word at- to say, that the same force by traction, or universal gravitation, which the planets tend incessantly the second by gravitation, and towards the sun, acts also upon the the third by the words affinity, satellites, and that they are car chemical attraction, or molecular ried towards the sun with the same attraction. Many philosophers are velocity as the planets. And since now of opinion, that it is the same the satellites tend towards the sun, force contemplated under different it follows that the sun tends toaspects, yet constantly subject towards them, because of the equathe same law. lity of action and re-action.

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.

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.

According to a law of Kepler, deduced from observation, the It therefore appears, that all the radii vectores of planets and co-heavenly bodies tend reciprocally mets describe about the sun areas towards one another: but this tenproportional to the times; but this dency, or rather the attractive law can only have place so long force which occasions it, apperas the force which incessantly tains not solely to their aggregate deflects each of these bodies from mass; all their moleculæ partake the right line is constantly direct- of it, or contribute to it. If the sun ed towards a fixed point, which is acted exclusively upon the centre the origin of the radii vectores. of the earth, without attracting The tendency, therefore, of the each of its particles, the undulaplanets and comets towards the tions of the ocean would be incom. sun, follows necessarily, from the parably greater, and very differproportionality of the areas de- ent from those which are daily scribed by the radii vectores to presented to our view. The tenthe times of description: this tendency of the earth towards the dency 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 is, therefore, the result of the sum of the attractions exerted upon all the moleculæ, which consequently attract the sun in the ra tio of their respective masses;

besides, every body upon the earth the diminution that is occasioned is attracted towards its centre pro- by the augmentation of the square portionally to its mass. It re-acts of the moon's distance. Now, it therefore upon it, the attraction may be shown that the revolution following the same ratio. If it of the moon about the earth is a were otherwise; if all the parts of phenomenon of the same kind the earth did not exert upon one and to be accounted for in the another a reciprocal attraction, the same manner (that is, by considercentre of gravity of the earth ing the joint operation of the prowould move by a constantly-accejectile and gravitating forces) as lerating motion, till at length it the curvilinear motion of a stone, would be lost beyond the limits of the system,

bullet, or any other projectile near the surface of the earth. If The attraction is therefore uni- we had engines of a sufficient versal, reciprocal, and propor-force to project a body in a right tional to the mass. It remains to line parallel to the horizon, with demonstrate, that this force is in- the velocity of 24326 Paris feet versely as the square of the dis- (nearly five English miles) in a tance. second of time, that body, setting Observations have shown, that aside the resistance of the air, the squares of the periodic times would revolve about the earth of the celestial bodies are propor-like a moon. For, 24326 is a mean tional to the cubes of the mean proportional between 39231600, the distances. Farther, it is rigorously diameter of the earth, and 151, the demonstrable, that when bodies space described in the first second circulate in such manner that the of time by a heavy body falling squares of the periodic times are from quiescence towards the earth. proportional to the cubes of the And the periodical time of such a distances, the central force which projectile would be nearly equal actuates them is in the inverse to 1 hour, 24 minutes, 27 seconds. ratio of the square of the distance: If this body could be carried to therefore, supposing the planets the distance of the moon, and proto move in circular orbits (from jected in the same direction as which they, in fact, differ but that in which the moon moves, little), they are solicited towards with such a velocity as would the sun by a force which varies carry it through 188489 Paris feet inversely as the square of the dis- in a minute, it would revolve about tance. This supposition is not ri- the earth in the same orbit as is gorous. But the constant relation described by the moon. We know of the squares of the periodic from experience, that the motion times, to the cubes of the dis-with which a body near the sur tances, being independent of the face of the earth tends to its ceneccentricity, would doubtless sub-tre, is such as in a second of time sist in the case where the eccen- makes it descend through 15 Paris tricity vanishes, that is, if the feet. planets moved in circular orbits. Indeed, the truth of the position may be readily established with regard to elliptical orbits: but we omit the demonstration, rather than protract this article to too great a length.

decrease inversely as the square Supposing this motion to of the distance; at the distance of semidiameters of the earth, it the moon, which is equal to 60 would be 60x60 times less than at the surface of the earth; and be sufficient to make a body detherefore at that distance would scend through 251 Paris feet in a

If the planets revolve about the sun in virtue of a central force, which is reciprocally as the square of the distance, it is natural to in-minute of time. This is, in fact, fer that the moon is retained in the space through which the moon her orbit by a central force direct-at the distance of 60 semidiameters ed towards the earth, and which of the earth, descends from the only differs from the gravity of tangent of its orbit, towards the terrestrial bodies, in the ratio of centre of the earth in a minute of