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ing many observations on the sun, í It was found, hy those who went moon, planets, and comets, and to the south, that the attraction of greatly improved the elements of the mountains of Peru had a sentheir motions. He also erected sible effect on the plumb-lines of the gnomon, and drew the celebra- their large instruments, which afted meridian line in the church of forded an experimental proof of Petronia, at Bologna.

the Newtonian doctrine of gravitaIn 1719, Mr. Flamstead was suc- tion, that has since been complete. ceeded by Dr. Hailey, who had ly verified by the observations of been sent, at the early age of 21, Dr. Maskelyne, made on the moun. to the island of St. Helena, to obtaju Schehallien, in Scotland. On set the southern stars, a cata- the death of Dr. Halley, in 1742, he logue of which he published in was succeeded by Dr. Bradley, 1679; and, a few years afterward, who has rendered himself celebrahe gave to the public his “Synopted by two of the finest discoveries sis Astronomiæ Cometicæ,” in which that have ever been made in astrohe ventured to predict the return nomy,-the aberration of light, of a comet in 1758, or 1759. He was and the nutation of the earth's the first who discovered the acce- axis. Among other things he also leration of the moon's mean mo-formed new and accurate tables of tion; and is the author of a very the motions of Jupiter's satellites, ingenious method for finding her as well as the most correct table parallax, by three observed places of refractions yet extant. Also, of a solar eclipse: he also showed with a large transit instrument, and the use that might be made of the a new mural quadrant of eight feet approaching transit of Venus, in radius, constructed by Bird, in 1761, in deterniining the distance 1750 he made an immense number of the sun from the earth; and re- of observations for settling the commended the method of deter places of all the stars in the Brimining the longitude by the moon's tish catalogue, together with near distance from the sun and cevtain 150 places of the moon, the greater fixed stars, which has since been part of which he compared with carried into execution at the in- Mayer's tables. Dr. Bradley was stance of the late Astronomer Roy: succeeded in 1762, in his office of al. Dr. Halley also composed astronomer royal, by Mr. Bliss; tables of the sun, moon, and pla. but who died in 1765, and was suc. nets, with which he compared the ceeded by Nevil Maskelyne, D.D. observations he made of the moon who rendered very considerable at Greenwich, amounting to near services to the science, by his pub1500, and noticed the differences. lication of the “Nautical AlmaAbout this time, an attempt was nac," the “Requisite Tables," &c.; inade in France to measure a de. and more particularly by his great gree of the earth, which was the assiduity and zeal, in bringing the occasion of a warm dispute con lunar method of determining the cerning its figure. M. Cassini con. | longitude at sea into general praccluded, from the measurement of tice. Picard, that it was an oblong sphe In the mean time, many other roid ; but Newton, from a conside, eminent mathematicians were asration of the laws of gravity, and siduously employed in endeavourthe diurnal motion of the earth, ing to promote the science of ashad determined its figure to be tronomy. Amongst these may be that of an oblate spheroid, flattened particularly distinguished, Clairat the poles, and protuberant at aut, d'Alembert, Euler, Simpson, the equator. To determine this Walmsley, Mayer, de la Cailie, ' point, Louis XV. ordered two de Manfredi, Lambert, &c. grees of the meridian to be mea Such was the state of astronomy sured ; one under or near the equa- when Dr. Herschel, by augment. tor, and the other as near as pos- | ing the powers of telescopes be sible to the pole: the result of this yond the most sanguine expecta. arduous undertaking was a confir- tions, opened a scene altogether mation of Newton's investigation. I unlooked for, by the discovery of

a new planet, 12th March, 1781, / when infinitely produced, or at the Georgium Sidus, or Uranus. an infinite distance. Two curves

On the 1st of January, 1801, ano- are also said to be asymptotical, ther new planet was discovered when they, thus continually apbetween Mars and Jupiter, by M. proach indefinitely to a coinciPiazzi, of Palermo, which is named dence: thus two parabolas, placed Ceres; and since this time three with their axis in the same right others have been observed, revolv-line, are assymptoles to eacia ing also between Mars and Jupiter, other. viz. Pallas, discovered by Dr. Of lines of the second kind, or Olbers, March 28, 1802 ; Juno, first curves of the first kind, thai is, observed by Mr. Harding, at the the conic sections, only the hyper. observatory at Lilienthal, near bola has asymptotes, which are Bremen, Sep. I, 1804; and Vester, two in number. All curves of the discovered by Dr. Olbers, 29th of second kind have at least one March, 1807, being the second that asymptote, but they may have we owe to this eminent astrono. three; and all curves of the third mer. For the particular elements kind may have four asymptotes, of these new planets, see the re- and so on. The conchoid, cissoid, spective articles URANUS Ceres, and logarithmic curve, thoughi PALLAS, JUNO, and VESTER. not geometrical curves, have each

Hence it appears, that within one asymptote; and the branch a few years the number of planets or leg of the curve that has an in our system have been nearly asymptote, is said to be of the doubled, and many other impor- hyperbolic kind. tant and interesting discoveries The nature of an asymptote is have been made during the same very difficult to be conceived, by period : yet it must be acknow-persons who are not acquainted ledged, that we are still unacquaint with the higher geometry: they ed with many particulars, and cannot comprehend how two lines which therefore still remain to shonld always continually apexercise the talents of modern proach each other, without the astronomers. We have not yet possibility of touching or coinciddetermined the times of rotation, ing; this mystery, however, may and the proper figures of some of be elucidated, and the nature of the planets and their satellites; these lines readily comprehended, nor do we know, with sufficient by considering the generation of precision, the masses of those the conchoid of Nicomedes. See bodies. The theory of their mo- Conchoid. tions also consists in a series of ASYMPTOTES, by some

are dis. approximations, of which the tinguished into various orders. convergence depends both upon The asymptote is said to be of the the perfection of the instruments first order, when it coincides with and the progress of analysis, and the base of the curvilinear figure; which for that reason ought to of the 2d order, when it is a right acquire continually new degrees line parallel to the base ; of the of exactness.

3d order, when it is a right line ASTROSCOPE, an astronomical oblique to the base; of the 4th instrument, composed of two cones, order, when it is the commion paraon whose surfaces are exhibited bola, having its axis perpendicular the stars and constellations, by to the base ; and, in general, of the means of which they are both n + 2 order, when it is a parabola easily found in the heavens. whose ordinate is always as the n

ASYMPTOTE, a right line to power of the base. The asymptote which some curve continually ap- is oblique to the base, when the proaches nearer, in such sort, that ratio of the first Auxion of the ordi. when they are both indefinitely nate to the fuxion of the base, approduced, they are nearer together proaches to an assignable ratio, as than by any assignable finite dis. its limit; but it is parallel to the tance; or it may otherwise be con- base, or coincides with it, when sidered as a tangent to the curve, I this limit is not assignable.

The areas bounded by curves figure of the atmosphere must be and their asymptotes, though in- come that of an oblate spheroid, definitely extended, have some because the parts that correspond times limits to which they may to the equator have a greater cenapproach indefinitely near: and trifugal force than the parts which this happens in hyperbolas of all correspond to the poles. Besides, kinds, except the first or Apollo- the figure of the atmosphere must nian, and in the logarithmic curve. represent such a spheroid, in conBut in the common hyperbola, and sequence of the sun striking the many other curves, the asymp- equatorial regions more directly totical area has no such limit, but than those about the poles: whence is infinitely great. Solids, too, it follows, that the mass of air, or generated by hyperbolic areas, re part of the atmosphere, about the volving about their asymptotes, polar regions, being less lieated, have sometimes their liniits; and cannot expand so much, por reach sometimes they may be produced so high ; nevertheless, as the same till they exceed and given solid. force which contributes to elevate Also the surface of such solid, when air, diminishes the pressure on the supposed to be infinitely produced, surface of the earth, higher cois either finite or infinite, accord- lumns of it at or near the equator, ing as the area of the generating all other circumstances being the figure is finite or infinite.

same, will not be heavier than The way of discovering whether those of the lower belonging to the any proposed curves have asymp-poles; but, on the contrary, with. totes, and the manner of drawing out some compensation they would them when they are inclined to be lighter, in consequence of the the axis, may be easily derived diminished gravity of the upper from the method of tangents. strata.

ATMOSPHERE, that gaseous or Weight or Pressure of the Atmos. aeriform fluid which every where phere.-Torricelli found that the invests the surface of the terraque- pressure of the atmosphere sustains ous globe; and partakes of all its a column of quicksilver, of an motions, both annual and diurnal. equal base and 39 inches height;

We have already considered the and as a cubical inch of quicksil? inechanical properties of this fluid, ver is found to weigh near half a under the article Arr; and it there-pound avoirdupoise, therefore the fore only remains to treat of it as whole 30 inches, or the weight of forming one body, viz. its figure, the atmosphere on every square pressure, altitude, &c.

inch, is nearly equal to 15ib. Again, Figure of the Atmosphere.-As it has been found that the pressure the atmosphere envelopes all parts of the atmosphere balances, in the of the surface of the earth, if both case of pumps, &c. a column of the one and the other were per- water of about 31 feet high; and, fectly at rest, and were not en: the cubical loot of water weighing dowed with a diurnal motion round just 1000 ounces, or 62ļlb. 34) iinies their axis, the atmosphere would 62, or 215815). will be the weight be exactly spherical, acco to of the column of water, or of the the universal laws of gravity ; for atmosphere on a base of a square the parts of the surface of a fluid foot; and, consequently, the iht. in a state of rest, must be equally part of this, or 151b. is the weight remote from its centre. But the ot the atmosphere on a square earth and the ambient atmosphere inch; the same as before. Hence are invested with a diurnal motion, the pressure of this ambient tuil which carries them round their on the whole surface of the earth, common axis of rotation; and the is equivalent to that of a globe úi different parts of both having a lead of 60 miles in diameter. And centrifugal force, the tendency of hence also it appears, that the which is more considerable, and pressure upon the human body that of the centripeta: force legs, must be very considerable; for, as the parts are more remote from admitting the surface of a man's the axis; and, consequently, the body to be about 15 square feet,

and the pressure about !5b, on feet, for the height of a uniform a square inch, he must sustain column; which is a little more 32,400lb. or nearly 114 tons weight than 54 miles. But the density for his ordinary load. And it decreases as the altitudes increase, might be easily shown, that the the former in geometrical, and the difference in the weight of air sus latter in arithmetical progression. tained by our bodies in different We have also, under the article states of the atmosphere, is often ALTITUDE, shown that the general near a ton and a half.

formula for ascertaining altitudes Height and Density of the Atmos: above the earth's surface, at the phere.—The densities of the air de. temperature of 31°, is 4 = 10000 x crease in geometrical progression, as the altitudes increase in arith: log. ; A being the altitude, and

M metical progression; and, therefore, if no other cause existed, it m and M the heights of the baro. would follow that the atmosphere meter, the former at the lower was of indefinite lieight. But this place and the latter at the top of caunot be, in consequence of the.

the eminence, which are also as

the densities of the air at those other planetary bodies : our atmosphere, for instance, cannot extend places, and therefore conversely beyond the common centre of at

to find the density of the air cortraction of the earth and moon; 1tudes, we may change the formula

responding to any particular allifor if in the first instance we co? into  = 10000 log. m - 10000 log. ceive it to surpass this limit, it is obvious, that as the earth revolves

M; whence ou its axis, and thereby turns all log. m.=

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 exhi. that 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. cuum between the terrestrial and Height in Miles. No. Times rarer. Junar atmospheres, or the limits of

0

1 both would be the common centre of attraction of the two bodies.

3} 7

4 Another cause, viz. the centrifugal

14

16 force, would also operate against

21 an indefinitely extended atmos

28 phere ; for as this fluid partakes of

35

1026 the diurnal motion of the earth, it

42

4096 is obvious, that beyond that point

49

16384 where the centrifugal force is equal

56

65536 to the force of gravity, the fluid

63

269144 would be thrown off by the rota

70

1048576 tory motion of the body, and the limits of the atmosphere terminated And by pursuing the calculation in th point.

in this table, it might easily be If the air was every where of shown, that a cubic inch of the air the sanie uniform density as at the we breathe would be so much raearth's surface, where its specitic refied at the height of 500 miles, gravity to that of water is about that it would fill a sphere equal in as 3 to 2500; or where a cubic foot diameter to the orbit of Saturn.

With regard to the extent of the weighs 1} ounces, it would follow, atmosphere, from the principles that its altitude would be about

l? pon which 54 miles: for the whole atmosphe founded it is indefinite; bulit must

calculation is ric pressure is equal to about 33 «r of necessity have a certain limit. 34 feet' of water; and the density for one of the principal effecis of of this latter fluid being about the atmosphere being the refrac833} times greater than that of air, tion of light, the particles of which we should have 833 X 33 = 27500 are the smallest of any we know

2

64

256

011

sun.

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 aunosphere 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 tiect 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 earth's surface; but how much thermometer, is 2.5

,which farther it may be extended, is

B totally unknown.

seems to agree well with observaRefractive and Reflective Powers Lion. of the Atmosphere. -- The almo The mean temperature of the sphere has a refractive power, atmosphere in any parallel ot lati. which 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 latipower, and this power is the cause tude is L, M the mean temperalure 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 en t=M + E. cos. 2 L; lightened sides so very bright, that whence the mean temperatore in probably we should only be able any latitude is readily ascertained. to see those parts of them which the mean temperature in latitude were absolutely exposed to the 45° is 58° = M, at the equator it.is sun's rays, if indeed the extreme 85', whence 859-58° = 27° = E; light in this case did not even therefore t = 58° + 27° X cos. 2 L, render them too powerful for the which, when 2 L> 90, the cosine delicacy of the optic nerve.

being negative, is less than 58o. Temperature of the Atmosphere. But if the place is at any height The temperature of the atmo-above the surface, then the for. sphere diminishes, as the distance mula becomes from ile earth increases, though

H apparently in a less ratio. M. de t=M + E, cos. 2 L; Saussure found, that by ascending

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 4o 4 ; and that, place in English teet. on ascending from thence to the On ascending into the almos. top of Mont Blanc, 1911 toises, it phere, at a certain height in fell 20° 71: this gives 221 feet En- every latitude a point is found glish for a diminution of 1° of Fah. where it always freezes, or where it renheit, in the first case, and 268 freezes more than it thaws, so that in the second. Nevertheless, from the mean temperature does not the accuracy which the rule for exceed 32°, and the curve joining barometical measurement pos- lor passing through all those points

64

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