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infinity of matter in the univerfe, and that it is inconfiftent with the phenomena of the planetary motions, which appear to be performed in a space void of all refiftance, and therefore of all matter. But this fluid muft be fo rare at great diftances, that the refiftance will be infenfible, even though the retardation occafioned by it has been accumu ated for ages. This being the cafe, it is reafonable to fuppofe the visible universe occupied by , which, by its gravitation, will accumulate itfelf round every body in it, in a proportion depending on their quantities of matter, the larger bodies attracting more of it than the fmaller ones, and thus forming an atmosphere about each. And many appearances warrant this fuppofition. Jupiter, Mars, Saturn, and Venus, are evidently fur manded by atmospheres. The conftitution of thefe atmospheres may differ exceedingly from other caufes. If the planet has nothing on its furface which can be diffolved by the air or volatilised by heat, the atmosphere will be continually clear and tranfparent, like that of the moon.

MARS has an atmosphere which appears precifely like our own, carrying clouds, or depofiting nows: for when, by the obliquity of his axis to the plane of his ecliptic, he turns his north pole towards the fun, it is obferved to be occupied by abroad white spot. As the fummer of that region advances, this fpot gradually waftes, and fometimes vanishes, and then the fouth pole comes in fight, furrounded in like manner with a white fpot, which undergoes fimilar changes. This is precifethe appearance which the fnowy circumpolar regions of this earth will exhibit to an aftronomer Mars.

The atmosphere of JUPITER is also very fimilar to our own. It is diverfified by ftreaks or belts parallel to his equator, which frequently change their appearance and dimenfions, in the same manner as thofe tracks of similar sky which belong to different regions of this globe. But the moft remarkable fimilarity is in the motion of the clouds on Jupiter. They have plainly a motion from E. to W. relative to the body of the planet: for there is a remarkable spot on the furface of the planet, which is obferved to turn round the axis in gh. 1' 16"; and there frequently appear variable and perifhing spots in the belts, which fometimes laft for feveral revolutions. These are ob. ferred to circulate in 9h. 55′ 05′′. Thefe numbers are the refults of a long feries of obfervations by Dr Herschel. This indicates a general current of the clouds weftward, precifely fimilar to what afpectator in the moon must observe in our atmosphere arifing from the trade-winds. Mr Schroeter has made the atmosphere of Jupiter a ftudy for many years; and deduces from his obfervations that the motions of the variable spots is fubject to great variations, but is always from E. to W. This indicates variable winds.

The atmosphere of VENUS appears alfo to be like ours, loaded with vapours, and in a state of continual change of abforption and precipitation. About the middle of the 17th century the furface of Venus was pretty diftinctly feen for many years chequered with irregular spots, which are defcribed by Campani, Bianchini, and other aftronomers in the fouth of Europe, and alfo by Caflin: at Paris,

and Hooke and Townley in England. But the spots became gradually more faint and indiftinét; and, for near a century, have disappeared. The whole surface appears now of one uniform brilliant white. The atmosphere is probably filled with a reflecting vapour, thinly diffufed through it, like water faintly tinged with milk. It appears to be of a very great depth, and to be refractive like our air. For Dr Herfchel obferved, by the help of his fine telescopes, that the illuminated part of Venus is confiderably more than a hemifphere, and that the light dies gradually away to the bounding margin. Venus may therefore be inhabited by beings like ourselves.

The atmosphere of COMETS feems of a nature totally different. This feems to be of inconceivable rarity, even when it reflects a very fenfible light. The tail is always turned nearly away from the fun. It is thought that this is by the impulfe of the folar rays. If this be the cafe, we think it might be discovered by the aberration and the refraction of the light by which we fee the tail: for this light must come to our eye with a much smaller velocity than the fun's light, if it be reflected by repulfive or elaftic forces, which there is every reason in the world to believe; and therefore the velocity of the reflected light will be diminished by all the velocity communicated to the reflecting particles. This is almoft inconceivably great. The comet of 1680 went half round the fun in ten hours, and had a tail at least a hundred millions of miles long, which turned round at the fame time, keeping nearly in the direction oppofite to the fun. The velocity neceffary for this is prodigious, approaching to that of light. SECT. VII. Of the MEASUREMENT of HEIGHTS by the BAROMETER.

We have shown how to determine a priori the denfity of the air at different elevations above the furface of the earth. But the denfities may be difcovered in all accessible elevations by experiments; namely, by obferving the heights of the mercury in the barometer. This is a direct measure of the preffure of the incumbent atmosphere; and this is proportional to the density which it produces. Therefore, by means of the relation fubfifting between the denfities and the elevations, we can difcover the elevations by obfervations made on the denfities by the barometer; and thus we may measure elevations by means of the barometer, and, with very little trouble, take the level of any extentive tract of country. See BAROMETER, § 1— 24: and Plate XXXVI.

If the mercury in the barometer ftands at 30 inches, and if the air and mercury be of the temperature 32° in Fahrenheit's thermometer, a column of air 87 feet thick has the fame weight with a column of mercury one 10th of an inch thick. Therefore, if we carry the barometer to a higher place, fo that the mercury finks to 29'9, we have afcended 87 feet. Suppose we carry it still higher, and that the mercury stands at 29°8; it is required to know what height we have now got to? We have evidently afcended through another ftratum of equal weight with the former: but it must be of greater thicknefs, because the air in it is rarer, being lefs compretled. We may call the den

fity of the firft ftratum 3co, measuring the denfity by the number of tenths of an inch of mercury which its elafticity proportional to its denfity enables it to fupport. For the fame reason, the denfity of the second stratum must be 299: but when the weights are equal, the bulks are inverfely as the denfities; and when the bafes of the ftrata are equal, the bulks are as the thickneffes. Therefore, to obtain the thickness of this fecond ftratum, say 299 300=87: 87°29; and this fourth term is the thickness of the fecond ftratum, and we have afcended in all 174'29 feet. In like manner we may rife till the barometer shows the denfity to be 298: then say, 298: 30=87: 87'584 for the thickness of the third ftratum, and 261875 or 2617 for the whole afcent; and we may proceed in the fame way for any number of mercurial heights, and make a table of the corresponding elements as follows: where the first column is the height of the mercury in the barometer, the second columo is the thickness of the ftratum, or the elevation above the preceding station; and the third column is the whole elevation above the first station. Strat. Elev.

Bar.

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feen that, upon the fuppofition of equal gravit the denfities of the air are as the ordinates of al garithmic curve, having the line of elevations f its axis. We have alfo feen that, in the true th ory of gravity, if the distances from the centre the earth increase in a harmonic progreffion, th logarithm of the denfities will decrease in an arit metical progreffion; but if the greateft elevatio above the furface be but a few miles, this harm nic progreffion will hardly differ from an arithm tical one. Thus, if Ab, Ac, Ad, are 1, 2, and miles, we fhall find that the correfponding elev tions AB, AC, AD, are sensibly in arithmetical pr greffion alfo: for the earth's radius AC is near 4000 miles. Hence it plainly follows, that BCof a mile, or 4000+4001' 16004000

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AB is of an inch; a quantity quite infignificant. W may therefore affirm, that in all acceffible place the elevations increase in an arithmetical progre fion, while the denfities decrease in a geometrica progreffion. Therefore the ordinates are propor tional to the numbers which are taken to meafur the denfities, and the portions of the axis are pro portional to the logarithms of theft numbers. I follows, therefore, that we may take fuch a scal for measuring the denfities that the logarithms o the numbers of this fcale fhall be the very portion of the axis; that is, of the vertical line in feet yards, fathoms, or what measure we pleafe: and we may, on the other hand, choose such a scale for measuring our elevations, that the logarithms of our scale of denfities fhall be parts of this feale of elevations; and we may find either of thefe fcales fcientifically. For it is a known property of the logarithmic curves, that when the ordinates are the fame, the intercepted portions of the abfciffe are proportional to their fubtangents. Now we know the fubtangent of the atmospherical logarithmic: it is the height of the homogeneous atmosphere in any measure we pleafe, fuppofe fathoms: we find this height by comparing the gra. vities of air and mercury, when both are of fome determined denfity. Thus, in the temperature of 32° of Fahrenheit's thermometer, when the barometer ftands at 30 inches, it is known (by many experiments) that mercury is 10423,068 times heavier than air; therefore the height of the balancing column of homogeneous air will be 10423,068 times 30 inches; that is, 4342,945 English fathoms. Again, it is known that the fubtangent of our common logarithmic tables, where I is the logarithm of the number 10, is 0,4342945. Therefore the number 0,4342945 is to the difference D of the logarithms of any two barometric heights as 4342,945 fathoms are to the fathoms F contained in the portion of the axis of the atmospherical logarithmic, which is intercepted between the ordinates equal to thefe barometrical heights; or that 0,4342945: D=4342,945: F, and 0,4342,945 : 4342,945=D: F; but 0,4342,945 is the ten-thoufandth part of 4342,945, and therefore D is the ten-thoufandth part of F.

Thus the logarithms of the denfities, measured by the inches of mercury which their elafticity fupports in the barometer, are juft the 10,0coth part of the fathoms contained in the correfponding por

tions of the axis of the atmospherical logarithmic. Therefore, if we multiply our common logarithms by repo, they will exprefs the fathoms of the axis of the atmospherical logarithmic; nothing is mareadily done. Our logarithms contain what is called the index or characteristic, which is an stager and a number of decimal places. Let us remove the integer-place four figures to the right band: thus the logarithm of 60 is 1.7781513, which is one integer and 7781513. Multiply

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both fuffer the fame change of temperature; and as the air may be warmed or cooled when the mercury is not, or may change its temperature independent of it, ftill greater variations of specific gravity may occur. The general effect of an augmentation of the specific gravity of the mercury must be to increafe the fubtangent of the atmospherical logarithmic; in which cafe the logarithms of the denfities, as measured by inches of mercury, will exprefs meafures that are greater than fathoms in the fame proportion that the fubtangent is increased; or, when the air is more expanded than 17781,513, the mercury, it will require a greater height of homogeneous atmosphere to balance 30 inches of mercury, and a given fall of mercury will then correfpond to a thicker ftratum of air.

The practical application of all this reafoning is obvious and eafy; observe the heights of the mercury in the barometer at the upper and lower tations in inches and decimals; take the logarithms of thefe, and fubtract the one from the other; the difference between them (accounting the four firft decimal figures as integers) is the difference of EXAMPLE.

elevation of fathoms.

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Such is the general nature of the barometric mafurement of heights firft fuggefted by Dr HALLEY; and it has been verified by numberlefs Comparisons of the heights calculated in this way with the fame height measured geometrically. It was thus that the precife specific gravity of air and mercury was moft accurately determined; namely, by obferving, that when the temperature of air and mercury was 32, the difference of the logarithms of the mercurial heights were precifely the fathoms of elevation. But it requires many corrections to adjust this method to the circumftances of the cale; and it was not till very lately that it has been fo far adjufted to them as to become ufeful. We are chiefly indebted to Mr DE LUC for the improvements. The great elevations in Switzerland enabled him to make an immenfe number of obfervations, in almost every variety of circumtances. Sir GEORGE SHUCKBOURGH alfo made a great number with moft accurate inftruments in much greater elevations, in the fame country; and he made many chamber experiments for determining the laws of variation in the fubordinate circumftances. General Roy also made many to the fame purpose. And to these two gentlemen we are chiefly obliged for the corrections which are now generally adopted.

This method, however cannot apply to every cafe; it depends on the fpecific gravity of air and mercury, combined with the fuppofition that this saffected only by a change of preffure. But fince all bodies are expanded by heat, and perhaps not equally, a change of temperature will change the relative gravity of mercury and air, even although

To perfect this method, therefore, we must learn by experiment how much mercury expands by an increase of temperature; we muft alfo learn how much the air expands by the fame, or any change of temperature, and how much its elafticity is affected by it. Both thefe circumftances must be confidered in the cafe of air; for it might happen that the elafticity of the air is not fo much affected by heat as its bulk is. It will, therefore, be proper to ftate the experiments which have been made for afcertaining these two expansions.

The most accurate, and the best adapted experiments for ascertaining the expanfion of mercury, are thofe of General Roy, published in the Philof. Tranf. vol. 67. He expofed 30 inches of mercury, actually supported by the atmosphere in a barometer, in a nice apparatus, by which it could be made of one uniform temperature through its whole length; and he noted the expanfion of it in decimals of an inch. Thefe are contained in the following table; where the first column expreffes the temperature by Fahrenheit's thermometer, the fecond the bulk of the mercury, and the third the expanfion of an inch of mercury for an increase of one degree in the adjoining temperatures. TABLE A.

Temp. Bulk of Expan. for 1°.

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The scale of the thermometer is conftructed on the fuppofition that the fucceffive degrees of heat are measured by equal increments of bulk in the mercury of the column; but that the correfponding expansions of this column do continually diminish, General Roy attributes to the gradual detachment of elastic matter from the mercury by heat, which preffes on the top of the column, and therefore hortens it. He applied a boiling heat to the vacuum a-top, without producing any farther depreflion; a proof that the barometer had been carefully filled. It had indeed been boiled through its whole length. He had attempted to meafure the mercurial expanfion in the ufual way, by filling 30 inches of the tube with boiled mercury, and expofing it to the heat with the open end uppermoft. But here it is evident that the expansion of the tube and its folid contents must be taken into the account. The expanfion of the tube was found fo exceedingly irregular, and fo incapable of being determined with precifion for the tubes which were to be employed, that he was obliged to have recourse to the method with the real barometer. In this no regard was necessary to any circumftance but the perpendicular height. There was, befides, a propriety in examining the mercury in the very condition in which it was used for meafuring the preffure of the atmosphere; be caufe, whatever complication there was in the refults, it was the fame in the barometer in actual ufe.

The most obvious manner of applying thefe experiments on the expanfion of mercury to our purpose, is to reduce the obferved height of the mercury to what it would have been if it were of the temperature 32. Thus, fuppofe that the obferved mercurial height is 29'2, and that the temperature of the mercury is 72° make 30°1302: 30=29'2:29*0738. This will be the true meature of the denfity of the air of the ftandard temperature. That we may obtain the exact temperature of the mercury, it is proper that the obfervation be made by a thermometer attached to the barometer-frame, fo as to warm and cool along with it. Or, this may be done without the help of a table, and with fufficient accuracy, from the circumftance, that the expanfion of an inch of mercury for one degree diminishes very nearly 6th part in each fucceeding degree. If therefore we take from the expanfion at 32° its thouf nd part for each degree of any range above it, we obtain a mean rate of expansion for that range.

There is another way of applying this correction, fully more expeditious and equally accurate. The difference of the logarithms of the mercurial heights is the measure of the ratio of thofe heights. In like manner the difference of the logarithms of the observed and corrected heights at any station is the measure of the ratio of thofe heights. Therefore this last difference of the logarithms is the measure of the correction of this ratio. Now, the obferved height is to the corrected height nearly as I to I'coo102. The logarithm of this ratio, or the difference of the logarithms of 1 and rcco102 is 00000444. This is the correction for each degree that the temperature of the mercury differs from 32. Therefore multiply o'0000444 by the difference

the mercurial temperatures from 32, and the

products will be the corrections of the respecti logarithms.

There is ftill an eafier way of applying the log rithmic correction. If both the mercurial temper tures are the fame, the differences of their logarith will be the fame, although each may be a good de above or below the ftandard temperature, if the e panfion be very nearly equable. The correction w be neceflary only when the temperatures at the tw ftations are different, and will be proportional this difference. Therefore, if the difference of t mercurial temperatures be multiplied by o'000044 the product will be the correction to be made the difference of the logarithms of the mercuri heights. But farther, fince the differences of the l garithms of the mercurial heights are alfo the di ferences of elevation in English fathoms, it follow that the correction is also a difference of elevation i English fathoms, or that the correction for one d gree of difference of mercurial temperature is of a fathom, or 32 inches, or 2 feet 8 inches.

This correction of 2.8 for every degree of diffe ence of temperature must be subtracted from th elevation found by the general rate, when the mer cury at the upper ftation is colder than that at th lower. For when this is the cafe, the mercuria column at the upper ftation will appear too fhort the preflure of the atmosphere too fmall, and there fore the elevation in the atmosphere will appea greater than it really is. Therefore the rule for thi correction will be to multiply o'o000444 by the de grees of difference between the mercurial tempera tures at the two ftations, and to add or subtract the product from the elevation found by the genera rule, according as the mercury at the upper ftation is hotter or colder than that at the lower.

If the experiments of Gen. Roy on the expanfion of the mercury in a real barometer be though most deferving of attention, and the expansion be confidered as variable, the logarithmic difference correfponding to this expantion for the mean temperature of the two barometers may be taken. Thefe logarithmic differences are contained in th following table, which is carried as far as 112, beyond which it is not probable that any obferva tions will be made. The number for each teuperature is the difference between the logarithm of 30 inches, of the temperature 32, and of 20 inches expanded by that temperature. TABLE B.

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its denfity is of much greater confequence than that of the mercury. The relative gravity of the two, on which the fubtangent of the logarithmic curve depends, and confequently the unit of our fcale of elevations, is much more affected by the heat of the air, than by the heat of the mercury. This adjustment is of incomparably greater difficalty than the former, and we can hardly hope to make it perfect. We shall relate the chief experiments which have been made on the expanon of air, and notice the circumftances which leave the matter ftill imperfe&.

Gen. Roy compared a mercurial and an air thermometer, each of which was graduated arithmetically, that is, the units of the fcales were equal bulks of mercury, and equal bulks (perhaps different from the former) of air. He found their progrefs as in the following table:

TABLE C.

1

Merc. Diff. Air. Diff.

he wished to examine the expanfion of air twice or thrice as denfe, he ufed a column of 30 or 60 inches long; and to examine the expanfion of all that is rarer than the external air, he placed the tube, with the ball, uppermoft, the open end coming through a hole in the bottom of the veffet containing the mixtures or water. By this pofition the column of mercury was hanging in the tube, fupported by the preffure of the atmofphere; and the elafticity of the included air was measured by the difference between the fufpended column and the common barometer.

The following table contains the expanfion of 1000 parts of air, nearly of the common density, by heating it from o to 212. The first column contains the height of the barometer; the ad contains this height augmented by the small column of mercury in the tube of the manometer, and therefore expreffes the denfity of the air examin ed; the 3d contains the total expanfion of 1000 parts: and the 4th contains the expanfion for 1°, fuppofing it uniform throughout.

TABLE D.

Denfity Expanfion Expanfion

examined by 212°.

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It has been established by many experiments that equal increments of heat produce equal increments in the bulk of mercury. The differences of temperature are therefore expreffed by the 2d column, and may be confidered as equal; and the numbers of the 3d column muft be allowed to exprefs the fame temperatures with thofe of the furt. They directly exprefs the bulks of the air, and the numbers of the 4th column exprefs the differences of these bulks. These are evidently of all when of the temperature 62 nearly. uraqual, and fhew that common air expands molt

The next point was to determine what was the heat. For this purpose he took a tube, having a actual increase of buik by forme known increase of narrow bore, and a ball at one end. He meafured the capacity of both the ball and the tube, and divided the tube into equal fpaces, which bore a determined proportion to the capacity of the ball. This apparatus was fet in a long cylinder filled with frigorific mixtures, or with water, which could be uniformly heated up to the boiling tem

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