704 Height to measure the respective densities of mercury and air; of the At- and in measuring the elevation which produces a fall of mosphere, one inch in the barometer, an error of of an inch would produce all the difference. We prefer the last, as depending on fewer circumstances. 281 832 But all this investigation proceeds on the supposition Make OD: OA=OA : Od; OC OB: OA=OA: Ob; &c.; ODXO d=OA'=OCXO c Oc: 0 d=OD: OC ; Oc: 0 c—0 d=OD : OD-OC, cd: CD=0c: OD; or, because OC and OD are ultimately in the ratio of cd: CD=Qc : OC=0A' : OC3, OA2 and c d=CD× OC2› But farther, this curve is the same with EGN. For Height Lastly, if OA, Ob, Oc, Od, &c. be taken in arithmetical progression decreasing, their reciprocals OA, of the At OB, OC, OD, &c. will be in harmonical progression mosphere increasing, as is well known: but, from the nature of the logarithmic curve, when O A, O b, O c, O d, &c. 233 are in arithmetical progression, the ordinates AE, bf, cg, dh, &c. are in geometrical progression. Therefore when OA, OB, OC, OD, &c. are in harmonical progression, the densities of the air at A, B, C, D, &c. are in geometrical progression; and thus may the density of the air at all elevations be discovered. Thus to find the density of the air at K the top of the homogeneous atmosphere, make OK: OA=OA : OL, and draw the ordinate LT, LT is the density at K. The celebrated Dr Halley was the first who observed the relation between the density of the air and the ordinates of the logarithmic curve, or common logarithms. This he did on the supposition of equal_gravity; and his discovery is acknowledged by Sir Isaac Newton in Princip. ii. prop. 22. schol. Halley's dissertation on the subject is in N° 185 of the Phil. Trans. Newton, with his usual sagacity, extended the same relation to the true state of the case, where gravity is as the square of the distance inversely; and showed that when the distances from the earth's centre are in harmonic progression, the densities are in geometric progression. He shows indeed, in general, what progression of the distance, on any supposition of gravity, will produce a geometrical progression of the densities, so as to obtain a set of lines OA, Ob, Oc, Od, &c. which will be logarithms of the densities. The subject was afterwards treated in a more familiar manner by Cotes in his Hydrost. Lect. and in his Harmonia Mensurarum ; also by Dr Brook Taylor, Meth. Increment.; Wolf in his Aerometria; Herman in his Phoronomia ; &c. &c. and lately by Horsley, Phil. Trans. tom. Ixiv. the earth An important corollary is deducible from these prin- The ar ciples, viz. that the air has a finite density at an in- has s fate density at finite distance from the centre of the earth, namely, such as will be represented by the ordinate OP drawn distance through the centre. It may be objected to this con- from the clusion, that it would infer an infinity of matter in the centre of universe, and that it is inconsistent with the phenomena of the planetary motions, which appear to be performed in a space void of all resistance, and therefore of all matter. But this fluid must be so rare at great distances, that the resistance will be insensible, even though the retardation occasioned by it has been accumulated for Even at the ages. moderate distance of 500 miles, very the rarity is so great that a cubic inch of common air expanded to that degree would occupy a sphere equal to the orbit of Saturn; and the whole retardation which this planet would sustain after some millions of years would not exceed what would be occasioned by its meeting one bit of matter of half a grain weight. This being the case, it is not unreasonable to suppose the visible universe occupied by air, which, by its gra vitation, will accumulate itself round every body in it, in a proportion depending on their quantities of matter, the larger bodies attracting more of it than the smaller ones, and thus forming an atmosphere about each. And many appearances warrant this supposition. Jupiter, Mars, Saturn, and Venus, are evidently surrounded by atmospheres. The constitution of these atmospheres may differ exceedingly from other causes. If the pla net 1 Atmo &c. 235 sphere of Mars. As net has nothing on its surface which can be dissolved spheres by the air or volatilized by heat, the atmosphere will be of the other continually clear and transparent, like that of the moon. Planets, Mars has an atmosphere which appears precisely like our own, carrying clouds, or depositing snows: for when, by the obliquity of his axis to the plane of his The atmo ecliptic, he turns his north pole towards the sun, it is observed to be occupied by a broad white spot. the summer of that region advances, this spot gradually wastes, and sometimes vanishes, and then the south pole comes in sight, surrounded in like manner with a white spot, which undergoes similar changes. This is precisely the appearance which the snowy circumpolar regions of this earth will exhibit to an astronomer on Mars. It may not, however, be snow that we see; thick clouds will have the same appearances. 236 Of Jupiter. 237 Of Venus. The atmosphere of the planet Jupiter is also very similar to our own. It is diversified by streaks or belts parallel to his equator, which, frequently change their appearance and dimensions, in the same manner as those tracts of similar sky which belong to different regions of this globe. There is a certain kind of weather that more properly belongs to a particular climate than to any other. This is nothing but a certain general state of the atmosphere which is prevalent there, though with considerable variations. This must appear to a spectator in the moon like a streak spread over that climate, distinguishing it from others. But the most remarkable similarity is in the motion of the clouds on Jupiter. They have plainly a motion from east to west relative to the body of the planet; for there is a remarkable spot on the surface of the planet, which is observed to turn round the axis in 9h. 51′ 16′′; and there frequently appear variable and perishing spots in the belts, which sometimes last for several revolutions. These are observed to circulate in 9h. 55'. 05". These numbers are the results of a long series of observations by Dr Herschel. This plainly indicates a general current of the clouds westward, precisely similar to what a spectator in the moon must observe in out atmosphere arising from the trade-winds. Mr Schroeter has made the atmosphere of Jupiter a study for many years; and deduces from his observations that the motion of the variable spots is subject to great variations, but is always from east to west. This indicates variable winds. The atmosphere of Venus appears also to be like ours, loaded with vapours, and in a state of continual change of absorption and precipitation. About the middle of the 17th century the surface of Venus was pretty distinctly seen for many years chequered with irregular spots, which are described by Campani, Bianchini, and other astronomers in the south of Europe, and also by Cassini at Paris, and Hooke and Townley in England. But the spots became gradually more faist and indistinct; 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 diffused through it, like water faintly tinged with milk. A great depth of this must appear as white as a small depth of milk itself; and it appears to be of a very great depth, and to berefractive like our air. For Dr Herschel has observed, by the help of his fine telescopes, that the illuminated part of Venus is considerably more than a hemisphere, and that the light dies gradually away to the bounding VOL. XVI. Part II. Planets, & c. margin. This is the very appearance that the earth Atmowould make if furnished with such an atmosphere. The spheres boundary of illumination would have a penumbra reach- of the other ing about nine degrees beyond it. If this be the constitution of the atmosphere of Venus, she may be inhabited by beings like ourselves. They would not be dazzled by the intolerable splendour of a sun four times as big and as bright, and sixteen times more glaring, than ours: for they would seldom or never see him, but instead of him an uniformly bright and white sky. They would probably never see a star or planet, unless the dog-star and Mercury; and perhaps the earth might pierce through the bright haze which surrounds their planet. For the same reason the inhabitants would not perhaps be incommoded by the sun's heat. It is indeed a very questionable thing, whether the sun would cause any heat, even here, if it were not for the chemical action of his rays on our air. This is rendered not improbable by the intense cold felt on the tops of the highest mountains, in the clearest air, and even under a vertical sun in the torrid zone. If this 238 The atmosphere of comets seems of a nature totally And of codifferent. This seems to be of inconceivable rarity, mets. even when it reflects a very sensible light. The tail is always turned nearly away from the sun. It is thought that this is by the impulse of the solar rays. be the case, we think it might be discovered by the aberration and the refraction of the light by which we see the tail for this light must come to our eye with a much smaller velocity than the sun's light, if it be reflected by repulsive or elastic 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 almost inconceivably great. The comet of 1680 went half round the sun in ten hours, and had a tail at least a hundred millions of miles long, which turned round at the same time, keeping nearly in the direction opposite to the sun. The velocity necessary for this is prodigious, approaching to that of light. And perhaps the tail extends much farther than we see it, but is visible only as far as the velocity with which its particles recede from the sun is less than a certain quantity, namely, what would leave a sufficient velocity for the reflected light to enable it to affect our eyes. And it may be demonstrated, that although the real form of the visible tail is concave on the anterior side to which the comet is moving, it may appear convex on that side, in consequence of the very great aberration of the light by which the remote parts are seen. All this may be discovered by properly contrived observations; and the conjecture merits attention. But of this digression there is enough; and we return to our subject, the constitution of our air. 239 We have shown how to determine à priori the densi- The baroty of the air at different elevations above the surface of meter used the earth. But the densities may be discovered in all heights. in taking accessible elevations by experiments; namely, by observing the heights of the mercury in the barometer. This is a direct measure of the pressure of the incumbent atmosphere; and this is proportional to the density which it produces. Therefore, by means of the relation subsisting between the densities and the elevations, we can discover the elevations by observations made on the densities by means + 4 U of 240 Barometer of the barometer; and thus we may measure elevations by means of the barometer; and, with very little trouble, take the level of any extensive tract of country. Of this we have an illustrious example in the section which the Abbé Chappe D'Auteroche has given of the whole country between Brest and Ekaterineburg in Siberia. This is a subject which deserves a minute consideration we shall therefore present it under a very simple and familiar form; and trace the method through its various steps of improvement by De Luc, Roy, Shuckburgh, &c. 241 Explana We have already observed, oftener than once, that if tion of its the mercury in the barometer stands 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 use, &c. 242 ry has the same weight with a column of mercury of an inch thick. Therefore, if we carry the barometer to a higher place, so that the mercury sinks to 29.9, we have ascended 87 feet. Now, 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 ascended through another stratum of equal weight with the former: but it must be of greater thickness, because the air in it is rarer, being less compressed. We may call the density of the first stratum 300, measuring the density by the number of tenths of an inch of mercuwhich its elasticity proportional to its density enables it to support. For the same reason, the density of the second stratum must be 299: but when the weights are equal, the bulks are inversely as the densities; and when the bases of the strata are equal, the bulks are as the thicknesses. Therefore, to obtain the thickness of this second stratum, say 299: 300-87: 87.29; and this fourth term is the thickness of the second stratum, and we have ascended in all 174.29 feet. In like manner we may rise till the barometer shows the density to be 298: then say 298: 30=87: 87.584 for the thickness of the third stratum, and 261,875 or 2617 for the whole ascent; and we may proceed in the same 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 column is the thickness of the stratum, or the elevation above the preceding station; and the third column is the whole elevation above the first station. Either of these methods is sufficiently accurate for most purposes, and even in very great elevations will not produce any error of consequence: the whole error of the elevation 883 feet 4 inches, which is the extent of the above table, is only of an inch. But we need not confine ourselves to methods of approximation, when we have an accurate and scientific method that is equally easy. We have seen that, upon the supposition of equal gravity, the densities of the air are as the ordinates of a logarithmic curve, having the line of elevations for its axis. We have also seen that, in the true theory of gravity, if the distances from the centre of the earth increase in a harmonic progression, the logarithm of the densities will decreas in an arithmeti cal progression; but if the greatest elevation above the surface be but a few miles, this harmonic progression will hardly differ from an arithmetical one. Thus, if Ab, A c, A d, are 1, 2, and 3 miles, we shall find that the corresponding elevations AB, AC, AD are sensibly in arithmetical progression also; for the earth's radius AC is nearly 4000 miles. Hence it plainly follows that BC-AB is I or I 4000 X 4001' 16004000 -of a mile, or of an inch; a quantity quite insignificant. We 250 may therefore affirm without hesitation, that in all accessible places, the elevations increase in an arithmetical progression, while the densities decrease in a geometrical progression. Therefore the ordinates are proportional to the numbers which are taken to measure the densities, and the portions of the axis are proportional to the logarithms of these numbers. It follows, therefore, that we may take such a scale for measuring the densities that the logarithms of the numbers of this scale shall be the very portions of the axis; that is, of the vertical line in feet, yards, fathoms, or what measure we please: and we may, on the other hand, choose such a scale for measuring our elevations, that the logarithms of our scale of densities shall be parts of this scale of elevations; and we may find either of these scales scientifically. For it is a known property of the logarithmic curves, that when the ordinates are the same, the intercepted portion of the abscissæ are proportioned to their subtangents. Now we know the subtangent of the atmospherical logarithmic: it is the height of the homogeneous atmosphere in any measure we please, suppose fathoms: we find this height by comparing the gravities of air and mercury, when both 243 rections to adjust this method to the circumstances of Taking the case; and it was not till very lately that it has been heights. so far adjusted to them as to become useful. We are chiefly indebted to Mr de Luc for the improvements. The great elevations in Switzerland enabled him to make an immense number of observations, in almost every variety of circumstances. Sir George Shuckburgh also made a great number with most accurate instruments in much greater elevations, in the same country; and he made many chamber experiments for determining the laws of variation in the subordinate circumstances. General Roy also made many to the same purpose. And to these two gentlemen we are chiefly obliged for the corrections which are now generally adopted. Barometer. both are of some determined density. Thus, in the temperature of 32° of Fahrenheit's thermometer, when the barometer stands 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 subtangent 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 these barometrical heights; or that 0.4342945: D =4342.945: F, and 0.4342945: 4342.945=D: F; but 0.4342945 is the ten-thousandth part of 4342.945, and therefore D is the ten-thousandth part of F. 444 245 246 This me And thus it happens, by mere chance, that the logarithms of the densities, measured by the inches of mercury which their elasticity supports in the barometer, are just the ten-thousandth part of the fathoms contained in the corresponding portions of the axis of the atmospherical logarithmic, Therefore, if we multiply our common logarithms by 1000, they will express the fathoms of the axis of the atmospherical logarithmic; nothing is more easily done. Our logarithms contain what is called the index or characteristic, which is an integer and a number of decimal places. Let us just remove the integer-place four figures to the right hand: thus the logarithm of 60 is 1.7781513, which is one in7781513 teger and Multiply this by 10.000, and we obtain 10000000 513 1001 The practical application of all this reasoning is obvious and easy: observe the heights of the mercury in the barometer at the upper and lower stations in inches and decimals; take the logarithms of these, and subtract the one from the other: the difference between them (accounting the four first decimal figures as integers) is the difference of elevation of fathoms. Example. Merc. Height at the lower station 29.8 1.4742163 upper station 29.1 1.4638930 Diff. of Log. X 10000 233 J000 0.0103.233 or 103 fathoms and of a fathom, which is 619.392 feet, or 619 feet 4 inches; differing from the approximated value formerly found about an inch. Such is the general nature of the barometric measurethod of ment of heights first suggested by Dr Halley; and it has measuring been verified by numberless comparisons of the heights heights now much calculated in this way with the same heights measured improved. geometrically. It was indeed in this way that the pre cise specific gravity of air and mercury was most accurately determined; namely, by observing, that when the temperature of air and mercury was 32, the difference of the logarithms of the mercurial heights were precisely the fathoms of elevation. But it requires many cor 247 on the It is easy to perceive that the method, as already It depends expressed, cannot apply to every case: it depends on specific gra the specific gravity of air and mercury, combined with vity of air the supposition that this is affected only by a change of and merpressure. But since all bodies are expanded by heat, cury. and as there is no reason to suppose that they are equally expanded by it, it follows that a change of temperature will change the relative gravity of mercury and air, even although both suffer the same change of temperature: and since the air may be warmed or cooled when the mercury is not, or may change its temperature independent of it, we may expect still greater variations of specific gravity. The general effect of an augmentation of the specifie gravity of the mercury must be to increase the subtangent of the atmospherical logarithmic; in which case the logarithms of the densities, as measured by inches of mercury, will express measures that are greater than fathoms in the same proportion that the subtangent is increased; or, when the air is more expanded than the mercury, it will require a greater height of homogenegiven fall of mercury will then correspond to a thicker ous atmosphere to balance 30 inches of mercury, and a stratum of air. In order, therefore, to perfect this method, we must learn by experiment how much mercury expands by an increase of temperature; we must also learn how much the air expands by the same, or any change of temperature; and how much its elasticity is affected by it. Both these circumstances must be considered in the case of air; for it might happen that the elasticity of the air is not so much affected by heat as its bulk is. It will, therefore, be proper to state in this place the experiments which have been made for ascertaining these two expansions. 248 on the ex for ascertaining the expansion of mercury, are those of Roy's exThe most accurate, and the best adapted experiments General General Roy, published in the 67th volume of the Phi-periments losophical Transactions. He exposed 30 inches of mer- pansion of cury, actually supported by the atmosphere in a baro- mercury. meter, in a nice apparatus, by which it could be made of one uniform temperature through its whole length; and he noted the expansion of it in decimals of an inch. These are contained in the following table; where the first column expresses the temperature by Fahrenheit's thermometer, the second column expresses the bulk of the mercury, and the third column the expansion of an inch of mercury for an increase of one degree in the adjoining temperatures. 4 U 2 TABLE. Barometer. 249 350 This table gives rise to some reflections. The scale of the thermometer is constructed on the supposition that the successive degrees of heat are measured by equal increments of bulk in the mercury of the thermometer. How comes it, therefore, that this is not accompanied by equal increments of bulk in the mercury of the column, but that the corresponding expansions of this column do continually diminish: General Roy attributes this to the gradual detachment of elastic matter from the mercury by heat, which presses on the top of the column, and therefore shortens it. He applied a boiling heat to the vacuum a-top, without producing any farther depression; a proof that the barometer had been carefully filled. It had indeed been boiled through its whole length. He had attempted to measure the mercurial expansion in the usual way, by filling 30 inches of the tube with boiled mercury, and exposing it to the heat with the open end uppermost. But here it is evident that the expansion of the tube, and its solid contents, must be taken into the account. The expansion of the tube was found so exceedingly irregular, and so incapable of being determined with precision 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 circumstance but the perpendicular height. There was, besides, a propriety in examining the mercury in the very condition in which it was used for measuring the pressure of the atmosphere; because, whatever complication there was in the results, it was the same in the barometer in actual use. The most obvious manner of applying these experiments on the expansion of mercury to our purpose, is to reduce the observed height of the mercury to what it would have been if it were of the temperature 32. Thas, uppose that the observed mercurial height is 29.2, and that the temperature of the mercury is 720, Taking make 30.1302: 30=29.2: 29.0738. This will be height the true measure of the density of the air of the staudard temperature. In order that we may obtain the exact temperature of the mercury, it is proper that the observation be made by means of a thermometer attached to the barometer-frame, so as to warm and cool. along with it. Or, this may be done without the help of a table,. and with sufficient accuracy, from the circumstance that the expansion of an inch of mercury for one degree diminishes very nearlyth part in each succeeding degree. If therefore we take from the expansion at 32° its thousandth part for each degree of any range above it, we obtain a mean rate of expansion for that range. If the observed temperature of the mercury is below 32°, we must add this correction to obtain the mean expansion. This rule will be made more exact if we suppose the expansion at 32° to be 0.0001127. Then multiply the observed mercurial height by this expan sion, and we obtain the correction, to be subtracted or added according as the temperature of the mercury was above or below 32°. Thus to abide by the former example of 72°. This exceeds 32° by 40: therefore take 40 from 0.0001127, and we have 0.0001087, for the medium expansion for that range. Multiply this by 40, and we have the whole expansion of one inch of mercury,=0.004348. Multiply the inches of mercurial height, viz. 29.2 by this expansion, and we have for the correction 0.12696; which being subtracted from the observed height leaves 29.07304, differing from the accurate quantity less than the thousandth part of an inch. This rule is very easily kept in the memory, and supersedes the use of a table. This correction may be made with all necessary exactness by a rule still more simple; namely, by multiplying the observed height of the mercury by the difference of its temperature from 32°, and cutting off four cyphers before the decimals of the mercurial height. This will seldom erry of an inch. We even believe that it is the most exact method within the range of temperatures that can be expected to occur in measuring heights: for it appears, by comparing many experiments and observations, that General Roy's measure of the mercurial expansion is too great, and that the expansion of an inch of mercury between 20° and 70° of Fahrenheit's thermometer does not exceed 0.000102 per degree. Having thus corrected the observed mercurial heights by reducing them to what they would have been if the mercury had been of the standard temperature, the logarithms of the corrected heights are taken, and their difference, multiplied by 10000, will give the difference of elevations in English fathoms. There is another way of applying this correction, ful- 253 ly more expeditious and equally accurate. The difference of the logarithms of the mercurial heights is the measure of the ratio of those 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 those heights. Therefore this last difference of the logarithms is the measure of the correction of this ratio. Now the observed height is to the corrected height nearly as 1 to 1.000102. The logarithm of this ratio,. or the difference of the logarithms of 1 and 1.000102, is 0.0000444. This is the correction for each degree that |