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when a compressing force 27 is employed, the air 0.8333, &c.? Sir Ifaac Newton shows piainly, that is compressed into one 29th of it's former bulk, this is not the cafe ; for if it were, the fenfibic the particles are at t of their former distance, and phenomena of condensation would be totally di. the force is distributed among 9 times the num. ferent from what we observe. The force necel. ber of particles; the force on each is therefore 3. sary for a quadruple condensation would be a In short, let -- be the distance of the particles, the force must be 27 times greater. Two spher

times greater, and for a nonuple condensation the number of them in any given vesel, and there. filled with condensed air must repel each othes

, fore the density will be as x, and the number pref. and two spheres containing air that is rarer than sing by their elasticity on its whole internal sur. the surrounding air must attract each other, &c. face will be as *?. Experiment shows, that the All this will appear very clearly, by applying to compressing force is as *), which being diftribu. air the reasoning which Śir Ifaac Newton has the ted over the number as x?, will give the force on ployed in deducing the sensible law of mutual each as x. Now this force is in immediate equi- tendency of two spheres, which consist of par. librium with the elasticity of the particle imme- ticles attracting each other with forces proposdiately contigaous to the compressing surface. tional to the square of the distance inversely. This elasticity is therefore as xi and it follows If we could suppose that the particles of air te from the nature of perfe& Auidity, that the para pelled each other with invariable forces at all dif. ticle adjoining to the compressing surface presses tances within fome small and insensible limit, this with an equal force on its adjoining particles on would produce a compressibility and elasticity 6. every side. Hence the corpuscular repulfions ex- milar to what we observe. But this law of core erted by the adjoining particles are inversely as puscular force is unlike every thing we observe in their diltances from each other ; or the adjoining nature, and to the last degree improbable. We particles tend to recede from each other with must therefore continue the limitation of this mur forces inversely proportional to their distances. tual repulsion of the particles of air, and be coll

Sir Isaac NEWTON was the first who reasoned tented for the present with having established it in this manner from the phenomena. Indeed he as an experimental fact, that the adjoining particles was the first who had the patience to reflect on of air are kept asunder by forces inveriely proporthe phenomena with any precision. His discove- tional to their distances; or perhaps it is better 19 •ies in gravitation naturally gave his thoughts this abide by the sensible law, that the density of air 4 turn, and he very early binted his suspicions that proportional to the compressive force. This law is all the characteristic phenomena of tangible mat. abundantly fufficient for explaining all the subo:ter were produced by forces which were exerted dinate phenomena, and for giving us a complete by the particles at small and insensible distances: knowledge of the mechanical constitution of our And he considers the phenomena of air as afford. atmosphere. ing an excellent example of this investigation, and sect. VI. Of the Height of the ATMOSPHERE. deduces from them the law which we have now demonstrated ; and says that air confifts of par The preceding view of the compressibility uk ticles which avoid the adjoining particles with air must give us a very different notion of the forces inversely proportional to their distances height of the atmosphere from what we deduced fron each other. From this he deduces (in the from our experiments. When the air is of the 2d book of his Principles ) several beautiful propo- temperature 32° of Fahrenheit's thermometer, and fitions, determining the mechanical conftitution the mercury in the barometer stands at zo inches, of the atmosphere. But he limits this action to it will descend one 10th of an inch if we take it the adjoining particles: and this is a remark of to a place 87 feet higher. Therefore, if the air immense consequence, though not attended to were equally dense and heavy throughout, the by the numerous experimenters who adopt the atmosphere would be 30 X 10 X 87 feet, or s miles law.

and 100 yards. But it must be much higher; beThe particles are supposed to act at a distance; cause every stratum as we ascend must be succesThis distance is variable; and the forces diminish fively rarer as it is less compressed by incumbent as the distance increases. A very ordinary air- weight. (See ATMOSPHERE, Ø 6.) Not know. pump will rarefy the air 125 times. The dif- ing to what degree air expanded when the comtance of the particles is now 5 times greater than pression was diminished, we could not tell the before; and yet they fill repel each other : for lucceffive diminution of density and consequent the air of this density will fill support the mer. augmentation of bulk and height ; we could only cury in a fyphon-gage at the height of 0-24 of say, tbat several atmospheric appearances indicaan inch ; and a better pump will allow this air to ted a much greater height. Clouds have been expand twice as much, and fill leave it elaftic. seen much higher ; but the phenomenon of the Thus, whatever is the distance of the particles of TWILIGHT is the most convincing proof of this common air, they can act five times farther off. There is no doubt that the visibility of the iky or The question tben is, Whether, in the state of air is owing to its want of perfect transparency, common air, they really do act five times farther each particle (whether of matter purely aerial or than the distance of the adjoining particles ? While heterogeneous) reflecting a little light. the particle a-aets on the particle b with the force Let b (fig. 49.) be the last particle of illuminated 5, does it also act on the particle e with the force air, which can be seen in the horizon by a fpece 2.5, on the particle d with the force 1*667, on the tator at A. This must be illuminated by a ray particle e, with the force 1.25, on the particles, SD b, touching the earth's surface at some point with the force s, cn the particle g, with the force D. Now it is a known fact, that the degree of

illumination

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llumination called twilight is perceived when the crease, or their depths under the top of the alfuo is 18° below the horizon of the spectator, mosphere decrease, in an arithmetical progresthat, when the angle E 6S or ACD is 18 degrees; fion, the densities decrease in a geometrical pro. therefore 6C is žhe secant of 9° (it is less, viz. greffion. about 81, on account of refraction.). We know Let ARQ (fig. 50.) represent the section of the the earth's radius to be about 3970 miles; hence earth by a plane through its centre O, and let m we conclude b B to be about 45 miles; nay, a OAM be a vertical line, and AE perpendicular to very fenfible illumination is perceptible much far. OA will be a horizontal line through A, a point ther from the sun's place than this, perhaps twice on the earth's surface. Let AE be taken to reas far, and the air is sufficiently dense for reflect. present the density of the air at A; and let DH, ing a sensible light at the height of nearly 200 parallel to AE, be taken to AE as the density at miles.

D is to the density at A: it is evident, that if a We have seen that air is prodigiously expansible. logistick or logarithmic curve EHN be drawn, ha. None of our experiments have diftinály hown us ving AN for its axis, and pasting through the any hint. But it does not follow that it is expan. points E and H, the density of the air at any fible without end. It is much more probable that other point C, in this vertical line will be reprethere is a certain distance of the parts in which sented by CG, the ordinate to the curve in that they would arrange themselves if they were not point : for it is the property of this curve, that if heavy. But at the very summit of the atmosphere portions AB, AC, AD, of its axis be taken in they will be a very small matter nearer to each arithmetical progression, the ordinates AE, BF, other, on account of their gravitation to the earth. CG, DH, will be in geometrical progression. It Till we know precisely the law of this mutual re is another fundamental property of this curve, palion, we cannot say what is the height of the that if EK or HS touch the curve in E or H, atmosphere. But if the air be an elastic fluid the fubtangent AK or DS is a constant quantity. whose denfity is always proportionable to the A 3d fundamental property is, that the infinitely compreffing force, we can tell what is its density extended area MAEN is equal to the rectangle at atiy height above the surface of the earth; and KAEL of the ordinate and fubtangent; and in we can compare the density fo calculated with like manner, the area MDHN is equal to SD X DH, e denfity discovered by observation: for this or to KA X DH; consequently the area lying behaft is measured by the height at which it sup. yond any ordinate proportional to that ordinate. ports mercury in the barometer. This is the direct These geometrical properties of this curve are meafare of the pressure of the external air; and all analogous to the chief circumstances in the conas we know the law of gravitation, we can tell ftitution of the atmosphere, on the supposition of what would be the preffure of air having the cal. equal gravity. The area MCGN represents the culated density in all its parts.

whole quantity of aerial matter which is above C: Suppose a prismatic or cylindric column of air for CG is the density at C, and CD is the thickness reaching to the top of the atmosphere. Let this of the stratum between C and D; and therefore be divided into an indefinite number of strata of CGHD will be as the quantity of matter or air in Tery small and equal depths or thickness; and let it; and in like manner of all the others, and of e suppose that a particle of air is of the same their sums, or the whole area MCGN; and as each weight at all distances from the centre of the ordinare is proportional to the area above it, so carth. The absolute weight of any of these stra. each density, and the quantity of air in each ftrata will on these conditions be proportional to the tum, is proportional to the quantity of air above number of particles, or the gravity of air contained it and as the whole area MAEN is equal to the in it; and face the depth of each stratum is the rectangle KAEL, so the whole air of variable denfame, this quantity of air will be as the denfity fity above. A might be contained in a column KA, of the stratum; but density of any ftratum is as the if, instead of being compressed by its own weight, compreffing force, i.e. as the pressure of the strata it were without weight, and compressed by an

ex. thove it; i.e. as their weight; i.e. as their quan. ternal force equal to the pressure of the air at the tity of matter therefore the quantity of air in surface of the earth. In this case, it would be of achu ftratum is proportional to the quantity of the uniform density AE, which it has'at the surair above it; but the quantity in each ftratum face of the earth, making what we have repeatedin the difference between the column incumbent ly called the homogeneous atmosphere. o its bottom and on its top: thefe differences Hence we derive this important circumstance, #e therefore proportional to the quantities of that the height of the homogeneous atmosphere is which they are the differences. But when there the subtangent of that curve whole ordinates are is a series of quantites which are proportional to as the densities of the air at different heights, on their own differences, both the quantities and the supposition of equal gravity. This curve may their differences are in continual or geometrical with propriety be called the ATMOSPHERICAL progreffion : for let a, b, c, be three such quanti- LOGARITHMIC; and as the different logarithmics ties that

are all characterised by their subsequents, it is of b: c-a-biber, then, by altern. importance to determine this one. It may be done B: a=b=c:-s and by compos. by comparing the densities of mercury and air. a=0 : b

For a coluinn of air of uniform density, reaching and a : b=b : C

to the top of the homogeneous atmosphere, is in etherefore the densities of these strata decrease in a quilibrio with the mercury in the barometer. Now

artetrical progression; that is, when the eleva- it is found, by the best experiments, that when itions above the centre or surface of the earth i- mercury and air are of the temperature 32° C.

Fahrenheit's

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A2

Fahrenheit's thermometer, and the barometer vitation of each particle. Therefore, id X og is as ftands at 30 inches, the mercury is nearly 10440 the pressure on C arising from the weigbt of the times den ser than air. Therefore the height of the stratum DC; but od X og is evidently the element homogeneous atmosphere is 10440 times 30 inches, of the curvilineal area AmnF, formed by the curve or 26100 feet, or 8700 yards, or 4350 fathonis, or Efghn and the ordinates AE, bf, cg, ah, &c. mn. 5 miles wanting 100 yards.

Therefore the sum of all the elements, such as Or it may be found by observations on the ba- edhg, that is, the area cmng below cg, will be as rometer. It is found, that when the mercury and the whole pressure on C, arising from the gravita. air are of the above temperature, and the barome- tion of all the air above it; but, by the nature of ter on the sea-shore stands at 30 inches, if we car- air, this whole pressure is as the density which it ry it to a place 884 feet bigher, it will fall to 29 produces, that is, as cg. Therefore the curve Egu ibches. Now, in all logarithmic curves having é is of such a nature that the area lying below or qual ordinates, the portions of the axes intercepted beyond any ordinate cg is proportional to that or. between the corresponding pairs of ordinates are dinate. This is the property of the logarithmic proportional to the subtangents. And the fub- curve, and Egn is a logarithmic curve. tangents of the curve belonging to our common But farther, this curve is the same with EGN. tables is oʻ4342945, and the difference of the loga. For let B continually approach to A, and ultimate. rithms of 30 and 29 (which is the portion of the ly coincide with it. It is evident that the ultimate axis intercepted between the ordinates 30 and 29), ratio of BA to Ab, and of BF to bf, is that of or oʻ0147233, is to oʻ4342945 as 883 is to 26058 equality; and if EFK, Egk, be drawn, they will feet, or 8686 yards, or 4343 fathoms, or s miles, contain equal angles with the ordinate AL, and wanting 114 yards. This determination is 14 will cut off equal subtangents AK, Ak. The yards less than the other, and it is uncertain which curves EGN, Egn are therefore the same, but in is the most exact. It is extremely difficult to oppofite positions. Lastly, if OA, Ob, Oc, Od, measure the respective densities of mercury and &c. be taken in arithmetical progression decrealair; and in measuring the elevation which produ- ing, their reciprocals OA, OB, OC, OD,' &c. ces a fall of one inch in the barometer, an error of will be in barmcnical progression increasing, as one 20th of an inch would produce all the differ- is well known; but, from the nature of the loence. We prefer the last, as depending on fewer garithmic curve, when OA, Ob, Oc, Od, &c. circumftances. But all this investigation proceeds are in arithmetical progression, the ordinates AE, on the supposition of equal gravity, whereas we bf, cg, dh, &c. are in geometrical progreffion. know that the weight of a particle of air decreases Therefore when OA, OB, OC, OD, &c. are in as the square of its distance from the centre of the harmonical progression, the densities of the air at earth increases. In order, therefore, that a supe- A, B, C, D, &c. are in geometrical progression; rior ftratum may produce an equal pressure at the and thus may the density of the air at all elevasurface of the earth, it must be denfer, because a tions be discovered. Thus to find the denfity of particle of it gravitates less. The density, there- the air at K, the top of the homogeneous atmorfore, at equal elevations, must be greater than on phere, make OK: OA=OA: OL, and draw the the supposition of equal gravity, and the law of ordinate LT, LT is the density at K. diminution of density must be different.

Dr HALLEY was the first who observed the reMake OD:OA=OA : Odia

lation between the density of the air and the ordiOC :0A=OA : Oc;

nates of the logarithmic curve, or common logaOB: OA=OA : Ob, &c.;

rithms. This he did on the supposition of equal so that Od, Oc, Ob, OA, may be reciprocals to gravity; and his discovery is acknowledged by Sir OD, OC, OB, OA; and through the points A, Isaac Newton in Princip. ii. prop. 22. fchol. His b, c, d, draw the perpendiculars AE, bf, cg, db, dissertation on the subject is in N° 185. of the Phil. making them proportional to the densities in A, Trans. Newton extended the same relation to the B, C, D, and let us suppose CD to be exceeding true state of the cate, where gravity is as the square ly small, so that the denlity may be supposed uni- of the distance inversely; and lowed, that when form through the whole ftratum. Thus we have the distance from the earth's centre are in harmo

OD X Od=OA?, =OC X Oc nic progression, the densities are in geometric proand Oc: Od-OD:0C:

grellion. He shows indeed, in general, what proand Oc : Oc-Od=OD:OD-OC, gression of the distance, on any lupposition of graor Oc : cd=OD:DC;

vity, will produce a geometrical progression of the and cd : CD=Oc: OD;

densities, so as to obtain a set of lines OA, Ob, or,' because OC and OD are ultimately in the ra. Oc, Od, &c. which will be logarithms of the dentio of equality, we have

sities. The subject was afterwards treated in a cd : CD-Oc: OC=OA? : OC?,

more familiar manner by Cotes in his Hydrof. Le&t. and cd=CDX OA?

AO? anded X-g=ÇDX cg X

and in his Harmonia Mensurar um ; also by Dr OC”,

Ocz; Brooke Taylor, Meth. Increment; Wolf in his A. but CD X cg XO.A`is the pressure at C arising from and lately by Horsley. Phil. Trans. tom. Ixiv.

crometria; Herman in his Phoronomia ; &c. &c. OC? the absolute weight of the fratum CD. For this deducible, viz. that the air has a finite density at

From these principles an important corollary is weight is as the bulk, as the density, and as the

an infinite distance from the centre of the earth, gravitation of each particle jointly. Now CD ex

namely, such as will be represented by the ordipresses the bulk, cg the density, and

GOA

nate OP drawn through the centre. It may be OC objected to this conclusion, that it would infer an

infinity

the ar

infinity of matter in the universe, and that it is in- and Hooke and Townley in England. But the confiftent with the phenomena of the planetary spots became gradually more faint and indistinct; motions, which appear to be performed in a space and, for near a century, bave disappeared. The void of all reliftance, and therefore of all matter. whole surface appears now of one uniform brilliBut this fuid must be so rare at great, distances, ant white. The atmosphere is probably filled that the relitance will be insensible, even though with a reflecting vapour, thinly diffused through the retardation occafioned by it has been accumu, it, like water' faintly tinged with milk. It appears lated for ages. This being the case, it is reason to be of a very great depth, and to be refractive able to suppose the visible universe occupied by like our air. For Dr Herschel observed, by the air, whicb, by its gravitation, will accumulate it. help of his fine telescopes, that the illuminated self round every body in it, in a proportion de- part of Venus is considerably more than a hemifpending on their quantities of matter, the larger phere, and that the light dies gradually away to bodies attracting more of it than the smaller ones, the bounding margin. Venus may therefore be and thus forming an atmosphere about each. And inhabited by beings like ourselves. many appearances warrant this fuppofition. Ju. The atmosphere of Comets seems of a nature piter, Mars, Saturn, and Venus, are evidently fur: totally different. This seems to be of inconceiva. rounded by atmospheres. The constitution of ble rarity, even when it reflects a very sensible these atmospheres may differ exceedingly from o- light. The tail is always turned nearly away from ther causes. If the planet has nothing on its sur- the sun. It is thought that this is by the impulse face wbich can be diffolved by the air or volatilised of the solar rays. If this be the case, we think it by heat, the atmosphere will be continually clear might be discovered by the aberration and the reand transparent, like that of the moon.

fraction of the light by which we see the tail : for Mars has an atmosphere which appears precise- this light must come to our eye with a much smaller ly like our own, carrying clouds, or depofiting velocity than the sun's light, if it be reflected by snows: for when, by the obliquity of his axis to repulfive or elastic forces, which there is every the plane of his ecliptic, he turns his north pole reason in the world to believe; and therefore the towards the sun, it is observed to be occupied by velocity of the reflected light will be diminished a broad white spot. As the summer of that region by all the velocity communicated to the reflecting advances, this spat gradually wastes, and some- particles. This is almost inconceivably great. times vanishes, and then the south pole comes in The comet of 1680 went half round the fun in ten fight, surrounded in like manner with a white spot, bours, and had a tail at least a hundred millions which undergoes fimilar changes. This is precise- of miles long, which turned round at the same ly the appearance which the snowy circumpolar time, keeping nearly in the direction opposite to regions of this earth will exhibit to an astronomer the fun. The velocity necessary for this is prodion Mars.

gious, approaching to that of light. The atmosphere of JUPITER is also very similar to our own. It is diversified by streaks or belts Sect. VII. Of the MEASUREMENT of Heights, parallel to his equator, which frequently change

by the BAROMETER, their appearance and dimensions, in the same man We have shown how to determine a priori the ner as those tracks of fimilar sky which belong to density of the air at different elevations above the different regions of this globe. But the most re- surface of the earth. But the densities may be difmarkable fimilarity is in the motion of the clouds covered in all acceslible elevations by experiments; on Jupiter. They have plainly a motion from namely, by observing the heights of the mercury E. to W. relative to the body of the planet : for in the barometer. This is a direct measure of the there is a remarkable spot on the surface of the pressure of the incumbent atmosphere; and this is planet, which is observed to turn round the axis proportional to the density which it produces. in gb. sI' 16"; and there frequently appear vari. Therefore, by means of the relation sublifting beable and perising spots in the belts, which some-tween the densities and the elevations, we can distimes last for several revolutions. These are ob. cover, the elevations by observations made on the ferred to circulate in 9b.55' 05". These num. densities by the barometer; and thus we may bers are the results of a long series of observations measure elevations by means of the barometer, and, by De Herschel. This indicates a general current with very little trouble, take the level of any exof the clouds westward, precisely limilar to what tensive tract of country. See BAROMETER, Ø 1

a spectator in the moon must observe in our atmof. 24: and Plate XXXVI. -- phere arising from the trade-winds Mr Schroeter. If the mercury in the barometer stands at 30

has made the atmosphere of Jupiter a study for inches, and if the air and mercury be of the temmany years; and deduces from his observations perature 32° in Fahrenheit's thermometer, a cothat the notions of the variable spots is subject to lumn of air 87 feet thick has the same weight with great variations, but is always from E. to W. a column of mercury one roth of an inch thick. This indicates variable winds.

Therefore, if we carry the barometer to a higher The atmosphere of Venus appears also to be place, so that the mercury links to 29*9, we have like ours, loaded with vapours, and in a fate of ascended 87 feet. Suppose we carry it itill higher, continual change of absorption and precipitation. and that the mercury itands at 2908; it is required About the middle of the 17th century the turface to know what height we have now got to? We of Venus was pretty diftinctly seen for many years have evidently ascended through another ftratum chequered with irregular spots, which are described of equal weight with the former : bur: it must be by Campani, Bianchini, and other astronomers in of greater thickness, because the air im it is rarer, the south of Europe, and also by Caflini at Paris,, being less compreiled. We may call the den

fity

1

or 9

88,475

89,079

fity of the first ftratum 300, measuring the density seen that, upon the supposition of equal gravity, by the number of tenths of an inch of mercury the densities of the air are as the ordinates of a lo. which its elasticity proportional to its density ena- garithmic curve, having the line of elevations for bles it to support. For the same reason, the den. its axis. We have also seen that, in the true thefity of the second ftratum must be 299: but when ory of gravity, if the distances from the centre of the weights are equal, the bulks are inversely as the earth increase in a harmonic progresfion, the the denlities; and when the bases of the strata are logarithm of the densities will decrease in an arithequal, the bulks are as the thicknesses. There- metical progression; but if the greatest elevation fore, to obtain the thickness of this second ftra- above the surface be but a few miles, this harmotum, fay 299 : 300=87: 87*29; and this fourth nic progresfion will hardly differ from an arithmeterm is the thickness of the second ftratum, and tical one. Thus, if Ab, Ac, Ad, are 1, 2, and 3 we have ascended in all 174'29 feet. In like manmiles, we shall find that the corresponding elevaner we may rise till the barometer Mows the den- tions AB, AC, AD, are fenfibly in aritbmetical profity to be 298 : then say, 298: 30=87: 87°584 for gression also: for the earth's radius AC is nearly the thickness of the third itratum, and 261:875 or 4000 miles. Hence it plainly follows, that BC2617 for the whole ascent; and we may proceed in the same way for any number of mercurial AB is

of a mile, or heights, and make a table of the corresponding

4000+4001' 16004000

250 elements as follows: where the first column is the of an inch ; a quantity quite insignificant. We height of the mercury in the barometer, the second may therefore affirm, that in all accessible places, column is the thickness of the stratum, or the ele- the elevations increase in an arithmetical progresvation above the preceding station; and the third fion, while the densities decrease in a geometrical column is the whole elevation above the first station. progression. Therefore the ordinates are proporBar. Strat.

Elev.

tional to the numbers which are taken to measure 30 00,000 00,000

the densities, and the portions of the axis are pro29,9

87,000 87,000 portional to the logarithms of these numbers. It 29,8 87,291 174,290

follows, therefore, that we may take such a scale 29,7 87,584 261,875

for measuring the densities that the logarithms of 29,6 87,879

349,754

the numbers of this scale shall be the very portions 29,5 88,176 437,930

of the axis; that is, of the vertical line in feet, 29,4

526,405

yards, fathoms, or what measure we pleafe: and 29,3 88,776 615,181

we may, on the other hand, choose such a scale 29,2

704,260

for measuring our elevations, that the logarithms 29,1 89,384 793,644

of our scale of densities fhall be parts of this scale 29 89,691 883,335

of elevations; and we may find either of these We can now measure any elevation within the scales scientifically. For it is a known property limits of our table, in this manner: Observe the of the logarithmic curves, that when the ordinates barometer at the lower and at the upper stations, are the same, the intercepted portions of the aband write down the corresponding elevations. Sub- sciffæ are proportional to their fubtangents. Now tract the one from the other, and the remainder we know the fubtangent of the atmospherical lo. is the beight required. Thus, fuppose that at the garithmic: it is the height of the homogeneous atlower ftation the mercurial height was 29,8, and mosphere in any mealure we please, fuppofe fathat at the upper station it was 29,1.

thoms: we find ihis height by comparing the gra. 29,1 793,644

vities of air and mercury, when both are of fome 174,291

determined density. Thus, in the temperature of

32° of Fahrenheit's thermometer, when the baro. 619,353=Elevation. meter stands at 30 inches, it is known (by many We may do the fame thing with tolerable ac- experiments) that mercury is 10423,068 times heacuracy without the table, by taking the medium vier than air; therefore the height of the balancing m of the mercurial heights, and their difference d column of homogeneous air will be 10423,068 in tenths of an inch; and then say, as m to 300, so times 30 inches; that is, 4342,945 English fais 87d to the height required h: or h=

300 +87d thoms. Again, it is known that the subtangent

of our common logarithmic tables, where I is the 2610od

logarithm of the number 10, is 0,4341945. ThereThus, in the foregoing example, m is fore the number 0,4342945 is to the difference D

of the logarithms of any two barometric heights 294,5, and dis = 7; and therefore b=

2+26100

as 4342,945 fathoms are to the fathoms F contain.

29455 ed in the portion of the axis of the atmospherical =620,4, differing only one foot from the former logarithmic, which is intercepted between the orvalue.-Either of these methods is sufficiently ac

dinates equal to these barometrical heights; or curate for most purposes, and even in very great that 0,4342945: D=4342,945 : F, and 0,4342,945 elevations will not produce any error of conse. : 4342,943=D:F; but 0,4 342,945 is the ten-thouquence: the whole error of the elevation 883 feet fandth part of 4342,945, and therefore D is the 4 inches, which is the extent of the above table, ten-thousandth part of F. is only of an inch.

Thus the logarithms of the densities, measured But we need not confine ourselves to methods by the inches of mercury which their elasticity fupof approximation, when we have an accurate and ports in the barometer, are just the 10,00oth part scientific method that is equally easy. We have of the fathoms contained in the corresponding por

29,8

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