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when a compressing force 27 is employed, the air 0·8333, &c.? Sir Ifaac Newton shows plainly, that is compressed into one 27th of it's former bulk, this is not the cafe ; for if it were, the senfibk the particles are at of their former distance, and phenomena of condensation would be totally dit the force is distributed among 9 times the num. ferent from what we observe. The force neceí. ber of particles; the force on each is therefore 3. sary for a quadruple condensation would be In short, let -- be the distance of the particles, the force must be 27 times greater. Two spheu

times greater, and for a nonuple condensation the number of them in any given vessel, and there. filled with condensed air must repel each othes, fore the density will be as x', and the number pres. and two fpheres containing air that is rarer than fing by their elasticity on its whole internal sur. the surrounding air must attract each other, &c. face will be as x?. Experiment shows, that the All this will appear very clearly, by applying to compresling force is as x?, which being distribu. air the reasoning which Śir Ifaac Newton has et 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 propos diately contigaous to the compresling surface. tional to the square of the distance inversely. This elasticity is therefore as x: and it follows If we could suppose that the particles of air refrom the nature of perfe& Auidity, that the par. 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 corerted by the adjoining particles are inversely as puscular force is unlike every thing we observe in their distances 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 mu. forces inversely proportional to their distances. tual repulsion of the particles of air, and be con

Sir ISAAC NEWTON was the first who reasoned tented for the present with having established it in this manner from the phenomena. Indeed be 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 invertely proporthe phenomena with any precision. His discove- tional to their distances ; or perhaps it is better to ries in gravitation naturally gave his thoughts this abide by the sensible law, that the density of air e turn, and he very early hinted his suspicions that proportional to the compresive force. This law is all the characteristic phenomena of tangible mat. abundantly fufficient for explaining all the suborter 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 of 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 from 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 sitions, 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 ioth 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 Aratum as we ascend must be succeithis 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, Ş 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 s times greater than presion was diminished, we could not tell the before; and yet they ftill repel each other: for luccessive diminution of density and confequent 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 o‘24 of say, that several atmospheric appearances indica an 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 sky or

The question then 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-acts 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 spec. 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, on 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 atfua is 18° below the horizon of the spectator, mosphere decrease, in an arithmetical progresthat, when the angle E OS or ACD is 18 degrees; fion, the densities decrease in a geometrical pro. therefore 6C is the secant of 9° (it is less, viz. greffion. about 84, 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 sensible 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 denfe for reflecto 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 palling 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 repre. there 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 tbe law of this mutual re- is another fundamental property of this curve, pulfion, 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 density 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 any height above the surface of the earth; and KAEL of the ordinate and subtangent; and in we can compare the density so calculated with like manner, the area MDHN is equal to SD X DH, the density 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 con33 we know the law of gravitation, we can tell ftitution of the atmosphere, on the supposition of what would be the pressure of air having the cal. equal gravity. The area MCGN represents the calated 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 very small and equal depths or thickness; and let it; and in like manner of all the others, and of - isppose 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 earth. The absolute weight of any of these stra. each density, and the quantity of air in each ftra

will on these conditions be proportional to the tum, is proportional to the quantity of air above cumber of particles, or the gravity of air contained it: and as the whole area MAEN is equal to the in it; and liace the depth of each ftratum is the rectangle KAEL, so the whole air of variable denfame, this quantity of air will be as the density fity above. A might be contained in a column KA, of the stratum; but density of any stratum is as the if, inftead 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 exo tove 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 ach Atratum 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 repeatedis the difference between the column incumbent ly called the homogeneous atmosphere. on its bottom and on its top: these differences Hence we derive this important circumstance, me 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 whose 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 6: c=a-biber, then, by altern. importance to determine this one. It may be done bia-b=c:c-b and by compor. by comparing the densities of mercury and air. a= : b

For a coluinn of air of uniform density, reaching and a : b=b : 0

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 Leonetrical progression; that is, when the eleva- it is found, by the best experiments, that when tions above the centre or surface of the earth iu- mercury and air are of the temperature 32° c.

Fahrenheit's

:

6:

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Fahrenfeit's thermometer, and the barometer vitation of each particle. Therefore, ed X og is as ftands at 30 inches, the mercury is nearly 10440 the pressure on C arising from the weight of the times der fer than air. Therefore the height of the ftratum DC; but cd 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 fathoms, or Efghn and the ordinates AE, bf, fg, ah, &c. ma. 5 miles wanting 100 yards.

Therefore the sum of all the elements, such as Or it may be found by observations on the ba. cdhg, 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 ahove 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 higher, it will fall to 29 produces, that is, as cg. Therefore the curve Egn ibches. Now, in all logarithmic curves having é is of such a nature that the area lying belaw 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 sub- 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 oo4342945, 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 o'0147233, is to oʻ4342945 as 883 i8 to 26058 equality; and if EFK, Efk, 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 reípective densities of mercury and &c. be taken in arithmetical progression decreas. air; and in meafuring 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 harmonical 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. circumstances. 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 progresion. know that the weight of a pariicle 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 progreflion; 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 denser, 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 atmosfore, at equal elevations, must be greater than op 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: 0A=OA : Odia

lation between the density of the air and the ordi. OC :0A=OA : Oc;

nates of the logarithmic curve, or common logaOB: OA=OA : 0b, &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, differtation on the subject is in No 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 showed, that when form tbrough the whole ftratum. Thus we have the distance from the earth's centre are in harmoOD X Od=0A?, -OC X Oc

nic progression, the densities are in geometric proand Oc: Od-OD: OC:

grellion. He Mows indeed, in general, what proand Oc : Oc-Od=OD: OD-OC, gression of the distance, on any fuppofition 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 den. tio of equality, we have

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

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

AO? andcd Xcg=ÇDX cg X

and in his Harmonia Menfurarum ; also by Dr OC,

OCZ; Brooke Taylor, Meth. Increment; Wolf in his A. but CD X cg XOA 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 ftratum 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 ordi. presses the bulk, cg the density, and OA

?

the ar. nate OP drawn through the centre. It may be OC2 objected to this conclusion, that it would infer an

infinity

a

a

a

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 fluid muft be so rare at great, distances, ant white. The atmosphere is probably filled that the relistance will be insensible, even though with a reflecting vapour, thinly diffufed 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 reasonto be of a very great depth, and to be refractive able to suppose the visible universe occupied by like our air. For Dr Herschel obferved, 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 hemis. pending 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 supposition. 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 conftitution 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 fur- the fun. 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 precife. 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 repulsive or elastic forces, which there is every the plane of bis 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 pale comes in The comet of 1680 went half round the fun in ten fight, surrounded in like manner with a white spot, hours, 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 aftronomer the sun. The velocity necessary for this is prodion Mars.

gious, approaching to that of light. The atmosphere of JUPITER is also very fimilar to our own. It is diversified by freaks 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 moft 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. St' 16''; and there frequently appear vari. Therefore, by means of the relation sublifting beable and perishing spots in the belts, which some- tween the densities and the elevations, we can distimes lalt for several revolutions. These are ob. cover, the elevations by observations made on the ferred to circulate in gb. 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 Dr 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 atmos- 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 co. that the motions of the variable spots is fubje& 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 aimosphere of Venus appears also to be place, fo that the mercury links to 29-9, we have like ours; loaded with vapours, and in a state of afcended 87 feet. Suppole we carry it still higher, continual change of absorption and precipitation, and that the mercury ftands at 2968; it is required About the middle of the 17th century the surface 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 : but it must be by Campani, Bianchini, and other astronomers in of greater thickness, because the air in it is rarer, the south of Europe, and also by Cassini at Paris,, being less compretied. We may call the den

а

I

or

00,000

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 lowhich 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 progression, the the denities; and when the bases of the Atrata are logarithm of the densities will decrease in an arithequal, the bulks are as the thicknesses. There- metical progreffion; but if the greatest elevation fore, to obtain tbe thickness of this second ftra- above the surface be but a few miles, this harmotum, say 299 : 300=87: 87029; and this fourth nic progreffion 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 man. miles, we shall find that the corresponding elevaner we may rise till the barometer Mhows the den- tions AB, AC, AD, are fenfibly in aritbmetical profity to be 298: then say, 298: 30=87: 840584 for gression alfo: for the earth's radius AC is nearly the thickneis of the third stratum, 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 firft 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 acceffible 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

the densities, and the portions of the axis are pro. 29,9 87,000 87,000 portional to the logarithms of these numbers. It 29,8 87,291 174,291

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

for measuring the densities that the logarithins 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, 2914 88,475 526,405

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 89,079 704,260

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 mealure 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 ftations, are the fame, the intercepted portions of the aband

write down the corresponding elevations. Sub- fciffæ are proportional to their fubtangents. Now tract the one from the other, and the remainder we know the subtangent of the atmospherical lois the beight required. Thus, suppose that at the garithmic: it is the height of the homogeneous atlower tation the mercurial height was 29,8, and mosphere in any measure we please, fuppose fathat at the upper station it was 29,1.

thoms: we find this height by comparing the gra. 29,1

vities of air and mercury, when both are of some 29,8 174,291

determined density. Thus, in the temperature of

32° of Fahrenheit's thermometer, when the baro619,353=Elevation. meter stands at 30 inches, it is known (by many We may do the same 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 1042 3,068 in tenths of an inch; and then fay, as m to 300, so times 30 inches; that is, 4342,945 English fais 87d to the height required h: or ha

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. There. Thus, in the foregoing example, m is fore the number 0,4342945 is to the differenee D

of the logarithms of any two barometric heights

2+26100 294,5, and dis=7; and therefore b=

as 4342,945 fathoms are to the fathoms F contain294,5

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 or value.- 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 confe- : 4342,945=D:F; but 0,4 342,945 is the ten-thou. quence: 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. But we need not confine ourselves to methods by the inches of mercury which their elasticity sup:

Thus the logarithms of the densities, measured of approximation, when we have an accurate and ports in the barometer, are just the 10,00oth part fcientific method that is equally easy. We have of the fathoms contained in the corresponding por

793,644

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