Gambar halaman



ments of Boyle, &c.



Experi pressing force by 4. In like manner, if we have com- ening the tube CD, and taking care that it be strong compressi. ments on pressed air into of its former bulk, and brought the enough to resist the great pressure. Great care must be bility, &c.

particles to of their former distance, we must divide taken to keep the whole in a constant temperature, be-
the compressing force by 9. In general if d express the cause the elasticity of air is greatly affected by heat, and
density, 5 Ja will express the distance ~ of the par- according to its density or compression


the change by any increase of temperature is different ticles ; ', or df, will express the vicinity or real others

, were not extended to very great compressions, density; and of will express the number

of particles of them; nor do they seem to have been made with very nicely made

the density of the air not having been quadrupled in any neither acting on the compressing surface : and if f express the great nicety. It may be collected from them in gene- nor extendaccumulated external compressing force, jy will express tioned to its density; and accordingly this law was al pression on

ral, that the elasticity of the air is very nearly propor-ed

to very

most immediately acquiesced in, and was called the the force acting on one particle ; and therefore the elas.

Boylean law: it is accordingly assumed by almost all ticity of that particle corresponding to the distance x.

writers on the subject as exact. Of late years, howExperi.

We may now proceed to consider the experiments by ever, there occurred questions in wbich it was of impor. ments esta- which the law of compression is to be established.

tance tbat this point should be more scrupulously settled, blishing The first experiments to this purpose were those made and the former experiments were repeated and extend2 the law of by Mr Boyle, published in 1661 in his Defensio Doc. ed. Sulzer and Fontana have carried them farther than

trince de Aeris Elatere contra Linum, and exhibited be- any other. Sulzer compressed air into one-eighth of its slon. fore the Royal Society the year before. Mariotte made former dimensions.

193 experiments of the same kind, which were published in Considerable varieties and irregularities are to be ob- Varieties, 1676 in his Essai sur la Nature de l'Air and Traité des served in these experiments. It is extremely difficult to &c. in Mouvemens des Eaur. The most copious experiments preserve the temperature of the apparatus, particularly periments, are those by Sulzer (Mem. Berlin. ix.), those by Fon- of the leg AB, which is most handled. A great quantana (Opusc. Physico-Math.), and those by Sir George tity of mercury must be employed; and it does not apShuckburgh and Gen. Roy.

pear that philosophers have been careful to have it pre196

In order to examine the compressibility of air that is cisely similar to that in the barometer, which gives us bility of air not rarer than the atmosphere at the surface of the earth, the unit of compressing force and of elasticity. The not rarer we employ a bent tube or syphon ABCD (fig. 66.), her- mercury in the barometer should be pure and boiled.

tban the metically sealed at A and open at D. The short leg If the mercury in the syphon is adulterated with bisorie atmosphere AB must be very accurately divided in the proportion of muth and tin, which it commonly is to a considerable earth's sur

its solid contents, and fitted with a scale whose units de- degree, the compressing force, and consequently the
note equal increments, not of length, but of capacity. elasticity, will appear greater than the truth. If the
There are various ways of doing this ; but it requires barometer has not been nicely fitted, it will be lower
the most scrupulous attention, and without this the ex than it should be, and the compressing force will ap-
periments are of no value. In particular, the arched pear too great, because the unit is too small; and
form at A must be noticed. A small quantity of mer this error will be most remarkable in the smaller com-
cury must then be poured into the tube, and passed pressions.
backwards and forwards till it stands (the tube being The greatest source of error and irregularity in the Heteroge-
held in a vertical position) on a level at B and C. Then experiments is the very heterogeneous nature of the air neous na-
we are certain that the included air is of the same den- itself. Air is a solvent of all Auids, all vapours, and ture of the
sity with that of the contiguous atmosphere. Mercury perhaps of many solid bodies. It is highly improbable
is now poured into the leg DC, which will fill it, sup- that the different compounds shall have the same elasti. source of
pose to G, and will compress the air into a smaller space city, or even the same law of elasticity: and it is well error.
AE. Draw the horizontal line EF: the new bulk of known, that air, loaded with water or other volatile
the compressed air is evidently AE, measured by the bodies, is much more expansible by beat than pure air ;
adjacent scale, and the addition made to the compres. nay, it would appear from many experiments, that cer-
sing force of the atmosphere is the weight of the column tain determinate changes both of density and of tempe-
GF. Produce GF downwards to H, till FH is equal rature, cause air to let the

vapours which it holds in
to the beight shown by a Toricellian tube filled with the solution. Cold causes it to precipitate water, as ap-
same mercury; then the whole compressing force is pears in dew; so does rarefaction, as is seen in the re-
HG. This is evidently the measure of the elasticity of ceiver of an air-pump.
the compressed air in AE, for it balances it. Now In general, it appears that the elasticity of air does The air's
pour in more mercury, and let it rise to g, compressing not increase quite so fast as its density. This will be elasticity
the air into A e. Draw the horizontal line ef, and best seen by the following tables, calculated from the
make fh equal to FH; then A e will be the new balk experiments of Mr Sulzer. The column E in each fast as its

AB of the compressed air,

set of experiments expresses the length of the column density. will be its new density, and GH, the unit being FH, while the column D expresses

hg will be the measure of the new elasticity. This


ration may be extended as far as we please, by length. AE

4T 2


a face.

Fig. 66.

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does not increase 30

Experiments on


Ist Set.






2.288 2.530

6.000 5.297


the differences are even greater than in Mr Sulzer's Elasticity 2d Set. 3d Set.


The second table contains the results of experiments 463 DI E DI E DIE

made on very damp air in a warm summer's morning.

In these it appears that the elasticities are almost pre1.000 1.000

cisely proportional to the densities + a small constant 1.093 | 1.236 1.224 1.091 1.076

quantity, nearly 0.11, deviating from this rule cbiely 1.222 1.211 1.294 1.288 1.200 1.183

between the densities 1 and 1.5, within which limits we 1.375 1.284 1.375 1.332 1.333 1.303

have very nearly D=E".0017. As this air is nearer to 1.571 1.559 || 1.466 1.417 1.500 1.472 the constitution of atmospheric air than the former, this 1.692 1.669 1.571 1.515 1.714 1.659

rule may be safely followed in cases where atmospheric 1.833 1.796 1.692 1.647

air is concerned, as in measuring the depths of pits by 2.000 1.958 2,000 1.964 2.000 1.900 the barometer.

The third table shows the compression and elasticity 104 2.444 2.375 | 2.444 2.392 2.400 2.241 of air strongly impregnated with the vapours of cam. 3.143 2.936 3.143 3.078 3.000 2.793 phire. Here the Boylean law appears pretty exact, or 3.666 3.391 3.666 3.575

rather the elasticity seems to increase a little faster than 4.000 3.706

4.000 3.631

the density. 4.444 4.035 4.444 4.320

Dr Hooke examined the compression of air by im-13 4.888 4.438

mersing a bottle to great depths in the sea, and weigh. 5.500 4.922 5.500 5.096

ing the water which got into it without any escape of 5.882 5.522

air. But this method was liable to great uncertainty, 7-333 6.694

on account of the unknown temperature of the sea at 8.000 6.835

great depths.

Hitherto we have considered only such air as is not There appears in these experiments sufficient grounds rarer than what we breathe ; we must take a very diffor calling in question the Boylean law; and the writer ferent method for examining the elasticity of rarefied of this article thought it incumbent on him to repeat air. them with some precantions, wbich probably had not Let g h (fig. 67.) be a long tube, formed a-top into Fiz, been attended to by Mr Sulzer. He was particularly a cup, and of sufficient diameter to receive another Nade of anxious to bave the air as free as possible from moisture. smaller tube af, open at first at boih ends. Let the Tam For this purpose, having detached the short leg of the outer tube and cup be filled with mercury, which wilien syphon, which was 34 inches long, he boiled mercury rise in the inner tube to the same level. Let af now rebed ar in it, and filled it with mercury boiling hot. He took be stopped at a. It contains air of the same density and a tinplate vessel of sufficient capacity, and put into it a elasticity with the adjoining atmosphere. Note exactly quantity of powdered quicklime just taken from the the space a b which it occupies. Draw it up into the kiln ; and having closed the mouth, he agitated the position of fig. 68. and let the mercury stand in it at the firs lime through the air in the vessel, and allowed it to re height de, while ce is the height of the mercury in the main there all night. He then emptied the mercury out barometer. It is evident that the column de is in equi. of the syphon into this vessel, keeping the open end librio between the pressure of the atmosphere and the far within it. By this means the short leg of the sy elasticity of the air included in the space a d. And phon was filled with very dry air.

The other part

since the weight of ce would be in equilibrio with the was now joined, and boiled mercury put into the bend whole pressure of the atmosphere, the weight of cd is of the syphon; and the experiment was then prosecuted equivalent to the elasticity of the included air. While with mercury which had been recently boiled, and was therefore ce is the measure of the elasticity of the surthe same with which the barometer had been carefully rounding atmosphere, c d will be the measure of the filled.

elasticity of the included air; and since the air originalThe results of the experiments are expressed in the ly occupied the space a b, and has now expanded into following table.

ab a d, we have


for the measure of its density. N. B. Dry Air. Moist Air. Damp Air. ce and c d are measured by the perpendicular heights of

the columns, but ab and a d must be measured by their DE D E DIE

solid capacities.

By raising the inner tube still higher, the mercury ***

will also rise higher, and the included air will expand 2.000 1.957 2.000 1.920

1.909 still farther, and we obtain another c d, and another 3.000 2.848 3.000 2.839) 3.000 2.845 a b

adi 4.000 3.737 4.000 3.7264.000 3.718

and in this manner the relation between the den5.500 4.930 5.500 5.000 5.500 5.104 sity and elasticity of rarefied air may be discovered. 6.000 5:342 6.000 5.452 6.000 5.463 7.620 6.490 7.620 6.775) 7.620 6.812 This examination may be managed more easily by as

means of the air pump. Suppose a tube a e (fig. 69.) Here it appears again in the clearest manner that the containing a small quantity of air ab, set up in a cisternation elasticities do not increase as fast as the densities, and of mercury, which is supported in the tube at the height

, we







1.000 2.000

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Fig. 70.

Esperi- eb, and let ec be the height of the mercury in the ba- ing to the interest which the philosophers bad in the Boylean ments on rometer. Let this apparatus be set under a tubulated result

. Those made by M. de Luc, General Roy, Mr Law. Air, receiver on the pump-plate, and let gn be the pump. Trembley, and Sir George Shuckburgh, are by far gage, and mn be equal to ce.

the most accurate ; but they are all confined to very Various ex. Then, as bas been already shown, cb is the measure

moderate rarefactions. The general result bas been, that periments of the elasticity of the air in ab, corresponding to the the elasticity of rarefied air

is very nearly proportional have been bulk ab. Now let some air be abstracted from the re to its density. We cannot say with confidence that any made to ceiver. The elasticity of the remainder will be dimi- regular deviation from this law has been observed, there nished by its expansion ; and therefore the mercury in being as many observations on one side as on the other;! the tube ae will descend to some point d. For the same but we think that it is not unworthy the attention of reason, the mercury in the gage will rise to some point philosophers to determine it with precision in the cases0, and mo will express the elasticity of the air in the of extreme rarefaction, where the irregularities are most receiver. This would support the mercury in the tube remarkable. The great source of error is a certain adae at the height er, if the space ar were entirely void hesive sluggishness of the mercury when the impelling of air. Therefore rd is the effect and measure of the forces are very small; and other fluids can hardly be elasticity of the included air when it has expanded to used, because they either smear the inside of the tube the bulk ad; and thus its elasticity, under a variety of and diminish its capacity, or tbey are converted into vaother bulks, may be compared with its elasticity when pour, which alters the law of elasticity. of the bulk ab. When the air has been so far abstract Let us, upon the whole, assume the Boylean law, viz. The Boyleed from the receiver that the mercury in ae descends to tbat the elasticity of the air is proportional to its density, an law may e, then mo will be the precise measure of its elasticity. The law deviates not in any sensible degree from the in general In all these cases it is necessary to compare its bulk truth in those cases which are of the greatest practical

be assumed. ab with its natural bulk, in which its elasticity balances importance, that is, when the density does not much the pressure of the atmosphere. This may be done by exceed or fail short of that of ordinary air.

213 laying the tube ae horizontally, and then the air will Let us now see what information this gives us with Investiga209 collapse into its ordinary bulk.

respect to the action of the particles on each other. tion of the Another Another


method may be taken for this examic The investigation is extremely easy. We have seen action of easy me nation. Let an apparatus abcdef (fig. 70.) be made, that a force eight times greater than the pressure of the partithod.

consisting of a horizontal tube a e of even bore, a ball the atmosphere will compress common air into the each othera.
dge of a large diameter, and a swan-neck tube hf. eighth part of its common bulk, and give it eight times
Let the ball and part of the tube geb be filled with its common depsity: and in this case we know, that
mercury, so that the tube may be in the same horizon the particles are at half their former distance, and that
tal plane with the surface de of the mercury in the the number which are now acting on the surface of the
ball. Then seal up the end a, and connect f with an piston employed to compress them is quadruple of the
air-pump. When the air is abstracted from the surface number which act on it when it is of the common den-
de, the air in a b will expand into a larger bulk ac, sity. Therefore, when this eightfold compressing force
and the mercury in the pump-gage will rise to some di. is distributed over a foursold number of particles, the
stance below the barometric height. It is evident that portion of it which acts on each is double. In like
this distance, without any farther calculation, will be manner, when a compressing force 27 is employed,
the measure of the elasticity of the air pressing on the the air is compressed into a's of its former bulk, the
surface de, and therefore of the air in ae.

particles are at of their former distance, and the force
The most The most exact of all methods is to suspend in the is distributed among 9 times the number of particles ;
exact mode receiver of an air-pump a glass vessel, having a very the force on each is therefore-3. In short, let be the
of exainin narrow mouth, over a cistero of mercury, and then ab-
ing this

stract the air till the gage rises to some determined distance of the particles, the number of them in any elasticity.

height. The difference e between this height and the given vessel, and therefore the density will be as x3,
barometric height determines the elasticity of the air in and the number pressing by their elasticity on its whole
the receiver and in the suspended vessel. Now lower internal surface will be as x. Experiment shows, that
down that vessel by the slip-wire till its mouth is im- the compressing force is as 2', which being distributed
mersed into the mercury, and admit the air into the re-

over the number as r', will give the force on each as r.
ceiver; it will press the mercury into the little vessel. Now this force is in immediate equilibrium with the
Lower it still farther down, till the mercury within it elasticity of the particle immediately contiguous to the
is level with that without ; then stop its mouth, take compressing surface. This elasticity is therefore as x:
it out and weigh the mercury, and let its weight be w. and it follows from the nature of perfect fuidity, that
Subtract this weight from the weight v of the mer the particle adjoining to the compressing surface presses
cury, which would completely fill the whole vessel; with an equal force on its adjoining particles on every
then the natural bulk of the air will be v~w, while side. Hence we must conclude, that the corpuscular
its bulk, when of the elasticity e in the rarefied receiver, repulsions exerted by the adjoining particles are inverse-
was the bulk or capacity w of the vessel. Its density ly as their distances from each other, or that the adjoin--

714 therefore, corresponding to this elasticity e, was

ing particles tend to recede from each other with forces Sir Isaac inversely proportional to their distances..

Neuton And thus may the relation between the density and ela Sir Isaac Newton was the first who reasoned in this was the sticity in all cases be obtained.

manner from the phenomena. Indeed he was the first first who A great variety of experiments to this purpose have who had the patience to reflect on the phenomena with properly been made, with different degrees of attention, accord- any precision. His discoveries in gravitation naturally on this saber



Eave jeres




None of our experiments have distinctly shown us any fies

Boylean gave his thoughts this turn, and he very early hinted same law of compression. But this law of corpuscolar Heiglee

his suspicions that all the characteristic phenomena of force is unlike every thing we observe in nature, and to tbe Atou tangible matter were produced by forces which were ex the last degree improbable.

sphere erted by the particles at small and insensible distances : We must therefore continue the limitation of this muAnd he considers the phenomena of air as affording an tual repulsion of the particles of air, and be contented excellent example of this investigation, and deduces from for the present with baving established it as an experithem the law which we have now demonstrated ; and mental fact, that the adjoining particles of air are kept says, that air consists of particles which avoid the ad- asunder by forces inversely proportional to their distan. joining particles with forces inversely proportional te ces : or perhaps it is better to abide by the sensible law their distances from each other. From this he deduces that the density of air is proportional io the compressing (in the 2d book of bis Principles) several beautiful pro- force. This law is abundantly sufficient for explaining

positions, determining the mechanical constitution of all the subordinate phenomena, and for giving us a com215 the atmosphere.

plete knowledge of the mechanical constitution of our Limits the But it must be noticed that he limits this action to the atmosphere. action to adjoining particles : and this is a remark of immense And in the first place, this view of the compressi- The height adjoining particles

consequence, though not attended to by the numerous bility of the air must give us a very different notion of of tbe az experimenters who adopt the law.

the height of the atmosphere from what we deduced on investiga-
It is plain that the particles are supposed to act at a a former occasion from our experiments. It is found, casiering
distance, and that this distance is variable, and that the that when the air is of the temperature 32° of Fab- its contre
forces diminish as the distances increase. A very ordi- renheit's thermometer, and the mercury in the barome- sibility, di
nary air-pump will rarefy the air 125 times. The dis ter stands at 30 inches, it will descend one-tenth of an
stance of the particles is now 5 times greater than be- inch if we take it to a place 87 feet higher. Therefore,
fore; and yet they still repel each other: for air of this if the air were equally dense and heavy throughout, the
density will still support the mercury in a syphon-gage height of the atmosphere would be 30 X 10 X 87 leet, or
at the height of 0.24, or

of an inch ; and a better

5 miles and 100 yards. But the loose reasoning addu.

ced on that occasion was enough to show us that it must pump will allow this air to expand twice as much, and be much higher; because every stratum as we ascend still leave it elastic. Thus we see that whatever is the must be successively rarer as it is less compressed by indistance of the particles of common air, they can act

cumbent weight. Not knowing to what degree air ex. five times farther off. The question comes now to be, panded when the compression was diminished, we could Whether, in the state of common air, they really do act

not tell the successive diminutions of density and consefive times farther than the distance of the adjoining par- quent augmentation of bulk and height; we could only ticles ? While the particle a acts on the particle with say, that several atmospheric appearances indicated a the force s, does it also act on the particle c with the much greater beight. Clouds have been seen much force 2.5, on the particle d with the force 1.667, on the bigher; but the phenomenon of the twilight is the most particle e with the force 1.25, on the particle f with convincing proof of this. There is no doubt that the vi

the force 1, on the particle g with the force 0.8333, &c. ? sibility of the sky or air is owing to its want of perfect 216

Sir Isaac Newton shows in the plainest manner, that transparency, each particle (whether of matter purely this is by no means the case ; for if this were the case,

aerial or heterogeneous) reflecting a little light. be makes it appear that the sensible phenomena of con

Letó (fig. 71.) be the last particle of illuminated air Fig. 71 densation would be totally different from what we ob wihch can be seen in the horizon by a spectator at A. serve. The force necessary for a quadruple condensa- This must be illuminated by a ray ŠD 6, touching the tion would be eight times greater, and for a nonuple earth's surface at some point D. Now it is a known condensation the

force must be 27 times greater. Two fact, that the degree of illumination called twilight is spheres filled with condensed air must repel each other, perceived when the sun is 18° below the borizon of the and two spheres containing air that is rarer than the spectator, that is, when the angle E 6S or ACD is 18 surrounding air must attract each other, &c. &c. All degrees; therefore b C is the secant of 9 degrees (it is this will appear very clearly, by applying to air the rea less, viz. about 85 degrees, on account of refraction). soning which Sir Isaac Newton has employed in dedu

We know the earth's radius to be about 3970

miles : cing the sensible law of mutual tendency of two spberes, bence we conclude b B to be about 45 miles; nay, a which consist of particles attracting each other with very sensible illumination is perceptible much farther forces proportional to the square of the distance in- from the sun's place than this, perhaps twice as far, and versely.

air is sufficiently dense for reflecting a sensible light 217

If we could suppose that the particles of air repelled at the height of nearly 200 miles. each other with invariable forces at all distances within We have now seen that air is prodigiously expansible

. Erçecerit some small and insensible limit, this would produce a For if we consider a row of particles, within this limit, out end ; nor is this at all likely. It is much more ability as compressed by an external force applied to the two ex- probable that there is a certain distance of the parts in tremities, the action of the whole row on the extreme which they no longer repel each other; and this would points would be proportional to the number of particles, be the distance at which they would arrange themselves ibat is, to their distance inversely and to their density: and if they were not heavy. But at the very summit of the a number of such parcels, ranged in a straight line, would atmosphere they will be a very small matter neares to constitute a row of any sensible magnitude having the each other, on account of their gravitation to the earth.


2 2 2


of, the


Height of Till we know precisely the law of this mutual repul It is another fundamental property of this curve, that Height of the Atmo- sion, we cannot say what is the height of the atmo- if EK or HS touch the curve in E or H, the subtangent the Atmosphere. sphere.

AK or DS is a constant quantity.

sphere. But if the air be an elastic fluid whose density is al And a third fundamental property is, that the infiniteFarther ob- ways proportionable to the compressing force, we can ly extended area MAEN is equal to the rectaugle KA

227 servations tell what is its density at any height above the surface ÉL of the ordinate and subtangent; and, in like man

on, and in- of the earth : and we can compare the density so calcu- ner, the area MDH N is equal to SDXDH, or to KA = vestigation lated with the density discovered by observation : for xDH; consequently the area lying beyond any ordi

height of this last is measured by the height at which it supports nate is proportional to that ordinate.
the atmo. mercury in the barometer. This is the direct measure These geometrical properties of this curve are all ana-

228 sphere. of the pressure of the external air; and as we know the logous to the chief circumstances in the constitution of

law of gravitation, we can tell what would be the pres the atmosphere, on the supposition of equal gravity.
sure of air having the calculated density in all its The area MCGN represents the

whole quantity of aerial,

matter wbich is above C: for CG is the density at C; 223 Let us therefore suppose a prismatic or cylindric co and CD is the thickness of the stratum between C and

lumn of air reaching to the top of the atmosphere. D; and therefore CGHD will be as the quantity of
Let this be divided into an indefinite number of strata matter or air in it; and in like manner of all the others,
of very small and equal depths or thickness; and let us, and of their sums, or the whole area MCGN: and as
for greater simplicity, suppose at first that a particle of each ordinate is proportional to the area above it, so each
air is of the same weight at all distances from the cendensity, and the quantity of air in each stratum, is pro-
tre of the earth.

portional to the quantity of air above it: and as the
The absolute weight of any one of these strata will whole area MAEN is equal to the rectangle KAEL,
on these conditions be proportional to the number of so the whole air of variable density above A might be
particles or the gravity of air contained in it; and since contained in a column KA, if, instead of being com-
the depth of each stratum is the same, this quantity of pressed by its own weight, it were without weight, and
air will evidently be as the density of the stratum : but compressed by an external force equal to the pressure of
the density of any stratum is as the compressing force; the air at the surface of the earth. In this


that is, as the pressure of the strata above it; that is, as would be of the uniform density A E, which it has at
their weight; that is, as their quantity of matter--there- the surface of the earth, making what we have repeat-
fore the quantity of air in each stratum is proportional edly called the homogeneous atmosphere.
to the quantity of air above it; but the quantity in Hence we derive this important circumstance, that

each stratum is the difference between the column in the height of the homogeneous atmosphere is the sub-
cumbent on its bottom and on its top: these differences tangent of that curve whose ordinates are as the densities
are therefore proportional to the quantities of which of the air at different heights, on the supposition of equal
they are the differences. But when there is a series of gravity. This curve may with propriety be called the
quantities which are proportional to their own differ ATMOSPHERICAL LOGARITHMIC; and as the different
ences, both the quantities and their differences are in logarithmics are all characterised by their subtangents,
continual or geometrical progression : for let a, b, c, be it is of importance to determine this one.
three such quantities that

It may be done by comparing the densities of mercury
CE_:boc, then by alter. and air. For a column of air of uniform density, reach-
b:bc:b and by compos.

ing to the top of the homogeneous atmosphere, is in

equilibrio with the mercury in the barometer. Now it
and a :

is found, by the best experiments, that when mercury
therefore the densities of these strata decrease in a geo- and air are of the temperature 32° of Fahrenheit's ther-
metrical progression; that is, when the elevations above mometer, and the barometer stands at 30 inches, the
the centre or surface of the earth increase, or their depths mercury is nearly 10440 times denser than air. There-
under the top of the atmosphere decrease in an arithme- fore the height of the homogeneous atmosphere is 10440
tical progression, the densities decrease in a geometrical times 30 inches, or 26100 feet, or 8700 yards, or 4350

fathoms, or 5 miles wanting 100 yards. 2 25

Let ARQ (fig. 72.) represent the section of the earth Or it may be found by observations on the barometer. 230 by a plane through its centre 0, and let m O AM be a It is found, that when the mercury and air are of the vertical line, and A E perpendicular to OA will be a above temperature, and the barometer on the sea shore horizontal line through A, a point on the earth's surface. stands at zo inches, if we carry it to a place 882 feet Let A E be taken to represent the density of the air at higher it will fall to 29 inches. Now, in all logarithA; and let DH, parallel to A E, be taken to A E as mic curves having equal ordinates, the portions of the the density at D is to the density at A: it is evident, axes intercepted between the corresponding pairs of orthat if a logistic or logarithmic curve EHN be drawn, dinates are proportional to the subtangents. And the having A N for its axis, and passing through the points subtangents of the curve belonging to our common tables E and H, the density of the air at any other point C, is 0,4342945, and the difference of the logarithms of in this vertical line, will be represented by CG, the or 30 and 29 (which is the portion of the axis intercepted dinate to the curve in that point : for it is the property between the ordinates 30 and 29), or 0.0147233, is to of this curve, that if portions AB, AC, AD, of its ax 0.4342945 as 883 is to 26058 feet, or 8686 yards, or is be taken in arithmetical progression, the ordinates, 4342 fathoms, or s miles wanting 114 yards. This deAE, BF, CG, DH, will be in geometrical progres- termination is 14 yards less than the other, and it is unsion.

certain which is the more exact. It is extremely difficult



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Fig. 72


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