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Meteor being investigated by the ardent enterprise of Man. To fix the values of the constants, he has recourse to Meteorology, Dalton imagined, however, that he could trace in the the absolute measures of the elastic forces at the con- ology.
columns of his elastic forces, the approximative law of venient intervals of 0°, 25°, 50', and 75o of the Centi-
+ 0.00000003385ť. ...(R).
F100 = 0.19918,
F19 = 0.200.
(430.) The formula (R) may be converted into Conversion obliged to limit the application of their own formula to degrees of Fahrenheit's scale by a well-known numerical of this for
into Remarks elasticities greater than a single atmosphere. * On the one
Fahren formulæ in hand, therefore, we see a series accommodated to the
heit's scale. general of elastic forces below the ordinary pressure of the atmo
log. Fe = log. 30 + af + bf +
93 this nature. sphere, deviating very widely from observation when
applied to forces above it; and on the other, a formula or by substituting the numerical values of the coefficients,
log. F, = log. 30
· 0.00002081212 ( + 0.0000000058 t...
(431.) We regret that our limits will not permit us to
same author's Précis Elémentaire de Physique, if it be F = 80 K,
desirable to pursue the subject free from its more scien
tific details. Formula of where F, denotes the elastic force corresponding to the Biot. temperature 100-t according to the Centigrade scale, the elastic force of vapour existing in the atmosphere at vapour in a
(432.) The preceding formulæ enable us to discover Weight of and k is a constant ratio connecting the elastic force at any temperature with that which precedes it. This any temperature. Let us, therefore, next inquire, what given vo
lume, at a ratio, it may be necessary again to remark, is not abso
is the absolute weight of vapour contained in a given lutely constant in the experimental results, but without volume, under given circumstances of density and tem- sityand tem sensible error may be assumed so, to bring all the perature. To accomplish this object, Gay Lussac perature. observations,—within of course the limits of a single employed small globules of glass of a nearly spherical Method of
One of these being accurately Gay Lusatmosphere, under the control of analysis. The series form, as B, B, fig. 2. hence employed by Biot is of the general form
weighed, had a portion of water introduced into it, the sac's.
contained air being expelled, and the narrow neck log. F, = log. 30 + at + b 2 + ct",
hermetically sealed. The weight of the ball in this and which he has limited to the third dimension of n,
new state, compared with its primitive weight, gave the on account of the coefficients of the higher powers of n exact weight of water contained in it. The globule becoming so minute.
being thus introduced into the glass vessel V V, pre
viously filled with mercury, was surrounded by the
vessel MM, containing water; and heat being applied
the external level, from the ordinary barometric column
measure of the elastic force of vapour produced.. 1+ 0.01878 1 ) 3-855
(433.) Such is Gay Lussac's accurate method of 2 878
performing this important experiment, and Biot has differs very little from that above given.
illustrated it by some equally beautiful investigations
Meteor of an analytical kind, and which we regret our limits ture of the boiling point, and under an atmospheric Meteordisgy. will not permit us fully to follow. He denotes the pressure of 29.9216 inches, weighs 257.7778 grains.
ology. weight of water in grammes, contained in one of the (435.) But the objects of Meteorology require that Biot's ic
glass globules by P, and by v the capacity in litres of a corresponding result should be found for any other weight of a on we same one of the equal divisions of the receiver, of which N is temperature. Accordingly Dr. Anderson, in his very of vapour at
their number. The resulting volume of vapour might able article on HyGROMETRY, published in the Edinburgh the boiling thus be truly represented by N v, did not the receiver Encyclopedia, has modified with some advantage, the point. itself undergo some change in consequence of the altered formula given by Biot for this purpose. If we denote Dr. Andercircumstances of temperature. Representing, therefore, with the author of the Paper alluded to, the weight in son's methe cubic dilatation of glass by k, the actual volume of grammes of a litre of vapour at the temperature t by P”, finding the vapour will become the corresponding elastic force by Fe, the weight in
same at ang grammes of a litre of vapour at the boiling point by P; other temNv(1 + 100 k).
and adopting moreover the principle of Gay Lussac, perature. But this volume, it should be further remarked, is not that vapours so long as they remain in the aeriform state, subject to the whole atmospheric pressure, and if we, expand by increase of temperature precisely in the same therefore, represent the height of the ordinary barometric manner as the permanently elastic fluids, and that they column by p, and that of the internal mercurial column suffer corresponding changes of volume by alterations of by h, reducing the whole volume to what it would pressure, and also that air uniformlyexpands three-eighths become under the standard pressure of om 76, we shall of its bulk from the freezing to the boiling point of the obtain for the volume of a single gramme of vapour, at Centigrade scale, we shall obtain by making the requithe temperature of the boiling point, the formula site substitutions
0.76 (1 +.00375 t)'
or by substituting for P its value 0.589483 grammes, (434.) This formula Biot illustrates by an appropriate and further reducing, enezpie example, the weight of water contained in the globule being 05.6, the number of divisions occupied by the
P = Fapour 220, and the capacity of one of them 0.00499316
1 +.00375 t litres. The barometric column also at the same time being Om7555 at a temperature of 15°, and the mercury
(436.) If again we are desirous of altering the tem-. within the vessel 0-.052 above the external level. By peratures into degrees of Fahrenheit's scale and the reducing these mercurial columns to the common tem- pressure of 0.76 metres, or 29.92196 inches, into the perature of zero, and allowing for the dilatation of pressure of 30 inches, to which that scale of temperature
is adapted, we shall obtain after the necessary correc
1 mercury for each degree of the centesimal scale
.0068544 F, of its bulk, we shall finally obtain the following elements, "!= 1+.002056 (-32)
(U), = 2.3424227 log. P = 1.7781513 and which, therefore, furnishes the desired weight in log. v = 3.6983755 log. Om.76 = 1.8808136 known terms of the temperature and elastic force. log. (p-1) = 1.8465660 log. p.om.76 1.6589649
To illustrate this useful formula by a single example, Numerical log. Nu (p-h)= 1.8873642
let it be required to determine the weight of a cubic inch example, log. p.Om 76 = 1.6589649
of vapour at the ternperature of 54°. In this case the 0.2283993 = 1!.6920
value of t being 54°, and Fs, computed by means of the log. 100 k = 3.4191865
formula (R) becoming .42779, we shall obtain 3.6478858 = 0.0044
.0068544 x .42779 11.6964
= .00280358 grains.
1.045892 from which it appears that a quantity of moisture, And by a similar method may the weight of a cubic equivalent in weight to a gramme, is contained in a inch of moisture be computed for any other temperavolume of vapour whose capacity is equal to 1.6964 ture. litres, at the temperature of the boiling point, and under (437.) But it may be useful, however refined and Dr. Anderan atmospheric pressure of 0.76 metres of mercury. perfect the system of computation, to discover how far son's expeWe know, moreover, that a gramme of water taken at
the processes of actual experiment will confirm it. riments to the temperature of the maximum of condensation, occu
Dr. Anderson accordingly made a large volume of determine pies precisely a cubic centimetre, of which the litre
saturated air to pass slowly in a small stream through contains a thousand; and that hence a cubic centimetre a sufficient quantity of sulphuric acid, or dry muriate of formula. of water of this degree of temperature, when reduced
lime, cut off from all communication with the atmointo vapour, will fill a space equivalent to 1696.4 cubic sphere; and then observing the increase of weight centimetres. It may also be added, that a litre of this which these substances acquired in consequence of the Vapour, under the pressure above mentioned, and of the
air transmitted through them. A complete descrip1
tion of his apparatus may be seen in his Paper temperature of 100', weighs
= 0.589483 gram
1.6964 mes. By reducing these results into English measures, have no room for in the text, may be seen at pages 275 and 276
* An exposition of these important reductions, which we regret we we shall find that a cubic foot of vapour at the tempera- of Biot’s Traité de Physique, tom. i.
racy of the
Graios of Moisture in a
By For mula D.
Meteor- before quoted, our limits only permitting us to record the (440.) To introduce the water we are desirous of Meteor. ology. results in
changing into vapour, another stop-cock R" is applied, ology. TABLE XCVI.
surmounted by a very small metallic vase V, in which
its centre as stop-cocks ordinarily are, but a small heTabular
mispherical depression O below the surface of the inresults. ture in Barome. Quintity
terior cone is made to contain a drop of the fluid. If
the stop-cock be then turned half a revolution, the
watery drop will be brought into the interior of A B,
and thus as many drops may be introduced as will pro
duce the desired effects on the volume of air submitted 3194 49 29.625 7.550.0023641.00235916 to observation.
(441.) The introduction of the first drop of water 10892 54 29.750 28.780.0026424.00278021
must evidently augment the elastic force of the air, and 10814 59 30.000 35.545.0032867 .00328366 cause the mercury in the tube TT to ascend. The
effect is sudden but not instantaneous, as it would be
if the liquid had been introduced into a vacuum; and
by which we perceive that the pressure of the air
single drop of the liquid be not sufficient to form all Remarkable
It is gratifying to observe how closely the results of the vapour necessary for the given space and temperacoincidence the experiment coincide with the numerical values of the ture, another may be added to increase the elastic force. of the expe- formula, affording at once a strong confirmation of After a certain number of drops, however, have been riments Dalton's researches on the elastic force of vapour, introduced, the addition of any greater quantity will with the
and of the relations which Gay Lussac nas established produce no effect, the excess remaining above the surformula.
between a volume of dry atmospheric air, and of the face of the mercury without being reduced into vapour.
some drops in excess have been added. By closing Union of
(438.) Let is next inquire into some of the condi- the cock R, and denoting the divisions of the tube occuvapour and tions relating to the union of vapour and atmospheric pied by the mingled volumes of air and vapour by N', atmospheric air. On this subject we may remark, as a general the elastic force of the two will be found equal to the air.
law existing among the dry gases, that if among any pressure p of the atmosphere, as at the commencement
divisions. Its elastic force is thus diminished, and,
into a volume of the same magnitude, we shall find must in its new state be represented by DenotElastic the elastic force P of the united volumes exactly equi
N" force of valent to the sum of the separate elastic forces; that is ing therefore the elastic force of the vapour by f, at the united volume equal
existing temperature, the measure of the whole elastic P = p + p' + p'..
force will become to sum of
and we shall now proceed briefly to show that the same separaie elasticities. remarkable principle holds good in the union of vapour
and atmospheric air. Gay Lus
(439.) To demonstrate this problem, Gay Lussac And since this is equal to the pressure p, which is sup-
a bent tube of glass TT', of a smaller diameter than and from which we have
In mechan ordinary density be now introduced into the globe, the with air preserves its own proper tension, and thus cal union mercury will not be depressed in the cylinder A B, and confirms the beautiful law announced, that in the sim- vapour an hence the stop-cock at R must be turned, to permit a ple mechanical union of vapour with air, each portion air, each portion of the quicksilver to descend, and thus allow of the mixture maintains its own elastic force dependent
tajos its some of the air to occupy its place. As soon as a on the volume it is made to occupy.
own elasti sufficient quantity of air has been introduced, its (443.) The preceding formula gives us the value of force. expansion is arrested by turning the stop-cock R; and the elastic force in functions of the whole atmospheric Further a by turning the other stop-cock at R’ at the same pressure, and the volumes occupied by the air in its ori- plication time, the dry air introduced into the cylinder A B is ginal state, and when united to vapour. By a simple
This prinprevented from escaping:
ciple. conversion, it may be made subservient, by aid of the
f+ N = P,
Meteor- beautiful law just_demonstrated, to another im- not, however, be equal to p as before, but to p + h, and Meteor Hogy
ology. portant purpose. That law enables us to conclude, hence we shall have that the elastic force of vapour in union with air, exercises its own elastic force, precisely as if no air were
present; and hence the absolute value of f, under and from which este mode of any circumstances of temperature and pressure, may be
N' m.cing calculated by aid of the formula (R). The value of f
P-fth 2 utnul thus becoming known, it is evident the formula before isme ci a alluded to will enable us to discover the actual volume This value of N' will always be greater than N, because Fize of which a mixture of vapour and dry air must occupy un- h - f must in all cases be a negative quantity. The
der the same conditions: for a simple transformation of entire coincidence of this formula with experiment, the formula gives us
furnishes a new confirmation of the law whose truth
we are endeavouring to demonstrate.
(446.) In the preceding experiments we have sup- Further mo-
dification of posed as much liquid to have been employed, as is in which all the elements of the right-hand member are
sufficient to furnish all the vapour admissible into the known.
space occupied by the air ; but let us now suppose that (441.) To apply this formula numerically, let it be
we only introduce a single drop, and that this quantity duoples
required to determine the actual increase which a given is not sufficient to saturate all the space capable of being volume of dry air undergoes, when saturated with va
filled with vapour.
After reducing this drop to vapour, pour at the temperature of 100° of Fahrenheit, and let the mingled volume be broughỉ back to the pressure under a pressure of 30 inches of quicksilver. Apply of the atmosphere, by allowing some of the mercury to ing this temperature to the formula (R), we have flow out by the inferior cock. The mixture will then f = 1.85241; and regarding the volume represented occupy some volume N', and the mercury in the two
branches will thus be reduced to the same level. Let by N as unity, we shall obtain
more of the quicksilver be now allowed to run out, so
that the mingled volume of vapour and air may occupy
nearly, 30 1.85241
any number of divisions N' greater than N'. The mer
cury in the smaller branch will thus be found depressed and from which it follows, that dry air at the tempera- below its level in the cylinder by a quantity h, the elastic lure of 100°, when saturated with vapour, is expanded force of the mixture being thereby reduced to p – h. one-fifteenth of its primitive volume.
But if the variation of the corresponding volume during
this change of the elastic force be observed, we shall
the volumes being inversely as the total elastic forces. and from which we obtain f=
= 15, a measure of the (447.) To discover the kind of variation this result elastic force corresponding to a temperature of about supposes in the elastic force of vapour, let us represent 180°. If we inquire in what case the volume will be it by f' in its new state of dilatation, its value in the quadrupled, we shall find it at a temperature of about case where the mixture occupied the space N' having 1990.
been f. The air contained in the mixture will thus If we suppose p=f, the value of N' becomes infi
sustain by itself only the pressure p - f; and since it nite. For when the elastic force of vapour is equal to occupies at present the space N", its elastic force will the whole pressure of the atmosphere, the air mingled
N with the vapour no longer bears any pressure, and con
become (p - f) * By joining this to the unknown
be equivalent to p – h, and hence we shall have
N of disclosed, may however be obtained without bringing
f' + (p-f) ne the mercury to the same level in both its branches,
р To accomplish this, let us suppose after the reduc. But experiment gives
р tion of the liquid to vapour, that the mingled vo
h lume occupies any number of divisions N', and that the
N' level of the quicksilver in the lateral tube
N" its height in the cylinder by the quantity h. In this
N' case, the elastic force of the air dilated into the space
f' = f
Quantity of N', will still be expressed by ; and by adding to
thus confirming the principle of Dalton, that the elastic vapour N
force of vapour in all cases varies with the volume, pre-existing in
PN cisely as the gases do. And hence we may further air, the it the tension f of the vapour, we shall obtain f +
same as in deduce also, that the quantity of vapour capable of exist
ing in air, is precisely the same as would be found in a of equal for the elastic force of the two. This elastic force will vacuum of equal capacity, under constant circumstances capacity.
of temperature and pressure, and that, therefore, the mum temperature of any period, therefore, whether it Meteor ology,
formula (U) which enables us to compute the weight be that of a day, a month, or a year, must set a limit to ology. of a cubic inch of vapour, will enable us also with equal the accession of watery vapour in the air ; and thus in
Minimum accuracy to find the actual weight of moisture in a cubic every region, the equatorial, the temperate, or the polar,
temperature inch of air, under the same measure of the elastic a strong and impassable barrier has been fixed by
Nature to the continued accumulation of moisture in the accumula. (448.) In making a practical application of the for- air. And that there is an equally impassable limit on tion of mula last quoted, the only thing requisite is a conve- the other hand—that of extreme dryness, also existing, vapour. nient mode of determining the elasticity of the vapour is evident, when we consider, that as every diminution already existing in the air, under any proposed circum- of temperature tends to saturation, so every increment stances. Mr. Dalton's simple method of filling a tall of heat must produce a tendency to dryness; and that
Maximum cylindrical glass jar with cold spring water, and repeat
temperatur as the maximum temperature of the day has itself a
being finite ing the observation until dew ceases to form on the ex- limit, and therefore governs this last condition of the
prevents ternal surface, first enabled us to obtain this interesting atmosphere, so the depression of temperature which entire dry. result; but we shall reserve the practical developements immediately follows, by at once increasing the humidity Dess. of this part of our inquiry, until we come to treat of of all the atoms of air which undergo that change, must Daniell's hygrometer.
remove at once the possibility of any long continuance Actual phe- (449.) Having thus briefly investigated some of the of comparative dryness. There are some occasional nomena ob- essential conditions of vapour, let us next inquire into anomalies, however, in the extreme conditions of humiserved in
a few of the interesting relations it presents, in its union dity and dryness to which Saussure has briefly alluded union of vapour with
with the great and perpetually changing body of the in his Essais sur l'Hygrométrie, and which sometimes
There are indeed two atmospheres which encompass stances of temperature will help us to trace some of the
Moisture increments of heat, and permeating the former, and would contain, when completely saturated, the same
diminisbez moving in its interstices, like water when in the process quantity of moisture. But since the temperature dimi- with the of filtration it passes through sand.
nishes with the latitude, a given volume of air in a state latitude. (450.) To supply the atmosphere with vapour, the of perfect saturation must contain less and less moisLimits set power of evaporation is in almost constant operation, ture as we approach the Poles. by Nature to and we might suppose that an agent possessing so
(453.) From a similar cause, the moisture of the Moisture aqueous
great an activity, would in time exhaust the store, atmospheric columns must diminish as we ascend ver- diminishe vapour, boundless as it is, by which that moisture is supplied. tically above the Earth ; and hence that the whole store ascetic
ascende But Nature has fixed limits beyond which the aqueous of moisture contained in a vertical equatorial column of element cannot pass, so as to prevent an undue accu- air, must exceed the quantity found in a polar column mulation of moisture on the one hand, and a state of of equal diameter and in the same state of perfect satu
long continued dryness on the other. These limits are ration. There are many difficulties, indeed, in the way
assigned by temperature, and which, whatever may be of proving experimentally the decreasing humidity of
To resolve the question perfectly, such observations