Meteor being investigated by the ardent enterprise of Man. ology, Dalton imagined, however, that he could trace in the columns of his elastic forces, the approximative law of the elasticities of steam increasing nearly in geometrical progression, at the same time that the temperatures augmented arithmetically; and Laplace adopting the same principle, represented the elastic force by an exponential whose exponent could be developed in a parabolic series. To the author of the Mécanique Céleste, the two first terms of the resulting series appeared sufficient; but Biot proved the necessity of a third; and while the series thus obtained, represented with considerable accuracy the measures of the elastic forces so long as they were confined within the limits of a single atmosphere, yet when the progress of inquiry ventured on loftier developements of the elastic power, the corrected series of Biot also deviated very widely from observation. At the same time it is worthy of observation, that the French Philosophers, with all the advantages which the formulæ of Prony, Laplace, Biot, Ivory, Roche, Auguste, Tregaskis, Creighton, Southern, Tredgold, and Coriolis could impart, found themselves obliged to limit the application of their own formula to Remarks on elasticities greater than a single atmosphere.* On the one formula in hand, therefore, we see a series accommodated to the general of elastic forces below the ordinary pressure of the atmothis nature. sphere, deviating very widely from observation when applied to forces above it; and on the other, a formula agreeing with wonderful accuracy up to twenty-four atmospheres-its greatest aberration amounting only to four-tenths of a centesimal degree when estimated in

Biot.

log. F= log. 30

0.0153741265 t-0.00006743127
+0.00000003385 ť. . . . (R).

(429.) Thus may the elastic force for any temperature
within the limits alluded to be computed, by substituting
successively proper values for t. If we take the case of
t = 100°, belonging to the elastic force of vapour at the
temperature of melting ice, we shall obtain
F100 0.19918,

and we know the actual observation of Dalton gives for
the same
F1000.200.

Considering the difficulty of the inquiry, this must be
regarded as a very close approximation.

degrees of Fahrenheit's scale by a well-known numerical of this for(430.) The formula (R) may be converted into Conversion relation, and which will give to it the form of

t

F, 30 K,

Formula of where F, denotes the elastic force corresponding to the temperature 100-t according to the Centigrade scale, and k is a constant ratio connecting the elastic force at any temperature with that which precedes it. This ratio, it may be necessary again to remark, is not absolutely constant in the experimental results, but without sensible error may be assumed so, to bring all the observations, within of course the limits of a single atmosphere, under the control of analysis. The series hence employed by Biot is of the general form

log. F= log. 30 +at+ b2 + c to,

and which he has limited to the third dimension of n, on account of the coefficients of the higher powers of n becoming so minute.

The formula adopted by Arago, Dulong, and their learned associates is e=(1+0.7153 )s, where e is the elasticity in atmospheres of 0m.76, and the temperature setting out from 100°. It is worthy of remark, that the late learned Dr. Young was the first who represented the elasticities by a certain power of the temperature aug. mented by a constant number. M. Coriolis adopted 5.355 for the exponent as deduced from Dalton's experiments below 212° of Fahrenheit; and it is remarkable that his formula

0.00002081212 +0.0000000058 ... in which t denotes degrees of Fahrenheit.

(S),

(431.) We regret that our limits will not permit us to pursue this branch of our subject further; but we strongly recommend to the reader's attention the whole of the XIIIth Chapter of the Ist Book of Biot's Traité de Physique, or the XIIth Chapter of the IId Book of the same author's Précis Elémentaire de Physique, if it be desirable to pursue the subject free from its more scientific details.

mula into Fahrenheit's scale.

(432.) The preceding formulæ enable us to discover Weight of the elastic force of vapour existing in the atmosphere at vapour in any temperature. Let us, therefore, next inquire, what given vo lume, at a is the absolute weight of vapour contained in a given given den volume, under given circumstances of density and tem- sityand ter perature. To accomplish this object, Gay Lussac perature. employed small globules of glass of a nearly spherical Method of form, as B, B, fig. 2. One of these being accurately Gay Lusweighed, had a portion of water introduced into it, the sac's. contained air being expelled, and the narrow neck hermetically sealed. The weight of the ball in this new state, compared with its primitive weight, gave the exact weight of water contained in it. The globule being thus introduced into the glass vessel V V, previously filled with mercury, was surrounded by the vessel M M, containing water; and heat being applied to it, necessarily caused the globule to break, and the resulting vapour to ascend to the summit of VV. Subtracting now the altitude of the mercurial column above the external level, from the ordinary barometric column existing at the same instant, must necessarily give the measure of the elastic force of vapour produced..

(433.) Such is Gay Lussac's accurate method of performing this important experiment, and Biot has illustrated it by some equally beautiful investigations

Meteor of an analytical kind, and which we regret our limits logy will not permit us fully to follow. He denotes the weight of water in grammes, contained in one of the sations glass globules by P, and by the capacity in litres of of the same, one of the equal divisions of the receiver, of which N is their number. The resulting volume of vapour might thus be truly represented by N v, did not the receiver itself undergo some change in consequence of the altered circumstances of temperature. Representing, therefore, the cubic dilatation of glass by k, the actual volume of vapour will become

Numerical

(434.) This formula Biot illustrates by an appropriate epie, example, the weight of water contained in the globule being 08.6, the number of divisions occupied by the vapour 220, and the capacity of one of them 0.00499316 litres. The barometric column also at the same time being 0.7555 at a temperature of 15°, and the mercury within the vessel 0.052 above the external level. By reducing these mercurial columns to the common temperature of zero, and allowing for the dilatation of mercury for each degree of the centesimal scale

log. N

log. v

log. (p-h)

1 5412 of its bulk, we shall finally obtain the following elements, = 2.3424227 log.p = 1.7781513 = 3.6983755 log. 0.76 1.8808136 = 1.8465660 log. p.0m.76 1.6589649

log. Nv (p-h)= 1.8873642

log. p.0m.76

= 1.6589649

from which it appears that a quantity of moisture, equivalent in weight to a gramme, is contained in a volume of vapour whose capacity is equal to 1.6964 litres, at the temperature of the boiling point, and under an atmospheric pressure of 0.76 metres of mercury. We know, moreover, that a gramme of water taken at the temperature of the maximum of condensation, occupies precisely a cubic centimetre, of which the litre contains a thousand; and that hence a cubic centimetre of water of this degree of temperature, when reduced into vapour, will fill a space equivalent to 1696.4 cubic centimetres. It may also be added, that a litre of this vapour, under the pressure above mentioned, and of the temperature of 100°, weighs

1

1.6964

0.589483 gram

mes. By reducing these results into English measures, we shall find that a cubic foot of vapour at the tempera

cubic foot

thod of

ture of the boiling point, and under an atmospheric Meteorpressure of 29.9216 inches, weighs 257.7778 grains. ology. (435.) But the objects of Meteorology require that a corresponding result should be found for any other Weight of a temperature. Accordingly Dr. Anderson, in his very of vapour at able article on HYGROMETRY, published in the Edinburgh the boiling Encyclopedia, has modified with some advantage, the point. formula given by Biot for this purpose. If we denote Dr. Anderwith the author of the Paper alluded to, the weight in son's megrammes of a litre of vapour at the temperature t by P', finding the the corresponding elastic force by F, the weight in same at any grammes of a litre of vapour at the boiling point by P; and adopting moreover the principle of Gay Lussac, perature. that vapours so long as they remain in the aeriform state, expand by increase of temperature precisely in the same manner as the permanently elastic fluids, and that they suffer corresponding changes of volume by alterations of pressure, and also that air uniformlyexpands three-eighths of its bulk from the freezing to the boiling point of the Centigrade scale, we shall obtain by making the requi

site substitutions

and further reducing, or by substituting for P its value 0.589483 grammes,

other tem

To illustrate this useful formula by a single example, Numerical let it be required to determine the weight of a cubic inch example. of vapour at the temperature of 54°. In this case the value of t being 54°, and F, computed by means of the formula (R) becoming .42779, we shall obtain

(437.) But it may be useful, however refined and Dr. Anderperfect the system of computation, to discover how far son's expethe processes of actual experiment will confirm it. riments to Dr. Anderson accordingly made a large volume of determine saturated air to pass slowly in a small stream through a sufficient quantity of sulphuric acid, or dry muriate of formula. racy of the lime, cut off from all communication with the atmosphere; and then observing the increase of weight which these substances acquired in consequence of the air transmitted through them. A complete description of his apparatus may be seen in his Paper

*An exposition of these important reductions, which we regret we have no room for in the text, may be seen at pages 275 and 276 of Biot's Traité de Physique, tom. i.

It is gratifying to observe how closely the results of coincidence the experiment coincide with the numerical values of the of the expe- formula, affording at once a strong confirmation of Dalton's researches on the elastic force of vapour, and of the relations which Gay Lussac has established between a volume of dry atmospheric air, and of the quantity of vapour contained in the space which that air occupies.

Union of

air.

(438.) Let us next inquire into some of the condivapour and tions relating to the union of vapour and atmospheric atmospheric air. On this subject we may remark, as a general law existing among the dry gases, that if among any number of elastic fluids incapable of being blended together at a given temperature, which separately sus tain the pressures p, p', p'', ... . &c., the same volume V of each be taken, and the whole afterwards reduced into a volume of the same magnitude, we shall find the elastic force P of the united volumes exactly equivalent to the sum of the separate elastic forces; that is Pp+p' + p'........

Elastic

force of united volume equal to sum of separate

and we shall now proceed briefly to show that the same elasticities. remarkable principle holds good in the union of vapour and atmospheric air.

Gay Lussac's expe

riment to

prove this.

(439.) To demonstrate this problem, Gay Lussac employed a cylindrical glass tube A B fig. 3, divided into parts of equal capacity, and having two stopcocks at R and R'. A little above the lower cock, a bent tube of glass TT', of a smaller diameter than the cylinder, communicated with its interior at T. The whole apparatus being perfectly dried, the stop-cock at R' is opened, and mercury well boiled and dried allowed to fill the cylinder, and to ascend to its proper level in the tube. A globe filled with air brought to a complete state of dryness, is then screwed on at R, and a communication opened between the cylinder and globe, by turning the stop-cocks at rand R'. If air of the ordinary density be now introduced into the globe, the mercury will not be depressed in the cylinder A B, and hence the stop-cock at R must be turned, to permit a portion of the quicksilver to descend, and thus allow some of the air to occupy its place. As soon as a sufficient quantity of air has been introduced, its expansion is arrested by turning the stop-cock R; and by turning the other stop-cock at R' at the same time, the dry air introduced into the cylinder A B is prevented from escaping.

(440.) To introduce the water we are desirous of Meteorchanging into vapour, another stop-cock R" is applied, ology. surmounted by a very small metallic vase V, in which the liquid is placed. This cock is not pierced through its centre as stop-cocks ordinarily are, but a small hemispherical depression O below the surface of the interior 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 produce the desired effects on the volume of air submitted to observation.

(441.) The introduction of the first drop of water must evidently augment the elastic force of the air, and 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 opposes a resistance to the formation of vapour. If a single drop of the liquid be not sufficient to form all the vapour necessary for the given space and temperature, another may be added to increase the elastic force. After a certain number of drops, however, have been introduced, the addition of any greater quantity will produce no effect, the excess remaining above the surface of the mercury without being reduced into vapour. Biot, with his usual ingenuity, supposes a case in which some drops in excess have been added. By closing the cock R, and denoting the divisions of the tube occupied by the mingled volumes of air and vapour by N', the elastic force of the two will be found equal to the pressure p of the atmosphere, as at the commencement of the experiment, the gas occupying, however, only N divisions. Its elastic force is thus diminished, and, since in its original condition it was equivalent to p, it must in its new state be represented by

Denot

PN N ing therefore the elastic force of the vapour by f, at the existing temperature, the measure of the whole elastic force will become

PN

f+ N

And since this is equal to the pressure p, which is supposed to remain constant, we shall have

(442.) If now, when the experiment is performed, the actual values of N, N' and p be observed, the same value for f will be found, as the elastic force of vapour in a vacuum would have afforded at the same temperature. Hence the vapour in its state of union In mecha with air preserves its own proper tension, and thus cal union confirms the beautiful law announced, that in the sim- vapour a ple mechanical union of vapour with air, each portion air, each of the mixture maintains its own elastic force dependent tains its on the volume it is made to occupy.

part mai

own elas

(443.) The preceding formula gives us the value of force. the elastic force in functions of the whole atmospheric Further pressure, and the volumes occupied by the air in its ori- plication this prin ginal state, and when united to vapour. By a simple ciple. conversion, it may be made subservient, by aid of the

Meteorology.

served in union of vapour with the atmosphere.

of temperature and pressure; and that, therefore, the formula (U) which enables us to compute the weight of a cubic inch of vapour, will enable us also with equal accuracy to find the actual weight of moisture in a cubic inch of air, under the same measure of the elastic force.

(448.) In making a practical application of the formula last quoted, the only thing requisite is a convenient mode of determining the elasticity of the vapour already existing in the air, under any proposed circumstances. Mr. Dalton's simple method of filling a tall cylindrical glass jar with cold spring water, and repeating the observation until dew ceases to form on the external surface, first enabled us to obtain this interesting result; but we shall reserve the practical developements of this part of our inquiry, until we come to treat of Daniell's hygrometer.

Actual phe- (449.) Having thus briefly investigated some of the nomena ob- essential conditions of vapour, let us next inquire into a few of the interesting relations it presents, in its union with the great and perpetually changing body of the atmosphere. Every volume of air, from whatever region it may be brought, is more or less charged with vapour. There are indeed two atmospheres which encompass the earth on every side, one of air, and the other of moisture. The union of these by Nature is mechanical only, and each is governed by its own peculiar laws. The atmosphere of air, as we have already seen, possesses permanent elasticity, expanding arithmetically by equal increments of heat, and decreasing in density and temperature as it recedes from the surface. The atmo sphere of vapour is also an elastic fluid undergoing condensation by cold, and at the same time evolving caloric, augmenting its force geometrically by equal increments of heat, and permeating the former, and moving in its interstices, like water when in the process of filtration it passes through sand.

Limits set

aqueous

vapour.

(450.) To supply the atmosphere with vapour, the power of evaporation is in almost constant operation, by Nature to and we might suppose that an agent possessing so great an activity, would in time exhaust the store, boundless as it is, by which that moisture is supplied. But Nature has fixed limits beyond which the aqueous element cannot pass, so as to prevent an undue accumulation of moisture on the one hand, and a state of long continued dryness on the other. These limits are assigned by temperature, and which, whatever may be its apparently capricious changes, is confined, in every climate, within definite bounds. The same heat, therefore, which warms and vivifies the air, and renders the earth an agreeable abode to Man, controls with admirable wisdom the rising moisture.

Tempera

ture the

cause.

(451.) This power of the air to acquire moisture is, however, modified by every alteration of temperature, any increase thereof augmenting its store, and every decrease of heat producing a proportional diminution. The greatest and least degrees of heat, whether it be that of a day or a year, must therefore afford some phenomena which influence the condition of atmospheric vapour. In the case of the minimum temperature of a given latitude, and a state of entire saturation of the air, no addition can possibly be made to the vapour it supports, so long as that temperature is maintained. Any augmentation of heat, however, from whatever cause it may proceed, is at once accompanied by an increased power of supporting moisture, and new accessions of vapour may be added to it. The mini

ology.

mum temperature of any period, therefore, whether it Meteorbe that of a day, a month, or a year, must set a limit to the accession of watery vapour in the air; and thus in every region, the equatorial, the temperate, or the polar, a strong and impassable barrier has been fixed by prevents

Minimum

temperature

Nature to the continued accumulation of moisture in the accumula air. And that there is an equally impassable limit on tion of the other hand-that of extreme dryness, also existing, vapour. is evident, when we consider, that as every diminution of temperature tends to saturation, so every increment of heat must produce a tendency to dryness; and that Maximum as the maximum temperature of the day has itself a temperatur being finite limit, and therefore governs this last condition of the prevents atmosphere, so the depression of temperature which entire dryimmediately follows, by at once increasing the humidity ness. of all the atoms of air which undergo that change, must remove at once the possibility of any long continuance of comparative dryness. There are some occasional anomalies, however, in the extreme conditions of humidity and dryness to which Saussure has briefly alluded in his Essais sur l'Hygrométrie, and which sometimes embarrass the inquirer.

(452.) This dependence of moisture on the circumstances of temperature will help us to trace some of the phenomena of its distribution. There is a gradation of heat, as we have before found, from the Equator to the Poies, and also from the surface of the globe upwards, into the loftier regions of the air. Generally speaking, Lowest atthe lowest stratum of the atmosphere, in whatever lati- mospheric tude it is found, must be most abundantly stored with stratum the watery vapour, on account of its being nearest the most abun dantly source from whence that moisture is supplied. If an stored wit equality of temperature existed therefore at the surface, moisture. a cubic foot of air, in whatever latitude it were taken, Moisture would contain, when completely saturated, the same diminishe quantity of moisture. But since the temperature dimi- with the nishes with the latitude, a given volume of air in a state latitude. of perfect saturation must contain less and less moisture as we approach the Poles.

diminishe

as we

(453.) From a similar cause, the moisture of the Moisture atmospheric columns must diminish as we ascend vertically above the Earth; and hence that the whole store ascend. of moisture contained in a vertical equatorial column of air, must exceed the quantity found in a polar column of equal diameter and in the same state of perfect saturation. There are many difficulties, indeed, in the way of proving experimentally the decreasing humidity of the air, and one of the most interesting Meteorological observations that can be made in the neighbourhood of a mountain is to determine the exact condition of vapour in the atmospheric strata at different elevations. To resolve the question perfectly, such observations should be made at the same instant at the two extremities of the same vertical line. This, however, is hardly possible to be done, and we must hence select such times and places of observation as are not widely separated from each other. Saussure made many among the Alps with this view, from the valley of Chamouni through several successive elevations, and in a general way found the law to hold good. He met with some instances, however, in which the absolute quantity of vapour was greater in the more elevated regions of the air. Thus by comparing the 75th and 76th Meteorological observation of his Voyage dans les Alpes, we shall find that his hygrometer advanced 10°.1 towards humidity, by ascending to a height of 291 toises above his first station, the thermometer of