APPENDIX.

APPENDIX.

Since the publication of the second part of the first volume, (1810) some important essays on the subject of heat have appeared, which have a direct bearing upon some points of the doctrine on that subject inculcated in the said volume. It may be proper to state the results, with such remarks and reflections as have occurred in the consideration of them.

In the Annales de Chimie for January 1813, also in the Annals of Philosophy, vol. 2, we find a Memoir on the specific heat of different gases, by M. M. De la Roche and Berard. This exhibits a most laborious and refined series of experiments on this most difficult subject. Great merit seems to be due to them, both for invention and execution.

It is unnecessary to describe the particulars of the apparatus and the mode of conducting the experiments, as a description may be found as above referred. It is sufficient to observe that thecalorimeterused was a copper cylinder of 3 inches diameter and 6 in length, filled with water, and having a serpentine tube 5 feet in length, running through the interior and opening at both ends on the outside of the vessels. By means of this tube a regular current of any gas of a giventemperature (212°) might be passed through the vessel so as to part with its excess of temperature to the water. The quantity of water and the capacity of the vessel for heat were previously determined; and the quantity of heated gas passed through the calorimeter was determinable at any time, as well as the temperature of the water, from the judicious arrangements.

It is easy to see that when an apparatus of this kind is at work, the gas will impart heat, more or less according to its capacity, to the water; and that the temperature of the calorimeter will gradually ascend till it arrives at a maximum; that is, till the refrigerating effect of the surrounding atmosphere upon the calorimeter is equal to the heating effect of the current of gas.

The following Table exhibits the results of their experiments.

They found the specific heats of equal volumes of air of the pressures 29.2 and 41.7 inches of mercury to be nearly as 1 ∶ 1.2396, differing from the ratio of the pressures or densities, which is 1: 1.358.

The above table of the specific heat of the permanent gases (excluding aqueous vapour) was corroborated by the results of another series of experiments in which the principle was varied a little: namely, to find how many cubic inches of each gas at a given temperature were required to raise the temperature of the calorimeter a given number of degrees, and inferring the capacities for heat to be inversely as the quantities of gas employed. The differences in the results were from 1 to 10 per cent., which may be considered small, in experiments of such delicacy.

The ratios of the specific heats of several gases being found, it was highly expedient to find the ratio of the specific heat of water, and that of some one gas, as common air. This was effected by passing a small current of hot water through the calorimeter, and comparing the effect of this current with that of the larger one of air, the requisite care being taken to ascertain the quantity of water passing in a given time and its temperature at the ingress. The result of thisexperiment was that the specific heat of water is to that of common air as 1 ∶ .25 nearly. By two other experiments, varied from the above, results not much differing were obtained, so that the average of the three gave, water to air, as 1 ∶ .2669.

Reducing the specific heats of the gases to the standard of water as unity, we have the following Table of the specific heats of equal weights of the respective bodies:

Before we animadvert upon these results, it will be expedient to give an abstract of the not less interesting experiments of Messrs. Dulong and Petit, on heat, as given in the Annales de Chimie and de Physique, vol. 7 and 10.

These gentlemen begin by an investigation of the expansion of air by heat. The absolute expansion of air from freezing of water to boilinghad been previously determined by Gay Lussac and myself to be from 8 to 11 nearly: they however extended the enquiry above and below these points of temperature, namely to those of freezing and boiling mercury. From the temperature of freezing mercury or thereabouts, to that of boiling water, they find the expansion of air to keep pace with that of mercury, as indicated by the common thermometer; but from the boiling point of water to that of mercury, the latter expands somewhat more in a proportion gradually increasing: as by the following Table.

TABLE I.

The absolute dilatation of mercury claims their attention. They quote nine authorities for the expansion from freezing to boiling water temperatures; the extremes of these nine are, Casbois ¹/₆₇ of originalvolume, and mine ¹/₅₀ of the same. They determine it to be ¹/₅₅.₅. By doubling and tripling the elevation of the temperature, they made observations from which are deduced the results of the following Table. The dilatations are for each degree of the thermometer centigrade, to which I have added the corresponding ones for Fahrenheit’s.

TABLE II.

By a series of observations on the apparent dilatation of mercury in glass vessels, compared with the results in the above tables, they deduce the absolute dilatation of glass for each degree of the thermometer, and the temperature that would be indicated by supposingthe uniform expansion of a glass rod adopted as the measure of temperature as under:

TABLE III.

The absolute dilatations of iron, copper, and platina were investigated with great address, from 0° to 100° and from 0° to 300° centigrade; and were found as per Table below, for each degree of the centigrade thermometer.

TABLE IV.

Connected with this subject was another important enquiry, whether the capacities of bodies for heat remain constant at different temperatures, or whether they diminish or increase as the temperatureadvances. In other words, does a body that requires a certain quantity of heat to raise it from 0° to 100° centigrade, require the same quantity to raise it from 100° to 200°, and from 200 to 300°, &c.; or does it require less or more as we ascend? This enquiry involves that of the measure of temperature. They adopt the uniform expansion of air, or the air thermometer, as the proper measure, and find the capacity of iron,

the capacity of an equal weight of water being 1.

The following Table exhibits the capacities of seven other bodies according to their results.

TABLE V.

According to this table the capacities of bodiesincreasewith the temperature in a small degree: and the increase, though it would still exist, would be less, if the common mercurial thermometer were the measure of temperature.

Also supposing that thermometers made of these bodies and graduated by immersion in freezing and boiling water into 100°; if these were all immersed in a fluid in which an air thermometer stood at 300°. Then the relative temperatures of the several thermometers would be as under, if measured by the absolute quantity of heat acquired, namely,

From these observations they infer that the law which has been promulgated for the refrigeration of bodies, cannot be strictly true: namely, that bodies part with heat in proportion as their temperature exceeds that of the surrounding medium.

Some animadversions on the general laws relative to the phenomena of heat, announced in my elements of Chemical Philosophy (page 13) thenfollow, together with a table drawn up to show the discordance between the air thermometer and the mercurial thermometer, both being graduated in the manner I proposed in the said elements. On these points I may have to remark in the sequel.

The first part of the Essay concludes with some remarks to shew why a preference should be given to the air thermometer, or more strictly, the thermometer whether of mercury or any other body, supposed to be graduated so as to correspond with an air thermometer of equal degrees.

The Second Part of the Essay is on

Adopting the air thermometer as the most eligible measure of temperature, Messrs. Dulong and Petit proceed to investigate the laws of the refrigeration of bodies, under a great variety of circumstances, invacuoand in air or gases of different kinds and densities. The inquiry abounds with experiments and observations evincing great skill and acuteness; but which it will not suit our purpose to detail. It may suffice for us to give a general summary of the Laws deduced by them from their experiments, at the same time recommending all those who feel sufficient interest in the subject to peruse the essay at large, which exhibits a profound philosophical train of experiments,the results of which are illustrated by the aid of mathematical generalization.

“Law 1.If one could observe the cooling of a body placed in a vacuum, and surrounded by a vessel absolutely destitute of heat, or otherwise deprived of the power of radiating heat, the velocities of cooling would decrease in geometrical progression when the temperatures diminished in arithmetical progression.”

“Law 2.The temperature of a vessel containing a vacuum being constant, and a body being placed in it to cool, the velocities of cooling for excesses of temperature in arithmetical progression, decrease as the terms of a geometrical progression diminished by a constant number. The ratio of this progression is the same for the cooling of all kinds of bodies, and is equal to 1.0077.”

“Law 3.The velocity of cooling in a vacuum for the same excess of temperature, increases in geometrical progression, the temperature of the vessel circumscribing the vacuum increasing in an arithmetical progression. The ratio of the progression is the same as above, namely 1.0077 for all kinds of bodies.”

“Law 4.The velocity of cooling due to the sole contact of a gas is entirely independent of the nature of the surface of the cooling bodies.”

“Law 5.The velocity of cooling due to the sole contact of a gaseous fluid varies in a geometrical progression, while the excess of temperature itself varies in a geometrical progression. If the ratio of this second progression be 2, that of the first is 2.35, whatever be the nature of the gas and its elastic force.”

“This Law may be likewise announced by saying that the quantity of heat carried off by a gas is in all cases proportional to the excess of the temperature of the heated body raised to the power whose index is 1.233.”

“Law 6.The cooling power of a gaseous fluid diminishes in a geometrical progression, when its tension itself diminishes in a geometrical progression. If the ratio of this second progression is 2, the rate of the first is 1.366 for atmospheric air; 1.301 for hydrogen; 1.431 for carbonic acid; and 1.415 for olefiant gas.”

“This law may also be presented as follows: The cooling power of a gas, all other things being alike, is proportional to a certain power of the pressure. The exponent of this power depends on the nature of the gas, and is for air 0.45; for hydrogen 0.315; for carbonic acid 0.517; and for olefiant gas 0.501.”

“Law 7.The cooling power of a gas varies with its temperature in such a manner that if the gas can dilate so as to preserve the same uniform tension, the cooling power will be as much diminished by therarefaction of the gas, as it is increased by its augmentation of temperature; so that definitively it depends only on its tension.”

Another ingenious Essay was published by Messrs. Dulong and Petit, in the Annal. de chimie et de physique, vol. 10, namely, “Researches on some important points of the theory of heat.”—One object is to ascertain the specific heats of bodies with superior precision. A table of the specific heats of certain metals, found by their method, is given, together with the weights of the atoms of those metals, and the products of the specific heats and weights of the atoms, as under:

The inference intended from this Table is pretty obvious, namely, that the atoms or ultimate particles of the above bodies contain or attach to themselves the same quantity of heat, or have the same capacity. This principle the authors think will apply to the simple atoms of all bodies, whether solid, liquid, or elastic; but they hold it does not apply to compound atoms. It differs therefore essentially from a suggestion of mine, made eighteen years ago, (see Vol. I. page 70,) thatthe quantity of heat belonging to the ultimate particles of all elastic fluids, must be the same under the same pressure and temperature. They seem to apprehend, from experience, that a very simple ratio exists between the capacities of compound atoms and that of the elementary atoms. They draw another inference from their researches, that the heat developed at the instant of the combination of bodies, has no relation to the capacity of the elements; this loss of heat, they argue, is often not followed by any diminution in the capacity of the compounds. They seem to think that electricity developes heat in the act of combination; but they do not deny that a change of capacity may sometimes ensue, and heat be developed from this cause.

Results nearly agreeing with those of De la Roche and Berard, on the capacity of certain elastic fluids for heat, were about the same time obtained by M. M. Clement and Desormes. (See Journal de Physique, Vol. 89—1819.) Such results, impugning some of the most plausible doctrines of heat, could not be admitted but upon very good authority. I remained doubtful, in some degree, till satisfied by my own experience. I procured a calorimeter of the construction of De la Roche’s, and to simplify the experiment, instead of forcing a given volume of hot air through the calorimeter to impart heat to the water, I drew, by means of an air-pump, a certain volume of atmospheric (or other air) of the common temperature, through the calorimeter filled with hot water, in order to find how much this process would accelerate the cooling. From several experiments of this kind, I am convinced that the capacity of common air for heat is very nearly such as the above ingenious French chemists have determined. That is, it is about ¹/₇ part only ofwhat Dr. Crawford deduced from his experiments, and nearly the same part of what I inferred from my theoretic view of the specific heats of elastic fluids. (See Vol. I. pages 62 and 74.)

Indeed M. M. De la Roche and Berard appear to have been puzzled with the admission of their own results. The combined heats of oxygen and hydrogen gases give only .6335 for the specific heat of water; whereas by experiment the heat of water is found to be 1, notwithstanding an immensity of heat is evolved during the combination of these gases.[26]

“It is necessary therefore,” they observe, “to abandon the hypothesis which ascribes the evolution of heat in cases of combination to a diminution of specific heat in the bodies combined, and admit with Black, Lavoisier, and Laplace, and many other philosophers, the existence of caloric in a state of combination in bodies.” I am not aware of any writer that denies the existence of caloric in a state of combination of bodies. Dr. Crawford, who would be thought the mostlikely to err in this respect, maintains, “that elementary fire is retained in bodies partly by its attraction to those bodies and partly by the action of the surrounding heat,” and that “its union with bodies will resemble that particular species of chemical union wherein the elements are combined by the joint forces of pressure and of attraction.” (On animal heat, 2d edition, page 436.) He is perhaps somewhat unfortunate in his instance in the combination of carbonic acid and water; muriatic acid or ammonia and water would have been more in point.

The truth is, these important experiments shew that in elastic fluids the increments of temperature are not proportional to the whole heat, compared with the like increments of temperature and whole heat in those bodies when in the liquid and solid states.

The specific heats of bodies, it is well known, are determined by means of the relative quantities of heat necessary to raise the temperature of those bodies a certain number of degrees. They are expressed by the ratios of those quantities. If the capacities of the same bodies for heat were permanent at all temperatures, then these ratios would also express those of the whole quantities of heat in bodies. In fact, mostauthors represent the specific heats as expressing both the ratio of the total quantities of heat in bodies, and of the relative quantities to raise their temperature a given number of degrees; but it is the latter only which they accurately represent, and the former only hypothetically.

In regard to bodies in the solid and liquid forms, all experience shews that their capacities for heat are nearly if not accurately constant within the common range of temperature; it seems therefore not unreasonable to infer that the whole quantity of heat in each is proportional to their increments. When, however, a solid body by an increase of temperature assumes a fluid form, and absorbs heat without any increase of its temperature, its total quantity of heat is thus increased; and it is contended by the writers on capacity, that the increments of heat afterwards are increased in the same proportion as the total quantities. This is probable enough; but it ought to be proved in several instances by direct experiment before it can safely be admitted as a general principle; more especially now since the analogy in the case of a liquid becoming an elastic fluid is found tofail in this particular. As an instance of uncertainty, the capacity of ice to water has been found as 9 to 10 by one person, and as 7.2 to 10 by others; such wide difference in the results shows there must be a difficulty in determining the specific heat of ice, and that it may even be doubted whether the specific heat of ice or water is greatest.

From the foregoing detail of experiments on elastic fluids, it appears evident that such fluids exhibit matter under a form in which it has the greatest possible capacity for heat, when capacity is understood to denote the total quantity of heat connected with the fluid; but if the capacity or specific heat is meant to denote the quantity of heat necessary to raise the body a given number of degrees of temperature, then the elastic fluid form of matter is that which has the least capacity for heat of any known form of the same matter. When therefore we use the termsspecific heatas applied to elastic fluids we should henceforward carefully distinguish in what sense they are used; but the terms may still be indifferently used in the one or the other sense as applied to liquids and solids, till some more decisive experiments shew that a distinction is required. Probably the anomaliesthat have occurred in investigations of the zero of cold, or point of total privation of heat, are in part due to the want of accordance between the ratio of the total quantities of heat in bodies, and the ratio of the quantities producing equal increments of temperature.

The greatest possible quantity of heat which a given weight of elastic fluid can contain is when the dilatation of the fluid is extreme. For, condensation, whether arising from mechanical pressure or from increased attraction of the atoms of matter for each other, tends to dissipate the heat, by increasing its elasticity. Hence increase of temperature, at the same time that on one account it increases the absolute quantity of heat in an elastic fluid, diminishes the quantity on another account by an increase of pressure, if the fluid be not suffered to dilate. This is well known from the fact that condensation produces increase of temperature in elastic fluids.

When it is considered that all elastic fluids expand the same quantity by the same increase of temperature, it might be imagined that all of them would have the same capacity, or require the same quantity of heatto produce that expansion. The results of De la Roche and Berard do not seem to admit of this supposition, though the differences of the capacities of elastic fluids of equal volumes are not very great. There is a remarkable difference too between their results and those of Clement and Desormes, in regard to hydrogen gas: namely, .9033 and .6640; also in carbonic acid gas, 1.2583 and 1.5. The subject deserves further investigation.

In reference to the experiments of Dulong and Petit, on the relative expansions of air and mercury by heat, I have no doubt their results are good approximations to the truth. My former experiments were chiefly made in temperatures between 32° and 212°, and I found, as General Roi had done, the expansion of air to be somewhat greater in the lower half than in the upper half of that interval, compared with mercury. On a repetition of the experiments, I think the difference is less than I concluded it to be, and I find that the like coincidence of the air scale and mercurial, continues down to near freezing mercury; at least the difference will not be so great as my new table oftemperature makes it atpage 14. I have made some experiments on the expansions of air above 212°, which lead me to adopt the results of Dulong. On a comparison of the air and mercurial thermometer upon the laws which I pointed out, namely, the former expanding in geometrical progression to equal intervals of temperature, and the latter expanding as the square of the temperature reckoned from its freezing point, it appears that in the long range of 600° from freezing water to boiling mercury, the greatest deviation of the two thermometers does not exceed 22°. However, the great deviation of the scales between the temperatures of freezing water and freezing mercury, is sufficient to shew, as Dulong and Petit have observed, that their coincidence is only partial. Like the scales of air and mercury, which are so nearly coincident from -40° to 212° that scarcely any difference is sensible, though no one doubts of its existence; yet afterwards the differences become obvious enough, and the greater the farther we advance.

Expansion of Mercury.See page 34, vol. I. I have overrated the expansion of glass bulbs (as will be seen presently,) and hence that of mercury; my expansion of mercury corrected on account of the glass,will be ¹/₅₃ nearly, which leaves it still greater than Dulong’s. The 2nd table of Dulong is valuable, on account of its affording us information of the rate of expansion in the higher degrees of temperature, from a given or standard air thermometer.

Expansion of Glass.—By the 3rd Table of Dulong and Petit, it appears these ingenious chemists found the expansion of glass for 180°, or from 32° to 212°, very nearly the same as had been determined previously by Smeaton and others. It also expands increasingly with the temperature, whether it is estimated by the air or mercurial standard. This was observed by Deluc, but more extensively by the present authors. The expansions of iron, copper, and platina, from 32° to 212° as detailed in the 4th table, agree nearly with the results of others; but the expansions in the higher part of the scale manifest some remarkable facts not before known. Platina not only expands the least of the above bodies, but its expansion is almost equable; iron expands more than glass and less than copper, but the most unequally of any one, the expansion increasing rapidly as the temperature advances.These facts explain some others which have fallen under my observation. I was formerly surprised to find glass and iron expand so nearly alike (see vol. I. page 31); but it now appears that iron increases more slowly in proportion than glass about the freezing point. More recently I procured a small thermometrical vessel of platina to contain water like those described at page 31, vol. I, and having filled it and treated it as the other metallic vessels, I was again surprised to find that the apparent greatest density of water in this vessel was at 43°, whereas I expected to have found it below 42°, the point for glass vessels. This observation, in conjunction with Dulong’s, shews, that platina expands more than iron at low temperatures, though for a range of 300° the whole expansion of the platina is to that of the iron as 2 to 3 nearly. Hence the error (for I now consider it as such) which I was led into with respect to the expansion of glass bulbs, (see vol. I. page 32) and subsequently into that of the expansion of mercury abovementioned. It is not the expansion of glass which approaches that of iron, but it is the reverse, which occasions the two bodies to meet so nearly in the table, page 31. This consideration will affect thepoint of greatest density of water also; for, the less the expansion of iron and glass, the nearer will be the points of real and apparent greatest density of water, contained in vessels of those materials. My observations on brown earthenware are scarcely to be relied upon from the difficulty of making such vessels water tight: but the common white ware I have verified repeatedly since the publication of that table, and am satisfied the point of apparent greatest density, is at or near 40° in such vessels; hence the real maximum density of water must be below 40°. I am inclined to adopt 38° as the most proximate degree.

Capacities of bodies for heat.In the 5th table of Dulong, we have the specific heats of glass and of six metals, determined between freezing and boiling water: that of iron is given before. So far the question does not involve that of the measure of temperature. Their results afford no striking differences from those previously determined; however, it is desirable to find a greater accordance amongst philosophers in this respect. The experiments which give the specific heats between 0° and 300° centigrade, are original and interesting. The results go to shew that the capacities of bodies increase in a small degree with the temperature. But supposing thatthese results may be relied upon as accurate (which can scarcely be affirmed of any former ones) still the character of them may be changed by adopting a different measure of temperature.

The Essay of M. M. Dulong and Petit, in the 10th vol. of the An. de chimie (see An. of Philosophy, vol. 14th, 1819) manifests great ingenuity. It does not appear, however, so fortunate either in theory or experiment as the former one. It would be difficult to convince any one, either by reasoning or by experience that a number of particles of mercury at the temperature of -40°, whether in the solid,, liquid, or elastic state, have all the same capacity for heat. Indeed the experiments of De la Roche and Berard, if they are to be credited, demonstrate the inferior capacity of condensed air to rarefied air; and if the same body changes its capacity in the elastic form, it may well be concluded that all the three forms have not the same capacity. M. M. Dulong and Petit have themselves shewn, in their former essay, (see page 276) that solid bodies vary in their capacities for heat, and that scarcely any two bodies, vary alike; hence it is impossible that the product of the weight of the atom and specific heat of the body shouldbe a constant quantity. Their specific heat of certain metals differ greatly from what is found by others. For instance, they make the specific heat of lead .0293; the lowest authority I have seen is Crawford, .0352, and the highest Kirwan .050; from repeated trials I have lately found it, upon an average, .032. The weights of some of the atoms in their table, differ materially from what are commonly received; for instance, bismuth is 13.3 instead of 9; also copper, silver, and cobalt, are only half the weights of some authors. The gases too are unfortunate examples. Oxygen gas gives a product of .236 instead of .375; azotic gas gives a product .1967, if oxygen be to azote as 7 to 5, but a product of .393 if oxygen be to azote as 7 to 10: by Dr. Thomson’s ratio of oxygen to azote, 4 to 7, the product will be .482, very different from .375. Hydrogen will give a product of .47 or .41 instead of .375. All these differences, it may be said, are occasioned by errors in the specific heats of the gases; but if errors of this magnitude can still subsist after all the care that has been taken, we shall scarcely know what to trust in experimental philosophy.

If M. Dulong would assume all his simple elements in an elastic stateand under one uniform pressure, the hypothesis would then make a part of mine (vol. 1. page 70), and there is great reason to believe it would be either accurately true or a good approximation; but to suppose that some of the bodies should be in a solid state, having their particles united by various degrees of attraction, others fluid, and others in the elastic state, without any material modifications of their heat arising from these circumstances, appears to me to be in opposition to some of the best established phenomena in the mechanical philosophy.

Their observations on the specific heat of compound elements, on the relation of the heat developed by combination, as compared with the heat of the elements before and after the combination, &c., are not supported by a detail of actual experience. Heat given out by chemical changes they suppose not to have been previously in a state of combination with the elements. As an argument, the heat given out by charcoal kept in a state of ignition, by a current of galvanic fluid, is adduced. It is true this case is most easily explained, by allowing that the galvanic fluid is in such circumstances converted into heat. But the charcoal does not undergo any chemical change, and therefore this is not a case in point.

All modern experience concurs in shewing that the heat of combustion is primarily dependent on the quantity of oxygen combining. The heat evolved by the combustion of phosphorus and hydrogen is very nearly, if not accurately, in proportion to the oxygen spent. The heat by the combustion of charcoal is not in a much less ratio: and I find the heat in burning carbonic oxide, carburetted hydrogen and olefiant gas is the same as in burning hydrogen gas,provided the combining oxygen is the same.

One difficulty seems to have occurred to M. M. Dulong and Petit. They all along conceive that the specific heats of bodies, that is, the heats producing equal increments of temperature, must necessarily be proportionate to their whole heat. This is purely hypothetical, till established by experiment. The generality of writers on specific heat had conceived it almost confirmed by experiment. The results of Delaroche and Berard have shewn that in elastic fluids the increments of heat are not proportional to the whole quantities, but on the contrary are less when a body is elastic than when liquid. Indeed some writers have argued this should be the case; because a body nearlysaturated with another has less affinity for it left.[27]It is plain then that oxygen gas or any other elastic fluid, may have a small specific heat in the sense above defined, and yet have an almost unlimited quantity of heat. I am not aware of any one established fact that does not admit of an explanation upon the hypothesis that heat exists in definite quantities in all bodies, and is incapable of any change, except perhaps into one of the other equally imponderable bodies, light or electricity.

NEW TABLE OF THEForces of Vapours in Contact with theGenerating Liquids at Different Temperatures.

This is an improved and extended table of the force of vapour, similar to that at page 14, vol. I. It shews that the different vapours increase inforce in geometrical progression, to certain intervals of temperature, the same to most or all liquids. These intervals of temperature were presumed in the former table, to be in realityequalto one another; but the accuracy of this last notion has been questioned.

TABLEShewing the expansion of air, and the elasticforce of aqueous and ethereal vapour,at different temperatures.

TABLE III.

Applications of the above Table.

These tables will be found of great use in reducing volumes of air from one temperature or pressure to any other given one: also in determining the specific gravities of dry gases from experiments on those saturated with or containing given quantities of aqueous or other vapours.

As several writers, and some of considerable eminence, have given erroneous or imperfect formulæ on these subjects, more particularly withregard to the effect of aqueous vapour in modifying the weights and volumes of gases, it has been thought proper to subjoin the following precepts and examples for the use of those who are not sufficiently conversant in such calculations.

The 5th column of the above table, or weight of aqueous vapour, is new, and may therefore require explanation. Gay Lussac is considered the best authority in regard to the specific gravity of steam; but it would be well if his results were confirmed or corrected, as they are of importance. According to his experience, the specific gravities of common air and of pure aqueous vapour,of the same temperature and pressure, are as 8 to 5, or as 1 to .625. Now I assume that 100 cubic inches of common air, free from moisture, of the temperature 60° and the pressure of 30 inches of mercury, weigh 31 grains nearly. It is an extraordinary fact that philosophers are not agreed upon the absolute weight of a given volume of common air. Most authors now assume the weight of 100 inches = 30.5 grains, whilst according to my experience it is more than 31 grains. If common air be assumed 31 grains, steam would be 19⅜ grains for 100 cubic inches, at the same temperature and pressure, could it subsist; but as it cannot sustainthat pressure at the temperature of 60° we must deduct according to the diminished pressure, the utmost force of steam at 60° being .65 parts of an inch of mercury, we have 30 inches ∶ 19⅜ grains ∷ .65 ∶ .420 grains = the weight of 100 cubic inches of aqueous vapour at 60° and pressure .65 parts of an inch; which is the number given above in the table. The like calculation is required for any other pressure: but in addition to this, there is to be an allowance for the temperature from the 2d column: Thus, let the weight of 100 cubic inches of steam at 32° be required. We have 30 inch. ∶ 19⅜ grs. ∷ .26 inch. ∶ .1679 grs.; the weight of 100 inches of steam at 60°; then if 480 ∶ 508 ∷ .1679 ∶ .178 grs. = weight of 100 cubic inches of steam at 32° and pressure .26 parts of an inch, the tabular number required.

Examples.

1. How many cubic inches of air at 60° are equivalent in weight to 100 cubic inches at 45°?

By the column headedvolume of airwe have this proportion, if 493 ∶ 508 ∷ 100 inch. ∶ 103.04 inches, the volume required.

2. How many cubic inches of air with the barometer at 30 inches height, are equal in weight to 100 cubic inches when the barometer stands at 28.9 inches?

Rule.The volume of air being inversely as the pressure, we have, 30 ∶ 28.9 ∷ 100 inches ∶ 96⅓ inches the answer.

3. How many cubic inches of dry air are there in 100 inches saturated with aqueous vapour, at the temperature of 50°, and pressure 30 inches of mercury?

Here the formula

applies, wherepdenotes the atmospheric pressure at the time, andfdenotes the utmost force of vapour in contact with water at the temperature. Hencep= 30,f= .49 per table, and we have

If the vapour of ether is assumed, thenf= 10.64, and we have

4. Suppose we find by trial the weight of 100 cubic inches of common air saturated with vapour at 60°, the barometer standing at 30 inchesto be 30.5 grains, and the weight of hydrogen gas in like circumstances to be 2.118 grains; query the weights of 100 cubic inches of each gas free from vapour, and their specific gravities, the temperature and pressure being as above?

If 30.5 ∶ 2.118 ∷ 1 ∶ .0694 = sp. gr. of vapourized hydrogen, that of vapourized air being 1. Subtracting .42 grs. (weight of vapour per table) from 30.5 grs., leaves 30.08 grains; and subtracting .65 parts of an inch from 30 inches, leaves 29.35 inches. Hence 100 cubic inches of dry air at the pressure of 29.35 inches, weigh 30.08 grains; and we have 29.35 ∶ 30 ∷ 30.08 ∶ 30.746 grains, the weight of 100 inches of dry air. Again, subtracting .42 grs. from 2.118, leaves 1.698 grains = weight of 100 cubic inches of hydrogen of 60° and sustaining the pressure of 29.35 inches; whence if 29.35 ∶ 30 ∷ 1.698 ∶ 1.736 grains, weight of 100 inches of dry hydrogen; and 30.746 ∶ 1.736 ∷ 1 ∶ .05645 = sp. gr. of dry hydrogen, that of dry air being unity. Or the results may be exhibited as under:

It frequently happens, especially in the decomposition of vegetable substances by heat, that the product consists of several combustible gases in mixture, and it is desirable to determine the proportions of each of those which collectively constitute the mixture. The following forms will be found useful for this purpose.

Letx= the volume of carbonic oxide,y= that of hydrogen,w= that of mixture, anda= that of carbonic acid, produced by exploding the mixed gases with oxygen over mercury.

Then the carbonic oxide, orx=a,and the hydrogen, ory=w-a.

Letx= the volume of sulphuretted hydrogen,y= that of hydrogen,w= that of the mixture, andg= the oxygen spent in the combustion ofw.

The notation being as above, we havex+y=w, and 2x+ ½y=g(see page 171): and,

The notation being as above, we have

Letx= carburetted hydrogen,y= carbonic oxide,z= the hydrogen,g= the oxygen spent in the combustion ofwvolumes of mixed gas, anda= the carbonic acid produced.

whence we have

andz=w-a.

Leta= the olefiant gas,y= the carburetted hydrogen, andz= equal the carbonic oxide,g= the oxygen enteringinto combination, anda= the carbonic acid produced; alsow= the whole volume as before.

7.Superolefiant gas,[29]carburetted hydrogen, and carbonic oxide.

Letx= volume of superolefiant,y= volume of carburetted hydrogen,z= volume of carbonic oxide,g= the oxygen combining,a= carbonic acid produced, andw= volume of mixed gas.

This is the mixture of gases obtained by a red heat from coal and oil, after being freed from carbonic acid, &c., by the usual means.

This mixture requires a very complicated formula, in consequence of the specific gravities of the gases entering into the calculus. The importance of the subject however may be an apology for the labour.

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