such part of the volume at any other temperature as is indicated by adding the number of degrees above 32° to 480.

879. The rule for correction to be applied to an observed volume of gas is, therefore, to add to 480 the number of degrees above 32°; to divide the observed volume by this sum, which gives the expansion or contraction for each degree at the observed temperature; to multiply this by the number of degrees between the observed temperature and the temperature to which the gas is to be corrected, which will of course indicate the whole expansion or contraction; and then to subtract this, if the observed be above the corrected temperature, or to add it, if the former be below the latter: thus allowing for the contraction or expansion which would actually take place, if the temperature of the gas were really to be brought to the point to which by calcu lation it may thus be corrected.

880. As an illustration, suppose 100 cubic inches of gas at 70° Fahrenheit are to be corrected to mean temperature, or 60°. The difference between 70°, the observed temperature, and 32°, is 38, which added to 40-518; the 100 inches divided by 518, gives 0.19305 of a cubic inch as the whole expansion for each degree; and this multiplied by 10, the difference between 70° and 60°, gives 1.9305 cubic inches as the whole expansion; which, subtracted from 100 cubic inches, leaves 98.0695 cubic inches as the volume which would be occupied by the gas at 60° Fahrenheit.

881. Or, again, suppose the 100 cubic inches were observed at 50° instead of 70°, then the expansion per degree is obtained by adding 18, or the difference of 32o and 50° to 480 this equals 499, and dividing 100 cubic inches by this, we obtain 0.2008032 of a cubic inch as the expansion per degree at 50°; and this multiplied by 10, the difference between 50° and 60°=2.008032 cubic inches, which would be the whole expansion for the 10° from 50° to 60°. Being added to 100, it makes 102.008032 cubic inches as the corrected volume of gas. The decimals have in these instances been calculated much farther than will be necessary, except in particular experiments, merely with a view of shewing the

difference in the amount of the corrections required for an equal number of degrees at different temperatures.

Correction for Pressure.

882. Boyle and Hooke were perhaps the first to observe that the volumes of gases varied inversely in proportion to the pressure exerted upon them, although the law, having been first distinctly announced and enlarged upon by Marriotte, has received his name. Its truth at high pressure, although sometimes doubted, has been confirmed by the results of Oersted,* and still more recently by those of MM. Dulong and Arago,† and no one has any doubt of its being accurately true at such pressures as occur naturally, and are indicated by the barometer, and also at the greater variations dependant upon the difference of level of the fluid within and without a jar standing over the mercurial or water trough (767, 782).

883. A pressure of 30 inches of mercury, as observed by an accurate barometer, has been assumed as the mean height or barometric pressure, and volumes of gas observed at any other pressure (780), frequently require to be corrected to what they would be at this point. For this purpose it is only necessary to compare the observed height with the mean height, or 30 inches, and increase or diminish the observed volume inversely in the same proportion. Thus, as the mean height of the barometer is to the observed height, so is the observed volume to the volume required. As an instance, suppose that 100 cubic inches of gas have been observed when the barometer stood at 30.7 inches: then, as 30 inches, or mean height, is to 30.7 inches, or observed height, so is 100, or the observed volume, to a fourth proportional obtained by multiplying the second and third terms together and dividing by the first: thus, 30.7 × 100= 3070, which divided by 30=102.333 cubic inches; this would be the volume of the gas at 30 inches of barometric pressure. Or, consider the gas as observed at 28.9 inches of the barometer: then 30 inches, or mean height, is to 28.9 inches, or observed height, as 100 is to 96.333 cubic inches, + Bib. Universelle, xlii. p. 338.

Phil. Mag., lxviii. 102.

that being the result of 28.9 multiplied by 100 and divided by 30, according to the rule. Again, suppose a quantity of gas amounting to 20 cubic inches standing over mercury in a jar, the level of the metal within being 3 inches above that without, and the barometer at 29.4 inches (800). Then the column of 3 inches of mercury within the jar, counterbalancing 3 inches of the barometric pressure, instead of being 29.4, the latter is effectively only 26.4, and the correction will be as 20 inches is to 26.4 inches, so is the 20 cubic inches observed to 17.6 cubic inches, the volume which the gas would really occupy if the mercury were level within and without the jar, and the barometer were at 20 inches.

884. It is constantly necessary to make corrections both for temperature and pressure in the same volume of gas. It matters not which correction is made first, the result being the same in either mode. Thus for instance, 100 cubic inches observed at the temperature of 40° Fahr. the barometer being at 28 inches, if first corrected for pressure, become 93.33 cubical inches: and then for temperature become 97.158469 which is the true volume. Or, if first corrected for temperature, it becomes 104.09826, and then for pressure, it becomes as before 97.158469 cubic inches.

which

885. Dr. M. Hall has constructed an instrument he has called an Aërometer, intended to give at once a correction for changes in the temperature of the atmosphere; in the barometrical pressure; in the external and internal

heights of the fluid in the pneumatic trough; and when this trough contains water, for the elevation and precipitation of aqueous vapour. It consists of a bulb of glass 4 cubic inches in capacity, attached to a long tube whose capacity is 1 cubic inch. This tube is inserted into another tube of nearly equal length, and supported on a stand, as in the figure. The first tube may be sustained at any height within the second, by means of a spring at the upper part. Five cubic inches of air

* Quarterly Journal of Science, v. 52.

at mean temperature and pressure are introduced into the bulb and tube of the latter, of which it will occupy one-half; the other half, and part of the tube into which it is inserted, are to be occupied by the fluid of the pneumatic trough, either water or mercury. The point of the tube at which the air and fluid meet is to be marked 5, and the upper and lower half divided into 5 equal parts, indicating tenths of a cubic inch each. The external tube is to be marked by a scale of inches.

886. When the volume of a gas confined over the pneumatic trough in jars is to be corrected by the indications of this instrument, the difference between the levels of the fluid in the jar and in the trough is to be measured, and the same difference occasioned in the external and internal heights of the fluid in the aerometer. The gas in the instrument, and that in the jar, are then precisely in the same condition, and by observing the volume of the former, the latter may be corrected. Thus, if it be 5.2 cubic inches in the aerometer, and 74 cubic inches in the jar, then as 5.2 is to 5, the volume in the instrument at mean temperature and pressure, so is 74 to 71.15, the corrected volume of gas in the jar.

§8. Weighing of Gases or Air.

887. The process of weighing a gas, which of all others is simplest in principle, is to exhaust a light globe or flask, fitted with a cap and stop-cock for the purpose, then exactly to counterpoise it (64, 65), to attach it to a graduated transfer jar containing the gas to be weighed (753), and after allowing as much as will enter to pass in, permitting the temperature to become that of the atmosphere (870), and equalizing the pressure within and without the jar, to estimate the volume that has entered, by the graduation. Then on weighing the vessel, it may be ascertained how much it has increased in weight, and the increase will of course be the weight of the observed volume of gas.

888. Globes or flasks of the kind required are sold by the instrument-maker. They should be perfectly clean and dry when used, nothing being allowed to adhere to the outside that may alter their weight during the process. The tem

perature should be noted, and its equality carefully preserved during the experiment; for this reason, the globe should be handled with all the delicacy possible (773). The pressure of the barometer is likewise to be noted. If the gas be in a jar standing over water, it must be let in carefully (871), the little piece of paper before recommended being introduced into the connecter; and it is advisable to let a small quantity of gas pass out there before the parts are closely screwed together, that the common air in them may be removed.

889. Gas when standing over water becomes saturated with aqueous vapour, the quantity being proportional to the temperature. In these cases, a part of the volume observed, and also a part of the weight, is due to the vapour, which therefore must be ascertained before the true weight of the gas under examination can be determined. The following table exhibits the proportion by volume of aqueous vapour existing in any gas standing over or in contact with water at the corresponding temperatures, and at mean barometric pressure of thirty inches.

890. By reference to this table, which is founded upon the experiments of Mr. Dalton and Dr. Ure, and includes any temperature at which gases are likely to be weighed, the proportions in bulk of vapour present, and consequently of the dry gas, may easily be ascertained. For this purpose the observed temperature of the gas should be looked for, and opposite to it will be found the proportion in bulk of aqueous vapour at a pressure of 30 inches. The volume to which this amounts should be ascertained and corrected to mean temperature. Then the whole volume is to be corrected to mean temperature and pressure (876), and the