represented by AF. The pressure at F is now the pressure of the atmosphere increased by the pressure measured by the height PQ of mercury. Suppose for instance that PQ is 18 inches; then the pressure at F is measured by 30+18 inches, that is by 48 inches, of mercury. It is found by trial that the volume represented by AF bears the same proportion to the volume represented by AD as 30 bears to 48; and a similar result holds whatever may be the relative positions of P, Q, and M. Thus in the language of Arithmetic the volume of the air varies inversely as the pressure exerted on it. For example, if the pressure were increased to 60 inches of mercury the volume would be reduced to half of the original volume; and if the pressure were increased to 90 inches of mercury the volume would be reduced to one third of the original volume; and so on.

495. The preceding experiments and results are of great importance in the subject, and a few remarks should be made on some incidental points. A condition must be carefully regarded to which we have not yet adverted; namely, the temperature must be the same throughout the experiment. For if the temperature of the air be changed the volume of the air will be changed on that account, while the pressure remains the same. The sudden compression of the air, when mercury is poured in, will raise the temperature of the air slightly, so that time must be allowed for the air in the shorter branch to cool down to its original temperature. We have used 18 inches for the sake of an example to measure the additional pressure, but the experiment may be varied by the use of more or less mercury, so as to introduce other numbers in the place of 18. Also we have taken 30 inches to measure the pressure of the atmosphere at the time and place of the experiment; but the real number may be somewhat greater or less than this, and would have to be accurately determined on the occasion. The volumes represented by AD and AF must be estimated with accuracy. If we are sure that the tube is of the same bore throughout we may take the volumes to be in the proportion of the lengths of the portions of the tube; but if this is not the case, we may determine the volumes accurately by weighing the quantities of mercury which they will hold.

496. In the experiment we supposed the air to be first under the ordinary pressure of the atmosphere, and afterwards under a greater pressure; in order to establish the law universally we ought to examine also the case in which the air is put under a pressure less than that of the atmosphere.

E

B

F

Take a glass tube and bend it so that the two branches shall be parallel. Let A, the end of the longer arm, be closed, and B, the end of the shorter arm, be open. Pour mercury into the tube, and by withdrawing air or adding mercury make the mercury in the two branches stand at the same level C and D; let this. level meet the vertical straight line MPQ at M. Then in AD we have a quantity of air sustaining the pressure of the atmosphere; we will suppose this to be measured by 30 inches of mercury. Withdraw some of the mercury from the tube, and let the mercury sink to the level E in the shorter branch, and to the level F in the longer branch. Let the level of E meet the vertical straight line MPQ at Q, and let the level of F meet the same straight line at P. Thus the air which formerly occupied the space represented by AD is now expanded into the space represented by AF. The pressure at F is now the pressure of the atmosphere diminished by a pressure measured by the height PQ of mercury. Suppose, for instance, that PQ is 9 inches; then the pressure at Fis measured by 30-9 inches, that is by 21 inches, of mercury. It is found that the volume represented by AF bears the same proportion to the volume represented by AD as 30 bears to 21.

497. The result which is established in Arts. 494...496 may be put in other ways which are equivalent to the statement that the volume varies inversely as the pressure. Thus since the density of a given body varies inversely as

its volume we may state the law thus: the density of air at a given temperature varies directly as the pressure exerted on it. Or again, the pressure to which air is subjected is resisted by the air, and in the state of equilibrium the resistance is equal to the pressure; now this resistance is ascribed to the elasticity of the air, and thus the law is sometimes expressed thus: the volume of the air is inversely proportional to its elasticity. The law itself is sometimes called Boyle's Law, and sometimes Mariotte's Law, from the names of two philosophers by whom it was discovered. The law was long held to be absolutely true for all gaseous bodies, as experiments had been made in which the pressure was carried on to an amount equal to twenty-seven times that of the atmosphere, and the results seemed to agree with the law. In more recent times however, in consequence of closer scrutiny, it has been found that the law is not absolutely true; for the gaseous bodies which are not liquefiable, such as air, hydrogen, and nitrogen, the deviations from the law are almost insensible; but in the case of liquefiable gases, as carbonic acid, the deviations may be considerable in all cases gases are rather more compressible than Boyle's law would indicate, but hydrogen is a remarkable exception, being less compressible.

498. We have alluded in Art. 495 to the fact that when the pressure remains unchanged the volume of air or a gas changes when the temperature changes. The law on which this depends may be stated with sufficient accuracy for our purpose thus: add 450 to the number of degrees in the temperature as expressed by Fahrenheit's thermometer, the volume is proportional to the sum. Thus, for an example, suppose that the pressure is kept unchanged and that the temperature has been increased from 50 degrees to 100 degrees; 450+50=500, and 450+100=550. Then the volume at the higher temperature bears the same proportion to the volume at the lower temperature as 550 bears to 500, that is, as 11 bears to 10.

XLV. THE BAROMETER.

499. The Barometer is an instrument for measuring the pressure of the atmosphere; we have already explained the principle of the instrument in Art. 489, and we have now to add a few practical remarks. The principle of the Barometer is that a column of mercury has a vacuum above it, and is exposed to the pressure of the atmosphere at its base. In the construction of the instrument it is necessary to be careful in securing as far as possible this vacuum above. Now it is found that mercury in its ordinary state frequently contains air or other elastic fluid combined with it; and moreover particles of air and moisture are sometimes adhering to the glass tube when the mercury is poured into it. Then when the pressure of the atmosphere is removed from the top of the column of mercury the moisture becomes vapour, and that and the air rise to the top of the tube, and occupy the space which ought to be a vacuum. In consequence of this there is a pressure at the top of the mercury which tends to force it down, and so the height of the column is less than it ought to be. To guard against this defect it is found advantageous to heat the tube before the mercury is put in; thus the particles of air become expanded and their elastic force is increased and they escape also the moisture is converted into vapour and escapes. The mercury is boiled, and this process expels from it any air or other elastic fluid which may have been combined with it. After all these precautions have been taken the portion of the glass tube above the mercury will be practically a vacuum; it is indeed highly probable that vapour may arise from the mercury itself and occupy this space, but it does not appear that this will exert any sensible pressure.

500. In the instrument, as we have described it in Art. 489, it is necessary to observe the level of the mercury at two points, namely, the place where it is exposed to the atmosphere, and the top of the column; and from the two observations we deduce the height of the column.

T. P.

14

Various methods however have been devised in order to obviate the necessity of the two observations.

501. If the area of a section of the vessel in which the lower end of the tube is immersed is very large compared with the area of a section of the tube, it is obvious that the level of the mercury in the vessel will remain almost unchanged when the column in the tube rises or falls a little. Hence we may consider this level as fixed, and measure from it upwards the height of the column. A small brass scale divided into inches and tenths of an inch may be fixed close to the glass, so that by looking at the mark nearest to the top of the mercury we may ascertain the height of the column; the brass scale need not extend beyond the heights between 28 and 31 inches, which is practically inclusive of the range under ordinary circumstances.

502. Another method of avoiding the necessity for two observations is to have the numbers recorded on the brass scale really exact. That is, the maker of the instrument must ascertain for any position of the upper end of the column what is the true distance between the level of that end and the level in the vessel, and must record it on the scale. We may conceive that this is done by actual examination of every case at which a mark is to be recorded; but practically the maker can assist himself by an easy principle. If the sides of the vessel are vertical, and the bore of the tube uniform, there will be a precise relation of a simple character between the changes of level in the vessel and the tube. Suppose, for instance, that the area of a section of the vessel, excluding the part occupied by the tube, is 100 times the area of a section of the bore of the tube; then when the level in the tube rises 1 inch, the level in the vessel will sink

1

100

of an inch,

and therefore the height of the column will be increased by 11 inches. Therefore a length which is actually 1 inch on the brass scale must be marked as 10; and so on in the same proportion. Hence by reading off the mark opposite to the top of the mercury we learn the accurate height of the column which measures the pressure of the atmosphere.