PNEUMATICS. 



PNEUMATICS. 



wqumtly, the compressing force, will vry w d- f . If D represent the 

 Oetuity of the fluid, d will ruy a* , or O~* ; therefore, nuWtituting 



o~t for d in the bit expreuion, the whole repulsive force varie* u 

 D -t(>-. But, agreeably to the Uw above mentioned, the compre**- 

 ing fore* varie* u o ; therefore the exponent i(n - 2) muit be equal 

 to unity, and hence = 1. It follow* therefore that the repulsive force 

 between MT two adjacent partielea rarie* aa d- 1 , or inversely a* the 

 dirinHMt of thuee particlM from each other. Sir I. Newton however 

 observe* (lib. ii., prop. 23, *choL) that this law hold* good only wh.>n 

 the repulsive power of any particle doe* not extend much beyond 

 those which are nearest to it. 



If F and P* represent the pressures exereUed upon a square unit of 

 the lupernce* bounding an elastic fluid, and the volume* of the fluid 

 under thoee pressures v and v' ; alao if the densities be D and D' 

 respectively, we ahall have 



t : r" : : v* : v, or P.v = p'.v', 

 and t : V : : D : D', or P.o'= P'.D ; 



whence, by equality of ratio*, 



v : V : : D' : D, or D.T = D'.V'. 



Conaiderable difficulty is found in determining the specific gravities 

 of gases with precision, and different experimenter* have obtained 

 reeult* which do not exactly agree. The value generally adopted when 

 the height of the column of mercury in the barometer is 30 inches, 

 and the temperature is 60* Kahr., IB 31*074 grains as the weight of 

 100 cubic inches of dry air. Other physicists have found it as low as 

 31-0117 and 30-935 grains ; but the former is probably most correct, 

 a* it agree* with the density of air as deduced from that of a mixture 

 of oxygen and nitrogen in the proper proportions to form air. Air U 

 therefore ,{, of the density of water. The experiments of Dalton have 

 led to the conclusion that the weight of a cubic foot of steam when at 

 the temperature of 212 Kahr., the height of the barometrical column 

 being 30 inches, is 253 grains troy ; by others it has been found to be 

 254'7 grains ; and it appears that within considerable limits the expan- 

 sion of the volume of any gas is proportional to the increments of 

 temperature, measured by the degrees of the thermometer. The 

 absolute value of the expansion is not precisely known ; that of air is 

 stated to be equal to about ,J;, and that of steam about fa of the 

 volume, for one degree of Fahrenheit's thermometer. [ AIR.] 



The following table, from the observations of MM. Dulong and 

 Petit, exhibits the volumes assumed by a given quantity of air at 

 different temperatures between the boiling-point and near the freezing- 

 point of mercury : 



Temperatures. 



SS" 



H 



ill 



Ml 



M 



481 



171 



(80 



Volume*. 



0-8650 



0000 



S750 



5576 



7389 



9189 



0976 



2-3115 



It has been mentioned that the rate of expansion of all gaaee U equal 

 and uniform at all degree* of temperature and pressure, and that the 

 amount of the expansion i* jfo of the bulk occupied at 82 Fahr., for 

 even decree of temperature, so that a quantity of any gas, which, at 

 82 Fahr., measured 491 part*, will, at 38 Fahr., measure 492 parte, 

 and so on. If, then, it were required to find the volume which 9 -2 

 cubic inches of any gas, measured at 70 Fahr., would have, when 

 reduced to 60 : since 70 - 82 = 38, 491 parts of the gas at 32, 

 would become 529 part* at 70. Again, 60 - 82 = 28, so that the gas 

 at 60 would, linularly, occupy 519 part*. Hence, we have the 

 pn.iortion, 629 : 619 : : 8"2 : *(= 9-026 cubic inches). 



From experiment* it ha* been concluded that, while (team is in 

 contact with the water from which it i* formed, it* expansive force 

 increaM in a geometrical progression, *o long a* its temperature is at 

 the "" time increased in an arithmetical progression, but the relation 

 btw*n the clastic force of this gas and its temperature, in that state, 

 i* a* yet far from being certainly known. Under the word ELASTICITY 

 i* given a table of the elastic force* of steam at temperature* between 

 111* freezing and boiling state* of water ; and the following table, 

 extracted from those which have been formed from the results of the 

 experiment* of Mr. Dalton, Dr. Ure, and the French physicists, may 

 also be useful as a mean* of affording a near estimate of the force at 

 high temperature*. The finrt. column contains the temperature of 

 th* water and steam in degree* of Fahrenheit's thermometer ; the second 

 is the measure of the expansive force by the number of inches in the 

 Might of the column of mercury which on a given superficies would 

 counterbalance it ; and the third, the like measure expressed by mul- 

 tiples of the weight of the atmospheric column when the air is in its 

 ordinary state : 



Tcnpmtwt. 

 Ill* 

 1*0 



140 



Sl-7 



Atmotphm*. 

 I 

 l-ll 



1-71 



Tfenpcnlurr. 

 100 

 ISO 

 300 

 111 

 IM 

 Ml 

 lit 

 401 

 ill 



Mi 



Inches EnglUh. 



71-3 

 101 

 139-7 

 IM1 

 111- 

 196-78 

 43S- 

 541-5 

 613-1 

 719-8 



Alniosphen. 



2-41 

 3.06 

 4-C6 

 5-51 



7-7 



m 



14-53 

 18-05 

 20-44 

 . -W4 



When steam is not in 'contact with the water from whence it is 

 formed, aud when it is subject to a constant pressure under which it 

 may expand in every direction (as when it is formed in the atmosphere), 

 an increase of temperature will not produce an increase of density, but 

 merely of its elastic power. Again, if steam be in contact with its 

 water, and the temperature remain constant, iU density, whether in 

 air r in eacuo, will remain constant, and its volume only will vary. 

 But if, in this case, its volume be kept constant, and the temperature 

 be increased, its density will rapidly increase, as before, until the 

 whole of the liquid U evaporated, and then the expansion of the steam 

 will follow the usual law* of permanent gases. The only difference in 

 these experiments between using a vessel containing air, and one 

 having a vacuum inside is, that in the former case the results do not 

 it tuft appear, until time has been all. '>wcd for diffusion. 



It has been found that the volume of gas disengaged from gun- 

 powder u equal to about 300 times the volume of the powder iUelf ; 

 and that its expansive force, when increased by the heat which is 

 generated at the time of the explosion, is about 1500 times as great aa 

 the pressure of the atmosphere in its ordinary state. It must con- 

 sequently exert a pressure againsta cannon-ball, and tbe interior of the 

 chamber of the gun, equal to about 15,000 pounds r,j...n every square 

 inch of the surface upon which it acts. 



The fact that the density of air varies with the compressing force is 

 sufficient to show that the atmosphere about the earth cannot be of 

 uniform density ; and it is also evident that the density must diminish 

 from the surface of the earth upwards, according to some law depend- 

 ing on the height of any point above the earth, or rather upm! the 

 weight of the mass of air above that point. It might, at nrst, be 

 supposed that the atmosphere would extend upwards to a height 

 at which the centrifugal force of the particles of air (by the diurnal 

 revolution) is equal to the force of gravitation; and it is shown 

 by Poisson (' Traite' de Me'canique,' torn, ii., 619) that, conformably 

 to this principle, the height of the atmosphere at the equator should 

 be equal to about five times the semi-diameter of the earth. But it 

 is probable that, long before this height is attained, the air loses its 

 elasticity by the cold in the upper regions, or that its expansion is 

 destroyed by the pressure of the ethereal fluid which is diffused 

 through infinite apace. By the duration of twilight it is inferred that 

 the atmosphere is capable of reflecting the sun's rays at the height of 

 about 45 miles above the earth, and it is probable that some light 

 is reflected from a still more elevated region. 



In order to determine the law by which the density of the atmo- 

 sphere diminishes at increasing distances from the earth's surface, on 

 the supposition that the action of gravity and the temperature of the 

 air are constant, let T be the centre of the earth, aud let A z be the 



height of a very slender column of air extending vertically upwards to 

 the top of the atmosphere. Also let the atmosphere be divide< i 

 an infinite number of concentric strata of equal thicknesses, wlii> Ii 

 latter are represented by A , B c, c D, Ac. ; and, as these thicknesses are 

 mall, let the density of the air in each stratum be supposed uniform 

 and equal to that which is due to the weight of all the strata above it. 



