in 



ELASTICITY. 



ELASTICITY. 



774 



Coulomb's torsion-balance it consists of a needle of gum-lac attached 

 perpendicularly to the string, as B F in the above figure, and a small 

 weight at B to steady the string ; the law of the times of oscillation 

 above found is sufficient to give the force of torsion in all cases if we 

 know it in one. It is thus that Coulomb used his balance in finding 

 the law of electrical attractions and repulsions; the electrised ball 

 acted on, being attached to the end of the needle of gum-lac, was 

 subjected to the joint action of electrical and elastic forces. [ELEC- 

 TRICITY, COMMON.] 



The range of the elastic force of fluids, in consequence of their great 

 resistance to compression, is extremely limited, and therefore few ordi- 

 dinary phenomena of nature are dependent on this cause. The great 

 pressure at considerable depths in the ocean must produce a corre- 

 sponding increase of density in the lower strata, if it is not in a great 

 measure compensated by the increase of temperature. 



Water expands in volume by an increase of temperature, and contracts 

 by a decrease ; but it has this peculiar property, that at a temperature 

 expressed by 39| degrees of Fahrenheit's thermometer it attains a 

 maximum of density. The quantity of water which at 60 would 

 occupy 1 cubic foot, at 40 occupies only 0'9907 cubic foot ; while 

 at the temperatures both of 45 and 35 (its fluidity at the latter 

 temperature being preserved by the avoidance of all agitation) the 

 volume is 0-9991 cubic foot (Gilpin, ' Phil. Trans.,' 1792) : the increase 

 of volume at temperatures below 40 is ascribed to some tendency of 

 the water to crystallise while it is still fluid. 



The variations produced in the volume by variations of temperature, 

 as well as the fact that water is a conductor of sound, and consequently 

 that it possesses some elasticity, are to be considered as arguments that 

 water may be capable of being compressed by mechanical means ; but 

 the quantities of compression which have been obtained by experiments 

 made for the purpose are so small as to render it very difficult to 

 determine its precise value. 



In 1661 some members of the Academia del Cimento at Florence 

 made experiments of different kinds in order to ascertain whether or 

 not water was compressible ; and one of these consisted in filling a 

 hollow globe of silver with water at the poult of freezing : an effort 

 was then made, by blows with a hammer, to diminish the volume of 

 the globe by altering its form, when it was found that the water 

 escaped through the pores of the metal. The like experiment was 

 made by Muschenbroeck in 1731 with a globe of gold, which was 

 attended with a like result ; and till the year 1762 it was considered 

 that water was incapable of being reduced in volume by pressure. In 

 that year Mr. Canton introduced water at a certain temperature into a 

 glass tube, and having, by an application of heat, made the water fill 

 the tube so as to expel the air, he sealed the tube hermetically : then, 

 having reduced the temperature to its former value, he broke off the 

 upper extremity of the tube in order that the atmosphere might press 

 on the top of the column of liquid, when the height of the iatter was 

 found to be thereby diminished. The like experiment was tried with 

 / alcohol, oil, and mercury ; and these fluids were found to suffer different 

 diminutions of volume by the pressure. 



It has been imagined that the apparent diminution of the volume of 

 water was only the result of an expansion of the tube in consequence 

 of the elasticity of the atmosphere, when the latter was allowed to 

 enter it ; but if such expansion alone had produced the effect it would 

 have been the same, and would have caused equal depressions, in the 

 columns of different kinds of fluid, whereas the depression of the water 

 was about fifteen times as great as that of the mercury. There is little 

 doubt, therefore, that the observed diminutions of height were results 

 of the compressions of the fluids by the weight of the atmosphere. 



The experiments of Canton show that, under a weight equal to that 

 of an atmospherical column in its ordinary state (29J inches of mer- 

 cury), the compressions of the four following fluids, hi millionth-parts 

 of their volumes, and at a temperature equal to about 50, are 



Alcohol 66 



Raul-water 46 



Sea-water 40 



Mercury 3 



The elasticity of a perfect fluid is such that its parts resist change o: 

 volume only, and not change of figure. The compressibility of a liquid is 

 the compression produced by a unit of elastic pressure, and its modulus 

 or co-efficient of elatticity in the ratio of the pressure applied to the 

 liquid, to the accompanying compression, and is consequently the reci 

 procal of the compressibility, which latter is measured by an instrument 

 called a PIEZOMETER. The empirical formula for the compressibility o 

 water at any temperature between 32 and 128 Fahr. has been obtaiuec 

 by Mr. Kankine from M. Grassi's experiments ; namely : 



c= I 



40(T + 461)D 



When c compressibility per atmosphere required, T= temperature in 

 degrees* of Fahrenheit, and D = density of water at that temperatur 

 under one atmosphere, its maximum density under one atmospher 

 being taken at unity. 



The elasticity of every tolid is sensibly perfect when the strain on it 

 does not exceed a certain limit. This has been proved even for solids 



ke clay, for which there are limits, which, if a strain exceed, set, or 

 ermanent change of figure is produced. It has been shown by 

 tfr. Hodgkinson that these limits depend on the duration of the 

 train, being less for a long continued strain than for a brief one, so 

 liat the elasticity of volume in solids is generally much more nearly 

 erfect than that of figure. There exists one simple and uniform law 

 or the elastic forces of dry air and all the permanent gases. From the 

 xperiments of Boyle, Mariotte, and Dalton, it is established that the 

 lasticity, which is proportional to the pressure, is inversely as the 

 olume, and therefore directly as the density, when the temperature is 

 onstant. 



But an increase of temperature produces an increase of the elastic 

 orce of gases : or, which is the same, under a given pressure it expands 

 he gas into a greater volume. Between the temperatures of melting 

 ce and boiling water this increase of volume is proportional sensibly 

 x> the additional temperature, measured by a mercurial thermometer, 

 is was well established by the experiments of Gay-Lussac ; but by the 

 more recent experiments of MM. Dulong and Petit, it appears that at 

 much higher temperatures the degrees of the mercurial and gas ther- 

 mometers no longer correspond ; for the expansion of the mercury 

 might be expected to become irregular when it tends to gassify, and 

 .herefore to have greater expansions for each degree of heat than in its 

 iquid state. 



In such experiments it is essential that the gas should be perfectly 

 Iry ; for if not, the elastic force obtained will be that of dry air plus 

 :hat of the contained aqueous vapour. For most observations on the 

 atter we are indebted to the researches of Dalton, who observed that 

 when the inside of a barometer is moistened, the elastic force of the 

 rapour, occupying the space which is a vacuum in ordinary barometers, 

 :auses a depression in the column of mercury proportional to itself. 



When a space is saturated with aqueous vapour or steam, the elas- 

 .icity remains the same when the volume is diminished, the only effect 

 of compression being to convert the surplus portion into water. The 

 contrary holds generally in gases, as we have seen that their elasticity 

 is inversely as their volume ; but it is probable that with very high 

 >ressures, such as that employed by Mr. Faraday to liquefy carbonic 

 acid gas, there exists a limit for each, beyond which it is impossible to 

 render them more elastic by compression. 



Moreover, the ratio of the elastic force of dry gas at the temperature 

 of boiling water to that at the freezing point is by no means the same 

 as in aqueous vapour ; but at very high temperatures it seems pro- 

 vable that similar ratios would approximate. The following is a table 

 " the elastic forces of thu latter, corresponding to degrees of the centi- 

 jnule thermometer : 



Elastic Force, 

 in inches. 



0-2 



0-297 



0-435 



0-63 



0-91 



1-29 



1-82 



2-54 



3-5 



4-76 



6-45 



8-55 

 11-25 

 14-6 

 18-8 

 24 

 30 



Temperatures. 

 

 61 



Successive 

 llatlos. 



25 



50 



56J 



62i 



68j 



75 



100 



1-485 



1-465 



1-448 



1-444 



1-418 



1-411 



1-395 



1-378 



1-36 



1-355 



1-326 



1-316 



1-298 



1-288 



1-277 



1-25 



The third column is given incorrectly in Biot's ' Physique ; ' and it 

 follows from inspection that the elastic force of steam increases nearly 

 in a geometrical progression when the temperature is increased in 

 arithmetical; from which property steam has now become a great 

 mechanical agent. 



When vapours are mixed with each other at the same temperature 

 and in the same space, the elastic force of the compound is the sum of 

 the separate elasticities, provided this sum is not sufficiently great to 

 render any of the vapours liquid, and provided these vapours have no 

 chemical affinity. 



The atmosphere which surrounds the earth is endowed with an 

 elastic power ; and partaking, moreover, of the earth's diurnal rota- 

 tion, its particles should, by their elasticity and centrifugal force com- 

 bined, recede from the earth till the whole is dissipated in space. Such 

 is not the fact ; and hence it is inferred, either that at a certain eleva- 

 tion above the surface of the earth, the elasticity of the atmosphere is 

 totally destroyed by the absence of caloric ; or that beyond the stratum 

 in which the centrifugal force of the particles is equal to their gravi- 

 tation, there may exist, in a state of rest, an etherial fluid occupying 

 the whole extent of space, and preventing the atmosphere from being 

 further expanded by its own elasticity. 



Now, by Mechanics, it may be found, that the distance from the 

 surface of the earth to the stratum of the atmosphere iu which the 

 centrifugal force of the particles is equal to their gravity 'is about five 



