380 Mathematical Principles of Chemical "Philosophy^ [TTov. 

 is A, let the volume = V ; 

 at A + i/4«iiti6^itaA±i V; 



at^X^¥i>^.?™Wfi^fV; 



atA + ;«a'''rT,?-5:!±!J~V 



Sitifce tlie elastic force is balanced ''by xlie pressure V 11^® 

 atmosphere, which is supposed to be constant, the elasticity of 

 the expanded gas is constant. Whilst the temperatures ^i^Pi., 



A -h f^rr^xik mjt^'^^^^^osQ the volumes r^pff »\\'Tf^{fi V, 



&c. be qcmjipressed till they occupy the same spape v ; tlie elas- 

 tic force f^ nearly proportional to the density, i. e. inversely as 

 the volume ; therefore, at A + a, the elastic force before com- 



pression : that 2ihebity*k -■' ■ ^ ^ ■> '> i-fitiifi^iris^i-jecij^s "W i\^ 1 at 



ijijiaangfim lo ^snil^olfi ?3tb 11 rr// loRlno nr ^h\oR oinodisO .1 

 4i ,*d^lcffe . 4^WP^X I f >^^ftw^ • .CompregsioBL ^^ tJ^jsg^RfecJft,^^; 



Therefor€> if a confined portiom off ti'^»'bei heated, the tempera- 

 ture is pfo^rtional to the logarithm of Uie elastic force ; or if it 

 be under a constant pressure, the temperature is the lo<j;arithm 

 of the volume. These conclusions depend upon the hypothesis 

 that the elastic force of a gas' is poportional to its density, 

 which is not quite correct ; but when the change of temperature 

 is not very great, it is an appt^iitimation sufficiently €xaotfei--^ll 

 practical purposes: ^■;Qfi^"^'^iJ^ n^iHOif ;lu;^.. 1o yliinfij 



The ^patios of the calonlfic'atmospheres of diflPerfeirf%o^^l=flaay 

 be found as follows : Take D proportional to the distance 

 between two adjacent particles in a solid, i. e. to the atomic 

 diamferkerfiff^eat the substance until it fuses : let this das tiftMl^be 

 lfe»<w»^ilhairt"itf/until the distance is increased by any kbdwn 

 sdT .gBfiiJnfjfm ^i'J .. i i i i --i; 



9m?l'fXi;8.Te;#ft.<iensitie8 are^, ^^rTn)^, (dTJ^3- ■^^''^^^^ 



%Sfi;,C^M^9t^W'^« proportional to ^, -^-^, ^-^^^,. ^.is 



66te^jf•^feyt<ftdV and it is equal to the force of repulsion. In 

 ail9itli(^ stiti^tance^ find the corresponding quantities rf, d •^7/1, 



^\mm:p^O;d\, and 92, oflib.l,of Newi6^A^4'Prfnciifia',ilbe 

 moil in9i9Bib a^onfiijsdqqfl ^aUididx^ fcl^javio Jg^rli^/^feTrrrT; 



