1825.] Mathemdticdi Principles of Chemical Philosophi/, 379: 



A D, A E, describe two circles : the space between the circles 



will be an annulus, whose breadth is t> E. Let the repulsive 



force at any point D in the annulus be D P". The force of the 



annulus unresolved will be D P" x area of the annulus. 



Through any other point B in P p, pass a plane similar and 



similarly situated to the former; when the distance Pp becomes 



2 P B, the plane E B F will divide the calorific atmospheres, 



because the angle D P A, and therefore 2 D P A is constant; 



thfe^eford BF : AD :: PB : PA. With radius BF and centre 



B describe a circle, also with radius B G. The force of this 



aftniilus is as FP" x area of the annulus. Since the forces are 



similarly resolved, the resolution may be neglected ;iq v, u|.* n 



and force at F : force at D :: P D" : P F'' '' '^M Juc- 



atid anriiilus F_G i anftulus D E :: P F^ : P D^ ;^herefor6i ^^^ 



force of annulus Fa,: that of annulus D ETTP B**-V: i^f^^f iS' 

 1 < 1 toi^ H?^ ^> i B Salens § (ii : acAffi^j 



P ir«-a • PDn-2 • ' •'''■ o'/' ,bnr/oqffloy j. 



And since the two planes maybe divided into the samef nuffi-'^ 

 ber of similar and similarly situated annuH, of which the forces 

 have all the same ratio to each other, the entire forces have the 

 same ratio. But at the same temperature, the whole force 

 between two adjacent particles of a gas is very nearly pro- 

 portional to the distance between them inversely; therefore 



py.dqlg^air jf^l. '' .:• j^<^-li^ ; thencew= 3 ; or the elastic for^vfe 



of the calorific atmosphere is very nearly proportional to the 

 cube of the distance inversely ; which is the ratio nearly of the 

 difference between the attractive force and the repulsive power 

 of caloric. The rate of expansion of gases by heat has been 

 obscurely expressed by most chemists : they lay down as the 

 datum, that the change of temperature of one degree produces a 

 change of the ^^th part of the volume of a gas ; and yet th6 

 differences of temperature being equal, the volumes given in 

 their tables are in arithmetical progression. Let V be the volume 

 of a gas, at any temperature A ; let the increments of tempera- 

 ture be a, 2 «, 3 a, &c. Then at temperature A, volume = V 5 

 when the temperature becomes A + a, let the volume b^ 



increased by - ; then at temperature A + a, the voluii^^ is' 

 ^ V ; at temperature A -f 2 a, it is ^^ ^ V ; ^ AJ^Jf|3|^|r 



is ]^^'V; M^ A + ma, it is ^^T"^' '"^^''^ If '^^^ 

 metric series, in which ^^ is the common ratio. By bifelri^^bf 



this formula may be found the elastic force of a confined portio,^ 

 of gas at different temperatures. Let the temperature^vaA4i 

 volumes be the same as before : when the temperature t 1 un 



