Mathematics to Chemistry. 279 



operation ; but the pressure at P also varies as that resultant, 

 because these forces sustain each other in equilibrium ; 

 therefore, the pressure at P varies as that at T, when the 

 volume is given ; but the pressure at P varies inversely as 

 the volume, when that at T is given (prop. 4. cor.) ; there- 

 fore, the pressure at P varies as that at T directly, and the 

 volume inversely: therefore, when the pressure at P is 

 given, the temperature varies as the volume. 



Cor. If any temperature T, and its corresponding volume 

 V, be assumed, and v be the increment of one volume, for 

 one degree of temperature, taken at T ; also t a given in- 

 crement of temperature taken from the same term T ; then, 

 T : T -f T ?; ^ :: V : V + V v ^ =V (1 + v 0=the volume 

 at the temperature T + ^ ; which is known, when V, v, 

 and t are given. 



This is a well known theorem, agreeing with experiment, 



Example, ifT = 32° Fahr. then ^ = 4L; let V =20, i = 



30; then Y {\ + v t)= 20 x ~= 21-25 = V, the new 



4oU , 

 / . V 

 volume: had V been given we should have had V=-; -— 



^ 1+ tv 



= >,-7r = 20, in this case, the volume at 32° Fahr. 



Prop. 6. If ethereal and electric atoms be compressed in 

 a vessel, fig. 1. the pressure and temperature being given, 

 and also the absolute force of a tenacious atom in it, while 

 its sphere of repulsion is supposed to vary ; then there will 

 be a certain magnitude in its sphere of repulsion, at which 

 it will collect and retain a maximum quantity of electric 

 atoms on its surface of repulsion. 



For, 1st, let the sphere of repulsion be extremely small, 

 then the attraction at the surface is very great, (1st. prin.) 

 therefore, the density of the ethereal matter at the surface 

 is very great, (prop. 1.), and, therefore, the electric atoms 

 at the surface obtain an increased atmospherule of ethereal 

 matter (prop. 1, cor.); hence, the relative attraction of the 

 tenacious and electric atoms is diminished, by their united 

 actions on the adjacent ethereal matter ; and this conjoined 

 with the extremely small surface of repulsion will operate 

 against the firm attachment of the electric atoms, which 



