278 Mr, Exleys Application of 



If the atomic weights of phosphorus and arsenic be 16 

 and 38, their vapours are in single groups of four atoms 

 each, probably in tetrahedrons, rendering them isomorphous. 



It is well known that experiment bears out these mathe- 

 matical conclusions. 



Prop, 4. Things being as in the preceding propositions, 

 and the tenacious atoms in a gaseous state compressed in 

 an inner concentric spherical vessel, which contains tena- 

 cious atoms, but admits a perfectly free communication to 

 ethereal atoms ; then the pressure on the exterior vessel 

 being given, the density of the gas will vary as the com- 

 pressing force on the inner vessel. 



Let the inner vessel be V W P, having the same centre s, 

 and let the tenacious atoms in it be compressed, as by a 

 piston, at P, such, that it shall continue to retain the 

 gaseous form. 



Then the internal pressure of the tenacious atoms on a 

 given surface, and, consequently, the compressing force on 

 the same, as on the piston P, will be as the number of 

 pressing atoms, and as the force of each ; but the number 

 of atoms on the given surface is inversely as the square of 

 their distance (geom.), and the force of each is inversely as 

 the distance (prop. 2) ; therefore, the compressing force is 

 inversely as the cube of the distance, but the density is 

 in that same ratio : therefore, the compressing force varies 

 as the density. 



Cor. The volume varies inversely as the pressure, be- 

 cause it varies inversely as the density. 



Def. The pressure at T answers to the effect of tempera- 

 ture, and the pressure at P to that of the usual pressure 

 on gases ; it arises from the re-action of the included tena- 

 cious atoms ; hence, the first at T may be called the pres- 

 sure of temperature, and the other at P, the pressure or 

 re-action ; or, for conciseness, simply the pressure and the 

 temperature. 



Prop. 5. The pressure or re-action at P, (fig. 1.) being 

 given ; the volume will vary, as the pressure at T, or the 

 temperature. 



For the volume being given, the temperature or pressure 

 at T, will vary as the resulting force determined in prop. 2, 

 because that is the sole cause which brings the forces into 



