Mathematics to Chemistry. 211 



of the spheres of repulsion as a surface of repulsion of 

 greater magnitude; hence, it will have a single distinct 

 atniospherule, and will act as a single atom, and occupy 

 (by this and the preceding proposition) the same volume ; 

 hence, the cor. is manifest. 



Cor. 2. When two tenacious atoms are connected chemi- 

 cally, yet so as not to form a single condensed group, they 

 will occupy, in a gaseous body, the same volume as they 

 did before the connexion took place. 



For, according to this and the last propositions, they 

 are kept apart by the same force, as that by which they 

 were before separated. 



The connecting link will be considered afterward : such 

 may be called cohesive combinations. 



Cor. 3. A double group will occupy in a gaseous body 

 exactly twice the volume of a single tenacious atom, or of 

 a single group. 



For the atom or single group connecting two others, as in 

 def. 2, displaces the ethereal atoms, and the parts of the 

 atmospherules between them ; and, because of the given 

 pressure, the same equilibrium will be maintained ; so that 

 the connecting atom will perform the effects of the dis- 

 placed ethereal matter, and, i^erefore, will not alter the 

 distance between the connected atoms; the same argu- 

 ments apply to single groups as to single atoms. 



Cor. 4. When gases are mixed, and no chemical unio», 

 or only cohesive combination occurs, the volume is not 

 changed. 



This is manifest from the proposition, since an alteration 

 in the absolute force or sphere of repulsion does not alter 

 the distance between the centres of the atoms, so that each 

 still occupies the same volume. 



Remark. — If an objection be made to this proposition 

 and its cors. by an appeal to fact, that the specific gravity 

 of sulphur vapour is 96, that of hydrogen being 1, while 

 the atomic weight of sulphur is only 32 ; it is easily ob- 

 viated ; for there will be perfect agreement, if the vapour 

 of sulphur consists of single groups of two atoms each ; 

 and this is likely, since sulphur has two fusing points, and 

 the liquid is less limpid after the second than after the first, 

 besides other peculiarities. 



