434 W.<A. Norton—Force of Effective Molecular Action. 
have already seen that when k=4'931, and «=1157, the effec- 
tive repulsion is 00000693»; and that this answers to one 
atmosphere of external pressure. en k=0 and x=116r, the 
effective repulsion is 0-00007561p ; and the distance « at which 
the repulsion becomes 0°0000693p is 1207. But the distances 
between the centers of the molecules must be much greater 
than these values of z It will soon appear that the law of 
Mariotte requires that the radius of the effective gaseous mole- 
cule, under a pressure of one atmosphere, be not less than 31r. 
This gives for the distance between the centers of the mole- 
cules, under this pressure, 177r when £=4°931 ; and 1827 when 
k=0. Now =) =1°086. This is the highest ratio of vol- 
umes of two simple gases, under atmospheric pressure, that 
would be theoretically possible; unless the effective size of the 
molecules be supposed to diminish as & increases. But this is 
only an ideal extreme result. It will appear in the sequel that 
the values of & for the simple gases, oxygen, hydrogen and 
nitrogen, for which Avogadro’s law, for a constant pressure and 
temperature, has been experimentally established, are included 
within narrow limits (probably 2 and 3). It thus becomes 
apparent that the extreme ratio of the number of molecules in 
the same volume cannot exceed 1°018, and may be much less. 
(2.) Avogadro’s Law, relative to compound gases; that the 
same volumes of these gases contain the same number of mole- 
cules, and the same number as equal volumes of the simple 
gases. The ordinary physical conception is that compound 
molecules are formed by the union of simple molecules, or of a 
certain number of their constituent atoms, and that these oc- 
cupy the same volume that the simple molecules did. In some 
instances of chemical combination it necessitates the supposi- 
tion that the formation of each new compound molecule is a 
result of the breaking up of several molecules of the combining 
substances. It also involves the improbable hypothesis that 
the space physically occupied by a molecule is wholly in- 
dependent of the number of its constituent atoms. Upon 
the conception of variable ultimate molecules adopted in 
this and my previous paper, Avogadro’s law simply im- 
plies that in the act of combination the effective molecules 
suffer a certain diminution of size, by the collapse of their 
envelopes. The same number of atoms may thus physi- 
cally occupy the same volume as if they were closely to unite 
aud form a compound molecule, upon the ordinary hypothesis. 
Thus in the formation of aqueous vapor by the combination of 
two volumes of hydrogen with one volume of oxygen, a 
two volumes of the compound, a condensation of the individua 
molecules would take place, and as the result two ultimate 
