404 J. P. Cooke on the Numerical Relation 
parent irregularities in solids have less influence, as we should 
naturally expect, probably because the atoms are removed out of 
the sphere of their action. We may therefore hope, on compar- 
ing together the properties of the liquid or gaseous states of the 
elements in any series, to discover some numerical relation .be- 
tween them. Unfortunately, however, we have not sufficient 
data for making such a comparison except in the case of one 
property, the specific gravity. The boiling point, which would 
be a very valuable property for the purpose, is known ouly in a 
few instances. 
That the specific gravity of the elements in their gaseous state 
varies in each series according to a numerical law, follows neces- 
sarily from what is already known. It is a well-known fact, that 
the specific gravities of the gaseous states of the elements divided 
by their atomic weights give quotients which are either equal, or 
which stand in a very simple relation to each other. For any 
series, as far as we have data, this quotient is the same for all the 
elements with only a few exceptions. That is ~y;=p. But 
we have found that At. W. may be expressed in general by a+nb, 
_and substituting this for for At. W. in the above equation, it be- 
comes =p, or sp. gr. =pa+npb; so that pat+npb isa 
general expression for the specific gravity of ail the elements of 
any series, in the same way that a+7 6 is-for the atomic weight. 
The value of p will differ according as the specific gravities use 
are referred to hydrogen or air. Below will be found tables which 
give the calculated and observed specific gravities of the elements 
of the Nine and Six Series referred to hydrogen, which has been 
taken as the unit instead of air, as we thus in a great measure 
avoid fractions. In the Nine Series p=1, so that the numbers 
representing the specific gravities are the same as those represent- 
ing the atomic weights. In the Six Series it equals two, so that 
the numbers represeuting the specific gravities are in this series 
twice as large as those representing the atomic weights. When 
the specific gravity has not been observed, the calculated number 
only is given. The observed numbers are taken from the “ Table 
of Specific Gravity of Gases aud Vapors,” in Graham’s & 
of Chemistry, which is a very complete collection of all known 
data. For the other series, we have only occasional data, $0 that 
no complete tables of their specific gravities are possible. sine 
It is evident, then, that at least one property of the elements 
varies in the series according to an ascertained numerical law. 
But, it may be said, this proves nothing, for these specific grav 
ties are connected so closely with the atomic weights t 
is true of one must be to the same extent true of the other. 
It must be remembered, however, that the specific gravities are 2” 
distinct set of observed facts, and that the probability of a law 
