252 THE NUMERICAL RELATION 



we are entirely unacquainted. Such in solids is undoubtedly the case with so simple and 

 fundamental a property as specific gravity, and most, if not all, of the other properties 

 of solids belong to the same category. It cannot therefore be expected that we should 

 point out the laws by which these properties vary, although the remarkable investiga- 

 tions of Dana, Filhol, Kopp, Schroder, and others, on the relations between the density 

 of substances and their atomic weights, and those of Kengott on the relation of hard- 

 ness to atomic volume, give grounds for expecting that even they will before long be 

 discovered. In liquids and gases, however, most of these molecular forces which pro- 

 duce the apparent 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 comparing together the properties of the liquid or gaseous 

 states of the elements in any series, to discover some numerical relation between 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 only 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 necessarily from Avhat 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 quo- 

 tient is the same for all the elements with only a few exceptions. That is ^y^' r=p. 

 But we have found that At. W. may be expressed in general by a + nh, and substituting 

 this for At. W. in the above equation, it becomes ^?^=/), or Sp. Gr.=paJ^np b; so 

 that p a -\-npb is a general expression for the specific gravity of all the elements of 

 any series, in the same way that a + n 6 is for the atomic weight. The value of p will 

 differ according as the specific gravities used 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 great measure avoid fractions. In the Nine 

 Series ^j = 1, so that the numbers representing the specific gravities are the same as those 

 representing the atomic weights. In the Six Series it equals two, so that the numbers 

 representing 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 and Vapors," in Graham's Ektiients of Chemistry, which is a very 

 complete collection of all known data. For the other series, we have only occasional 

 data, so that no complete tables of their specific gravities are possible. 



