242 THE NUMERICAL RELATION 



which should be the same function of the same variables, and what mathematics 

 teaches we ought reasonably to expect in the case of this curve, we ought to expect 

 also in the variations of solubility of these substances. Now every mathematician 

 is familiar with the remarkably rapid changes which a curve undergoes that is a 

 function of several variables, and we cannot be surprised that similarly rapid changes 

 should be observed in the solubility of homologous substances in passing from one to 

 the next in the series. In the curve which corresponds to the relative solubility of CaO, 

 CaFl, CaCy, CaCl, CaBr, and Cal, it would seem that at CaFl there is a singular point 

 where the curve, after rising for some distance above the axis, bends down again 

 towards it. Several of the other series of compounds of these elements present sim- 

 ilar anomalies ; for example, KO, KFl, KCy, KCl, KBr, and KI. Here the solubility 

 diminishes until we come to KCl, which is less soluble than KCy ; then it increases 

 to the last. Here, of course, the singular point is at KCl. With the corresponding 

 compounds of Sodium, the solubility diminishes to XaFl, which is the least soluble of 

 the series, and then increases constantly to the end. 



These facts at least seem to show that apparent variations from the law of series 

 in properties, which evidently are unknown functions of several variables, should not 

 be allowed to outweigh strong analogies, and certainly the analogies between Fluorine 

 and the other haloids are very marked. Fluorine itself possesses properties such as 

 we should expect to find in a member of the series above Chloiine. The strong and 

 active affinities of Fluorine might be indeed predicted, after seeing the rapid increase 

 both in the strength and activity of the affinities in passing from Iodine to Chlorine. 

 In passing from Bromine to Chlorine, we pass from a liquid to a gas, permanent under 

 any natural conditions ; and we should expect, therefore, in rising still higher in the 

 series, to find in Fluorine a gas less easily reduced to a liquid than Chlorine. Now 

 although, on account of its remarkably active affinities, this fact cannot be demon- 

 strated on the gas itself; it can, nevertheless, be inferred with perfect certainty from 

 its compounds. Finally, the isomorphism of Fluorine and the other haloids may be 

 urged as indicating close analogy. From these considerations, I cannot but think that 

 those chemists who have questioned the propriety of classing Fluorine with the other 

 haloids will, on reviewing the facts, and regarding the haloids in the light of a series, 

 and not simply as a group of elements possessing certain general properties, be led 

 to change their opinion. 



Cyanogen, though a compound radical, has been classed with the other haloids, not 

 only from its atomic weight, but also from its other analogies. Its properties are in 

 most cases those which we should expect from an element occupying its position in 



