142 MR J. Y. BUCHANAN ON THE 



cases of potassium and rubidium iodates being that of contraction on dilution, while 

 the iodate of caesium simulates the character of the iodide of the same base, though to 

 a modified degree ; as though the dominating influence were the expansive effect of the 

 basic radical. 



§ 62. If we consider the solutions of the salts of the double ennead MR, MRO3, we 

 have eighteen solutions for each value of m. Owing to the sparing solubility of some 

 of the salts of the ennead MRO3, the highest value of m available for all the salts is 

 1/16. The eighteen salts can be divided into three hexads, the members of each 

 hexad containing a common metallic element, K, Rb, or Cs, and into three other hexads 

 having a common metalloidal element, CI, Br, or I. The values of v ( = A— 1000) for 

 the solution of 1/16 gram-molecule of each of the salts in the three hexads having 

 the common elements K, Rb, Cs are arranged in the tables, and the graphic effect is 

 illustrated in the diagram of § .38. When we wish to compare the solutions having 

 different values of m, it is convenient to use the values of v/m, that is, the increment 

 of displacement (A — 1000) reduced to the value which it would have if m = 1. This is 

 found in the general tables of Class E (§ 30) ; and for the solutions of 1/32 gram-molecule 

 salt and under, with nucleus CI, Br, or I, the values of vjin are represented graphically 

 in the diagram § 61, in which the ordinates are values of v/m, and the abscissse 

 values of m. 



When this diagram is studied, it is seen that the arrangement of the curves is 

 different in each of the three compartments which correspond to the solutions of salts 

 having as common elements the metalloids CI, Br, I respectively, and that their 

 differences are not altogether irregular. In the first diagram, the common element 

 being CI, the values of vjm follow the same order as that of the arrangement for 

 m= 1/16 in the tables, namely, KCl, RbCl, CsCl, KCIO3, RbClO^, CsClOg. This order 

 is maintained for m= 1/64, 1/128, 1/256. When the common element is Br or I, the 

 arrangement of the salts with respect to the values of vjm is different. 



The values of vim recorded in the general tables of Class E, with the curves in 

 the above diagram, furnish the means of appreciating the changing characters of the 

 difierent solutions with change of concentration, having regard to the numerical values 

 of the constant vjm for the different salts for the different values of m. 



§ 63. It is instructive to consider the order in which the salts of each hexad follow 

 each other when arranged in ascending order of values of vjm, without paying particular 

 attention to their actual numerical values. 



For this purpose it is convenient to represent each hexad of salts by a hexagon, 

 the centre of which is occupied by the common element, metal or metalloid, as nucleus. 

 The angles of the hexagon are then supposed to be occupied by the residues of the 

 respective salts after abstraction of the common element, arranged in ascending order 

 of magnitude of vjm, the lowest value occupying the lowest angle on the paper, and 

 the other values of vjm occupying the other angles seriatim in ascending order of 

 magnitude, and going round from left to right. 



