184 



MR J. Y. BUCHANAN ON THE 



A very remarkable feature exhibited by this table is the pronounced expansion 

 which accompanies the dilution of solutions of beryllium chloride for which ■m<l/16. 



§ 103. In columns 5, 9, and 10 of the tables, § 99, we have the data forjudging 

 the degree of conformity of the displacements of the solutions of these salts with 

 the laws of the two hypotheses, Section VII. They do not agree at all with the 

 arithmetic law of the first hypothesis, and their departure from the logarithmic law of 

 the second hypothesis is considerable, as may be seen in the columns headed (x — m) 

 and (llm—l/x). Thus, in the strong solutions of MgClg and CaCls, taking the ex- 

 ponent for m = 1 as unity, we see that the exponents for the solutions of higher 

 concentrations increase more rapidly than the corresponding concentration factors m, 

 but for both strong and weak solutions x^m. Considering the solutions of BeClg, we 

 see that the values of {l/m— '[/a)) change sign for a value of m lying between 1/16 

 and 1/32. The behaviour of the solutions of BeClj is, in this respect, quite remarkable. 

 If column 6 be referred to, it will be seen that for 



1/128. 

 0-2999 



1/256. 



0-2295 



1/512. 

 0-1992 



1/1024. 

 0-1720 



A - 1000 = 



so that for these very different concentrations the displacements are very nearly the 

 same. This depends on the remarkably low specific gravities of these solutions, which 

 was commented on in § 100. 



In the following table, which is constructed on the same scheme as Table VIII., § 45, 

 the solutions of each salt are taken in successive pairs. The numbers in it represent 



the values -^ — - 



log A 



2 



A^ is taken as unity 

 of x should be 2. 



= x, or the exponent of the displacement A^ when the exponent of 

 If the solutions conformed to the logarithmic law, the value 



Table giving the Values of ^ '" for the three Salts, Beryllium Chloride, 









Mag 



nesium Chloride, 



and Calcium Chloride. 









m. 



6-0. 



4-0. 



2-0. 



1-0. 



1/2. 



1/4. 



1/8. 



1/16. 



1/32. 



1/64. 



1/128. 



1/256. 



1/512. 



BeClj 



MgClg 

 CaClj 



2-154 

 2-149 



2-200 

 2-253 



2-204 

 2-175 



2-145 

 2-132 



2-038 

 2-127 

 2-089 



2025 

 2-091 

 2-054 



2-049 

 2-093 

 2-057 



1-807 

 2 051 

 1-804 



1-795 

 2-107 

 2-263 



1-692 

 2-321 

 2-251 



1-307 

 1-440 

 2-484 



1-152 

 4-888 

 1-473 



1-158 

 1-362 

 2-454 



Here again the radical changes which take place in the properties of the solutions 

 when the values of m fall below 1/16 are apparent, and particularly so in the case of 

 the solutions of BeCL. 



