360 REPOET— 1886. 



solution dimiuishes when it is diluted with water to double its volume, are laid 

 down in table B. This quantity we name the exponent of dilution.' 



B is a long table wherein, after all, .r does not turn out a constant — though it 

 is roughly so, several values of x being given for each substance according to its 

 degree of dilution. The values of x for all the substances range from 17 to 2-3, 

 and their average value would seem to be about 1-95. 



The above introduction to the formula for calculating x loses all meaning 

 unless X is intended to be constant ; but, in so far as .r is intended to be constant, 

 the' gist of the introduction may be paraphrased thus : — 



The first approximation to the relation between k and vi (conductivity and 

 concentration) is that made by Kohh-ausch, viz., that the two are proportional.' 

 This is roughly true for very dilute salt (not acid) solutions, but it breaks down in 

 a manner shown by Kohlrausch's experimental curves for more concentrated ones, 

 so that he suggests the formula — 



kltn = A — A.in\ 



as a closer, though still rough, approximation. Arrhenius, however, prefers to 

 assume {i.e., practically, though unconsciously, does assume by his reasoning) that k 

 is nearly proportional to m', where r is an index to be determined by experiment. 

 This is fair enough as an hypothesis, and should have been set forth clearly, and 

 then negatived by the result of his experiments : or, as a clumsier and bulkier 

 proceeding, the value of ?• might be tabidated for every substance at various 

 strengths. Instead, however, of determining r, Arrhenius determines 2' ; which 

 he calls x, and tabulates. This number x, his exponent of dilution, he calculates 

 from the equation — 



log^' ^ log mfm' ^ logw y^-. 



log 2 log ?n/OT' log u 



I confess that it has cost me a good deal of trouble to disentangle the real 

 meaning of this said dilution-exponent, and of the ideas involved in it.'^ 



I ought here to say that in 1884 M. Bouty independently expresses his results 

 in terms of this same number, which he calls the ratio X ; showing that it has some 

 experimental convenience. Bouty, however, does give absolute concentrations, 

 and he really doubles the dilution each time. Arrhenius gives no absolute con- 

 centration ; he dilutes largely, and then calculates what woidd have happened 

 if he had only doubled the dilution, by means of a formula which, after all, 

 is not reidly correct.' Perhaps the idea in not gi\-iug absolute concentrations is 

 that it is impossible accurately to tell them, unless absolutely pure water were 

 available to start with. But the difficulty of impure water tells just as much at 

 every dilution, for it is a medley of things you are really adding. A great part 

 of the merit of Kohlrausch's work is that he takes such immense pains over the 

 quality of his water. 



§ 10. List of bodies examined. 



§11. Table A, giving resistance and temperature of different strengths of 

 solution of the various substances, but no absolute strengths are given ; ratios of 

 dilution are all that are specified. The columns, in fact, show 1/n and l/i«. 



Table B contains the ' exponents of dilution/ x, calculated for the different 

 substances ; it shows a slow increase in .r as the solution becomes weaker. 



Table B' contains similar numbers, calcidated from some experimental results 

 of Lenz for stronger solutions. 



The net result of these tables is that they help to confirm the later results of 

 Kohlrausch. For all salts other than hydrates the value of .r becomes practi- 

 cally equal to 2 as the solutions become very weak, i.e., r becomes unity ; and 

 this means simply that A/w for such solutions is approximately a constant. 



' See § 4 of letter on p. 385. 



^ In his letter on p. 386 below, § 4, Dr. Arrhenius denies that he had any theoretical 

 idea in introducing the ' exponent of dilution.' I accept his statement of course, and 

 regret the time spent over the troublesome, and now apparently unmeaning, intro- 

 duction quoted above. 



3 See § 4 of letter on p. 386. 



