Eobertson. — On certain Maxima and Minima, 465 



even compounds alone are considered the association de- 

 creases, reaches a minimum, and then rapidly rises again. 

 The initial molecular depression, however, steadily falls to 

 a minimum, and then rises again after about the twelfth 

 member. 



(3.) Disubstituted acetic acids associate less rapidly than 

 mono-derivatives. The trisubstituted acids have the smallest 

 rate of association. 



(4.) Dicarboxylic acids associate more strongly than the 

 monocarboxylic acids. 



(5.) Hydroxyl and nitroso groups tend to increase the rate 

 of association. 



(6.) The rate of association of the substituted acetic acids 

 shows a qualitative relationship with their velocity of esteri- 

 fication. 



(7.) The dicarboxylic and a amido acids are characterized 

 by their sparing solubility. 



In conclusion, I wish to express my thanks to Professor 

 Easterfield for the encouragement and advice which he has 

 given me during the course of my work. 



Art. LVII. — The Exhibition of a Maximum or Minimum in 

 the Properties of certain Series of Organic Compounds. 



By P. W. Eobertson, Sir George Grey Scholar, Victoria 



College. 

 [Read before the Wellington Philosophical Society, 18th March, 1903.] 



The aim of the following paper is to collect the various data 

 in which a maximum or minimum is exhibited in an homo- 

 logous series, and to show that in many cases the cause is due 

 to the influence of molecular association. For the sake of 

 convenience two main subdivisions are made : A. When the 

 maximum or minimum is clearly seen. B. When it is 

 hidden. 



A. (1.) When the Compounds are in the Gaseous State. — 

 The only example of this yet observed is described in the 

 preceding paper. The molecular association of the fatty acids 

 in phenol solution first increases as the series is ascended, and 

 then, having reached a maximum, continues to decrease. 



Assuming for the present that the molecular weight of 

 acetic acid is normal when the freezing-point of its solution 

 is depressed 1°, and that the molecular depression is in- 

 versely proportional to the amount of association, the fol- 

 lowing values are obtained for the association factors : — 

 30 



