Bobertson. — On certain Maxima and Minima. 467 



(3.) When the Compounds are Solids. — (a.) The Melting- 

 points of the Phenyl Fatty Acids : — 



Table III. 



Acid. Melting-point. 



Benzoic ... ... ... ... 121° 



Phenylacetic ... ... ... 77 



Phenylpropionic ... ... ... 49 



Phenylbutyric ... ... ... 47 



Phenylvaleric ... ... ... 52 



Now, molecular complexity raises the boiling-point ; and, in 

 general, when the boiling-point of an isomer rises the melting- 

 point is found to fall. Consequently, when the melting-point 

 falls in an homologous series (a rise being expected) it may 

 naturally be concluded that the association of the molecules 

 becomes greater with the fall of melting-point. 



(b.) The Solubilities of the Calcium Salts of the Fatty 

 Acids:* In the case of the normal acids the salts increase 

 in solubility from formate to propionate, and then decrease 

 quickly with the increase of the number of carbon atoms. In 

 the following table the values of the solubilities are given for 

 the temperatures 0° and 100° : — 



Table IV. 



Salt. 

 Calcium formate 

 „ acetate 

 „ propionate 

 „ butyrate 

 „ valerate 



hexoate 

 „ heptoate 

 „ octoate 



nonoate 



Solubility (0°). Solubility (100°). 



. 16-15 (increase) 18-40 



. 37-40 (decrease) 29-65 



. 42-80 (increase) 48-44 



. 20-31 (decrease) 15-85 



9-82 (decrease) 8-78 



2-23 (increase) 2-57 



095 (increase) 1-26 



0-33 (increase) 0-50 



0-16 (increase) 0-26 



Near the member where the maximum solubility occurs it 

 is found that there is alternate increase and decrease of solu- 

 bility between 0° and 100°. This is comparable with the 

 association of the fatty acids (A (1) ) where the rate alternates, 

 but the association reaches a maximum. 



Lumsden states that one of the causes that determines the 

 solubility is osmotic pressure. Now, osmotic pressure is in- 

 fluenced by association ; so we see in this case also that 

 there is a possibility of the cause of the phenomenon being 

 molecular association. 



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

 Again, the only example of this type is furnished by the fatty 



Lumsden, Journ. Chem. Soc, 1902, 350. 



