Table I. Acid. No. of Carbon Atoms in Molecule. Association Factor. Acetic 2 1·00 Propionic 3 1·01 Butyric 4 1·03 Valeric 5 1·05 Hexoic 6 1·06 Heptoic 7 1·07 Lauric 12 1·11 Stearic 18 1·01 On the other hand, the rate of association alternately increases and decreases; thus in this case there is an intimate relationship between the attainment of maximum association and the wavy nature of a closely related property. Generally speaking, association decreases with rise in molecular weight. This was observed by Ramsay and Shields and by Traube in the case of liquids, and is also true for the association of the fatty acids in the gaseous state as measured by their vapour densities.* Easterfield and Robertson, Trans. N.Z. Inst., 1901, 499. An increase of molecular complexity which extends to far up the series, as in the case of the aliphatic acids in phenol, has never been previously observed. (2.) When the Compounds are in the Liquid State.—Examples of this are exceedingly numerous for the rotary power of optically active compounds. Guye showed that in many cases the explanation may be given from his hypothesis of the product of asymmetry. Frankland,† Trans. Chem. Soc., 1899, 347. on the other hand, explains the maximum or minimum in many cases as due to the association of the initial members of the series. A clear case of this is exhibited by the esters of active amyl alcohol (Guye and Chavanne). The association factor is calculated according to Traube's formula:— Table II. Ester. [a]. Association Factor (15°) Amyl formate + 2·01 1·08 " acetate + 2·53 1·02 " propionate + 2·77 1·00 " butyrate + 2·69 0·94 " valerate + 2·52 0·92 " hexoate + 2·40 0·90 Here it is seen that when there is no association the values of [a] regularly increase.