Liebig's Law of the Minimum in Relation to General Biological Problems.

MSS. Intended for publication and books, etc., intended for review should be senit to Professer J. McKeen Cattell, Garrison. on-Hudson. N. Y. LIEBIG'S LAW OF THE MINIMUM IN RELATION TO GENERAL BIOLOGICAL PROBLEMS' TmE Law of the Minimum has never been accurately defined, although the idea that it involves is relatively simple. Professor B. E. Livingston says in a recent paper2 that "this prilnciple is still quite incomplete logically and its statement will assuredly become much more complex as our science advances." In order to get a clear understanding of the law so that it may be stated accurately, we will begin with a simple application to chemical reactions. One molecule of KOH reacts with one molecule of HCI to form one molecule of KC1 and one of H20. If only one molecule of KOH is present, only one molecule of KCI can be formed, no matter how many molecules of HC1 are present; and likewise if only one molecule of HC1 is present, only one molecule of KCI can be formed, no matter how many molecules of KOH are present. By considering the weights of the reacting substances, the situation is somewhat complicated: 56.1 grams of KOH react with 36.5 grams of HC1 to form 74.6 grams of KCI and 18 grams of H20. In round numbers 3 parts by weight of KOH and two of HC1 give 4 parts by weight of KCI and one of H20: 3/4 gr. of KOH and 1/2 gr. of HC1 are necessary to form a gram of KCI. Let us call these fractions, 3/4 and 1/2, the specific reactive weights of KOH and HC1 in respect to the formation of a unit quantity of KCI. Suppose x amount of KOH and y of HC1 are given. If x and