[Rrprinfed from iSciENCK, N. S., Vol.XLVI., A'o. 

 1183, Pages 197-204, August 31, 1917] 



LIEBIG'S LAW OF THE MINIMUM IN 

 RELATION TO GENERAL BIOLOG- 

 ICAL PROBLEMS 1 



The 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 paper^ that 

 ' ' this principle is still quite incomplete log- 

 ically and its statement will assuredly be- 

 come much more complex as our science 

 advances." In order to get a clear under- 

 standing 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 HCl to form one molecule of 

 KCl and one of H2O. If only one molecule 

 of KOH is present, only one molecule of 

 KCl can be formed, no matter how many 

 molecules of HCl are present ; and likewise 

 if only one molecule of HCl is present, only 

 one molecule of KCl can be formed, no mat- 

 ter how many molecules of KOH are pres- 

 ent. By considering the weights of the 

 reacting substances, the situation is some- 

 what complicated: 56.1 grams of KOH 

 react with 36.5 grams of HCl to form 74.6 

 grams of KCl and 18 grams of H2O. In 

 round numbers 3 parts by weight of KOH 

 and two of HCl give 4 parts by weight of 

 KCl and one of H,0 : 3/4 gr. of KOH and 



1 Paper read before the Biological Club of Tale 

 University, April 19, 1917. 



2 Plant World, 20 : 1-15, 1917. 



