198 



SCIENCE 



[N. S. Vol. XL VI. No. 1183 



y are divided by their respective specific 



4 

 reactive weights, we get ^ x and 2y. The 



smaller of these quantities is a direct meas- 

 ure of the weight of KCl that can be 

 formed from x KOH and y HCl. If, for ex- 

 ample, X and y are both equal to three 

 grams, four grams of KCl can be obtained. 



These facts can be generalized. If A, B 

 and C are substances which react to form S 

 and uA,vB and w C are necessary for the 

 formation of a unit amount of S, then u, v 

 and w may be called the specific reactive val- 

 ues of A, B and C, respectively. They may 

 be weights, volumes, numbers of molecules 

 or what not. In any particular case, where 

 pA, gB and rC are reacting, the amount of 

 S formed is the smallest of the fractions 

 p/u, q/v, r/w. When the amounts of the 

 reacting substances are divided by their 

 specific reactive values, the smallest quan- 

 tity so obtained is equal to the amount of 

 the product formed. 



This conclusion is directly applicable to 

 the problem of fertilizers. It is known that 

 most of the higher plants must obtain 

 seven elements in combined form from the 

 soil. They are S, P, N, K, Ca, Mg and Fe. 

 If aS, PV, yN, 8K, eCa, fMg and tjFc are 

 required for a unit amount of growth in 

 some particular plant, say wheat, and if 

 cS, 5P, cN, dK, eCa, /Mg and g-Fe are pres- 

 ent in a particular soil in available form, 

 the maximum amount of wheat that can be 

 grown in that soil will be the smallest of 

 the fractions a/a, i/fS, c/y, d/S, e/e, f/^, 

 g/rj. In this case a, j8, y, etc., may be called 

 specific growth values for the plant under 

 consideration. When the available amounts 

 of the essential inorganic food constituents 

 are divided by their respective growth 

 values, the smallest quantity obtained gives 

 the maximum amount of growth possible. 



It was in this connection that Liebig^ first 



3 ' ' Die Chemie in ihre Anwendung auf Agricul- 

 tur und Physiologie, " 7'" Auflage, 2: 225, 1862. 



formulated the Law of the Minimum which, 

 as commonly stated,* says that "the yield 

 of any crop always depends on that nutri- 

 tive constituent which is present in mini- 

 mum amount. ' ' The use of the term mini- 

 mum is not strictly accurate, as can be seen 

 from the example of KOH and HCl. If 

 three grams of each are present, the amount 

 of KOH determines the yield of KCl, al- 

 though both HCl and KOH are present in 

 equal amount. However, the above state- 

 ment of the law is convenient because of its 

 simplicity. 



A much broader application of the Law 

 of the Minimum was indicated by the work 

 of P. F. Blackman, whose conclusions are 

 summarized in his paper on "Optima and 

 limiting factors. ' ' ^ Blackman called atten- 

 tion to the complexity of the process of car- 

 bon assimilation, the rate of which depends 

 on at least six factors — 



1. Temperature, 



2. Light intensity, 



3. Carbon-dioxide supply, 



4. Water supply, 



5. Chlorophyll, 



6. Enzymes. 



Where it is possible to vary one of these 

 factors independently of the rest, its effect 

 on the rate of assimilation can be measured, 

 under suitable conditions, and a curve 

 plotted. In this way a temperature-as- 

 similation curve, a light-assimilation curve 

 and a carbon-dioxide-assimilation curve 

 can be constructed. The other factors 

 are more difficult to control. The fol- 

 lowing curves were constructed by Black- 

 man and Smith" from a study of the 

 rate of assimilation in Elodea. 



The light curve and the carbon-dioxide 

 curve are straight lines. The rate of as- 

 similation varies directly with the inten- 



* Cf. F. Czapek, ' ' Biochemie der Pflanzen, " 2 : 

 841, 1905. 



5 Annals of Botany, 19 : 281-295, 1905. 

 Proc. S. Soc, B., 83 : 389-412, 1910. 



