60 THE QUANTITATIVE METHOD IN BIOLOGY 



are in play, the indiscriminate use of the above-mentioned 

 terms may result (and has resulted) in inexact conceptions. 

 For instance, in the comparative study of male and female 

 individuals of the same species, clearer views would certainly 

 be obtained if the terms infantile [juvenile), progression and 

 retrogression were used for each property separately. The 

 investigation of this important subject, which is in close rela- 

 tion with the secondary sexual characters, has been initiated by 

 DARWIN. It has been considerably spoiled by the obsession 

 of adaptation and other preconceived ideas, and it is rather 

 overlooked by many biologists. 



§ 48.— THE MEASUREMENT OF A STATE OF EQUI- 

 LIBRIUM. — In § 43 a primordium (simple property) is defined 

 as a state of equilibrium. This is further explained in § 44, 

 and in § 45 the property length of a petal is given as example. 

 Just as the latter property, the primordia mentioned in §§ 46- 

 47, during their period of development are passing through a 

 series of values till a certain state of equilibrium is reached. 



This view is based upon a mechanical conception. It may 

 be asked how it is possible to express a state of equilibrium by 

 measurement. 



A state of equilibrium coincides with the simultaneous action 

 of a certain number of forces. Strictly speaking, it ought to be 

 expressed by an equation in terms of the forces. In the 

 present state of biological science it is impossible to enumerate 

 and to measure the forces which are at play. Therefore we 

 must have recourse to an indirect method, measuring the 

 material parts which are maintained in equilibrium by the 

 acting forces. We may count the similar parts (organs, seg- 

 ments, etc.) which are in equilibrium, measure their dimensions, 

 their form (any form may be expressed in terms of dimensions), 

 their relative position (angles of divergence, etc. See, on 

 phyllotaxis, § 40), their physical properties (elasticity, etc.), etc. 

 The chemical properties properly so called, which depend on 

 the presence of certain abiotic substances or mixtures (§8), are 

 quantitatively known as soon as we know the chemical con- 

 stitution and the quantity of the substances under considera- 

 tion.^ In many cases the abiotic chemical properties may be 

 measured indirectly (scale of colours, transparence, etc.). But 

 whatever may be the object of the measurement, it must always 

 be borne in mind that we are measuring something which coin- 

 cides with a state of equilibrium. 



The principles upon which the measurement of the primordia 

 of the living beings is based are expounded in Part VI. (prob- 

 ability). Part VII. (variation steps) and Part VIII. (gradation). 

 1 This may be discovered by chemical research. 



