PREFACE vii 



must be provided, and the preparation of a pure specimen may 

 last several months. Moreover, many figures obtained by the 

 measurement of inorganic objects are variable according to 

 the external conditions, in the same way as the dimensions 

 and other properties of living beings. For instance, the density 

 of a given substance varies according to temperature ; pressure 

 has an influence on the boiling-point ; etc. Therefore, in order 

 to establish constants, certain conventions have been made ; 

 this renders the task still more laborious and delicate. Biologists 

 should not allow themselves to be discouraged by the prospect 

 of " such lengthy work " ; they should always remember what 

 the students of inorganic nature have already carried out. 



When an index of refraction, a coefficient of expansion or a 

 given angle of a crystal has been exactly measured, work and 

 perseverance find their reward, because a precise notion has 

 been acquired once for all. In Biology, on the contrary, 

 especially in the descriptive (systematic) part of Zoology and 

 Botany,! numerous objects have been described again and 

 again as new ; contradiction and hesitation prevail everywhere ; 

 an enormous amount of labour has been wasted. We should 

 follow the example given by physicists, chemists and mineralo- 

 gists. Otherwise it may be feared that the work, like that of 

 Penelope, will go on indefinitely. 



It may be remarked that the present book is NOT in reality 

 a treatise on mathematical biology : mathematical notions 

 (Part VI.) are used only in order to find the primordia and the 

 methods of measuring them. We may hope that when a 

 sufficient number of constants have been collected the power- 

 ful machinery of mathematical science will become applicable 

 to biological problems. 



I have, in conclusion, the pleasant duty of acknowledging the 

 assistance received from various friends. 



To Professor F. E. Weiss, who has kindly read through 

 the manuscript and has made numerous corrections in the 

 language, and to Professor W. H. Lang, in whose laboratory 



1 See on Embryology, § 50. 



