410 SIR NICHOLAS YEPv:\IOLOFF OX SOME IXTERMEDIATE FORMS 



iana to be a sort of " integral" to begin with, and the Cymhella 

 microcephala the last "derived function" of the series. Indeed, 

 we may say that Nature herself is a great and patient mathema- 

 tician, one whose integrals are primordial forms and whose derived 

 functions are what naturalists call " species." And from this 

 point of view it would perhaps be permissible to introduce, I 

 should not say a new, but a different defiintion of v/hat in natural 

 history is meant by the word " species " : it is a definition which 

 was advocated in Russian scientific circles before the war : 



" A species in Nature corresponds to what in the Differential 

 Calculus is meant by a ' derived function ' : it is a certain type- 

 limit, to which tend, without even sometimes quite identically 

 attaining it, certain varying intermediate forms." 



The distinguishing features upon which are founded the sys- 

 tematic classification of Diatoms belong to seven categories : 



(1) Habitat. — Whether freshwater, brackish water or marine^ 

 This is a very constant and definite feature. 



(2) Modus Vivendi. — Whether free, stipitate, enclosed in mucila- 

 ginous tubes, living individually, or in colonies, bands, chains 

 and the like. This is a very uncertain and changeable feature of 

 distinction. 



(3) Size. — A fairly constant featm'e within certain limits. 



(4) Exterior structure of the valves as to : raphe, nodules, costae 

 or striae, also as to hyaline axial and central zones. This is a 

 very important category, liable to many variations, yet usually 

 constant within certain limits. 



(5) Interior structure and arrangements : septa, loculi, zone 

 details in the frustule view. 



(6) Outline form of the valves, of the margins and ends. A 

 most important category of distinctive features. 



(7) The distribution of the endochrome as regards chromatophores, 

 pyrenoids, etc. 



All the above seven categories are important for the deter- 

 mination of forms, but not equally so. Some are more, some are 

 less, constant and reliable. To show how careful the observer 

 has to be even with such a comparatively constant distinctive 

 feature as habitat^ whether a diatom is freshwater, brackish water 

 or marine, I vvill state the case of the so-called Fragillaria rntarc- 

 tica. Now nearly all Fragillariae are freshwater. Vet Fragillaria 



