408 SIR NICHOLAS YERMOLOFF ON SOME INTERMEDIATE FORMS 



" variable." No reverse process of synthetic grouping, or, if I 

 may again use a term of mathematics, no process of " integration" 

 is possible and thinkable without the previous exhaustive exam- 

 ination of the elemental " differentials." It would therefore seem 

 to me that the consummation devoutly to be wished would lie in 

 another direction — not in the curtailing of the differentiating 

 operations, but in a process of reverse character, namely, in a 

 process of synthetic integration, undertaken after the study of 

 variations had been thoroughly mastered. This reverse process 

 ought to be performed, as is again done in mathematics, according 

 to some definite method and plan within certain limits. 



One of your illustrious writers has truly said : "111 can he 

 rule the great that cannot reach the small." Nothing is more 

 true in a scientific sense : before undertaking any work of inte- 

 gration we must thoroughly master variation in all its forms. 



To return to Diatoms, it is to be noted that the variations of 

 intermediate forms by no means appear as a rule to be abrupt ; 

 on the contrary, they are usually very gradual, and, I should say, 

 continuous, insensibly passing from one form into another. But 

 that peculiarity in Nature is most precious, and immediately 

 gives us guidance as to how to proceed farther : on the one hand 

 it leads us towards Darwin's doctrines of Evolution ; on the 

 other hand it brings the study of a biological subject closer to 

 the ideas of abstract mathematics. 



The work of synthetic integration I am speaking about cannot 

 of course be done, so to say, accidentally or at random : it must 

 be done according to some guiding idea, and must follow some 

 definite formula or plan. At the present stage of diatom sys- 

 tematics it is perhaps feasible to make an attempt in that direc- 

 tion. Such an attempt, however small, forms the subject of this 

 paper. 



In the course of my paper I shall have occasion to explain that 

 a certain fossil Diatom, found in the freshwater deposits of the 

 American State of Maine — Navicula Monmouthiana — may be con- 

 sidered as an ancestral form of a whole series of species of 

 Cymljella which I am about to describe. It would seem that this 

 ancestral form, through the course of many centuries, had passed 

 through a long series of many slight transformations, evolving 

 about fifteen forms of Cymbella extremely near and similar to 

 each other, and closing the series in a very small form, Cymbella 



