370 



Literarisch=kritische Rundschau. 



Mathematics and Mitosis. By Prof. Marcus Hartog. From the 

 Biological Institute of University College, Cork. Mit 7 Textfiguren. 



There is nothing more liarmful to the progress of science 

 than the parcelling of its area into a series of watertight compart- 

 ments, each labelled "a distinct science'\ of which the cloors are 

 too offen rusted up and immoveable. The reception of my own 

 work on the cell-field has illustrated this evil. The reasoning 

 therein was difficult to the biologist who has forgotten bis elem- 

 entary mathematics and physics: the physicists (to whom the work 

 should appeal on many grounds) have no knowledge of cytology ; 

 and, accustomed as they are to arrange for themselves the actual 

 conditions of experiment, can hardly realise in what bonds we 

 biologists labour, who must needs base our conclusions on the 

 logical, quasi-historical synthesis of collections of fixed specimens 

 into an inferred series of changes. On these grounds we most 

 heartily welcome Dr. Geigel's visit to our little domain of 

 cytology ^) and hope that he may continue bis interest in our doings. 



Yet we cannot accept bis reasoning as convincing, because 

 bis Store of biological facts has been inadequate for bis precise 

 calculations. Huxley once said that mathematics is likeamill: 

 the quality of the grist depends largely on that of the corn that 

 is poured into the hopper. But, even before going into the facts, 

 there are some important criticism, of method. Geigel has attempted 

 to obtain the accuracy of an equation. In such complex case 

 equations are quite out of the question: usually all that we can 

 arrive at is the Statement that one factor is a '"function" of 

 another, "direct" or "inverse", as the case may be. Moreover 

 Geigel's precise equation is arrived at for a field about a Single 

 centre whereas the cell-field is essentially dicentric. Thirdly, 

 as I have shown, on the assumption of a centred action, we must 

 assume that the chromosomes are of high "permeability" to the 

 force; and bis equations ignore this fact. What w^ould be thought 

 of an equation dealing with gravity in which account was taken 



1) Richard Geigel: Zur Mechanik der Kernteilung und der Be- 

 fruchtung. Arch. f. mikr. Anat.. Bd. LXXX, 1912, II. Abt. 



