THE VITAL PHENOMENA OF BACTERIA. 103 



two of these groups of facts, indeed, I was able 

 some time since to infer the existence of the 

 other group as a probable contingency, before 

 such existence was directly ascertained. I 

 mention this only to show how, in principle at 

 least, the biologist is at no disadvantage in 

 the matter of accurate prediction as compared 

 with the physicist or astronomer. His method 

 of reasoning is just as precise as that of a 

 mathematician, but his material is for the most 

 part too complex to admit of the use of math- 

 ematical signs. The demonstration of the pos- 

 sibility of such accurate forecasting establishes 

 for us a certain security as regards the nature 

 of our work. The unreasoning pride that too 

 often hirks in a onesided mathematical for- 

 mula need impose upon us no longer. There 

 is, perhaps, a mathematics without the usual 

 symbols. Far-seeing physicists, like R. 

 Mayer, Helmholtz and E. Mach, have already 

 recognized that, in order to be intelligible, 

 physical observation must have its indispen- 

 sable physiological side. In the monistic 

 theory we possess a bond uniting not only 

 all natural sciences with one another, but all 

 the natural sciences with the so-called psycho- 

 logical sciences. 



The cells of those animals and plants that 

 lack chlorophyl are able, according to the cur- 



