§ 3] CHEMOTAXIS 43 



From this table it appears that the strength of solution 

 necessary to provoke a certain response depends upon the 

 strength of solution to which the protoplasm has been pre- 

 viously subjected 'and increases proportionately with it. It is 

 clear that the capillary solution of 0".1%, which produces a 

 marked chemotaxis in bacteria reared in a culture solution of 

 0.01%, would awaken no response in bacteria reared in 0.1%. 



We are now in a position to appreciate the importance of 

 still another addition to our terminology of stimuli — the dif- 

 ferential threshold stimulation (Reizunterscheidsschwelle) — 

 which may be defined as the minimum increase of a preexisting 

 stimulus which is capable of calling forth a just noticeable 

 reaction. In the case just cited, the differential threshold 

 stimulation lies just above 3 times the preexisting (culture) 

 stimulus, and this is true whatever the degree of the preexist- 

 ing stimulus ; and it is shown by experiment that, in general, 

 as the preexisting stimulus increases, the differential threshold 

 stimulation increases in the same proportion. This observa- 

 tion is in perfect accord with the law formulated long ago by 

 Weber with especial reference to sight. This law runs : The 

 smallest change in the magnitude of a stimulus which will call 

 forth a response (differential threshold stimulation) always 

 bears the same proportion to the whole stimulus. We may 

 express this law mathematically, as Fechner has done, by the 

 following considerations : Let us take the case of a protoplas- 

 mic body, as, for example, that of a spermatozoid, living in a 

 stimulating medium (s) of a certain concentration and experi- 

 encing a certain reaction r' ; then s corresponds to r'. In 

 order just to get a chemotactic response (threshold stimulation), 

 a solution of say 30 times the concentration must be brought 

 to the solution affording the stimulation s. This will give a 

 reaction which is greater than r' by a quantity which we may 

 designate r, so that the quantity of the whole reaction may be 

 designated as ?•' -t- r. If the organisms are now placed in this 

 stronger solution (31 s), the solution in the capillary tube must 

 be 30 times stronger (80 x 31 s) in order to give the differential 

 threshold stimulation. The reaction following this stimulation 

 may be designated, according to Fechner's conception, as 

 yi j^r + r. The relation of the successive stimuli and the reac- 



