It is not always easy to distinguish these two classes of phenomena.
Jennings, in his studies on Reactions to Stimuli in Unicellular Organisms (1899-1900), has shown that whatever be the nature of the repellent stimulus, chemical or mechanical or thermal, the reaction of Paramecium and many other Protista is always the same. It swims backward a short distance, turns towards the aboral surface, and then having thus reversed swims on again in the new direction, front foremost as before. Apparent "positive taxies" are often really negative ones; for if the Paramecium be placed in water containing CO2 it shows the reaction not on entering the part charged with this acid, but on passing away from it into purer water, so that it continually tends to turn back into the acid part, while within it or in the water at a distance not yet charged it swims about irregularly. It appears due to this that the individuals become aggregated together, as they excrete this gas into the water. If a repellent substance diffuse towards the hinder end of a Paramecium, the response, instead of carrying it away, brings it into the region of greater concentration, and may thus kill it.
"Galvanotaxis and Chemotaxis," Journ. of Physiol. vol. xxvi. 1900-1901, p. 291.
Let us take the case of a 1-centimetre cube, growing to the size of a 2-centimetre cube. The superficial area of the 1 cm. cube measures 6 square centimetres, and its bulk is 1 cubic centimetre. The superficial area of the 2-centimetre cube measures 24 square centimetres, while its volume measures 8 cubic centimetres. Thus the larger cube has only 3 cm. sq. of surface to every cubic cm. of volume, instead of 6; in other words, the ratio of surface to volume has been halved by growth. Three successive bipartitions of the larger cube will divide it into eight separate 1-centimetre cubes, each now possessing the original ratio of surface to volume.
The nucleus is regarded by some as equivalent to a central nervous organ for the cell; by others, such as G. Mann and Verworn, as the chief chemical centre of the cell, and notably the seat of the secretion of the zymases or ferments that play so important a part in its life-work; for it is found that a Protist deprived of its nucleus can execute its wonted movements, but can neither digest nor grow. This conclusion may appear to be rather sweeping and premature, but we have seen that the changes of surface tension are the direct antecedents of the motions of the cytoplasm, we know that such changes are induced by chemical changes; and thus the nucleus—if it be the central laboratory to which such changes are ultimately due—would really in a certain sense be a directive centre.