38 



cording to size. The experiments were satisfactory, as they gave him the 

 data which he sought, thus enabling him to solve the problem. 



That the tendency of botanical work is in the direction of mathematical 

 preciseness is seen in the works of Sachs, Nageli, Wiesner and many others. 

 Sachs* has worked out cell division in a masterly manner. By means of 

 periclined and anticlined planes he has demonstrated the direction of the 

 cell-divisions in a growing organ, the outline of the organ taking the form 

 of a parabola, a hyperbola, or an ellipse. By this means he has proven 

 that the mode of cell-division depends entirely upon the increase in vol- 

 ume and the configuration of the growing organ, and not upon its physi- 

 ological or morphological significance. From his work he has formulated 

 two important laws, (1) that the daughter-cells are usually equal to one 

 another in volume, and (2) that the new cell-walls are situated at right 

 angles to those already present. 



Previous to Sachs' work it was supposed that it was possible to charac- 

 terize the true morphological or phylogenetic nature of an organ by the 

 way in which cell division took place. 



Sachs has also studied the growing apex of stems and roots so as to de- 

 termine the zone of greatest growth. From the tables compiled by him 

 there are certain facts deduced which, when the successive zones are rep- 

 resented by A. N. V x. the apical zone beinu A, the zone of greatest 

 growth X, and the last zone of the growing region N+x, are clearly ex- 

 pressed by the formula : 



A A 1 A 2 . . . <N N 1 N 2 . . . X x. 



The formula indicating the relation of their respective increments. 



The following general expression is used by Sachs to express the relative 

 lengths of the different tissues after isolation, where E, C. V, P, stand re- 

 spectively for epidermis, cortex, vascular tissue and pith : 

 E<C V P V C>E. 



The expression also states the relation active tension of the layers, for 

 the greater the compression, the greater will be the length upon isolation. 



Xiigelit has demonstrated the movements of bacteria in air and water. 

 He classifies them into groups and applying the general formula for ve- 

 locity v=l / 2^, he has deduced the formula- v='^— i in which// is 



.1. Sachs. Arbeiten des bot. lust, in Wurzburg, 1878. On the Physiology of Plants. 

 1887, pp. 431-459. 

 tC. v. Xiigeli. Untersuchuugen iiber niedere Pllze aus dem Pflanzenphysiologischen 



Institut in Miinchen. 1882. 



