308 Researches in the Theory and Calculus of Operations. 



nuclei, while convoying the larger freight to reinforce the 

 central nucleus; during which process of evolution and 

 subsequent involution, the different mineral elements of 

 each plant had their genesis and fixation of quality, such 

 as now to admit the determination of new or secondary 

 creations of germs out of the results of the primitive one : 

 so in the example of the specimen microcosm or little world 

 of vegetal matter and form whose secondary creation and 

 subsequent development we are endeavoring to trace, the 

 process started by the expansion of force, but encountered 

 other than void conditions. The primal germ-force, origin- 

 ated by the union of certain elements existing in a turbid 

 water, must push its way against a resisting or reactive 

 medium, incorporating sundry elements therefrom as it 

 goes and meets with feebler reactions at successive steps, 

 until finally the acting and reacting forces come to an 

 equality, a limit is reached, and a new turn of action must 

 take place. One phase of the system is formed, and, just as 

 in the macrocosmal example, a return towards the origin 

 becomes necessary. 



The unique direction of the reacting force of the soil 

 against the deposited germ of the plant compels the forces 

 of the latter to take the direction of the normal to the sur- 

 face, while the equable horizontal pressure of the surround- 

 ing atmosphere determines the cylindric form of the ascend- 

 ing stem; the nodes and # spiral arrangement of the buds of 

 which respectively betray the wave -form of the impulses 

 from below and the rotative influence of the sun's chang- 

 ing direction. Eeaching a higher and rarer medium, the 

 spherical form of expansion becomes easier, and branches 

 radiate accordingly, while still obeying the cylindrically 

 imprinted forces. At the limiting region, therefore, there is 

 discontinuity of substance, each separate twig carrying on 

 its leaves, and terminating in a flower-bud, which now re- 

 sumes a miniature of all the resultant forces gathered dur- 



