298 Researches in the Theory and Calculus of Operations. 



a change of quality without removal of the body or sub- 

 stance, as in the formation of chemical equilibrium by com- 

 bination of different elements, the undisturbed result or 

 which terminates in crystallization on the spot, in the case 

 where the combining elements find their mutual intensi- 

 ties satisfied; but if one of the combiners possesses or is 

 supplied with an overplus of force, this overplus is trans- 

 mitted unreduced to the next contiguous particle, which 

 now holds the same quantity of overplus of force as was 

 held by the first atom, and consequently a new combina- 

 tion takes place outside of the first atom, which may now 

 settle down into equilibrium : thus the process of combi- 

 nation and subsequent equilibration may go on in a linear, 

 superficial or radiating series according to the constitution 

 of the surrounding medium, until arrested by encounter ot 

 some heterogeneous opposing force. The branching of some 

 forms of crystal, the propagation of fermentation by means 

 of yeast, the growth of the joints of the tapeworm, the 

 communication of disease by inoculation, etc. etc., are 

 pregnant examples in which physical and mechanical 

 changes are combined, change of place with change of 

 quality. A force of the second degree is also requisite to 

 the origination of any of these phenomenal results, and we 

 now have at our successive stages in fig. 38, an elementary 

 crystal, or a drop of acid, or a joint of worm, or a pustule 

 of variola, etc. 



The operations hitherto considered have been conducted 

 by means of linear forces, that is, by forces of the first de- 

 gree, themselves each the product of a single act of a con- 

 stant force of the second degree, while their phenomenal 

 results are uniform in time, are of the degree zero of force, 

 and are susceptible of linear or spacial measures. But as 

 we now approach the boundary between physical and vital 

 forces, beyond which border variable forces of the second 

 degree come into play, it becomes incumbent to inquire 



