Researches in the Theory and Calculus of Operations. 297 



together that the direction of rotation shall of the same 

 direction throughout, as in the solenoid ; in which position, 

 the extremities of the crystal are specially related as the 

 north and south poles of a magnet. We are thus led to the 

 supposition that the atomic elements of this mineral sub- 

 stance quartz, while in the fluid state, were so composed by 

 the three cosmical forces above named as to take on this 

 helicoidal form of action, arranging themselves in a mag- 

 netical shape, and subsequently dropping adhesion between 

 the poles. External pressure or other forceful action upon 

 the atomical forces of a nascent fluid may originate therein 

 a system of one, two, three, etc. axes, around which the 

 intensity of the forces may differ, and thus give rise to a 

 spheroidal or polyhedral shape of atom, instead of simply 

 spherical or cubical. Planes of cleavage evidently consist 

 as the boundary between molecular systems of atomical 

 forces, and are superficial nodes corresponding to the linear 

 nodes of linear forces. 



We have seen (section 5) that a single impulsion applied 

 to the unit mobile 1^ generates a velocity (a force of the 

 first degree <p' = 1 J which carries the mobile the distance 

 nl t in the time nl provided no resistance be encoun- 

 tered ; but if the operation has place in a resisting medium, 

 a renewed and persevering application of the force which 

 gave the first impulse is required to continually overcome 

 this resistance. Here the phenomenal result (fig. 38) con- 

 sists simply in the arrival and departure of the burthen at 

 the successive stations 1, 2, 3, 4, etc., and is the first kind 

 of change offered for investigation in the study of the me- 

 chanical and physical sciences. The primitive force which 

 starts the movement, being capable of a continued renewal 

 of its application, is therefore a force of the second degree 

 <f)", constant if the renewals are of the same intensity, 

 variable if otherwise. A mechanical change consists in a 

 displacement in space, while a physical change consists in 



Trans. vii~\ 38 



