Researches in the Theory and Calculus of Operations. 257 



density and particular form of combination of emanatory 

 forces, the latter determined by geological or cosmical 

 position and interfering forces while in the nascent state of 

 equilibration. 



All bodies or substances, at whatever temperature, con- 

 tinually radiate (emanate) caloric or matter of heat 

 (Fourier); so that matter or substance and heat are related 

 as cause and effect. We may then define substantial matter 

 as a constant force of the second degree, which constantly 

 emanates or generates force of the first degree, and accept 

 fig. 46 to assist in explaining the different kinds of the last 

 named force thus generated. It is abundantly proved, both 

 physically and mathematically, that all material bodies 

 constantly radiate and absorb heat (Prevost) : this is the 

 usual condition of mutual exchanges, undisturbed by the 

 introduction of new forces. But we have seen that certain 

 interferences, such as the application of severe friction upon 

 the surface of the body 01, evolves the heat with greater 

 rapidity ; while a much slighter friction evolves the electric 

 force (figs. 8 & 12). 



1° At and within the circle 1 (fig. 46), the atomic forces 

 are as represented in fig. 44 a', with centers merged; the 

 opposing hemispheres of the body 1 holding each other 

 in equilibrium, rendering the repulsion infinite at the sur- 

 face (the radii proportioned to the distance of the center, 

 1 : 0= oo), and becoming finite at an infinitesimal distance 

 outside. 



2° The spherical shells 1 3, 3 3', 3' 3", etc. represent the 

 departing calorific waves, which are exchanged by giving 

 and receiving with any exterior emanating substance in the 

 vicinity. The generated calorific atomical forces are as 

 represented in fig. 44 b (radius to the distance between the 

 centers as 1:1=1); and in fig. 46, by the small circles 3' 3', 

 3", etc. inscribed between the spherical shells 13,33',3'3", 



Trans. vii.~\ 33 % 



