Researches in the Theory and Calculus of Operations. 299 



into their origination. To this end, it is again necessary to 

 anticipate on Part EE of these researches. 



Referring to fig. 3, let A represent a plane section of the 

 globe of the Sun, D the same thing for the Earth, and the 

 circumference stand for the vastly remote boundary of 

 equilibrium between ours and a neighboring solar system. 

 I assume the Sun to be a force of a very high degree of in- 

 tension ; variable originally, but subsequently constant for 

 very long secular periods down to the present. Radiating 

 and diffusing uniformly in time, equably in all directions 

 of space, and filling the sphere to its boundary with force, 

 the volume of this force is proportional to the cube of the 

 radius r 3 , while the extension and intension at any surface 

 is proportional to the reciprocals of the squares of the 

 radii r 2 and r -2 . During several secular periods prior to the 

 present, the action of the Sun upon the Earth was* more 

 intense, and has decreased down to the constant energy it 

 now puts forth as a force of the second degree <p". In its 

 capacity as such force, the Earth reacts against the Sun, 

 forming a border of equilibrium between the two at S', 

 which averts further approach ; while the force destroyed 

 by the encounter liberates as much in the opposite direc- 

 tions DE' and OA', which prevents further departure, and 

 the planet keeps its orbit (See section 3). As the Sun is the 

 greatest force, an overplus of its emanation reaches the 

 superficial strata of the Earth, where action and reaction 

 ensues, one of the results of which is the production of 

 light and heat as forces of the first degree 

 4 Digression 3. The primeval germ of the planetary uni- 

 verse was posited in a state of incandescence, and rushed 

 to fill the void (Nature abhors a vacuum) by one single 

 spherically advancing wave, reaching and meeting the boun- 

 dary of reaction at a single leap ; not by emanation now, 

 but by actual expansion of substance (nebula of Herschel 

 and Laplace), a completed spherical wave with venter at 



