234 Researches in the Theory and Calculus of Operations. 



of the two elements commences as in chemical combination, 

 and continues under the influence of the cause that initiated 

 the operation. 



As an application of our forceful theory to the interpreta- 

 tion of one of the most familiar cosmical phenomena, let 

 (fig. 2) OA represent the solid globe of the earth, and If, C 

 spheres of emanated force, D being put for the limiting 

 sphere. E is a small sphere of matter placed within the 

 limiting sphere OD. The spheres CA and E being free to 

 act upon each other, the encounter of the emanating forces 

 during a first instant of time annihilates a portion of each 

 which acted in the opposing directions OE and EO, liberat- 

 ing respectively an equal portion to act during the second 

 instant in the mutually opposing directions OC and E C. 

 As the action and reaction hold between the spherical shells 

 as well as through the diameters (see 6), the liberated force 

 in OC draws E towards O and the force EC draws to- 

 wards E ; but as the mass of is very much greater than 

 that of E, the latter is moved bodily towards the former. 

 In the succeeding moment of time, the process is reiterated ; 

 and so for every succeeding moment, the velocities being 

 continually added, whereby the body E describes a distance 

 increasing as the square of the time of the fall. Thus with- 

 out resorting to the hypothesis of attraction (in which the 

 force "looks one way, and rows the other"), the so-called 

 law of gravitation is demonstrated from the principle of 

 emanation alone (fig. 3). 



The principles in question are directly available for the 

 interpretation of the daily occurrence of the ebb and flow 

 of the waters of the ocean. -Let A represent the Earth and D 

 the Moon. Suppose the arc R to indicate the boundary of the 

 Earth's emanation , and S the boundary of the Moon's emana- 

 tion, in all relative positions of these bodies, and in all direc- 

 tions from their centres except that particular one which con- 

 nects their centres for the time. When the Moon approaches 

 the terrestrial meridian of any place, the terrestrial emanation 



