kixetic theories of gravitation. 211 



Conditions of the Problem. 



It is well to bear in mind that every hypothesis directed to the expli- 

 cation of gravity, is required in limine to give a satisfactory account of 

 the following six characteristics of this mysterious influence : 



1st. Its direction is radial toward the acting mass, or rectilinear — in- 

 definitely. This rectilinear traction is incapable of deflection by any 

 intermediate force. It suffers neither disturbance nor interference from 

 any multiplication of similar lines of action, and admits neither of re- 

 flection, refraction, nor of composition. 



2d. Its quantity is exactly proportional to the acting mass — indefi- 

 nitely. Corollary: hence, 



2d b. Its integrity of action is complete with every accumulation of 

 additional demand — indefinitely ; that is to say, no multiplication of 

 duty in the slightest degree impairs its previous tensions. 



3d. Its intensity is diminished by recession, in proportion to the square 

 of the distance through which it acts — indefinitely ; in a manner some- 

 what analogous to — but (as modified by the second condition) radically 

 different from — the action of light. 



4th. Its time of action is instantaneous throughout all ascertained dis- 

 tances, and therefore presumably — indefinitely. Corollary : hence, 



4th b. Its rate of action (if the expression may be tolerated) is precisely 

 the same on bodies at all velocities — indefinitely. It no more lags on a 

 comet approaching the sun at the inconceivable speed of two hundred 

 miles in one second than on a body at the lowest rate of motion, or than 

 on the same comet receding from the sun at the same velocity. 



5th. Its quality is invariable under all circumstances — indefinitely. 

 It is entirely unaffected by the interposition of any material screen, 

 whatever its character or extent ; or in other words, it can neither be 

 checked by any insulator nor retarded by any obstruction. 



Gth. Its energy is unchangeable in time, certainly for the past two 

 thousand years; presumably — indefinitely. Corollary: hence, 



Gth b. Its activity is incessant and inexhaustible — indefinitely ; the 

 ceaseless fall of planets from their tangential impulses involving no 

 dynamic expenditure in the sun or in other known matter. 



It is scarcely necessary to add, as the necessary outcome of the latter 

 propositions, that gravitation is a property immutable and inconvertible. 

 As in the 1st proposition, two terminal elements (m' and m") are neces- 

 sarily assumed for determining the direction and measure of the radial 

 straight line of action ; and as in the 2d proposition, u the acting mass' ; 

 (m) is the product of these two elements, (m'.m" 7 ) — the action being 

 reciprocal; so in the 3d proposition, the measure of the diminution of 

 intensity (d 2 ) has reference to the same two elements, between whose 

 dynamic centers the value of the distance d is taken. And the expres- 

 skm for these propositions considered collectively is ' as the measure 

 of the combined quantity and intensity of the traction between the two 

 given elements. If we regard m" as incomparably smaller than m', (as 



