THE THEORY OF GRAVITATION. 159 



the orthogonal projection of the visible universe upon the plane of this 

 section. 



Sixth. The different parts of a single current are sensibly of equal 

 density, either where contemporary portions of sensible magnitude or 

 successive portions occupying sensible times in traversing a given 

 surface are compared. The densities of different currents are also 

 equal. 



Seventh. The mean velocity determined in the same manner as the 

 mean density is also sensibly constant. 



Eighth. This velocity is several thousand times as great, relative to 

 the velocities of the planets, as is the gravitation of the planets toward 

 the sun relative to the greatest resistances which secular observations 

 permit us to suppose they experience. For example, several hundred 

 times greater relative to the velocity of the earth than the gravitation 

 of the earth toward the sun multiplied by the number of times the 

 firmament would contain the disc of the sun is greater than the greatest 

 resistance which the secular differences in the length of the year permit 

 us to suppose the earth experiences from celestial matter. 



CONCEPT, WHICH FACILITATES THE APPLICATION OF MATHEMATICS 

 TO DETERMINE THE MUTUAL INFLUENCE OF THE HEAVY BODIES 

 AND THE CORPUSCLES. 



First. Decompose all heavy bodies into equal masses so small as to 

 allow them to be treated without sensible error as attractive particles 

 are treated in those theories of gravitation in which no hypothesis is 

 made as to its cause. In such a small mass the effects of unequal dis- 

 tance and position of its particles relative to those of the mass which is 

 conceived to attract it, and to be attracted by it, may be neglected. 

 Such masses will have a diameter no more than one one-hundred- 

 thousandth as great as the mutual distance of the two masses under 

 examination. Thus the apparent semidiameter of one as viewed from 

 the other does not exceed one second. 



Second. For the surfaces of this mass, accessible but impermeable 

 to the gravitational fluid, substitute a single spherical surface equal to 

 their sum. 



Third. Decompose these first surfaces into facets sufficiently small 

 to be treated as planes without sensible error. 



Fourth. Transport all these facets to the spherical surface above 

 mentioned. Each one of the facets should in this transformation 

 occupy that point of the spherical surface at which the tangent plane 

 is parallel to the original position of the facet. 



REMARKS. 



First. It is not necessary to be very expert to deduce upon these 

 suppositions all the laws of gravitation, both terrestrial and universal 

 (and consequently those of Kepler and some others), with as much of 



