154 THE THEORY OF GRAVITATION. 



tioual to the density of the medium made up of these atoms and their 

 interstices. Now, the gravitation of the body (exclusive of all other 

 elements than this atomic mass) is proportional to this same mean den- 

 sity. How, then, can it be that the retardation is imperceptible while 

 the gravitation is so sensible? The objection is rendered the more 

 forcible when we consider that the retardation of a revolving body is 

 brought about by all the atoms which it meets in its orbit, while its 

 gravitation is produced only by those which at any one position in its 

 orbit are directed toward the central body. 



XXIV. 



Reply: Other things being equal, the force of gravitation, being pro- 

 duced by the single stream of atoms deprived of antagonists, is propor- 

 tional to the square of the velocity of the atoms (by a proposition demon- 

 strated generally), while the retardation above spoken of, being caused 

 by the stream opposing the planet in its motion, is proportional to the 

 product of this velocity of the atoms by that of the revolving body (as 

 we shall prove directly). Consequently (things being equal) the gravi- 

 tation is to the retardation as the velocity of the atoms is to that of 

 the revolving body. 



Now, it is not hard to believe that the velocity of the atoms is greater 

 than that of the revolving body; and, indeed, all that we have hereto- 

 fore said would lead to the presumption that it is incomparably greater. 

 Hence the system of thin-sown atoms moving in every direction agrees 

 very well with a condition of gravitation incomparably greater than 

 the retardation, and it agrees still, despite the consideration which for- 

 tifies the difficulty which we are considering, since a velocity has always 

 been assigned to the atoms greater than would have been necessary to 

 obviate this latter difficulty alone. 



Remark: I have said that the retardation of a great body caused by 

 the opposing stream of atoms moving much more rapidly than the 

 body itself would be proportional to the product of the velocity of the 

 atoms by that of the great body. I shall first demonstrate this propo- 

 sition with respect to the couple of opposed streams parallel to the 

 direction of the great body, and in so doing I shall have proved it for 

 the case of opposing streams oblique to this direction, since their 

 motions may be decomposed in two directions, the one parallel and the 

 other perpendicular to the direction of the body, of which the first is 

 nearly always much greater than the motion of the body, and of which 

 the second produces no effect. 



Demonstration : The total retardation of the body is the excess of 

 the simple retardation it experiences from the stream which it encoun- 

 ters over the simple acceleration which it experiences on the part of 

 the stream which pursues it. Now, these simple factors are propor- 

 tional to the squares of velocities, which are respectively the sum and 

 difference of the absolute velocity of the atoms and the absolute veloc- 



