JtfARS AS A WORLD. irj 



planot to swerve from a rectilinear path, and thus con- 

 strains it to move in a circular orbit. The more rapid the 

 motion, the more intense must be the force which is con- 

 tinually drawing the planet aside from the rectilinear 

 path, and consequently, the greater must be the mass of 

 the central sun by which the attraction is produced. The 

 proportion is, however, not a very simple one. If the mass 

 of the sun be doubled, the speed of the planet will not be in- 

 creased in the same proportion. The true law is that the 

 mass of the central attracting body will be proportional to 

 the square of the velocity, or inversely proportional to the 

 square of the periodic time. Hence it follows that if the 

 mass of the central sun be increased fourfold, the speed of 

 the satellite will be doubled, or what comes to the same 

 thing, the periodic time of the satellite will be reduced to 

 one-half. 



Returning now to our figure. We have seen that the 

 two bodies revolve in periods of 8,000 months and thir- 

 teen months respectively ; that their distances from the 

 primaries are equal ; and from these data it is required to 

 conclude the relative masses of these primaries. One of 

 these numbers is about 615 times the other. Hence we 

 have to determine the relative masses of two central 

 attracting bodies, such that the relative periodic times of 

 their planets at equal distances shall be 615. We have 

 shown that the masses of the central bodies must be 

 inversely proportional to the squares of the periodic times ; 

 hence we learn that the more rapidly moving of these two 

 bodies must be controlled by a central force which is 

 615 X 615 times greater than that necessary for the 

 slower motion. We have used approximate numbers in 



N 



