38 THE POPULAR SCIENCE MONTHLY. 



either increased or diminished by the fact that at the same time it 

 also exerts an attraction on C, D, or E. Now, let B, C, D^ and E, be 

 united into one mass, F, and it will be readily perceived that the 

 truth of the foregoing statements cannot thereby be affected. 



As a general formula the law of gravitation may be enunciated as 

 follows : " If one of the masses contain m units of mass, and the other 

 one unit, the force will be m times as great as though they were both 

 units of mass ; but if the second body contain n units of mass, the 

 attraction will be n times as great as before ; that is, m n divided by 

 the square of the distance between the bodies." 



Now, suppose A and F fi-ee to move, then on meeting A will have 

 moved over four-fifths of the distance between A and F, and F during 

 the same time will have moved over one-fifth of the same distance ; 

 tiiat is tc say, the velocity of A has just been equal to four times that 

 of F, and this is just what might have been expected from what is 

 known of the laws of force. Suppose A and F to be placed where 

 friction and other obstacles to motion do not exist, the velocities of 

 the bodies will be indirectly as their masses, if the respective forces 

 exerted on the bodies be equal ; that is, a force which would propel a 

 body with a certain velocity would proj)el another body one-quarter 

 of the mass of the former with four times the velocity. In the case 

 sujjposedj since A is one-quarter of the mass of F, a given force must 

 necessarily move A over four times the space and with four times the 

 velocity that it is able to move F, and when A and F meet the mo- 

 menta of A and F will be respectively equal. 



The truth that two bodies mutually and equally attract each other 

 is also abundantly proved in astronomy. Take the case of the earth 

 and moon. The earth by its attraction compels the moon to make 

 around it as a centre her monthly revolution ; but it is equally true 

 that the moon compels the earth to move around the centre of gravity 

 of the earth and moon, which centre, on account of the earth's mass 

 being over eighty times that of the moon, is distant from the earth's 

 centre a little pv^er 2,000 miles, and this motion of the earth is per- 

 formed in precisely the time of the lunar revolution, namely 27^ 

 days. Now, it will require but little reflection to perceive that to 

 move the earth in a circle with a radius of a little more than 2,000 

 miles, and the moon in a circle with a radius of nearly 240,000 miles, 

 would requii-e equal forces. The same thing is true of the sun, which 

 is obliged by the combined forces of the planets to revolve around 

 the centre of gravity of the solar system, and on making the neces- 

 sary calculations we find that the force exerted on the planets by the 

 sun just equals the force exerted by the j^lanets on the sun. 



Weight has been defined as the measure of the earth's attraction. 

 A body weighing one pound attracts the earth and is attracted by it 

 with a force of one pound, but the same body at the sun's surface 

 would attract the mass of the sun with a force of twenty-seven pounds. 



