BOW TO WEIGH THE SUN. 691 



just before Newton, what is the law of variation ? And there was not found one 

 among men able to solve the problem. 



Before we proceed, it will be well to remark that physicists at that time did 

 not know the amount of variation of velocity at different points on the earth's 

 surface as we do now. They did not have mathematically exact clocks nor re- 

 fined instruments of measurement; all they had as a basis to work on was an im- 

 pression, simply, that gravity varied slightly, and that this variation depended in 

 some way on distance from the centre of the globe. These things render more 

 remarkable the achievement of Newton. Let us now, along with that great man, 

 begin a search for hidden law, and propound such questions as these to our own 

 minds, as he did : How great a velocity will a falhng body attain in one second 

 if let fall from heights of five, ten or fifty thousand miles above the surface of the 

 earth ? How shall we learn ? we cannot reach these altitudes ; is there no way 

 to .find out? There is, — but none save Newton can tell us. Let us see; the 

 moon is above the surface of the earth, and if gravity reaches that far, it must be 

 a faUing body. Conceive the earth and moon to be called into existence instant- 

 ly, then the moon must begin to fall toward the earth at once, smce our world 

 contains eighty times as much matter. And if the attraction of the earth is as 

 strong there as it is on its surface, the moon, at the termination of the first second 

 of its fall, must be moving with a velocity of 386 inches per second, directly to- 

 ward the centre of the earth. Now we all know that the moon does not approach 

 the earth, although terrestrial gravity is exerted upon it all the time, making it 

 tend to fall; and fall it would, did there not exist some force able to hold it back. 

 What is this force ? Tie a cord to a stone, and revolve it rapidly around the 

 hand ; the string will be found to pull with a force which varies in some ratio to 

 the velocity. Make the stone revolve twice as fast, and even with the hand it 

 can be detected that the pulling sensation is more than twice as strong as before ; 

 while with instruments it is demonstrated that the centrifugal force varies as the 

 square of the velocity. So with the moon ; its velocity generates centrifugal force 

 which draws against the attraction of the earth precisely as the stone against the 

 hand. Behold ! we are in the midst of an inductive process which leads to a law 

 of Nature. Is it not clear, that, if we can find how much centrifugal force is 

 evolved by the motion of the moon, we shall at once know how strong the earth 

 attracts at that distance, since we already know these two forces are equal, because 

 the moon does not come nearer the earth ? But how shall we find the centrifugal 

 force of the moon ? It is developed by analysis that if a body in space revolves 

 around another with velocity sufficient to prevent gravity from causing them to 

 approach, the velocity of the revolving body must equal the square root of the 

 product of gravity multiplied by the radius of its orbit. The mean equatorial 

 radius of the earth is 3962.72 miles, and the mean distance of the moon is just 

 sixty times as much, or 15,064,676,352 inches. And the force of gravity exerted 

 by the earth at the distance of the moon, let us assume, is equal to a force which, 

 acting one second, could make the moon move in centripetal fall, at its close, 

 with velocity of 386 inches per second. Now multiply the above number by 386, 



