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228 THE POPULAR SCIENCE MONTHLY. 



the centre. There is no force acting directly from the centre. That 

 which is often called centrifugal is really centripetal force, for the 

 tension of the string in the following experiment is hot caused by any 

 force acting on the ho^y from the centre, but it is caused by a force 

 drawing the body out of its rectilineal course, and toward the centre, 

 compelling it to move in a curve. 



Suppose the body E (Fig. 1) moves with a certain velocity in the 



curve I? CD, and that the string 



ES feels a known tension, just 



"*\ A equal to its strength. Now, 



*\ double the velocity, and the 



strength of the string must be 



increased fourfold to keep it 



\ from breaking, for the force 



\ drawing the body toward the 



i centre must then be four times 



\ J as great to keep it moving in 



\ : d the curve. Or, suppose the body 



C\ / moves from A toward B with 



y'' a known velocity, and that on 



''..^ ,.'''' reaching E\% is acted upon by 



"f"ig"i" tne strm g- 1' ne body is then 



made to take a curvilinear mo- 

 tion, and the string feels a tension drawing the body not directly 

 from but toward the centre, and equal to a force necessary to keep 

 the body from moving in a straight line. It may be remarked that, as 

 action and reaction are equal, the tension is felt both ways. But the 

 reader can easily see what I mean. 



This law of motion can be still better illustrated by a reference to 

 one of the satellites of the planet Neptune. The mean distance of 

 this satellite is nearly equal to the distance of our moon from the 

 earth. We may assume these distances to be exactly equal. Then, 

 as at the same distance the centripetal force must increase as the 

 square of the velocity, to keep the body moving in the curve, and as 

 the velocity of this moon of Neptune is about four and a half times 

 greater than that of our moon, the centripetal force, or the force of 

 gravity produced by Neptune on this moon, must be (4.5) 2 about 

 twenty times as great as is the centripetal force or the gravitating 

 power our earth produces on its moon. In other words, the planet 

 Neptune is about twenty times as heavy as our earth, for weight is 

 nothing else than the measure of gravity. 



The preceding statements are sufficient to show what is meant by 

 centrifugal and centripetal forces. Let us now see how these act on 

 bodies moving in large and small curves, and how the waters on the 

 earth's surface are driven by centrifugal force toward a line tangent 

 to her orbit. Since the length of the orbital curve of the earth is 



