?74 THE POPULAR SCIENCE MONTHLY. 



a centrifugal force that is in excess of the centripetal force felt at this 

 same point ; and the matter of her surface facing the sun, l^eing near- 

 est to it, feels a centripetal force that is in excess of the centrifugal 

 force felt at this same point. But these two excesses are equal ; hence 

 there are equal solar tides at these points, while at the eartli's centre 

 there is an exact balancing of the two forces. 



Suppose the matter of the earth were all condensed into the vol- 

 ume of a cubic inch, and that this small volume were jjlaced at the 

 eartli's present centre ; then suppose it received an impulse carrying 

 it forward with a velocity equal to that which moves the centre of the 

 earth, and that it were influenced by the sun, according to the law of 

 gravity. This small volume, though equal in mass to the entire mass 

 of the earth, would then move in the same curve in which the centre 

 of the earth moves, and with the same velocity. But suppose this 

 solid inch of matter were to be placed 4,000 miles farther from the 

 sun, namely, at that point in space where the earth's surface is most 

 remote from tlie sun. This solid inch, or whole mass of the earth, 

 would then move in a longer curve than it would when at her present 

 centre, as under the first supposition. But completing, nevertheless, 

 in this longer curve, one revolution in the same time in which one 

 revolution is completed in the shorter curve, at the earth's centre, the 

 centrifugal force would be much increased ; and, the centripetal force 

 being also diminished in tlie same ratio, this cubic inch of matter would 

 either abandon the sun's companionship entirely or make a new orbit 

 of motion. In like manner are the waters of the earth operated on by 

 centrifugal force at this point of the earth's surface. They have a ten- 

 dency to fly off" in a line tangent to the earth's orbit. 



Now, suppose again that this condensed matter of the earth were 

 placed at that point in space where the earth's surface is nearest the 

 sun, namely, 4,000 miles nearer the sun than the centre of the earth 

 is : then the whole mass of the earth's matter woidd move in a 

 shorter curve than when placed at the centre, but, completing one 

 revolution in no shorter period, the centrifugal force would be dimin- 

 ished ; and, being also nearer to the sim, the centripetal force would 

 be much increased by the central power of attraction. Therefore, this 

 body of matter would, under this supposition, also leave its orbit, but 

 it w^ould be drawn toward the sun, and probably plunge into it. In 

 the one case, the centrifugal being greater than the centripetal force, 

 the body would fly/rom its centre of controlling power; in the other 

 case, the centripetal being equally superior to the centrifugal force, 

 the body would also be drawn out of its orbit, but dragged to the 

 centre of controlling power. These suppositions are made to show, 

 by w^ay of illustration, the excessive force of each kind over its oppo- 

 site, at opposite sides of the earth. And these equally excessive 

 forces, acting in such opposite directions, cause the opposite solar 

 tides. The particles of water, moving easily among one another, are 



