2 78 THE POPULAR SCIENCE MONTHLY. 



gravity exerted directly on her by the moon. And, on the side of 

 the earth facing the sun, she feels a centrifugal force produced hy 

 revolution around the centre of gravity of herself and the moon, and 

 also a centripetal force produced by the gravitating influence of the 

 sun. Hence there must be high tide also when sun and moon are in 

 opposition. 



It is a known fact that the solar are less than the lunar tides. 

 How must we account for this fact ? The sun is a body so large that 

 the mass of the moon is not much more than a grain of sand in com- 

 parison with it. But it must also be remembered that gravity dimin- 

 ishes as the square of the distance increases ; and as the moon is very 

 near the earth, and the sun a great way ofl\, the lunar influence is 

 much more strongly felt in tlie phenomena of tides than the solar in- 

 fluence. 



The amount of centrifugal force felt by a body moving in space 

 around a centre depends, not only on the velocity with which it moves, 

 but also upon the size of the curve in which it moves. If the circum- 

 ference of the curve is very large, it differs not much from a straight 

 line. If a body moves in space in the direction of a straight line, it 

 feels no centrifugal force at all. If it is deflected from the direction 

 of this straight line, only a very little, the circumference of the curve 

 will be very long, and the centrifugal force will be small. But, if it 

 is very much deflected, the curve becomes very small, and the body, 

 turning around very " short corners," has a strong tendency to fly 

 "off" the track." In other words, in a short curve the centrifugal force 

 is very great. 



Now, let us make an examination of the orbital curve of the earth 

 made in its motion around the sun. The length of tlie circumference 

 of this curve is, in round numbers, about 5*70,000,000 miles. A 

 straight line, 10,000 miles in length, tangent to this curve at one end, 

 is only about .526 of a mile distant from the circumference at its other 

 end. Therefore, the earth, moving in this orbital curve, feels rather 

 a small amount of centrifugal force. But, in her motion around the 

 centre of gravity between herself and the moon, she turns very " short 

 corners," and hence under this influence she experiences a greater 

 amount of centrifugal force than in her motion around the sun. For 

 this reason, also, the lunar are greater than the solar tides. 



If the earth had only one rotation in one revolution around the 

 sun, there would be, as already stated, one solar tide by virtue of cen- 

 trifugal force occurring at midnight, and another by virtue of centrip- 

 etal force occurring at noon. That is, perpetual night and high tide 

 would occur at one side, and perpetual day and liigh tide at precisely 

 the opposite side of the earth. But now let us suppose the earth ro- 

 tates on her axis once every twenty-four hours, and from west to east, 

 as she actually does rotate : then there wnll be motion of the waters ; 

 but this motion will be only apparent motion, and from east to west. 



