276 THE POPULAR SCIENCE MONTHLY. 



earth's surface nearest the sun, beicg acted upon more powerfully by 

 the gravitating influence of this central force than the remote part, 

 will show a less tendency to move on in a line tangent to the earth's 

 orbit. Hence there will be another tide produced by gravity di- 

 rectly. 



I have thus far spoken only of the solar tides. It will be necessary 

 also to say something of lunar tides, or what influence the moon has 

 on the phenomena of the tides. 



It is a well-known fact that there is a jioint between the earth and 

 her moon called their centre of gravity. The distance between the 

 centres of these two bodies is about 240,000 miles. A rough calcula- 

 tion brings the centre of gravity of these bodies about 2,687 miles 

 from the centre of the earth, and 237,313 miles from the centre of the 

 moon. This point describes the curve of an ellipse around the sun ; 

 and the earth and moon revolve around this point, while they both 

 sweep through space in their majestic journey around the sun. It is 

 therefore evident that the earth, in her ceaseless motions, is influenced 

 by three different centrifugal forces. The one is produced by rotation 

 on her axis ; the other by her revolution around the sun ; and the third 

 by her revolution around the centre of gravity between herself and 

 the moon. 



Let us suppose that the earth and moon have no other motion in 

 space than that of revolving around their common centre of gravity, 

 and that the same side of the earth is always facing the moon. The 

 earth will then feel a centrifugal force on her side farthest from the 

 moon, and equal to the centripetal force felt on her side facing the 

 moon. These two equal forces, acting in opposite directions, will 

 cause tide-waves on opposite sides of the earth ; and they will be pro- 

 duced in the same manner as the opposite ones, spoken of already, are 

 produced by centrifugal and centripetal forces felt by the earth in her 

 orbital motion around the sun. 



Let us now place the earth and moon in their proper position with 

 respect to the sun ; and let us suppose the moon to be in conjunction 

 with the sun, as at A^ Fig, 2. It is then new moon, and the moon's 

 centre is 237,313 miles within and the earth's centre 2,687 miles out- 

 side the elliptic orb described by their centre of gravity. At this 

 point of her path the earth feels, therefore, the greatest amount of 

 centrifugal force on the side of her surface farthest from the sun. This 

 large amount of centrifugal force is produced by axial rotation, by 

 revolution around the sun, and by i-evolution around the centre of 

 gravity already named. The direction of these three forces is in the 

 same line. The motion of this part of her surface, which is in this 

 line of direction, is therefore the most rapid ; consequently, the cen- 

 trifugal force felt here is also the greatest. Therefore^ we have one of 

 the highest tides when the moon is in conjunction with the sun ; and, 

 since centripetal is always equal to centrifugal force, the side of the 



