526 THE POPULAR SCIENCE MONTHLY 



it is the difference between the moon's attraction upon the given unit 

 mass and the moon's attraction upon the entire earth divided by the 

 mass of the earth. Because the depths of the oceans are small in com- 

 parison with the length of the earth's radius, and because of the small- 

 ness of the tidal forces, only the horizontal components of such forces 

 are effective in the production of tides; and so these may, without im- 

 propriety, be spoken of as the tidal forces. 



The vertical forces alter the intensity of the earth's gravity upon 

 the waters of the ocean in a way similar to the alteration which would 

 be occasioned were the density of the waters to undergo a fluctuation 

 having a range of less than one ten-millionth part of itself. Now the 

 greatest known ocean depth occurs near Guam Island and measures 

 5,269 fathoms or 31,614 feet; and it is obvious that the small density 

 fluctuation just mentioned, and so the vertical forces, can create no 

 sensible disturbance in the existing ocean. 



For simplicity's sake, we shall here ignore that alternation in the 

 forces which depends upon the declination of the moon, and is respon- 

 sible for what is called the " diurnal inequality " in the tides. We 

 shall also, as a rule, ignore that portion of the tidal forces resulting 

 from the sun's attraction. 



It is evident that at moonrise or moonset at a given point or local- 

 ity upon the earth's equator, the horizontal forces vanish because the 

 given point is then (very nearly) as remote from the moon as is the 

 earth's center. On account of the moon's parallax, the moon at the 

 times of rise or set does exert a downward disturbing force at the given 

 point or locality ; but, as already stated, this does not concern the tides. 

 When the moon is on the meridian above or below the horizon, the 

 disturbing force is all vertical and so the horizontal component does 

 not exist. Therefore the tidal forces vanish four times during each 

 lunar day. From moonrise to moon culmination, the force is directed 

 eastward; and from culmination to moonset, westward. Also from 

 moonset to lower culmination, the force is directed eastward, and from 

 lower culmination to moonrise, westward. 



For a point not upon the equator, there is also a meridional 

 periodic force. In north latitude this force has its maximum south- 

 ward value at the time of either culmination, and its maximum north- 

 ward value at moonrise and moonset. The reverse of this is true for a 

 point situated in the southern hemisphere. 



In accordance with what has been said, a suspended plumb bob 

 will, at the equator, make two complete oscillations daily in an east- 

 and-west direction. The average amount of deviation either way from 

 its undisturbed position will be about one thirteen-millionth part of the 

 length of the line measured from the point of suspension to the center 

 of inertia of the bob. 



