832 



SCIENCE 



[N. S. Vol. XEEI. No. 1093 



In the early spring of the present year 

 (1915) I had so far completed the construction 

 of mathematical formulas for the computation 

 of the tides, that I actually computed the lati- 

 tude at which the two tidal waves crossed each 

 other at noon of each day during the limation 

 between May 13 and June 13. This calcula- 

 tion led to the discovery that, whatever may 

 be the relative declinations of the sun and 

 moon at the moment of conjunction or oppo- 

 sition in right ascension, the two tidal waves 

 will always cross each other exactly at the 

 equator; and at the distance of 90° both east 

 and west from the meridian on which the sun 

 and moon are situated. During this limation 

 the two tidal waves crossed each other at an 

 angle which varied between 4° 20' and 90° ; 

 and the latitudes at which they crossed each 

 other were less than 40° during about three 

 days, at the times of new and full moon; 

 while during the twenty-six or twenty-seven 

 remaining days of the lunation the high water 

 was confined within the latitude of 45° and 

 Y0°, making a typical high-water zone of about 

 25° in breadth. 



I^ow it will be remembered by readers who 

 are familiar with tidal history, that both New- 

 ton and Laplace were greatly embarrassed by 

 the fact that the highest tides did not occur 

 at the time when the acting forces were the 

 greatest, but about a day and a half later; 

 and in order to explain this default of theory, 

 they were obliged to assume the operation of 

 fictitious or imaginary causes. The observa- 

 tions on which their theories were based were 

 made in southern England or northern France, 

 in latitudes in which the united tidal wave did 

 not usually reach until about a day and a half 

 after the time of new or full moon; and the 

 reason it was not observed was not on account 

 of its non-existence but because it was on duty 

 in another place. 



We shall now consider the united tidal wave 

 during the lunation beginning with the full 

 moon of July and ending with that of August. 

 According to the data given in the American 

 Ephemeris, the two tidal waves at the instant 

 of conjunction on August 10 made an angle 

 with each other amounting to only 43.8"; so 



that they were practically superposed the one 

 upon the other throughout their whole extent 

 and reaching entirely around the earth. But 

 as the lunar tidal wave travels over the earth's 

 surface about thirteen times as fast as the 

 solar tidal wave, they soon part company near 

 the equator, each wave revolving around its 

 own polar axis ; and at the end of a single day 

 the latitude of the united tidal wave will be 

 found at 61° 40' and the two tidal waves will 

 cross each other at an angle of about 11° 20'. 

 The united tidal wave will then remain on or 

 very near to the parallel of 62° of latitude 

 mitil near the end of the lunation; and there 

 would be a daily succession of uniformly high 

 tides on that parallel of latitude during nearly 

 a whole month. 



We have thus far considered only that por- 

 tion of the tidal waves which rises ahove the 

 normal surface of the ocean ; but the water can 

 not rise at any given place on the earth's sur- 

 face without an equivalent depression at some 

 other point; and a correct theory of the tides 

 will explain equally well all the conditions 

 incident to their formation. ITow we know 

 that the earth's surface-gravity is diminished 

 by the attraction of the sun and moon at all 

 points of the surface that are less than 54° 44' 

 of angular distance from those bodies, and in- 

 creased for all greater distances. It therefore 

 follows that all fluids that are under the sun 

 and moon and are free to flow, will flow away 

 from the point directly under the sun or 

 moon, instead of towards it, as required by the 

 present accepted theory of the tides. This fol- 

 lows for two reasons : First, because the 

 earth's gravity is greater in that direction, 

 and, second, because the tangential forces of 

 the sun and moon actually push all bodies in 

 that direction. This is one of the most beau- 

 tiful and interesting consequences arising 

 from the gravitation of matter; for, were the 

 manner of its action to be reversed, the earth 

 would no longer be habitable by man or beast ; 

 for the sun would be hidden by a perpetual 

 cloud by day, and the moon by night; and 

 neither of the luminaries would be visible ex- 

 cept at rare and uncertain intervals. 



Sir John Herschel in his " Outlines of 



