haemo:n'ic analysis and peediction of tides. 9 



the earth opposite the moon, the tide then becoming diurnal and 

 remaining such for all latitudes north of this. If we were to proceed 

 southward from the Equator while the moon is still in north declina- 

 tion, we should find similar conditions prevailing, except that the 

 unequal high waters of the semidiurnal tide and the single high and 

 single low waters of the diurnal tide would have their positions 

 reversed; that is, the higher high water of the semidiurnal and the 

 single high water of the diurnal tide would occur on the side of the earth 

 farthest from the moon instead of on the side nearest to that body. 

 If the moon is. in south declination, the conditions in respect to the 

 Northern and Southern Hemispheres will, of course, be exactly re- 

 versed. 



In this discussion only the moon has been considered. The sun 

 alone should have an exactly similar effect, except that, on account 

 of the greater distance, the magnitude of the tide would be only 

 about one-half as great as that due to the moon. Theoretically, the 

 height of the tide at any place due to each body can be computed 

 separately and the sum taken to represent the height due to the com- 

 bined effect. 



As already stated, the actual conditions that exist on the earth 

 differ so greatly from the ideal conditions assumed for the equilibrium 

 theory that tHe tides as derived from that theory are expected to 

 differ greatl}^ from tides as actually observed. It will be interesting 

 to note here some of the agreements and differences. 



1. Generally two high waters and two low waters occur during each 

 day, but the high waters do not necessarily occur when the moon 

 and sun are on the meridian. The interval between a transit of the 

 moon and the occurrence of a high water varies in different parts of 

 the earth without any apparent regard for the equilibrium theory, 

 and high water may occur at any hour between successive transits 

 of the moon; but for any particular place the interval between the 

 time of transit and the time of high water remains approximately 

 constant. 



2. Usually the alternate high waters or the alternate low waters 

 are nearly equal in height when the moon is near the Equator and 

 have an increasing diurnal inequality as the moon's declination 

 increases north or south of the Equator. According to the equilibrium 

 theory there should be a diurnal inequality in the high waters only, 

 and with any given declination this inequality should depend upon 

 the latitude. As an actual fact we find that at many places there is 

 a much larger inecj[uality in the low water heights than in the high 

 water heights, and that the magnitude of the inequality apparently 

 has no direct relation to the latitude of the place. 



3. By the equilibrium theory the diurnal tides would be expected 

 only in latitudes near the poles, but observations show that stations 

 near the Equator as well as those near the poles have diurnal tides. 



In the following chapter a formula will be obtained which will 

 represent the approximate height of the tide at any time and place, 

 based upon the equilibrimn theory. Although it is recognized that 

 any calculations of the tide based solely upon this theory ma}^ give 

 results entirely at variance with the real tide, because the actual 

 conditions on the earth differ so much from the assumed ideal con- 

 ditions, 5^et such a formula is very useful, inasmuch as v,-e may intro- 

 duce into it certain factors and differences determined from actual 



