8 , U. S. COAST AND GEODETIC SURVEY. 



rise until the point is again directly under the moon. The time 

 required for the point P^ to pass completely around the circle and 

 back to its original position directly under the moon is approximately 

 one day. During this period there have been two high waters of 

 equal height and two low waters of equal depression. The height of 

 the high waters above the mean level, however, is greater than the 

 depression of the low waters, indicating that the average elevation of 

 the water at the Equator has been raised above the normal by the 

 presence of the moon. If we take a point P/ in latitude 30° N., we 

 again find two high waters of equal height and two low waters of 

 equal depression occurring during the day, but the height of the high 

 waters is more nearly equal to the depression of the low waters. In 

 latitude 60° we again find two equal maximum and two equal mini- 

 mum heights, but in this case the equilibrium surface is below the 

 mean undisturbed surface during the entire rotation of the earth. 

 From the foregoing we may conclude that under the equilibrium 

 theory, when the moon is on the Equator, there will usually be in all 

 latitudes two equal high waters and two equal low waters during 

 each day, and that the presence of the moon will tend to raise the 

 average level near the Equator and to lower it near the poles. It will 

 also appear evident that the amount of these variations will depend 

 upon the distance of the moon from the earth; the nearer the moon 

 is to the earth the greater will be its effects. 



Let us now examine Figure 5, which illustrates the tidal condition 

 when the moon is near its greatest north declination. If we take a 

 point Pi in the Equator, as before, we find that in this case also we 

 have two equal high waters and two equal low waters during the day, 

 but the increase in the average height of water on the Equator is not 

 as great as that shown in Figure 3. If we take the point P/ and 

 follow it around the small circle in latitude 30° N., we pass through 

 a low water at Pj', a high water at Pg', a low water at P/, and return 

 to the high water at P/. We still have two high waters and two low 

 waters during the day, but it will be noted that one high water is 

 somewhat higher than the other, while the two low waters are of 

 equal height. In latitude 60° N. we have during a single day only 

 one high water, which is at P/', and a low water at Pa". In this 

 case the tide is said to be diurnal, while in the usual case of two high 

 waters and two low waters each day the tide is called semidiurnal. 

 If we were to take sections in the Southern Hemisphere corresponding 

 to those for the Northern Hemisphere, with the moon still in its north 

 declination, we would obtain ellipses similar to those in Figure 5, 

 except that the centers of the ellipses instead of being on the side of 

 the earth's axis nearest the moon would be displaced by an equal 

 amount on the opposite side. From these figures we may conclude 

 that, according to the equilibrium theory, there will be a semidiurnal 

 tide with equal high and equal low water heights at all places on the 

 Equator for any declination of the moon. If the moon is in north 

 declination, and we travel from the Equator northward, we should 

 expect to find the semidiurnal tides continuing with equal low waters, 

 but with an increasing difference between the heights of the two high 

 waters, the higher high being on the side of the earth toward the 

 moon and the lower high on the opposite side. After reaching a 

 certain latitude the lower high and the two low waters should, 

 according to this theory, blend into a single low water on the side of 



