62 REPORT OF THE SECRETARY. 



The investigation of the half-monthly inequality, or of the effect of 

 the action of the sun in modifying the effect of the moon in time as 

 well as in height of tide, gave the following results: The range of 

 the inequality in time is one hour and twenty-six minutes. The mean 

 establishment of high water is found to be eleven hours thirteen min- 

 utes and eight-tenths, and that of low water seventeen hours nineteen 

 and a half minutes. The range of the variation in the height of the 

 water, due to the action of the sun and moon, is two feet and a half. The 

 absolute average variation in the height of water at Port Foulke is 

 7,7 feet, while Dr. Kane found at Van Rensselaer harbor 7.9 feet as 

 the variation at that place. The extreme fluctuation observed in the 

 water level was 13.8 feet. The retardation or the difference between 

 the theoretic and observed time of high water is comparatively small. 



The effect of the greater or less distance of the moon or parallax 

 on the half-monthly inequality shows that diminution of distance 

 produces a decrease in the time of the lagging of the water, and that 

 the range of the tide is increased by three-tenths of a foot for an 

 increase of one minute of parallax. The action of the sun must ev- 

 idently be relatively less, with an increase of the declination of the 

 moon, and the amount of this is found from the discussion of the 

 observations to be in height of the value of only a fraction of a foot, 

 and in time but a few minutes. 



The moon, as it is well known, produces two high tides, at nearly 

 the same moment, on opposite sides of the earth, and these must vary 

 in altitude and extent from day to day, with the change of position 

 of the moon in the heavens. The difference of these two tides in time 

 and height is called the diurnal inequality. Mr. Schott has made 

 of this phenomenon a special graphical study, and has found that the 

 diurnal variation in height is greater for high water than for low 

 water — that is, two successive high waters differ from each other 

 more than two successive low waters. The maximum variation in 

 height is found at Port Foulke to be 3.8 feet, and only 2.4 in low 

 water, while this variation entirely disappears about two days after 

 the moon passes the equator. This is for the high water ; but for 

 low water the disappearance does not take place until after a lapse 

 of nearly ten days, and this fact is connected with a remarkable one 

 relative to the magnitude of the variation. On the one hand, the less 

 interval of time between two tides is accompanied in high water 

 with a greater difference of height, while in low water a greater 

 interval of time is connected with a smaller difference in the level 

 of the two tides. The diurnal inequality is due to two waves, a 



