TIDAL OBSERVATIONS. 



149 









Ilalf-monthly inequality in time. 











In higli 



water. 







In low water. 





C's transit. 



Observed. 



Computed. 



Difference. 



C's transit. 



Observed. 



Computed. 



Difference. 



0" 



2'?" 



+ 3- 



+ 3- 



Qm 



Qh 2r 



+ 4- 



+ 4" 



0" 



1 



29 



—15 



—13 



2 



1 29 



— n 



—12 



— 5 



2 



29 



—34 



—28 



—6 



2 29 



—29 



—27 



2 



3 



29 



—39 



—39 







3 28 



—35 



—38 



+ 3 



4 



28 



—46 



—42 



—4 



4 28 



—48 



—43 



— 5 



5 



30 



—24 



—32 



+ 8 



5 27 



—28 



—35 



+ 1 



6 



30 



— 5 



— 5 







6 26 



— 9 



— 9 







1 



26 



+ 31 



+ 24 



+ 7 



1 26 



+ 24 



+ 23 



+ 1 



8 



22 



+ 35 • 



+ 40 



—5 



8 21 



+ 50 



+ 40 



+ 10 



9 



30 



+ 40 



+ 41 



—1 



9 30 



+ 34 



+ 41 



— 7 



10 



29 



+ 33 



+ 32 



+ 1 



10 29 



+ 32 



+ 33 



— 1 



11 



28 



+ 19 



+ 18 



+ 1 



11 25 



+ 22 



+ 20 



+ 2 



The comparison is shown to better advantage in the diagrams. 



For high water. For low water. 



i+50- 



_M M 1 1 M M 1 1 M 



1 M 1 1 I ' M^l 1 _'J 1 



+50° 



■2 40 

 i 30 



I ./^\ 



/\ - 



40 

 30 



S 20 



— 1 \ ' 



/ \ ~ 



20 



& 10 



— 1 \ ' 



/ \ ~ 



10 



■S 



\ 1 



\ / 





 10 



3 10 



- \ / 



- \ / 



g 20 



- \ / 



\ / ~ 



20 



1 30 



— \ y 



\ */ - 



30 



S 40 



- \_y 



\_y _ 



40 



—50 



1 1 M !• 1 M 1 1 1 1 1 1 



M M I.I M 1 1 1 1 1 1 



—50 



Oi" 1 2 



3 4 5 



Moon' 



6 7 8 

 3 transi 



9 10 11 12'' 

 t. 



0" 1 2 3 4 5 6 7 8 9 10 11 121' 

 Moon's transit. 



The range of this inequality amonnts to 1'' 26" for either the time of hign or of 

 low water; this is about a normal value. At Van Rensselaer Harbor it amounted, 

 however, to the unusually large value of 1'' 52". 



The determination of the constants for the half-monthly inequality in height is as 

 follows : First, for the retard ; the epoch of the highest and lowest reading of high 

 water differs from that of the syzygy and quadrature, on the average by 52", hence 

 a = 13°, similarly the epoch of the extreme readings of low water differs nearly 32", 

 hence a = 9°. Second, for the range ; the inequality in the height of high water is 



2.4 feet; half of this, or 1.2 is the coefficient: the inequality in the low water is 



2.5 feet; its coefficient, therefore, 1.25. The mean of all the heights of high water 

 being 20.55, and of all the heights of low Avater 12.83, Ave have at once the approxir 

 mate expressions for the half-monthly inequality in height, for the high Avaters 



y = 20.55 + 1.2 cos 2{cp — 13°) 

 for the loAv Avater 



?/= 12.83 — 1.25 cos 2 (?> — 9°) 



