RECORD AND REDUCTION OF THE TIDES. 



77 



The mean declination corresponds to an epoch 1.6 days anterior, which remark 

 applies also to the formula dh = C sin. 2 iV, representing the diurnal inequality dh 

 in two successive high or low waters, 6' heing the moon's declination. For the 

 value of C we ohtain 3.3, which gives us the following comparison : — 



DIURNAL INEQUALITY IN HEIGHT. 



(Epoch l.C clays.) 



The diurnal inequality in time I have tried to exhibit by numbers as well as by 

 diagrams; it seems, however, that the incidental irregularities in the observations 

 themselves, coupled with the fact that the observations generally were only made 

 half-hourly and at other times hourly — so far exceed in magnitude the inequality 

 itself as to make the effect of the changes of the moon's declination exceedingly 

 obscure. The lunitidal intervals (for high and low water) between Oct. 17 and 

 Dec. 28, 1853, between Jan. 28 and March 7, 1854, and between June 1 and July 

 7, 1854, were tabulated in vertical columns; the means of the alternate values 

 were tabulated in the 2d column, and placed in the horizontal line opposite the 

 intermediate value of column one. The numbers in the first column were next 

 subtracted from the corresponding numbers in the second column, if the interval 

 belonged to the inferior transit ; if belonging to the superior, the values in the 

 second column were subtracted from those in the first. The moon's declination, 

 for noon each day, was also set down. The 276 values for diurnal inequality in 

 time, thus obtained, were plotted. After attempting to deduce an epoch and 

 arranging the values for different assumptions for epoch, no satisfactory result 

 could be obtained in any way according with the expression 



d^ = 9 tan - h ' „ (see Lubbock, Phil. Trans. 1837), 



I -{- A cos. -<£> 



and the results of the investigation must be confined to the following general 

 remark. The diurnal inequality in time is in maxima probably not exceeding two 

 hours ; it seems to be less in amount for the times of high water than for the times 

 of low water, a result the reverse of that belonging to the inequality in height. 

 A similar conclusion was arrived at in the discussion of the tides at San Francisco, 

 Cal. (Prof. A. D. Bache in Coast Survey Report for 1853, p. *81), when the smaller 

 inequality in height of high water (when compared with that for low water) cor- 

 responded to the greater inequality in time of high water (when compared with 

 the inequality for low water). "Whether the inequality of the height for high or 

 low water is the greater or smaller depends only on the epoch of the diurnal wave 

 compared with the epoch of the semi-diurnal wave. There is no regular increase 



