350 -F*ro/! A. D. Bache on Tidal Observations. 



for seven hours (m) and backwards for seven (n). The same is 

 done for low waterj (m' and n'.) The half sunns and half differ- 

 ences are taken in each case, and then the means. The compu- 

 tation of the diurnal curve is made in the upper part of the table, 

 and that of the semi-diurnal curve in the lower part. The num- 

 ber representing the mean level is eliminated by the mode of 

 taking the means in each table, and the ordinates below the axis 

 are treated as if having the same sign as those above. The 

 semi-diurnal curve is turned over on its maximum ordinate, and 

 the mean value of a single branch of it found. Then each curve 

 is reduced to zero, in the mean level of the period. The last, 

 two columns of the upper and lower part of the table contain 

 respectively the curves of sines corresponding to the diurnal and 

 semi-diurnal curves. 



In the case shown in the first diagram, the ordinates of the 

 semi-diurnal curve from mean water to high water, and corres- 

 ponding nearly to a minimum of declination, and new moon, are 

 000 feet, + 002, + 0-03, + 005, -f- 004, ~ 0*03, + 0-02. The 

 moon's declination during the period being about from 2*^ 54' S., 

 to 1^ 45^ S.; this curve obviously contains a residual of the 

 semi-diurnal curve, not taken out, but supposing it to be deduced 

 from a just mean, the corresponding ordinates of a semi-diurnal 

 curve, calculated with 04 feet as the maximum would be 000 

 feet, 001, 0-02, 0'03, 0-03, 004, 004, differing at the most, 0-06 

 of a foot, or about three-quarters of an inch, and in a single in- 



stance, the sum of all the six differences being 03 feet, and the 



average '004. 



The ordinates of the semi-diurnal curve are O'OO feet, 014, 

 0-28, 0-32. The curve of sines computed with the greatest or- 

 dinate has in this case for its corresponiding ordinates 000 feet, 

 0-16, 0-28, 0-32, differing but -02 feet at the greatest. 



At the next period of declination nearly zero, and full moon 

 in the month of March, the ordinates of the diurnal curve de- 

 duced are 000 feet, 005, 006, 006, OOS, 0*06, 0-09, and the 

 corresponding computed ordinates 00 feet, 002, 0'043 OOo, 

 07, 0-09, 009, differing at the greatest 003 feet, and on the 

 average, 0-004 feet, the observed ordinate being this time i^^^^' 

 cess as it was before in defect. The ordinates of the semi-diur- 

 nal curve are 000 feet, 12, 0-22, 026, and the computed ones, 

 00 feet,013, 24, 0*26, the greatest difference being 02 feet, 

 and the average 0007 feet in excess, as was the former. 



For March 12, corresponding to the maximum of the diurna 

 curves, and to neap tides (one day after last quarter), the ordi- 

 nates of the hourly diurnal curve from mean to high water ai 

 0-00 feet, 0-21, 0-36, 0-51, 063, 0-69, 71, the corresponding or- 

 dinates of the curve of sines being 0-00 feel, 0-18, 035, Ot)^» 

 0-69, 71, in which the greatest difference is 03 feet, and tn^ 



1 



p 



