\ 



Prof. A, D. Bache on Tidal Observations. 349 



ditiates of six and eighteen hours from the first mean. The 

 means present the best criterion because not displaced in ihis 

 combination as the equation shows. This mode of proceeding, 

 however, throws the test too much on the weak part of the re- 

 suItSj the times of occurrence of high and low water, or of mean 

 water, and does not take in all the points of the curve, and I 

 have therefore preferred a different form of discussion. 



7. Placing the maximum of the semi-diurnal curve at hours, 

 m the hypothesis that the high water of the diurnal curve is nine 

 hours in advance of that of the semi-diurnal curve, the two 

 curves cross the line of mean water at three hours, the diurnal 

 curve rising and the semi-diurnal falling; at six hours, the semi- 

 diiirual curve has reached its maximum, and rises again at nine 

 hours to its intersection with the mean water line, at which time 

 the diurnal curve has reached its maximum; the semi-diurnal 

 curve attains its greatest rise at twelve hours, and the mean level 

 at fifteen; the diurnal curve also descending to the same point at 

 that time. 



Within these two intervals from mean level to mean level, the 

 combinations of the ordinates forming the actual tidal curve are 

 exhausted; the part of the curve below the mean level being 

 syrnmetrical with that above. From three to nine hours, the 

 ordinates of the semi-diurnal curve are subtractive ; from nine to 

 fifteen hours, additive. The mean is the average between high 

 and low water. The tides of each day will give the forms of 

 the component curves, beginning with the mean, and ending 

 ^ith itj considering as symmetrical the parts above and below 

 the axis of X. 



In tabulating, the branch above the axis should be referred to the 



1 + 1' 



niean of the preceding and succeeding low water j ^ 



and of the high water which it includes, and that below to the 

 ^ean of the two high, and of one low water. From three to 

 nine hours, the difference of the ordinates giving the actual curve, 

 and from fifteen to nine in the reverse order the sum of the same 

 ordinates, half the sum of the two series of ordinates gives the 

 value of the ordinates of the diurnal curve, and half the differ- 

 ence, the ordinates of the semi-diurnal curve. The same being 

 repeated wiih the second branch of the curve, the average will 

 giv^e two results for each day's observation. 



1 he case given in the table on the board, for March 5, will 

 serve to illustrate the simple nature of this method of proceeding. 



The mean ordinate for the first and second branches of the 

 enrve having been obtained, and the hourly observation which 

 coincides most nearly with it having been found before and after 

 n^gh water, the hourly observations are arranged from it forwards 



Second Series, Vol. ZII, ^o. 36.— Nov., 1851. 46 



