TIDAL DATUM PLANES 43 
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between the higher low and lower high is small, and even moderate weather effects so 
disturb the curve as to make it difficult to determine whether there are a true high 
water and a true low water intervening between the higher high water and lower 
low water. 
In the latter case it is the practice to disregard adie lower high waters and higher 
low waters when the difference between them is less than a tenth of a foot. While 
this practice furnishes a definite, even if an arbitrary criterion, in the tabulation of 
the tide curve, it does not altogether resolve the difficulty when it comes to the deter- 
mination of the datums of mean bigh water and mean low water. Further considera- 
tion will be given this matter in the detailed discussion of these datums. 
Interpolation of Breaks in the Record 
Since the time and height of tide varies from day to day, it is desirable both for 
the purpose of determining mean values and for purposes of comparison to interpolate 
any breaks that may occur in the tide record at stations where the series of observations 
cover several months or more. Various methods may be used, depending on the loca- 
tion of the station and the duration of the break. In general the procedure is to tabulate 
the hourly ordinates and the high and low waters for such portions of the record as are 
complete, leaving the interpolations to be made later. 
To distinguish interpolated values from those derived directly from the tide record, 
the interpolated values are tabulated in red ink or they are inclosed in parentheses. 
If the duration of the break is no more than a day or two, a convenient method is to 
interpolate linearly the times and heights of the high and low waters. These inter- 
polated values are then used for constructing the tide curve on cross-section paper, 
from which the hourly ordinates are tabulated. An example will make this method clear. 
Suppose that on June 26, 1944, the tide gage at Boston had failed to function. 
In tabulating the record for that month, the tabulator would leave that day blank 
in both the hourly heights and in the high and low water tabulations (figs. 15 and 16) 
and complete both tabulations before making the interpolations. The tabulation of 
the high and low waters illustrated in Figure 16 shows that on the day preceding the 
assumed break the morning high water came at 2.9 hours with a height of 14.3 feet, 
while on the day succeeding the break these values were, respectively, 4.6 hours and 
12.6 feet. A direct mean of the above values gives for the time of the missing high 
water 3.8 hours and for the height 13.4 1O8L, as compared with 3.9 hours and 13.3 feet, 
the values actually observed. 
In the same way the morning low water for the 26th would be determined as 10.2 
hours and 4.4 feet, while the afternoon high and low waters interpolated from the 
corresponding Alles the day previous and the day following are, respectively, 16.4 
hours and 12.5 feet, and 22.4 hours and 5.2 feet. 
To interpolate the hourly ordinates for the day in question, the values determined 
above for the times and heights of the high and low waters are plotted on cross-section 
paper and a curve drawn through these points as maxima and minima, the shape of 
the curve being made to conform to the curves of the days preceding and following. 
The hourly heights are then tabulated directly from this curve. 
The linear method of interpolation obviously can be used only for relatively short 
breaks—rarely more than for 3 days. Breaks of greater duration may be interpolated 
