88 U.S. COAST AND GEODETIC SURVEY 
high water above sea level for the period of observations. The second correction is to 
derive the value of mean sea level from the sea level of the period of observations. 
In the tabulation of the high and low waters from the tide observations at any 
place, half-tide level is derived directly from this tabulation. The derivation of sea 
level requires the tabulation of the hourly heights of the tide. But as was found in the 
discussion of half-tide level, the variations in the latter follow closely those of sea level. 
Hence it is more convenient in determining mean high water to use half-tide level 
rather than sea level. . 
The method of comparison of simultaneous observations is generally the more 
satisfactory method and will be taken up first. 
Comparison of Simultaneous Observations. 
To exemplify the determination of mean high water by this method, the procedure 
used and the accuracy attainable will be illustrated below for periods of various lengths. 
Day.—Suppose that tide observations were made at Seaveys Island, Maine, near 
the mouth of the Piscataqua River, each fifth day of the month of May 1946 and that 
it was desired to determine mean high water from each of these days of observations 
using the primary tide station at Boston for comparison. In tabular form the data 
would appear as follows: 
Mean high water fron 1 day of observations 
Boston Seaveys Island 
Date Height on stafi Corrections for— Height on staff 
BW OO —F ‘AW- MHW 
ATL oi HTL above |MHTL| MHW 
HW | LW | HTL Wasi) Sees || ety || may |) lem SE 
1946 Feet Feet Feet Feet Feet Factor Feet Feet Feet Feet Feet Feet Feet 
Mayl1...-| 14.10 1 7) 7. 92 6.18 0. 28 0. 764 IU By 0. 85 6. 10 Da 2D 4.01 6. 38 10.39 
May 6_--- 13. 55 3.15 8.35 5. 20 —0.15 0. 908 10. 90 2.10 6. 50 4.40 4.00 6. 35 10. 35 
Mayll_..| 12.70 3. 95 8. 32 4.38 | —0.12 1.079 10. 20 2.80 6. 50 3. 70 3.99 6. 38 10. 37 
May 16...|. 12.95 53, ‘Za 8.35 4.60 | —0.15 1. 027 10. 40 2. 50 6. 45 3.95 4.06 6. 30 10. 36 
May 21_-- 12. 40 4.75 8. 58 3. 82 —0. 38 UPB) 10.05 3. 40 6. 72 3.33 4.12 6. 34 10. 46 
May 26_-- 12. 85 4.25 8. 55 4.30 | —0.35 1.099 10. 35 2. 90 6. 62 3 733 4.10 6. 27 10. 37 
May 31-_-- 15. 05 2.35 8. 70 6.35 | —0. 50 0. 744 12.15 1. 60 6. 88 5. 27 3. 92 6.38 10. 30 
From the high and low water tabulations the average height of the two high waters 
for each day is entered in the 2d column for Boston and in the 8th column for Seaveys 
Island. The 3d and 9th columns similarly give the average heights of the two low 
waters for each day. The 4th and 10th columns give the half-tide levels for each day, 
derived from the corresponding high and low waters, and the 5th and 11th columns give 
the heights of high water for each day above half-tide level, or the semi-range of the tide. 
For the 19-year period 1930-1948, mean high water on the tide staff at Boston reads 
12.920 feet, and mean half-tide level 8.196 feet. Hence the primary determination of 
mean high water above half-tide level, or the semi-range of the tide is 4.724 feet. In 
column 6 is entered the correction for the half-tide level to bring it to mean value, and 
in column 7, the factor by which the half range in column 5 is to be multiplied to give 
the mean value of the half range. The latter value obviously is derived by dividing 
4.724 by the value in column 5. . 
The factors in column 7 are then applied to the corresponding values of column 11 
