44 U. S. COAST AND GEODETIC SURVEY 
by use of the observations at some other tide station, not too far away, which has a 
tide of the same type. The differences in the time and height of the tide at the two 
stations are determined from simultaneous observations and these differences applied 
to the observed times and heights of the high and low waters for the days in question, 
the hourly ordinates being interpolated as before. 
Another method of interpolating a break of more than 3 days is to take a mean 
of the times and heights of the high and low waters 29 days before and after. This 
method is based on the fact that the three principal lunar cycles, the phase cycle, the 
parallax cycle, and the declinational cycle are, respectively, 29% days, 27% days, and 
27% days in length. As an example of this method, it may be used for interpolating 
the high and low waters at Boston for June 26, 1944, the day used to exemplify the 
method of linear interpolation. 
Twenty-nine days prior to June 26th is May 28th, and 29 days after June 26th 
is July 25th. For May 28, 1944 the high waters at Boston occurred at 4.5 and 17.0 
hours, the heights being 12.5 and 11.8 feet, respectively. For July 25th the correspond- 
ing values were 3.5 and 15.9 hours, and 12.8 and 12.4 feet. Hence the interpolated 
high waters for June 26th would be 4.0 and 16.4 hours, and 12.6 and 12.1 feet. The 
observed values were 3.9 and 16.4 hours, and 13.3 and 12.5 feet, so that the interpolated 
times are very close, but the interpolated heights differ by 0.7 and 0.4 foot, respectively. 
Means of the times and heights of the low waters on May 28 and July 25, 1944, are 
10.2 and 22.4 hours, and 3.9 and 4.9 feet. The observed times and heights of the low 
waters on June 26th were 10.1 and 22.4 hours, and 4.4 and 5.1 feet. Again the times 
of the interpolated tides agree well with the observed, but the heights differ by 0.5 
and 0.2 foot. 
