308 On the Tides of Key West. 
a zero, were tabulated, and the maximum ordinates S and D of 
the semi-diurnal and diurnal curves of sines found, taking (E) 
generally at its mean value. From these the ordinates of each 
which gave the sum of the differences of computation aud ob- 
servation, without regard to sign, the smallest. 4 
was next intended, treating this as a first approximation, to 
take a different zero-point for the semi-diurnal curve, but the 
labor necessary has prevented this idea from being followed up 
thus far, and the agreement of the computed and observed curves 
is quite satisfactory in the cases in which E is not varying too 
rapidly for safe deductions. The labor and uncertainty of deduc- 
ing E from the observations in the manner just referred to is very 
considerable, and, after one full comparison made in this way, 
the vafftes will be deduced from theory, and applied to the curves. 
The approximate compound curve was next projected on a 
diagram of suitable scale, and the outline cut from the paper 80 
as to apply it to the curve of observation, and thus to find its 
best position in reference to that curve, and to determine the 
times of high water. The work referred to in the paragraphs pre- 
ceding the last is mechanical, but this latter requires much judg- 
ment, and has been executed by Mr. W. W. Gordon. Supposing 
that some discrepancies observed might result from a sort of pet- 
sonal equation in making these comparisons, a second person was 
engaged to repeat them for verification, and the result showed 
that the comparison could be depended upon in individual cases 
to within about five minutes in time in the position of the max 
mum ordinates. 
Semi-diurnal Tides. 
the curves, and from the formula-for the half-monthly inequality 
Teferred to in the previous part of this paper: a 
fe eer a 
