260 THE REV. W. WHEWELL’S RESEARCHES ON THE TIDES. (SERIES XII.) 
P.S. I will add to the above memoir two tables, giving the height of the surface 
of the sea at any time, as affected by the tide at Plymouth and at Liverpool. In con- 
structing these tables I have supposed the rise and fall of the surface to follow the law 
of the sine of the time from mean water, as already explained. For although there 
exists in many places a displacement of the summit of the curve of rise and fall, this 
displacement is small, and would not much affect the height at any time. Whether 
it arise from the combination of the solar with the lunar tide-wave, or of the diurnal 
with the semidiurnal wave, or from the form of the channel and local circumstances, 
it may be disregarded or postponed in a statement like the present. 
The height is given in these tables according to hours before and after high water, 
the curve being supposed symmetrical, as we have said. The unit of height (ex- 
pressed in the table by 1000) is the height of the high water at spring tides above the 
mean water , or half the total rise of the surface at spring tides. The table must be 
adapted to any particular place by multiplying each tabular number by this quantity 
(the height of spring tide high water above mean water) for the place (cutting off 
three decimal places). 
The highest spring tides and the lowest neap tides take place at different intervals 
after the moon’s syzygies and quadratures at different places, the interval varying 
from a few hours to a few days. In like manner the tides corresponding to the moon’s 
octants (when her transit takes place three hours after the sun’s) follow the time of 
the octants at different intervals at different places ; but they may be very intelligibly 
designated as octant tides, which term is employed in the tables. 
In the table for Plymouth, the spring tide is to the neap tide as 5 to 3 ; which 
supposes the solar tide to be one fourth of the lunar tide. In the table for Liverpool, 
the spring tide is to the neap tide as 7 to 3 ; which supposes the solar tide to be two 
fifths of the lunar. These are the proportions given by observation at those places 
I will add an Example of the use of the following tables. Let it be proposed to 
find the height of the surface at Plymouth If hour before high water at octant tides. 
The range of spring tides at Plymouth is sixteen feet ; hence the unit of heights is 
eight feet; and at If hour before high water the tabular number (by interpolation) 
is ‘515. Hence the height above mean water is 4‘12 feet, or four feet one inch ; and 
since mean water is at nine feet ten inches on the scale, the height of the surface on 
the scale is thirteen feet eleven inches at the time proposed. 
