46 
DISCUSSION OF TIDES IN BOSTON HARBOR. 
t.h. w=E-+m are the times of high water; the days and hours, being the same as in E, are not 
written. . . 
Q, the coefficient of the semi-diurnal tide, independent of the effect of F, is obtained either by 
construction, as has been explained, or from log Q in the latter part of the example, when 
obtained by computation. The different steps in the example, by which log Q is obtained, 
need no explanation. _ : 
n—=Q—4.90 ft.; that is, it is the excess of Q above its mean value. One-third of this sub- 
tracted from Q gives A,=4.90+ = 
affected by F. 
4}, 4? are the first and second differences of A,, used as a check, and also in interpolating for 
the lower transits. 
o' are the first differences of A, after interpolation, used as a check, and for interpolating to 
low water. 
Ho+ Ag, in which H) is taken from Table II, with the day of the year as an argument, is the 
height of high water of the semi-diurnal tide. 
p is taken from the first part of Table IV, with the declination, D, one day in advance, and is 
the effect of the lunar diurnal tide upon the height of high water. 
q is taken from Table X, with B and the day of the year as arguments, and is the effect of the 
solar diurnal tide upon the height of high water above the zero of the tide-gauge. 
r=p+q is the effect of the whole diurnal tide upon the height of high water. The values of r 
for the lower transits are readily obtained by interpolation, and must be used with the 
contrary sign. 
h.h. w=H)+A.+r is the height of high water. 
HY’ is obtained from Ei by interpolation to the time of low water by means of 61, using only the 
first differences. 
k’ is taken from the first part of Table IV for low water, using the argument D one day in 
advance. 
lis taken from Table LX, with the arguments B and the day of the year. 
m =k'+V is the whole effect of the diurnal tide upon the times of losy water. The values of m 
for lower transits are obtained by interpolation and must be used with the contrary sign. 
t.1.w=E+m’ are the times of low water, the days and hours being the same as in Bi’. 
A’, is obtained from A, by interpolation to the time of low water. 
H,— A”, is the height of the iow water of the semi-diurnal tide. 
pis taken from the first part of Table IV for low water, using the argument D one day in 
advance, and is the effect of the lunar diurnal tide upon the height of low water. 
q is taken from Table XII, with B and the day of the year as arguments, and is the effect of 
the solar diurnal tide upon the height of low water. 
7’ =p'+q/ is the effect of the whole diurnal tide upon the height of low water. The values of r 
for lower transits are obtained by interpolation, and must have the contrary sign. 
h.l.w=H,)—A’,-+7 is the height of low water. 
, or the coefficient of the semi-diurnal tide as 
CONCLUSION. 
50. In the preceding discussion all the results have been brought out which can be of much 
interest to any one in any theoretical tidal investigations: and much attention has been given to 
the arranging and presenting of the whole matter in as systematic and concise a manner as pos- 
sible, and with a convenient and appropriate notation. These results must be found to be the more 
interesting to investigators on account of the great peculiarities due to local circumstances which 
make them differ so much in many respects from the results obtained in most of European ports. 
A comparison of these results has also been made with both the equilibrium and the dynamical 
theories of the tides, so far as it could be done, where it is neither convenient nor proper to enter 
very thoroughly into the discussion of tidal theories; and the great defects of the equilibrium 
theory have been shown, and also various discrepancies of a small order between the results and 
