HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 91 
we have omitted from our schedule, because of the smallness of the tides 
to which they refer. The entries of the tides of long period, Nos. 3 and 
4, are given with the opposite sign from that here adopted ;' thus those 
entries require alteration by 180° to bring them into accordance with our 
schedule. 
The following corrections have to be made in Table II.: No. 8, for 
Qy read 3v; No. 15, add 4y; Nos. 17 and 19, add 2(v—€); Nos. 18 and 
20, subtract 2(7—é). ; 
The K,, K, tides, Nos. 9 and 16 of both tables, are entered separately 
as to their lunar and solar parts. The two parts of the M, tide, Nos. 7 
and 11, are entered separately. Also No. 14 only gives one part of the 
tide here entered as L. 
The reader is warned that the definition of « on p. 293 is incomplete, 
and incorrect for proper reference to the equilibrium theory of tides. 
The definition of a’ on p. 302 is incorrect. 
§ 8, On the Reductions of the Published Results of Tidal Analysis. 
In the Tide Tables pablished by the Indian Government, it is stated 
that each tide is expressed in the form R cos (nt—e«), where R is the 
semi-range in feet, n the speed of the tide, and «/ is the time in mean 
solar hours which elapses, after an epoch appropriate to the tide, until the 
next high-water of that tide. Tables are then given for R and « at each 
station for each year. 
The mode of tabulation is the same as that followed in the Tidal 
Reports of the British Association for 1872 and 1876. 
It is advisable that all the results should be reduced according to one 
system, such that the observations of the several years and the values 
for the several speeds of tide may be comparable inter se. 
: In § 5 it has been proposed that the tide should be recorded in the 
orm 
fH cos (V+u—k). 
It appears from the statements in the Reports for 1872 and 1876 and 
from an examination of the reductions of the published results that the 
e of the tables is equal to «—w, and that the R of the tables is equal to 
fH. Thus in order to reduce the published results to proper forms, com- 
parable inter se, it is necessary to add to « the appropriate w, and to divide 
RB by the proper f. Following this process we obtain at once the following 
additive corrections to the «’s to obtain the «’s. The values of 1/f by which 
the R’s are to be multiplied to obtain the H’s, are those given in the pre- 
ceding schedule [1]. 
For all tides not mentioned here, « is identical with «, and H with R. 
1 See the passage in §2 between equations (28) and (29). 
