( 10 ) 
or, after applying the augmenting factor R 2 and the astronomical 
argument, as the result of this investigation: 
j Calculated 0".00504 cos (t — 286°.2) 
Kl j Observed 0".00518 cos (t — 249°.2) 
Calculated 0".00187 cos (t — 286°.2) 
r j Observed 0".00192 cos (*— 249°.2) 
and then for the monthly means of the diurnal inequality the 
0".01296 {1 + 0.361 co* (30 a? - 248°.7)} co* (15 t - 245°.5) 
6. Just as for watertides the superposition of the .partial tides 
S 2 and K 2 causes a maximum in March and September (the equi¬ 
noctial tides known to every mariner) and a minimum in January 
and July, here too such a semi-annual variation must appear in the 
expressions for the semi-diurnal inequality . Indeed this variation makes 
its appearance clearly at first sight in the amplitudes of Table I. 
If we assume that the S 2 tide is constant during the whole year, 
then the general expression for the monthly means is: 
S 2 cos (30 t—Cj + K 2 cos (SO t—C 2 k + 60.r) 
where 
= F 0 , V 0 = 2h 0 — 2v". 
We have then to do nothing but to analyse the expressions of 
Table I, after subtraction of the mean for the whole year, into the 
components: 
A cos 30 t + B sin 30 t 
A = cos (60 x — C 2 fc) 
B = — sin (60 x — C 2 k) 
If we bring through the differences A and B doubly-periodic 
curves, we obtain for each of the quantities to be found: 
K 2 sin Cm and K 2 cos Cm . 
two values which must be about equal and from which we deduce, 
after applying the augmenting factor 
R. = - 1.0472 
4 6 sin 30? 
and the astronomical argument 
F, = 2 A, — 2 v" == 229°.68 — 0°.25, 
the quantities K, and x 
The astronomical coefficient calculated according to the tables of 
and if 
we put 
