38 REPORT—1885. 
15 Beas 
io 15° p{4yg+-Agl cos (mma) P+ e081 (m1 —R2) (+ ey 
Ny 
+ cos[ (nm —79) (2+ 22) 1+ e .]+B: [&e.]} +sin 15°p {&e} (a) 
ny ny 
And for semidiurnal tides the arguments of all the circular functions in 
(a) are to be doubled. 
Now, we want to choose such a number of terms that the series by 
which A, and B, are multiplied may vanish. This is the case if the series 
is exactly re-entrant, and is nearly the case if nearly re-entrant. 
The condition is exactly satistied for diurnal tides, if 
9 
(ny, —1y)q— =277, 
ny 
where ¢ is either a positive or negative integer. And for semidiurnal 
tides, if 
Ar 
—I5 ——=9; e 
(n, ma) wr 
That is to say, 
(2, —n2)qg=,", for diurnal tides, 
or 
(n; —n2)qg=43n,", for semidiurnal tides. 
It is not worth while attempting to eliminate the effect of the semi- 
diurnal tides on the diurnal tides, and vice vers, because we cannot be 
more than a fraction of a day out, and on account of the incommensurability 
of the speeds we cannot help being wrong to that amount. 
S Series. 
Now suppose we are analysing for the S, tide, and wish to minimise 
the effect of the M, tide. 
Then ,=2(y—n)=2 x 15° per hour, 
ny=2(y—2), 
Ny —Ng=2(o—n)=1°'0158958 per hour. 
The equation is 
1°-0158958q¢=15° r. 
Tf r=25, q=369-13. 
Thus 25 periods of 2(¢—n) is 369°13 mean solar days. It follows, 
therefore, that we must sum the series over 369 days in order to be as 
near right as possible. 
Now this is equally true of all the columns, and each should have 369 
entries. ; 
Hence, in order to have 369 entries in each column, the present S, 
computation form should have the last three entries cut off. The divisors 
are to be, of course, changed accordingly. 
M Series. 
Now consider that we are analysing for M,, and wish to minimise the 
effect of the S, tide. Hence 
