36 REPORT—1885. 
advice of great value for the prosecution of tidal observation in other 
countries. The work also explains the method of measuring the tide 
diagrams, entering the figures in the computation forms, and the sub- 
sequent numerical operations. 
TI. Cerrain Factors anp ANGLES USED IN THE ReEpucTION oF TIDAL 
OBSERVATIONS. 
In completing the reduction of the results of harmonic analysis to the 
standard form, a number of angles and factors are required which de- 
pend on the longitude of the moon’s node. Tables of these angles and 
factors have been computed under the superintendence of Major Baird.' 
It may happen, however, that the tables are inaccessible to the computer, 
and the computation from the full formule might be somewhat laborious. 
It happens that the angles », £, »’, 2v’’ (the meanings of which are ex- 
plained in the Report of 1883) are all expressible in the form 
A sin N+B sin 2N+C sin 3N+...., 
where N is the longitude of the moon’s node, and that the coefficients 
diminish with such rapidity that the first two terms are probably sufficient 
for all practical purposes. 
Also the several factors f are reducible to the form 
A+B cos N+C cos 2N+...., 
and three terms are practically sufficient. 
I have obtained the approximate formule given below in this form. 
The rigorous results having been tabulated, it appeared easier to work 
from them instead of from analytical expressions in terms of the longitude 
of the moon’s node. I find, then, the following results :— 
Schedule I. Approximate Formule for Angles. 
vy =12°°9 sin N—1°3 sin 2N, 
£ =v—1°-07 sin N, 
(for K,) »’ =8°8 sin N—0°6 sin 2N, 
(for K,) 2v’=17°8 sin N—0%5 sin 2N. 
Also A =16°51+43°44 cos N—0°19 cos 2N, and 4,=16°'36. 
For the meanings of A and A, the reader must refer to Part IV. 
Approvimate Formule for Factors f. 
For M, and other tides, 
cos4 47 
=1-0003—:0373 cos N+'0002 cos 2N. 
: A, 
For 0, £2 Leos’ 2 _.1.00884:1886 cos N—-0146-c0s AN. 
sin w cos” 4 cos! 47 
ForK, ... .. «. + f=1:0243+-2847 cos N+:'0080 cos 2N. 
ForK, . .. . . . ~ £=1-0060+-1156 cos N—:0088 cos 2N. 
m2 
ForMf . . f=—S™/ __1.04994-4135 cos N—-0040 cos 2N. 
sin? w cost 47 
1 Some of these are given in the Report of 1883. 
