82 U. S. COAST AND GEODETIC SURVEY 
Substituting the above in (851) 
— Aa sin 6+ Bb sin (¢—8@) 
—— Aa sin 6+ Bb sin ¢ cos 6— Bb cos ¢ sin 6 
=—(Aa+Bbd cos ¢) sin 6+ Bb sin ¢ cos 6=0 (353) 
Then i 
ee Sbysinge 
tan USGI GOS © (354) 
239. For the resultant amplitude at the time of this maximum sub- 
stitute the values of ¢ from (850), in (846), and we have 
y=A cos (2n r—0)+8B cos E (2n 70-0) +8 
=A cos 6+ B cos [= (2n x00) +6—a—0| 
=A cos 06+ B cos (¢—8) (855) 
=A cos 6+ B cos ¢ cos 6+B sin ¢ sin 8 
=(A+B cos ¢) cos 6+B sin ¢ sin 6 
bah =) ep sin 
= A?+ B?+2AB cos ¢ cos (o—tan : te 
240. From (354) , . 
(ins 2 eee ee (356) 
A, +B cos ¢ Bet 68 ? 
A : sae 
In the special cases under consideration the ratio 7 is near unity, 
B sin $ 
A+B cos @ 
small, so that the cosine may be taken as unity. 
The resultant amplitude may therefore be expressed by 
and the difference between @ and tan7! is therefore very 
J A?+ B?+2AB cos b=Aq/1 4d = cos ¢ (357) 
The true amplitude of the constituent sought being A, the resultant 
amplitude must be divided by the factor 
y 1 go cos ¢ (358) 
in order to correct for the influence of the disturbing constituent. 
241. The corrections for acceleration and amplitude as indicated 
by formulas (356) and (358) may to advantage be applied to the con- 
stants for constituent K, for an approximate elimination of the effects 
of constituent P, and to the constants for S, for an approximate 
elimination of the effects of constituents K, and T,. By taking the 
relations of the theoretical coefficients for the ratios s and the differ- 
ences in the equilibrium arguments as the approximate equivalents 
of the phase differences represented by ¢, tables may be prepared 
giving the acceleration and resultant amplitudes with the arguments 
referring to certain solar elements. 
Thus, from table 2, the following values may be obtained. 
