238 REPORTS ON THE STATE OF SCIENCE, ETC. 
We now form A cos p,T, A sin p,T, B cos p,T, B sin p,T, as in Table IIf. When 
M is large we shall have from (7) § 18, 
Asymptotic mean of A cos p,T =3Ac2 
Asin p,T =3Ag. 
B cos p,T = $By2 
B sin p,l =3Bee 
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Determining these means as nearly as possible we have 
F,cos7,= 4A,,—-}B,.= —'003—"012= —"015 
F,sin7,= 34A,+3B%,= “000+ -044= 044 
and 
¥F’, cos 7',= 44A.+3Be.=—'003+-012= 009 
¥’, sin 7',= —}A,,+4B*%,= —"000+ O14= “O44 
Hence we have two constituents 
F,, cos (12— p21) =-047 cos (109° —p,T) 
F’, cos (n',+ pal) = 045 cos (78° + p, 1’) 
The latter of these gives the constituent A,. 
Now using the table of §17 we have (R,«) respectively equal to (047, 135°), and 
(:045, 52°), the latter giving A,. 
The presence of the constituent ‘conjugate’ to A, with p=1:778° in L, time is very 
interesting, especially when it turns out to be as important as A,. Again we have 
an unsuspected constituent, but a word of caution must be given. Our analysis has 
assumed the presence of two constituents with equal and opposite values of p, and 
indeed this is often the case, but here we can assert nothing about the unknown 
constituent except that it has p approximately =2°, and without more definite 
information as to the value of p the above figures are not to be considered as definitive 
for this constituent. It is not inappropriate to add that though we may not get 
pairs of values of p to be equal and opposite in sign yet the tidal constituents in- 
dicated by the potential are such that the relation is nearly true, and any correction 
necessary could easily be applied, provided that the true values of p are known. 
It was considered to be of interest to see the results after the two disturbing 
constituents had been removed, and cols. 10 and 11, Table II., give the residual A 
and B; these are plotted in fig. 8. An independent deduction of A,, and B,, from 
these figures confirms the values previously obtained from the original A and B; we 
get 
Aq ='010, B, =-025 
whence the L, constituent in the residue is 
RAR ConA 
‘027 cos (ct —68°). 
These examples are sufficient to illustrate the methods. In practically all cases 
approximate quarter-annual perturbations in the A and B have been found. The 
cause of these is obscure and the matter is still under investigation. 
Oe See 
igo e 
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Kite 
