72 REPORT—1883. 
A tide of greater importance than some of those retained here is that 
referred to where the approximation with regard to I was introduced, 
viz. with speed 2y+o—a; the value of its coefficient is ‘00323. There 
is also the larger variational diurnal tide, which has been omitted: it 
would have a coefficient ‘00450; also an evectional termensual tide, 
1oeme + sin? I cos (3s—2h+p), with coefficient of magnitude -00292. 
All other tides in a complete development as far as the second order of 
small quantities, without any approximation as to the obliquity of the 
lunar orbit, would have smaller coefficients than those comprised in the 
above list. Such a development has been made by Professor J. C. Adams, 
and the values of all the coefficients computed therefrom, in comparison 
with the above. 
Besides the tides above enumerated, the predicter of the India 
Office also has the over-tides M, and M,, of speeds 4 (y—c), 6 (y—c), and 
the compound tides 2MS, 2SM, MS, of speeds 2y—40+42n, 2y +2c0—4n, 
4y —2o—2n, and the meteorological tides 8,, Sa, of speeds y—, ». 
If this schedule is worth anything, it seems probable that the India — 
Office predicter would do better with some other term substituted for A. 
If further examination of the tidal records should show that the tide M, 
is in reality regular, it should be introduced. 
§ 3. Tides Depending on the Fourth Power of the Moon’s Parallaz. 
Tue potential corresponding to these tides is 
vatt p (& cos? PM—3 cos PM). 
We may obviously neglect the eccentricity of the lunar orbit, and it 
will appear below, when the principal terms are evaluated, that the 
declinational tides may be safely omitted. 
By these approximations we may put r=c, and M,=0, and neglect 
the terms in M,, M, which involve g?. Following the same plan as in 
the previous development of § 2, we have, when M,=0, 
M 
v= 
3 (& —3én?) (M,3—3M, M,”) + 2 (9? — 32?) (M03 —3M 2M) 
+3 (8+ 52-4667) (13+ MM?) 
+ 3 (fn +? —4n5?) (1,?M,+ M3) 
The four functions of &, n, £, in this expression are surface spherical 
harmonics of the third order, and therefore, corresponding to these four 
terms, there will be four tides of the types determined by those functions. 
Now, we have approximately 
M,=p? cos (x-1), M,=—p? sin (x—l). 
From which we have 
M,?—3M,M,?= p* cos 3(x—1) 
M,?+ M,M,?=p5 cos (x—/) 
When n=0; &?—35n?=cos3d, €3+ £1)? —4622=cos A (1—5 sin?A). 
