5U REPORT—1885. 
a term varying with the speed. Hence all the retardations may be 
expressed in terms of ¢ and p, and 
It is ag that « differs very little eae g, and that 
kK—M_2(m—¥) Sp 
o o—@ o—)7 
The time ({—,)/(¢—n) is called ‘the age of the tide,’ for reasons 
explained below, and «—p, p—v, not being large angles, do not differ 
much from these tangents. Hence the ages of the declinational and 
parallactic inequalities are both approximately equal to the age of the 
tide. 
Let «, then, denote ({—)/(o—»), the age of the tide. 
Now, as an approximation, we may suppose that heights of the lunar 
K, tide, the N and L tides bear the same ratio to the M, tide as in the 
equilibrium theory ; and that the solar K,, the T and R tides bear the 
same ratio to the 8, tide as in that theory. Then reverting to the nota- 
tion with J, w, i in piace of A, A,, and writing 
( cos $1 \'= f 
cos Sw cos ti : 
we have 
sin? A x7 sin? Toye 087A zp ae cet pM, 
ea cost 32” cos? A, 
K!'= 3sin? mS, T=3eS, R=1eS. 
cos*sw 
Also, since (22) may be written 
‘ N sin 2(u—v)+Dsin 2(A—p) 
tan(22—2c)=—__ = : 
mag a) N cos 2(up—v)—Lcos2(A—p)’ 
we have, treating p—v, \—p, p—e as small, approximately, 
e=p—2e(o—c)=p—Z(A—r). 
Also 
cos?A Ncos 2v—L cos 2X 
cos? A , cos 2¢ re 
Then reverting 1o mean longitudes, and substituting the age of tide 
where required, we find, on neglecting the difference between « and a 
For the lunar declinational term, 
2 tan? $7 £M cos 2[s—#o—<] cos 2(—Z) ; 
For the solar declinational term, 
2 tan? dw S cos 2h cos 2(W,—Z); 
For the lunar parallactic term, 
3efM cos [s—p—a(c—a)] cos 2h Y—p+3e(e—c)];5 
