MR. LUBBOCK ON THE TIDES. 
223 
h = D + E {A cos (2 p — 2 <p) -f- cos 2 4 1 } 
E A varies as P 3 cos 2 &, E varies as P' 3 cos 2 S'. 
If (A) and (E) denote the values of those quantities for the mean parallaxes and 
declinations, that is, when & = h' = 15°, P = sin 8"*8, P' = sin 57', the semimenstrual 
inequalities in the interval and in the height are given by the expressions 
tan 2 p 
(A) sin 2 <p 
1 -f- ( A ) cos 2 <p 5 
h = D + ( E ) {(A) cos (2 p — 2 <p) + cos 2 p } ; 
D being a constant which depends only on the zero line, from which the height is 
reckoned. The value of (A) obtained from observations of the interval at different 
places should be the same, unless neap tides are transmitted with a different velocity 
from that of spring tides. 
The difference in height between the morning and evening tide depends upon the 
angles p — <p and p ; if this difference be called d h, considering only the quantities 
multiplied by P 3 and P' 3 , 
d h == B {(A) sin 2 S cos (p — <p) + sin 2 S' cos p } ; 
B being a constant. The quantities multiplied by P' 4 may also, perhaps, give some 
sensible term in the diurnal inequality ; and the term 
m'RP' 3 
o m ' ma y & lve an ine qoabty 
in the height depending upon the moon’s parallax and independent of her age or time 
of transit. The diurnal inequality of the interval may be put in the form 
. , F cos2rJ/ f(^)sin2 8 . x . . 1 
d ^ = i + (A) cos ' ei { cos* 8- sm ( 4 - - t) + 2 tan 8’ sin ^ j 
F being a constant. 
The inequalities of the heights at different places depending upon the angles 
2 p — 2 <p and 2 p are proportional to the quantity (E ) ; so that if they have been 
obtained for any place P, they may be obtained for any other place P', by multi- 
plying the former by ^-gy. The inequalities in the interval are the same everywhere, 
according to the theory above explained ; but in both cases the argument may 
require to be shifted. 
The British Association for the Advancement of Science having placed at my dis- 
posal for the purpose a sum of money, I employed Mr. Jones and Mr. Russell, two 
excellent computers, to discuss nineteen years’ observations made at the London 
Docks, with reference to the moon’s transit two days previous, and the results have 
been arranged in the accompanying tables. I now proceed to compare these with 
theoretical results deduced from the preceding expressions. 
First, with respect to the semimenstrual inequality. From the column headed 
“ Mean” in Table II. it appears that 
For the transit happening at 9 h 30 ra the interval is 3 h 48 m- 9 
3 30 2 25 *1 
3 h 48 m, 9 — 2 h 25 m, l = l b 23 m *8, which, converted into space, = 21° nearly. 
