SPHEROIDS, AND ON THE OCEAN TIDES UPON A YIELDING NUCLEUS. 33 
where © is a certain definite integral, depending on the distribution of land and 
water, but which has not yet been evaluated. 
The latitude of evanescent fortnightly tide is 36° 15' if (£ is zero; and if we bear 
in mind that © may be negative, it is clear that the observations at Cat Island 
(lat. 30° 23') are made too near the critical latitude to be trustworthy for determining 
the true fortnightly tide. It is also hardly possible to believe that the observations at 
Toulon should show a true tide of this denomination, because the Mediterranean must 
be regarded as a virtually closed sea. The observations at Cat Island, and at Toulon, 
will therefore be set aside. 
The first process to be applied to the above observations is obviously to divide each 
value of R by ^ sin 2 (lat.) ; the following are the factors for reducing the values 
of R:— 
[r^sin^lat .)]- 1 
Ramsgate. 
3-62 
Liverpool. 
3T 7 
Hartlepool. 
3-01 
Brest. 
3-07 
Kurrachee. 
6-40 
These factors will be applied to the values of R in the table first given. 
The next point to consider is the phase of the tide. The formula we have given 
shows that the fortnightly tide consists in an alternate deformation of the ocean level 
into an oblate and prolate spheroid of revolution, when the tide is deemed to be 
superposed on a true sphere, instead of on an oblate nucleus. 
7T 
When t is zero the spheroid is oblate, and this may be called high-tide; when 
it may be called low-tide. It follows, therefore, that N. of lat. 36° 15' high -tide is 
low-water, and vice-versd; but S. of this latitude the tide and water agree. But the 
formulae in the tidal reductions always refer to high -water, hence to find the retarda¬ 
tion of the tide we must subtract 180° from all the e’s for places N. of 3C° 15'—that is 
to say (Cat Island being rejected) for all except Kurrachee. 
For Kurrachee, we may observe that any retardation e may be regarded as a retarda¬ 
tion e—27r, which, if negative, is an acceleration of tide. If 2it —e be less than 180°, 
this appears to be the more correct light in which to look at it. 
Now if we reduce all the observations in the way indicated, so that the fortnightly 
tide is given by R'(^—cos 2 6) cos (2 nt — rj), we find the following results :—- 
MDCCCLXXTX. 
F 
