134 
THE REV. W. WHEWELL ON THE SOLAR INEQUALITY 
pute, the approximate circumstances of the solar correction for the height. I have 
also obtained, though by no means with the same certainty, evidence of the existence 
and laws of the solar inequality of the times. These inequalities, as thus discovered, 
exhibit the same general agreement with the equilibrium-theory which has been dis- 
closed in all the inequalities hitherto detected*. 
9. But though the equilibrium-theory thus seems to suggest and express the laws 
of the various inequalities of the tides, I would by no means be understood to rate 
this theory above its true value. It is not the true theory, but a very inaccurate and 
insufficient substitute for it, which we are compelled to adopt in consequence of the 
extremely imperfect state of the mathematical science of hydrodynamics. The tides 
are a problem of the motion, not of the equilibrium of fluids ; and we can never fully 
explain the circumstances of the phenomena till the problem has been solved in its 
genuine form. This solution is perhaps not beyond the powers of modern mathe- 
matics, but it has certainly never yet been given. Laplace’s solution, besides being 
obtained by means of a precarious assumption, rests upon several arbitrary hypo- 
theses, fatal to it even as a first approximation ; and, I believe it will be found, leaves 
out of consideration an essential portion of the forces. To obtain any useful result, 
tlie question must be taken up afresh and treated in another manner. 
10. I hope some mathematician will be found able and willing to execute this task. 
But in the mean time I may be permitted to observe, that what has been already done 
in the discussion of tide observations, and in bringing to light the empirical laws of 
the phenomena, has entirely altered the position of this branch of science with respect 
to the mathematical theory. A little while ago the theory was in advance of obser- 
vation ; at present observation is in advance of theory. A very few years since, the 
equilibrium-theory and the Laplacian theory were in a condition to assign laws regu- 
lating the changes of the times and heights under given astronomical circumstances, 
and it had not been shown from observation whether these laws were obeyed. We 
can now state what the agreement and disagreement is between such theoretical laws 
and the facts ; and we call upon the mathematician to substitute for these two theo- 
ries, both confessedly false, some other, which shall come nearer to the true state of 
the case, and, by that means, nearer to the laws of the phenomena. The performance 
of this task is requisite for the completion of the Newtonian theory of the universe. 
^ 2. On the Effect of the Moon's Declination on the Tides at Liverpool 
11. In order to obtain the Solar Inequality, it was necessary to eliminate the effect 
of the variations of the lunar tidal forces; the results of the two sets of forces being 
combined in the tides when tabulated according to months, as is done in Mr. Lub- 
• While I write this, I am informed by Mr. Bunt that he has obtained the law of the solar inequality of the 
times at Bristol. The agreement with my results is very remarkable. 
t In the calculations of this Memoir, I have been assisted by Mr. Naylkk of Queen’s College in this Uni- 
versity. 
