The present state of our knowledge of the tides is remarkably at variance with the complete and scientific character which Physical Astronomy is, in common opinion, supposed to have attained. We may, perhaps, most easily figure to ourselves the real condition of this subject, by imagining what the condition of other branches of astronomy would be, if some great natural or moral convulsion should sweep away our existing science, and replunge us in the ignorance of the dark ages, leaving extant only a few general notions concerning the theories which are at present established. In such a state of things, we may suppose that some tradition of the doctrine of universal gravitation would survive the change, and that learned men would still go on asserting that the various astronomical phenomena of the universe were owing to that cause; but the resources of mathematical art being, for the time, lost, they would be unable to prove the truth of such assertions: and, both the collected stores of observation, and the habit and apparatus of observing, being, in such a case, supposed to be annihilated, it would be long before there would arise persons able and willing to supply such deficiency; the more so as those who might make such collections would have still to seek for the mode of turning them to any use. If, in this state of things, a few persons should, by their own sagacity and labour, or by the aid of some traditionary secret, attain to the power of predicting phenomena with tolerable correctness, we may imagine that they would use their peculiar skill for purposes of gain, and that they would not readily admit the world at large to the knowledge of the secret which gave them a superiority over the rest of their countrymen. Our knowledge of the tides, at the present time, exactly realizes this imaginary condition which we have supposed for astronomy in general. Our philosophers assert, without hesitation, that this phenomenon is the result of the law of the universal gravitation of matter; yet no one has hitherto deduced, from this law, the laws by which the phenomena are actually regulated with regard to time and place. Analysis has been largely used; but it has been employed only to deduce the consequences of certain assumed suppositions, which suppositions are acknowledged to be utterly different from the real state of the case: and where is the immediate advantage, for the purposes of sound philosophy, of analysis which does not solve the problem proposed, over no analysis at all? Some observations of the tides have no doubt been made, and more are now making; but it is not too much to say, that these are only a commencement of the collections which the subject will require, to place it on a par with the other provinces of physical astronomy. The laws which connect the course of the observed tides with the motions and distances of the sun and moon are not known for any single port; and the tables, which in every other province of physics are the result of the knowledge which our men of science have accumulated for us, are, in this department, published by persons possessing and professing no theoretical views on the subject; and the methods by which they are calculated are not only not a portion of our published knowledge, but are guarded as secrets, and handed down as private property from one generation to another.
II. On the empirical laws of the tides in the port of London; with some reflexions on the theory