fix the value of those which are uncertain; and develope phenomena which before were obscured in the errors of observation. The tides are not less interesting to understand, than the inequalities of the heavenly bodies, and equally merit the attention of observers. We have hitherto neglected to follow them with sufficient precision, because of the irregularities they present. But I can assert, after a careful investigation, that these irregularities disappear by multiplying the observations; nor is it necessary that their number should be extremely great, particularly at Brest, whose situation is very favourable for this species of observation. I have now only to speak of the method of determining the time of high water, on any day whatever. We should recollect, that each of our ports may be considered as the extremity of a canal, at whose embouchure the partial tides happen at the moment of the passage of the Sun and Moon over the meridian, and employ a day and a half to arrive at its extremity, supposed eastward of its embouchure, by a certain number of hours.-This number is what I call the fundamental hour of the port. from the hour of the establishment of the port, by considering this as the hour of the full tide, when it coincides with the sysygy. The retardation of the tides, from one day to another, being then * 2705", it will be † 3951" for one day and a half, which quantity is to be added to the hour of the establishment, to have the fundamental hour. Now, if we augment the hours of the tides at the embouchure by It may easily be computed 15 hours, plus the fundamental hours, we shall have the hours of the corresponding tides in our ports. Thus, the problem consists in finding the hours of the tides. in a place whose longitude is known, on the supposition that the partial tides happen at the instant of the passage of the Sun and Moon over the meridian. For * 14' 36". + 21' 20". ‡ 36". this purpose analysis affords very simple formulæ, which are easily reduced to tables, and very useful to be inserted in the ephemerides that are destined for navigators. CHAP. XI. On the Stability of the Equilibrium of the Ocean. SEVERAL irregular causes, such as hurricanes and earthquakes, agitate the sea, elevate it to a great height, and sometimes oblige it to forsake its limits. Nevertheless, observation shews us that it has a tendency to return to its former state of equilibrium, and that the friction and resistances of all kinds that it experiences, would very soon bring it to this state, without the action of the Sun and Moon. This tendency constitutes the stable equilibrium, which we mentioned in the Third Book. We have there shewn that the stability of the equilibrium of a system of bodies may be absolute, or take place, whatever small derangement it may receive; or it may be relative, and depend ance. on the nature of the primitive disturb. To which class belongs the stability of the ocean? This is what observation cannot teach us with absolute certainty; for, although in the almost infinite variety of disturbances to which the ocean is liable, from the action of irregular causes, it may appear to return to its former state of equilibrium; yet we may ne vertheless apprehend, that some extraordinary cause may communicate to it a shock, which though inconsiderable at its origin, may augment continually, and elevate it above the highest mountains: this would explain several phenomena in natural history. It is therefore interesting to investigate the conditions which are necessary for the absolute stability of the ocean, and to examine if these conditions exist in nature. In submitting this object to analysis, I have assured myself that this equilibrium is stable, if its density is less than the mean density of the Earth, which is extremely probable, for it is natural to think, that the strata are more dense as |
