(I.) If we do not know on what quantity those changes depend which we are studying, we may fail entirely in detecting the law of the changes, although we throw the observations into curves. For the true _argument_ of the change should, in fact, be made the _abscissa_ of the curve. If we were to express, by a series of ordinates, the _hour_ of high water on successive days, we should not obtain, or should obtain very imperfectly, the law which these times follow; for the real argument of this change is not the _solar hour_, but the _hour_ at which the _moon_ passes the meridian. But if we are supposed to be aware that _this_ is the _argument_, (which theory suggests and trial instantly confirms) we then do immediately obtain the primary Rules of the Time of High Water, by throwing a series of observations into a Curve, with the Hour of the Moon's Transit for the abscissa. In like manner, when we have obtained the first great or Semi-mensual Inequality of the tides, if we endeavour to discover the laws of other Inequalities by means of curves, we must take from theory the suggestion that the Arguments of such inequalities will probably be the _parallax_ and the _declination_ of the moon. This suggestion again is confirmed by trial; but if we were supposed to be entirely ignorant of the dependence of the changes of the tide on the Distance and Declination of the moon, the curves would exhibit unintelligible and seemingly capricious changes. For by the effect of the Inequality arising from the Parallax, the convexities of the curves which belong to the {209} spring tides, are in some years made alternately greater and less all the year through; while in other years they are made all nearly equal. This difference does not betray its origin, till we refer it to the Parallax; and the same difficulty in proceeding would arise if we were ignorant that the moon's Declination is one of the Arguments of tidal changes. In like manner, if we try to reduce to law any meteorological changes, those of the Height of the Barometer for instance, we find that we can make little progress in the investigation, precisely because we do not know the Argument on which these changes depend. That there is a certain regular _diurnal_ change of small amount, we know; but when we have abstracted this Inequality, (of which the Argument is the _time of day_,) we find far greater Changes left behind, from day to day and from hour to hour; and we express these in curves, but we cannot reduce them to Rule, because we cannot discover on what numerical quantity they depend. The assiduous study of barometrical observations, thrown into curves, may perhaps hereafter point out to us what are the relations of time and space by which these variations are determined; but in the mean time, this subject exemplifies to us our remark, that the method of curves is of comparatively small use, so long as we are in ignorance of the real Arguments of the Inequalities.