19. If for example, we wish to learn whether the Height of the Barometer exerts any sensible influence on the Height of the Sea's Surface, it would appear that the most satisfactory mode of proceeding, must be to subtract, in the first place, what we know to be the effects of the Moon's Age, Parallax and Declination, and other ascertained causes of change; and to search in the _unexplained Residue_ for the effects of barometrical pressure. The contrary course has, however, been adopted, and the effect of the Barometer on the ocean has been investigated by the direct application of the Method of Means, classing the observed heights of the water according to the corresponding heights of the Barometer without any previous reduction. In this manner, the suspicion that the tide of the sea is affected by the pressure of the atmosphere, has been confirmed. This investigation must be looked upon as a remarkable instance of the efficacy of the Method of Means, since the amount of the barometrical effect is much smaller than the other changes from among which it was by this process extricated. But an application of the Method of Residues would still be desirable on a subject of such extent and difficulty. 20. Sir John Herschel, in his _Discourse on the Study of Natural Philosophy_ (Articles 158-161), has pointed out the mode of making discoveries by studying Residual Phenomena; and has given several illustrations of the process. In some of these, he has also {219} considered this method in a wider sense than we have done; treating it as not applicable to quantity only, but to properties and relations of different kinds. We likewise shall proceed to offer a few remarks on Methods of Induction applicable to other relations than those of quantity. {{220}} CHAPTER VIII. METHODS OF INDUCTION DEPENDING ON RESEMBLANCE. APHORISM XLIX. The Law of Continuity _is this:--that a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate magnitudes according to the intermediate conditions. This Law may often be employed to disprove distinctions which have no real foundation._ APHORISM L. The Method of Gradation _consists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. This Method is employed to determine whether the extreme cases are really distinct or not._ APHORISM LI. _The Method of Gradation, applied to decide the question, whether the existing_ geological _phenomena arise from existing causes, leads to this result:--That the phenomena do appear to arise from Existing Causes, but that the action of existing causes may, in past times, have transgressed, to any extent, their_ recorded _limits of intensity._ APHORISM LII.