To the Editor of the Popular Science Monthly.
I HAVE read with a good deal of interest Prof. Schneider's article on "The Tides," in the July number of the Monthly. I was pleased with his method of approaching the problem, because it deals with the planetary bodies as we actually see them in motion, not demanding that effort of the imagination required in studying the problem simply as one of static equilibrium. He has succeeded in rendering tolerably intelligible from a new standpoint a subject which is perhaps left for the average reader in a somewhat unsatisfactory state in our popular works on astronomy and physical geography.
In proportion as he has done this portion of his work well, is any error of statement into which he may have been led liable to prove mischievous. This is my only excuse for venturing to offer any criticism on the work of one who has really done valuable service in presenting familiar truths in new aspects.
Nowhere is our author more clearly wrong than in his own criticism of the commonly-accepted theory of the causation of the tides. He admits, apparently, that the attraction of the moon, or of the sun, is capable of lifting into a tidal protuberance the waters that lie, in popular parlance, directly beneath them; but that the earth itself should be drawn away from the waters upon its opposite surface, he pronounces preposterously absurd. "It has been proved experimentally," he says, "that all bodies on the surface of the earth are heavier at midnight than at any other hour of the twenty-four." He cites no authority for this statement, which is simply inconsistent with the observed fact that at midnight, leaving out of account the influence of the moon, the tide is rising instead of falling. The state of the tide, however, as we shall perhaps have occasion to indicate hereafter, is not a trustworthy measure of the local variations in that gravitative force which manifests itself as weight. Unless, therefore, delicate experiments with the pendulum have actually demonstrated the existence and amount of such diurnal variations, we can only infer them from our knowledge of the forces which may produce them.
It is in his attempt to do this that our author falls into the fatal confusion of thought which leads him to pronounce absurd a theory which to the clear-sighted Newton was simply the truth. This confusion seems to arise wholly from a careless use of the term weight or gravity. On the side of the earth facing the sun, all particles of matter feel the attraction of the earth and that of the sun as forces acting in opposite directions. "The weight of a body situated at this point then will be diminished by precisely the amount of the sun's attractive force." Yes, if meanwhile the earth's centre remain stationary. But this is not the fact; the whole mass of the earth has simultaneously yielded to the solicitation of the same attraction. If these motions are equal, they can produce no change in weight, for weight is simply the force with which a body tends to approach the earth's centre, not simply the force with which it advances through space in the direction of that centre. Prof. Schneider himself points out the distinction, but proceeds immediately to ignore it in his reasoning. He says: "As the particles of the earth most remote from the sun feel its attraction plus that of the earth herself, they are drawn with greater force toward the centre of the earth than any other particles. Hence," he triumphantly asserts, "it cannot be true that the whole earth is drawn away from the waters, and that any tide is produced by the waters being left behind."
Having thus convincingly (?) shown the necessity for a more satisfactory hypothesis regarding the causation of the tides, he proceeds to offer one of his own. The first thing we remark, however, in examining this is that it embodies all that was contained in the old "absurd" hypothesis, while it complicates the problem by compelling us to consider not only the attraction of the sun or moon, but also the antagonizing force which prevents the earth from moving in the direction of the attracting body. It is true that by an ingenious misstatement of his own theory the writer avoids what to him seems paradoxical in that which he rejects. One of the tides—that on the side of the earth facing the disturbing body—he tells us, is produced by centripetal, the other by centrifugal force. In an explanatory paragraph he admits, although he does not distinctly state, what is the fact, viz., that in each case coinciding effects are produced by simultaneous variations in opposite directions of both these forces. Recognizing, however, the supreme value of directness and simplicity of statement in all popular expositions of scientific truth,