Popular Science Monthly/Volume 11/October 1877/Correspondence

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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, we are disposed to overlook inaccuracies such as these, lying merely on the surface. It is otherwise with anything that betrays confusion of thought in regard to the fundamental elements of the problem. This, it seems to me, the writer has done in ascribing to centrifugal force a primary place in the causation of tides. It is only as the waters upon the earth's surface have freedom of motion—are acted upon, therefore, as independent of the earth's mass—that tides are possible. On the other hand, only in so far as the waters take up by friction and cohesion of their particles the motion proper to the portion of the solid earth underlying them, will they acquire the increased tangential momentum which constitutes the so-called centrifugal force. When it is understood that the force in question operates only in this indirect manner, it becomes plain that it ought not to be classed with gravitation as a primary cause of the tides, but rather with the rotation of the earth as an important secondary factor, necessary to be studied in tracing out the actual operation of their real cause.

The new mode of explaining the observed phenomena is, however, on the whole, quite intelligible and satisfactory in its application to the solar tides. It requires a greater effort of the imagination to see exactly how the same principles operate in the causation of the lunar tides. It is easy to understand how centrifugal force will predominate on the side of the earth opposite the moon, and how the waters on the nearer side will tend to insphere themselves about the centre of gravity of the rotating system, a point only 2,687 miles from the earth's centre. There is some difficulty in taking on trust the statement that the earth will feel on the side facing the moon a centripetal force equal to the centrifugal force which is said to cause the tide on the opposite side, when we remember that the moon itself is a part of the rotating system, and must itself claim a share, however small, of the forces, centrifugal and centripetal, whose balancing equivalents are to be sought on the remote side of the earth. And it is far from clear to the tyro in mathematics why high tide should occur directly under the moon, where centrifugal force, acting in a direction away from the earth's centre, is but slight, while centripetal force, acting in the opposite direction, is at its maximum so far as it is dependent on proximity to the centre of rotation. Although the explanation of this latter apparent paradox is by no means difficult, it will certainly prove to many a fertile source of perplexity.

The interest I have myself taken in applying Prof. Schneider's hypothesis to the numerous practical problems which arise the moment we pass in our study from hypothetical tidal waves to the actual movement of the waters of existing oceans, has led me to jot down the above points in the way of friendly criticism. For the rest, I would rather listen to some abler critic.

A. B. Lyons, M. D.
Detroit, June 27, 1877.


To the Editor of the Popular Science Monthly.

Dear Sir: The letter of Prof. G. B. Halsted, of Johns Hopkins University, in your number for July, 1877, in regard to the imaginary geometry of Gauss, Lobatchewsky, and Beltrami, brings to my mind the fact that there is no necessary truth in many things that we have regarded (at least we mathematicians) as necessary truths.

Sir George Airy investigated the conditions under which perpetual motion might exist (Cambridge "Philosophical Transactions," 1880, vol. iii., pp. 369-372).

Newton's notion of negative density ("Principia," book ii., sec. ii., prop, x.) is another case.

Laplace, in the "Mécanique Céleste," has indulged in a remarkable speculation as to what the laws of motion would have been if momentum, instead of varying simply as the velocity, had been a more complicated function of it.

These things seem to overturn current metaphysics, and that is about all the good in them. Yet Reid, in what he calls the Geometry of Visibles, chapter xli. of his "Inquiry," raised a question of like nature. Hamilton, as noticed by George Lewes ("Problems of Life and Mind," vol. ii. . Appendix), has avoided any comment.

By reason of the superb contempt which this extraordinary man affected for mathematics, I presume he thought it beneath his notice. Your obedient servant,

Lewis Kennon, M. D.
Fort Bayard, New Mexico, July 29, 1877.


We give below an important letter from Prof. Wilder, of Cornell University, on the Woodruff Scientific Expedition, and would call the attention of those interested to the assurances it contains concerning the opportunities for study and the facilities for original work which the expedition is expected to afford. Prof. Wilder is a member of the faculty of scientific instructors, and also one of the trustees of the expedition. The letter, as will be seen, is in response to our inquiries:

To the Editor of the Popular Science Monthly.

Sir: In answering your inquiry as to the nature and extent of scientific work to be attempted on the Woodruff Expedition, and the facilities therefor, I must premise: first, that the published list of professors does not include several who are expected to conduct special departments of botany and zoölogy; second, that the faculty have had no official conference, so that I can speak only for myself.

My own duties will include—1. General lectures on the habits and structure of vertebrates. These will be nearly free from technicalities, so as to be intelligible to all. 2. Special instruction of those who may wish to go more deeply in certain directions; this by superintendence of dissections, and occasional lectures. 3. Instruction in methods of collecting, preparing, and preserving specimens. 4. Preparation of, and research upon, embryos, brains, hearts, and other soft parts, which are usually neglected by foreign collectors.

The students will provide their own dissecting instruments, cans, and preservatives; but, as stated on page 21 of the announcement, the management engages to furnish a library and apparatus for instruction.

I understand such requisite apparatus to include nets, dredges, and sounding arrangements, chemical and physical instruments, microscopes, diagrams, blackboards, stereopticon, and the means of preserving certain typical forms for illustration of lectures.

To insure the fulfillment of the promises made in the announcement, the trustees are to control the transfer of the fees to the director. The trustees are also members of the faculty, and their interests are therefore identified with those of the students.

From what I know or have heard of those concerned in the management of the expedition and the instruction, I feel confident that all possible facilities will be afforded for the acquisition of general information, and for the pursuit of special lines of investigation.

Respectfully yours,
Burt G. Wilder.
Ithaca, New York, September 1, 1877.