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. |
THE NEW IDEAS ABOUT SPACE.
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. |
THE WOODRUFF SCIENTIFIC EXPEDITION.
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
