cular motion, is impressed upon it. "Centrifugal force" is a misnomer—a convenient fiction to represent resistance. Resistance or inertia only opposes motion; it never produces it; and is, therefore, not force. Hence any explanation of phenomena that assigns "centrifugal force" as the real cause in producing motion or change of motion is wholly erroneous, and subversive of Newton's first law. No such resort to "centrifugal force" is necessary in the explanation of the tides.
I must confess entire ignorance of the experimental demonstration that bodies weigh more or are heavier at midnight than at any other hour of the twenty-four. If that be true, and the cause assigned by Prof. Schneider a sufficient explanation, then the lunar midnight should produce the same effect as the solar. On this point allow me to quote from Sir William Thomson and Prof. P. G. Tait's "Treatise on Natural Philosophy," vol. i., page 662. The authority of these physicists must be acknowledged: "Hence as the moon or anti-moon (an imaginary moon 180° from the real one) rises from the horizon to the zenith of any place on the earth's surface, the intensity of apparent gravity is diminished by about 16000000 part; and the plummet is deflected toward the point of the horizon under either moon or anti-moon by an amount which reaches its maximum value when the altitude is 45°. The corresponding effects of solar influence are of nearly half these amounts."
Does Prof Schneider mean to subvert Newton's third law that action and reaction are always equal? If he can prove that the centripetal force for any point of a revolving body is greater or less than its reaction, the "centrifugal force," he will certainly disprove Newton's law, and compel a reconstruction of most, if not all, mechanical propositions.
His statements respecting the value of "centrifugal force" (properly centripetal force or acceleration toward the centre) as depending on the radius of curvature are incorrect. It is not unconditionally true that "in a short curve the centrifugal force is very great." On the contrary, if the time of revolution is constant, the "centrifugal force" varies directly as the radius, increasing as the radius increases. If the velocity of rotation is constant, "centrifugal force" varies inversely as the radius, increasing as the radius decreases. Neither of these conditions is met in the comparison of the revolutions of the earth and the moon in their orbits, since neither times nor velocities are the same in the two orbits. In fact, the acceleration of the earth (and, therefore, of the moon) toward the sun is about 23100 of an inch; while that of the moon toward the earth is a little less than 11100 of an inch a second. The acceleration of the earth toward the common centre of gravity of earth and moon is only a small fraction of the moon's acceleration toward the same point. These accelerations are the measures of "centrifugal force." Hence, according to Prof. Schneider's theory, the solar tide should be many times greater than the lunar.
My amazement reaches a climax when I read, near the close of the article in question, that "centrifugal force acts in a line tangent to the earth's orbit;" or, "in a direction at right angles with the radius-vector." Really, Mr. Editor, your compassion should have saved Prof Schneider from making such an egregious blunder.
In reference to the true explanation of the tides, the length of this communication will allow me to add only that, if Prof. Loomis, in his admirable "Treatise on Astronomy," had applied to the tides the same explanation and figure, mutatis mutandis, that he uses in estimating the amount of the sun's disturbing effect on the moon's motion, no uncertainty would remain in the mind of teacher or student respecting the cause of the tides.
| H. S. Carhart. |
| Northwestern University, Evanston, Illinois, July 2, 1877. |
"THE ZODIACAL LIGHT."
To the Editor of the Popular Science Monthly.
Prof. Brame's article on "The Zodiacal Light," in The Popular Science Monthly for July, may make a recent observation of that phenomenon of interest. About eight o'clock in the evening of July 3d my attention was called to a peculiar appearance of the sky. The sun had been below the horizon about an hour. From the point in the horizon where it was last seen a broad band of pink or rose-colored light followed the ecliptic across the sky to the opposite horizon. Its south limit was sharply defined—its intensity nearly the same from horizon to horizon. Its north limit was not determinable, the pinkish light extending nearly or quite to the horizon, filling the entire northern sky. The southern sky from the ecliptic was of the normal blue color, with the exception of a single streak of a darker blue, extending from the point where the sun sank below the horizon about 90° into the southern sky, making an angle of say 30° with the southern limit of the rose-colored light, or the ecliptic.
There were none of the auroral characteristics. The light was steady, and the entire exhibition as described lasted for twenty minutes, when it all faded away gradually, leaving a perfectly clear sky, with only a trace of the pink in the west.
| Charles A. Morey. |
| Winona, Minnesota, July 5, 1877. |
