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is much to be regretted that no observations were made by any of the large Munich refractors, as they might, at the least, have been able to fill out a great part of the series up to Professor Challis's last observation. “ The three orbits are as follows:Epoch. June 16.5 Berlin M. T., M. Eq. 1848.0.
III. M 1576 53.25 156 15 45^9 156°8 485 8 68 28 32.6 68 28 3.3 68 27 56.1
70 56 50.8 71 35 14.75 71 41 2.2 i 5 35 32.88 5 35 33.4 5 35 34.4 9 7 2 52.73 7 6 43.85 7 7 14.52 962".647 963".244
9634.272 “ These three orbits satisfy the series of observations almost equally well, Orbit I. giving the majority of the Right Ascensions somewhat too large, and II. and III. somewhat too small. The sum of the errors is smallest in II., – the sum of their squares in III. The Orbit III. gives the following absolute places, to which is annexed the aberration in decimals of a day.
“ The comparison of this ephemeris with observation is contained in the following table. “ COMPARISON OF ORBIT III. with OBSERVATION.
“For this orbit the perturbations by Jupiter, since the opposition of 1848, have been computed. The influence of Saturn was found quite unappreciable, and that of Mars very insignificant, although the latter planet will be nearly in heliocentric conjunction with Metis during the month of April next. Their difference of latitude is, however, very considerable.
" The variations of the osculating elements are as follows. They are to be algebraically added to the elements in Orbit III.
“ Hence result the following osculating elements for April 6.5 :
lle . 962".985 Log. e 9.0924492 “These elements give the following ephemeris for the reappearance of Metis in 1849. The great diversity of the elements calculated from normal places so little different would of itself indicate that great exactness cannot be expected. And, were it not so, the unavoidable insecurity of the extrameridional observations at the discovery, and immediately before the disappearance, of the planet, would warn us to expect at least an uncertainty of one or two minutes in the predicted place.
“Metis. Mean BERLIN Midnight.
“ The elements computed by me on the 28th of May last, and published in No. 639 of the Astronomischen Nachrichten (XXVII. p. 237), gave the right ascension, at the beginning of August, a minute and a half of arc too large, and the declination nine seconds too far south. These elements were deduced from meridian observations at an interval of but thirty days, and furnish a strong testimony to the importance of basing the orbits computed from a small arc upon meridian observations alone, if possible.”
Professor Lovering read a paper on the “Law of Continuity,” and a seeming exception to it, and illustrated it by various magnetical experiments.
“ The law of continuity supposes that, in the operations of nature, a body passes from one state to another distinct state only by going through all the intermediate states. As to motion, this is obviously true. We cannot conceive of a body getting from one place to another, except by moving, in successive instants of time, through the intermediate positions.
“ Leibnitz, who claimed to be himself the originator of this principle, considered it applicable, not only to the position of a body, but to the chemical and physical arrangement of its molecules. He supposed the foundations of this principle to be laid so deep in the arrangements of nature and the structure of the human mind, that man could not, when he reasoned upon the subject, conceive of its non-existence or of any exception to its application. The extreme length to which the law of continuity was pressed by Leibnitz and Bernouilli, in their attempts to demonstrate the laws of mechanics, led Maclaurin and others to reject it altogether. It must be admitted, notwithstanding, that this law of continuity has a firm foundation in truth ; and that, under its guidance, man is put into the right path in the investigation of the plan of nature. The method of analysis which began with Leibnitz and Newton, and which in England has been known, under the name of fluxions, rests upon this law of continuity. For it supposes a line to flow out from a point, a surface from a line, and a solid from a surface ; and this, like any other motion, involves the law of continuity. If we admit the usefulness of the principle only in cases of motion, we still give it a wide range ; since so many problems, not strictly dynamical, are reduced to cases of motion when investigated by the rules of modern analysis.
“ The object of the present communication is not, however, to ex. plain or defend the law of continuity as a sound principle in physical investigation, but to call attention to a few real or apparent exceptions to it with which I have become acquainted in studying the physical forces.
- If we place a bar-magnet on a table, and move over it lengthwise a small compass-needle which is free to move on a horizontal axis only, when this axis is parallel to the axis of the large magnet, the law