Also receipts for Catalogue, as follows: Boston Public Library (Part III); Amer. Antiquarian Society (Part III); Wisconsin State Historical Society (Part III); Regents of the University of New York (Part I); and the U. S. Naval Observatory (Parts I, II, III).

A letter requesting exchange of catalogues was received from the Public School Librarian at St. Louis.--On motion the exchange was ordered.

Letters of envoy were received from the Royal Society of New South Wales, Sydney, Sept. 11, 1878; Royal Bavarian Academy, Munich, March 30, 1878; and Holland Society of Sciences, Harlem, Jan., 1877.

A letter was received from Mr. Walter White, Assistant Secretary of the Royal Society, dated London, Sept. 23d, 1878, presenting a copy in bronze of the newly instituted Davy Medal; and letters from the U. S. Department of State transmitting the same.

Donations for the Library were received from the R. Bavarian Academy; R. Accademia dei Lincei; R. Academy at Lisbon; Kansas Academy at Topeka; and Academy at San Francisco; the Department of Mines, Melbourne; Royal Danish Society; Revue Politique, and M. M. Delesse and Lapparant, Paris; London Nature; Mr. O. Fisher, F. G. S.; Essex Institute; Boston Society of Natural History; Harvard College; American Antiquarian Society; Yale College; Prof. Geo. J. Brush; Ed. S. Dana; Lyceum of New York, (N. Y. Academy of Natural Science); Prof. J. S. Newberry; Polytechnic Review; Brooklyn Entomological Society; Franklin Institute; American Journal of the Medical Sciences; Medical News and Library; Penn Monthly; Prof. E. D. Cope; Dr. J. B. Cox; Mr. Edwin A. Barber; U. S. Coast Survey; U. S. Engineer Department; Bureau of Education; Weather Bureau; University of Virginia; Georgia Historical Society; Kansas State Horticultural Society; Ministerio de Fomento, and Geological and Statistical Society, Mexico; and Ministerio de Fomento, Madrid.

A bronze medal, a copy of the newly instituted Davy

1878.]

Medal, was presented to the Cabinet by the Royal Society of London. On the obverse a head of Sir Humphrey Davy. On the reverse the following legend:-"The Royal Society to Robert Wilhelm Bunsen. Gustav Robert Kirchhoff. In accordance with the will of Humphrey Davy, who devoted the testimonial presented to him by the Coalowners of the Tyne and Wear to the encouragement of Chemical research -1877."

The Secretary offered for publication in the Transactions a memoir entitled, "The Upper Carboniferous Flora of West Virginia. With 23 plates. With 23 plates. By W. M. Fontaine and I. C. White," and exhibited proof sheets of the quarto plates.— On motion the paper was referred for examination and report to Dr. Leidy, Dr. J. S. Newberry, and Mr. Lesquereux.

The Secretary read by title a communication entitled "On the limiting Constant of Gravitation. By Pliny E. Chase."

Prof. Lesley read a communication entitled "Notes on a series of analyses of the Dolomitic Limestone rocks of Cumberland Co., Pa."-The subject was discussed by Dr. König, Prof. Frazer, and Mr. Walter.

Mr. Briggs read from a MSS. part of his discussion of the economical problem of force and fuel applied to Electric Lighting as compared with Lighting by Coal Gas.

Mr. Briggs invited attention to the remarkable fact that all the exhibitors of Artificial Ice Machines at Paris (six in number, of which Pictet's seems to be best) claimed for their several machines twice or three times the maximum efficiency to be expected, if the accepted theory of the coefficient of heat be true.

Prof. Frazer communicated the fact that in his use of the local telephone circuit during the Summer he had observed a continued resonance of over tones.

In the course of some experiments on a telephone line with a view to decrease the crackling due to atmospheric disturbance, an observation was made by Prof. Frazer which will seem to illustrate to what an infinitessimal motion the sounds heard through the telephone are sometimes due. A telephone was selected in which the diaphragm was held fast at only two

[Oct. 18,

or three points instead of on a flat surface, which usually binds the outside of the metal plate. The diaphragm gave to one note a clear resonance, in which the overtones so characteristic of metal plates in vibration were distinctly heard (middle A of piano). On sounding this note into the mouthpiece, while keeping the other telephones covered so as not to be directly affected by the air-waves, it was found that the overtones were audibly traceable in one of the other telephones with which connection was had over a line of about one-third of a mile with a ground return circuit.

It is difficult enough to understand how the minute waves into which a metal plate is thrown by a vigorous note of the voice can reproduce sound through the intermediate agency of maxima and mimima of resistance in the medium of current transmission; but that the minute wavelets which are produced upon the backs of these, should at the extremity of a long line produce sufficiently powerful variations of conductivity to cause the mechanical fluttering of the diaphragm of another instrument to a sufficient degree to cause the effect of sound could scarcely have been foreseen.

Pending nominations 864, 867, 868, 869, 870, and new nomination 871 were read.

In the absence of Prof. Houston the consideration of his motion to amend the minutes was postponed to the next regular meeting.

The Secetary read a letter from Prof. Henry Morton, dated Hoboken, Oct. 7., drawing attention to a marked word, "Fourou's," in an enclosed original letter, written to him by Prof. Sadtler, dated Dec. 31, 1877; and for the purpose of showing that he (Prof. Morton) did Prof. Sadtler no injustice in quoting this word (instead of Fouqué) in his letter of May 15, 1878, commented upon in Prof. Sadtler's reply as published in the Proceedings A. P. S., Vol. XVII, page 724.

The pending nominations 864, 867 to 870 were balloted for, and, after scrutiny of the ballot boxes by the presiding officer, the following were declared duly elected members of the Society :

Dr. Albert H. Smith, of Philadelphia.

Rev. Saml. Longfellow, of Germantown.

Rev. Ed. A. Foggo, D. D., of Philadelphia.

M. A. Descloizeaux, of Paris.

Dr. C. Schorlemmer, of Manchester, England,

and the meeting was adjourned.

The Limiting Constant of Gravitation. By Pliny E. Chase. (Read before the American Philosophical Society, October 18, 1878.) Newton and Lesage both thought that gravitation might be due to some action of an æther or " æthereal spirit." If such supposed action is uniform it should be capable of representation by some uniform or constant value, toward which planetary or gravitating motion should constantly tend.

Faraday sought in vain to find such a value, and his want of success led him to the belief that the "correlation of forces" could not include the force of gravity. It is true that a kind of constancy is observable in bodies at rest, and another kind in circular orbits; but if the distance from the principal center is changed, the former varies inversely as the square of the distance, the latter inversely as the square root of the distance. Inasmuch as there is no known limit of possible density, there is no obvious limit to the possible velocity of gravitating motion.

My various investigations have shown that heat, actinism, kinetic laws, spectral lines, the arrangement and masses of planets, interstellar nodes, barometric fluctuations, centers of inertia, terrestrial magnetism, chemical combinations, and the aggregation or dissociation of stellar systems, all point to the velocity of light as a limiting constant. Weber, Kohlrausch and Maxwell having found a like pointing, in the relations which exist between electro-static and electro-dynamic phenomena, it seems probable that the goal of Faraday's search may also have been the velocity of light, and that such velocity is the fundamental basis of universal correlation.

I have already pointed out three methods of approximation to the limit : 1, by the tendency towards equality in planetary revolution and in the mean moment of solar inertia of rotation; 2, by the tendency to equality between mean radial oscillatory velocity and the velocity which marks the limit between complete solar dissociation and incipient nucleal aggrega tion; 3, by the tendency to uniformity in dissociative velocity at each of the three principal centres of nebular condensation in the solar system.

Against the first of these methods the objection has been urged that it supposes the sun to be homogeneous. The validity of this criticism cannot be determined until the problem has been subjected to a rigid mathematical analysis. If such analysis should hereafter show that the objection is well taken, it may be found that the sun is more homogeneous than the dense planets, and sufficiently so to satisfy all the requirements of the method. Draper's recent photograph of the corona indicates a diameter twice as great as that of the sun. This is in exact accordance with the supposed gascous nature of the sun, and, consequently, with its homogeneity, as well as with the relations which I have pointed out between Jupiter's mass and position.

Some have thought the second method faulty, because it involves a consideration of hypothetical conditions of nebular condensation, such as are inconsistent with the common notions of the nature of matter. But those conditions were introduced merely to indicate joint tendencies, without

PROC. AMER. PHILOS. SOC. XVIII. 102. F. PRINTED DEC. 12, 1878.

Chase.]

[Oct. 18, any regard to the variety of possible or impossible forms which the tendencies may be supposed to assume or to indicate. In all mathematical physics an ideal completeness is assumed, such as is never found in nature. The method in question is analogous to the one which has been satisfactorily adopted in investigating the laws of elastic undulation.

It seems to have been generally admitted that the third method may be accepted as lending probability to the indications of the other two, but it involves the same question of dissociative velocity, and is, therefore, open to the same criticism as the second method. For this reason it seems desirable to see whether the problem can be successfully treated in some other way.

If gravitating movements have any common limit, either of originating efficiency or of ultimate tendency, which is uniform in all stellar systems, that limit should evidently be sought in the direction of phenomenal maxima, and with special reference to the principal center of the system. If the ethereal hypotheses are correct, we may reasonably presume that the gravitating constant is dependent upon some æthereal constant.

La Place established the general principle that the state of a system of bodies becomes periodic when the effort of the primitive conditions of movement has disappeared by the action of resistances. This principle, which is a necessary consequence of the third law of motion, is well illus trated in elliptical planetary orbits, in which the cyclical movement may be resolved into alternate oscillations, of approach to perihelion and retreat to aphelion. The duration of all such oscillations, whether circular, slightly elliptical, or as nearly radial and rectilinear as the central nucleus will allow, is determined by the length of the major axis, varying as the power of the length. If the major axes are equal, the oscillations are synchronous.

If orbital collisions of particles, in the neighborhood of the focus, shorten the major axes, cosmical rotation may be substituted for free planetary revolution. But the limiting value, which is to be alternately overcome and renewed, will not be changed thereby; the period for destroying or acquiring that limiting value should still be one-half of the cyclical period, or the period of a half rotation.

The equation of constant velocity, in an elastic atmosphere or in an æthereal medium, is

denoting the wave-velocity; g, the acceleration of gravity at the point of observation; h, the modulus of elasticity, or the height of a homogeneous atmosphere; t, the time of rise or fall, throughh, under the constant retardation or acceleration g; t is also, as has just been shown, the time of a half-rotation which is supposed to be due to æthereal impulses. Challis has found that if all the ordinary central forces are due to transformed æthereal vibrations, "the actions of such forces on atoms are in every in stance attributable to æthereal currents, whether the atoms be immediately acted upon by steady motions of the æther or by ethereal vibration."

* Phil. Mag., Sept., 1872; Sept., 1876: June, 1876.