OFFICERS OF SECTION A.

Vice President.

J. R. EASTMAN' of Washington.

Secretary.

HENRY M. PAUL of Washington.

Member of Council.

HENRY FARQUHAR of Washington.

Members of Sectional Committee.

G. W. HOUGH of Chicago, ORMOND STONE of Univ. of Virginia,

1 To fill vacancy caused by the absence of WILLIAM FERRELL.

PAPERS READ.

ON A METHOD OF COMPUTING THE SECULAR CONTRACTION OF THE EARTH. By R. S. WOODWARD, U. S. Geological Survey, Washington, D. C.

[ABSTRACT.]

THE nature and difficulties of the problem are first set forth.

The method is based on four assumptions, viz.: 1. An initial uniform temperature for the earth's mass; 2. A constant coëfficient of diffusion for that mass; 3. The sufficiency of the first approximation to the roots of Fourier's transcendental equation; 4. A constant coëfficient of cubical contraction. The grounds for these assumptions are discussed and the desirability of certain experimental information indicated.

The main features of the mathematical work are explained and their correctness tested. The resulting expression for the contraction is given two principal forms, the one applicable to the earlier and the other to the later stages of cooling.

Some numerical results dependent on Sir Wm. Thomson's coëfficient of diffusion are given.

A COMPLETED NOMENCLATURE FOR THE PRINCIPAL ROULETTES. By Prof. F. N. WILLSON, Princeton, N. J.

[ABSTRACT.]

THE paper discusses the anomalies of both early and recent definitions of trochoidal curves; demonstrates, kinematically, the property of double generation of all epi- and hypo-cycloids and trochoids, establishing the identity of curtate and prolate forms; shows the inadequacy of the existing nomenclature to suggest the mode of generation of all curves of this class, and presents the following completed nomenclature in a tabular form (see next page) suggested by that of Kennedy, and of which it is both a modification and extension. The last three columns are the new and completing feature.

The demonstrations above alluded to establish the identity of the curves whose names are preceded, in the following table, by the same letter.

STANDARD DIMENSIONS IN ASTRONOMICAL AND PHYSICAL INSTRUMENTS. By J. A. BRASHEAR, Allegheny, Pa.

IN a paper read before the Franklin Institute by Mr. George M. Bond, the present secretary of Section D, the following words were quoted from Mr. Forney's report to the Master Car Builders' Association, on standard bolts and nuts:

"It is worthy of note that a remedy for the evil complained of by the Master Car Builders, that nuts, made by some firms, would not screw on bolts made by other firms, at first baffled the ability of the most prominent manufacturers of tools in the country, and to provide an adequate remedy it was necessary to secure the assistance of the highest scientific ability in the country, which was supplied through the coöperation of the professor of astronomy of the oldest and most noted institution of learning in the land. The man of science turned his attention from the planets and the measurements counted by millions of miles, to listen to the imprecation perhaps of the humble car repairer, lying on his back and swearing because a 5-8 nut a trifle small would not screw on a bolt a trifle large." We all know this professor of astronomy and the noble work he has done in the way of giving us standards of the highest accuracy, which in turn have been carried out into practical mechanism by some of the honored members of the American Association, especially by Mr. Bond of the mechanical section.

Paradoxical as it may seem, though the astronomer has furnished the most accurate standards for the mechanician, thus facilitating the construction of interchangeable machinery all over the world, the astronomer himself has yet to put up with an eye-piece that is just a little too large for a sliding tube that is just a little too small; or, in other words, that branch of science, which has furnished the standard for all other work, is without any standard for the construction of its own instruments.

How many of the parts of an astronomical or physical instrument should be made interchangeable, I am not now willing to say, but every worker with the telescope, spectroscope, or other instrument for physical research, will bear me out in this fact that there is a sore need of standard dimensions in many of the parts of our apparatus. Indeed, our president, Professor Langley, was one of the very first to call my attention to the matter, and suggested that it would be a very excellent plan for this Association to appoint a committee to discuss, and, if possible, decide upon some standard dimensions of the more important parts which should at the earliest date be made interchangeable. I might urge many reasons in support of standard dimensions in many of the parts of our astronomical and physical instruments, but it is not necessary, as the day has passed when we are satisfied with anything but interchangeable parts in modern machinery; therefore we should not be satisfied with anything less for our astronomical and physical instruments.

As an illustration of what is needed, I have constructed four spectroscopes within the past year for six inch aperture telescopes. The diameter of the tail piece of these telescopes has varied from two and one-half

inches to six inches, requiring a new pattern to be made for every clamp that holds the spectroscope to the telescope.

We have indeed only to look at the great variety of eye-pieces and their varied diameters for which we are constantly called upon to make adapters, so that they may be used with any degree of pleasure, to see how far we are from the ideal astronomical or physical instrument. We shall, in all probability, have to call to our assistance the "mandrel drawn" tube makers to give us standard tubes; and perhaps the founder to give us a standard metal, but we should make a move in the matter, and everything will come out right. These very mechanicians, to whom the astronomer has furnished the data, have given us standard reamers, standard gauges, and every facility for making our own work standard, and so we are without a subterfuge, without a valid excuse for doing our work in a "haphazard" way.

I should hope that whatever parts of our instrument we make of standard dimensions, that the basis should be a decimal system, preferably the metric; indeed, is it not possible that these standards might be made international, as they should most surely be? The greater then the value of the metric basis.

This paper is only suggestive, but I trust will serve to call attention to a fault in the construction of our apparatus that is not in accord with the progress in other lines of mechanical art.

THE PHENOMENA OF SOLAR-VORTICES.
Racine, Wis.

[ABSTRACT.]

By Prof. FRANK H. BIGELOW,

THE theory of the sun-spots as vortex rings admits certain tests which are here indicated. The spots are supposed to originate in the following manner-the sun is composed of an ellipsoidal nucleus of viscous material with a figure corresponding to the period of rotation; surrounding this is a convectional region filled with currents of radiated gases and surmounted at the end of the cooling radius by a spherical envelope of condensation. The low specific gravity of the sun, the invariability of its apparent diameters under rotation, the acceleration of the equatorial belts point to this conclusion. The general contraction of the nucleus and other causes of constriction produce great bubbles all over its surface, but most vigorously near parallels of structural weakness where the tangential tension on the surface is a maximum. The escape of the gases occurs in the form of vortex rings which finally impinge upon the envelope, the strongest being able to break through. The spot belts and their periodicity depend upon the special energies of the nucleus.

Spots are distinguished as of the normal type and of the irregular forms. Each spot passes through three stages: the formation, the quiescence and the degeneration. The natural development of a vortex is that ordinarily observed, an apparition with local disturbance of the surface, including a lifted space gradually streaked with cleavages; the appearance of the true ring, umbra, penumbra and photosphore, with their respective