XIV. "Account of the Construction of a Standard Barometer, and of the Apparatus and Processes employed in the Verification of Barometers at the Kew Observatory." By JOHN WELSH. Communicated by J. P. GASSIOT, Esq., F.R.S., Chairman of the Kew Observatory Committee of the British Association.

(Abstract.)

After stating the results of experiments, made under the superintendence of the Kew Committee, for the construction of a barometer tube of large diameter by the usual method of boiling the mercury in the tube, the author proceeds to describe a method of filling a tube with the aid of an air-pump. In this process, which is fully detailed in the paper, the tube is so constructed, that when the air has been extracted from it, the mercury enters by atmospheric pressure, provision being made for entirely removing the air which the air-pump has failed to extract. By this method a barometer tube of 1.1 inch internal diameter has been satisfactorily prepared at the Kew Observatory. The author then describes the mounting and mode of observing the standard barometer, proceeds to explain the processes adopted in the verification of barometers, and gives a detailed description of the apparatus for determining the errors of barometers at different atmospheric pressures.

XV. "On the Aurora." By REUBEN PHILLIPS, Esq. Communicated by Professor STOKES, Sec. R.S. Received March 7, 1856.

In this paper the author enters into various speculations as to the formation and motion of auroral arches. Since it has been found by experiment that the maximum length of the voltaic arc with a given battery is nearly the same in atmospheric air and in highly rarefied air, forming a very perfect vacuum, the author conceives that a streamer begins as a disruptive discharge of finite and very moderate length, (the maximum length very nearly of a continuous discharge,) which starts upwards from the auroral arch, which he

regards as the discharging train. If this first portion be not parallel to the dipping-needle, it is moved laterally by virtue of the earth's magnetism, and thus wrenched, as it were, from the spot where it was formed, and extinguished. If, however, the discharge, or any portion of it, be parallel to the dipping-needle, it is not influenced by the earth's magnetism, and remains. To this first length another length may be added by a similar process, and so on, these successive lengths being all parallel to the direction of the first, since otherwise the streamer would be torn asunder by the lateral motion resulting from the earth's magnetism. Thus a straight streamer extends upwards in a direction parallel to the dipping-needle.

If, from some increase in the power of conduction of the arch, the base of the streamer be not necessarily confined to a single spot, then a streamer may be formed which is somewhat inclined to the dippingneedle; but the consecutive elements of such a streamer must be in the same direction, otherwise they would have different lateral motions, the streamer would be divided, and the discharge would cease. The streamer, as a whole, will move from east to west, or from west to east, according to circumstances. Those streamers which would tend to move north or south cannot exist, because their bases would be severed from the auroral arch.

If the discharge take place in air not so very highly rarefied, so that the disruptive discharge is not quite of its maximum length, consecutive elements need not be quite in the same direction in order that the streamer may be unbroken, and thus curved streamers may be formed. It is stated by M. Biot that such have sometimes been observed.

The author then enters into some speculations as to the nature of the auroral arch, which he conceives to consist of nebulous matter highly charged with electricity, and accounts, according to his views, for the motion of such arches from the pole towards the equator.

The remainder of the paper is occupied with speculations as to the nature of fire-ball lightning, and other subjects relating to ordinary electricity.

XVI. "On the Lunar-diurnal Magnetic Variation at Toronto." By Major-General EDWARD SABINE, R.A., D.C.L., Treas. & V.P.R.S. Received June 13, 1856.

(Abstract.)

This paper contains the results of an investigation into the moon's diurnal influence on the horizontal and vertical components of the magnetic force at Toronto, and the consequent deduction of the lunardiurnal variations of the inclination and of the total force at that station. The observations from which the results were obtained consisted of five years of hourly observation of the bifilar and vertical force magnetometer, ending June 30, 1848, from which the disturbances of largest amount had been separated as described in a paper previously communicated (Phil. Trans. 1856, Art. XV.). The results derived from the mean of the five years are confirmed by the accord which is shown of the means of each of the half-periods into which the observations of the five years are divided for that purpose.

To complete the view of the moon's diurnal influence on the magnetic elements at Toronto, a recalculation has been made of the lunar-diurnal variation of the declination from the mean of six years of hourly observation, ending June 30, 1848, employing the more perfect normals derived from the exclusion of the larger disturbances, as described in the paper above referred to (Phil. Trans. Art. XV. 1856); and the confirmation is shown of the mean result of the six years by the accordance of three separate portions of two years each, into which the whole period of six years has been divided for that purpose.

From these premises the author draws the following conclusions:

1. The three magnetic elements concur in showing that the moon exercises a sensible magnetic influence at the surface of the earth, producing in every lunar day a variation which is distinctly appreciable, in each of the three elements, by the instruments adopted and recommended in the Report of the Committee of Physics of the Royal Society, when due care is taken in conducting the observations, and suitable methods are employed in elaborating the results.

2. That the lunar diurnal variation in each of the three elements constitutes a double progression in each lunar day; the declination having two easterly and two westerly maxima, and the inclination and total force each two maxima and two minima between two successive passages of the moon over the astronomical meridian; the variation passing in every case four times through zero in the lunar day. The approximate range of the lunar-diurnal variation at Toronto is 38" in the declination, 4"-5 in the inclination, and 000012 parts of the total force.

3. That the lunar-diurnal variation thus obtained appears to be consistent with the hypothesis that the moon's magnetism is, in great part at least if not wholly, derived by induction from the magnetism of the earth.

4. That there is no appearance in the lunar-diurnal variation of the decennial period, which constitutes so marked a feature in the solar diurnal variations.

XVII. "On Autopolar Polyedra." By the Rev. THOMAS P. KIRKMAN, M.A. Communicated by ARTHUR CAYLEY, Esq., F.R.S. Received June 19, 1856.

(Abstract.)

An autopolar polyedron is such, that any type or description that can be given of it remains unaltered, when summits are put for faces, and faces for summits. To every ẞ-gon B in it corresponds a ẞ-ace b (or summit b of ẞ edges), which may be called the pole of that B-gon; and to every edge AB, between the a-gon A and the ß-gon B, corresponds an edge ab, between the a-ace a and the B-ace b. Two such edges are called a gamic pair, or pair of gamics.

The

The enumeration of autopolar p-edra is here entered upon as a step towards the determination of the number of p-edra. theorems following are established, and shown to be of importance for the solution of the general problem.

THEOREM I.-No polyedron, not a pyramid, has every edge both in a triangle and in a triace.

Def. An edge of a polyedron is said to convanesce, when its two summits run into one; and it is said to evanesce, when its two faces revolve into one.

An edge (AB) is said to be convanescible, when neither of the faces A and B is a triangle, and (AB) joins two summits which have not two collateral faces, one in either summit, besides A and B.

An edge (ab) is said to be evanescible, when neither a nor b is a triace, and the two faces about (ab) are not, one in either, in two collateral summits, besides a and b.

THEOREM II.-Every polyedron, not a pyramid, has either a convanescible or an evanescible edge.

THEOREM III.-Any p-edral q-acron, not a pyramid, can be reduced by the vanishing of an edge, either to a (p-1)-edral q-acron, or to a p-edral (q—1)-acron.

By such a reduction of a p-edral q-acron P to P', of P' to P", &c., P can be shown to be generable from a certain pyramid II; by which it is meant that Il is the highest-ranked pyramid to which P can by such reduction be reduced.

Hereby it is evident that the problem of enumeration of the x-edra is brought down to this: to determine how many (r+m)-edra are generable from the r-edral pyramid.

The autopolars so generable are first considered, as the heteropolars are obtained by combination and selection of those operations with which the theory of the autopolars makes us acquainted.

Autopolarity is of three kinds, nodal, enodal, and utral.

Every even-based pyramid is nodally autopolar; i. e. it cannot but have two nodal summits. For example, the 5 edral and 7-edral pyramids have the signatures of their faces and summits thus arranged,—

the upper line showing the triangles, and the lower the triaces about the base, which as well as its pole the vertex, is signed zero. The two triaces in the triangle 5 are 3 and 2; the two triangles in the triace 1 are 6 and 1 in the 7-edron, and 4 and 1 in the 5-edron. The nodal summits and faces are 3 and 1 in the 5-edron, and 4 and 1 in the 7-edron. No other mode of autopolar signature is possible in these.