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Looking, therefore, on the stars as severally in motion, with velocities exceeding the sun's on the average, it cannot but be looked upon as highly significant that in any large region of the heavens there should be a community of motion such as I have described. We seem compelled to look upon the stars which exhibit such community of motion as forming a distinct system, the members of which are associated indeed with the galactic system, but are much more intimately related to each other.

In other parts of the heavens, however, there are instances of a stardrift opposed to the direction due to the solar motion. A remarkable instance may be recognized among the seven bright stars of Ursa Major. Of these, the stars ß, y, d, e, and are all drifting in the same direction, and almost exactly at the same rate, towards the " apex of the solar motion," that is, the point from which all the motions due to the sun's translation in space should be directed. If these five stars, indeed, form a system (and I can see no other reasonable explanation of so singular a community of motion), the mind is lost in contemplating the immensity of the periods which the revolutions of the components of the system must occupy. Mädler had already assigned to the revolution of Alcor around Mizar (Ursæ) a period of more than 7000 years. But if these stars, which appear so clear to the naked eye, have a period of such length, what must be the cyclic periods of stars which cover a range of several degrees upon the heavens?

In like manner the stars a, 6, and y of Arietis appear to form a single system, though the motion of a is not absolutely coincident either in magnitude or direction with that of ẞ and y, which are moving on absolutely parallel lines with equal velocity.

There are many other interesting cases of the same kind. I hope soon to be able to lay before the Society a pair of maps in which all the wellrecognized proper motions in both hemispheres are exhibited on the stereographic projection. In the same maps also the effects due to the solar motion are exhibited by means of great circles through the apex of the solar motion, and small circles or parallels having that apex for a pole.

It appears to me that the star-drift I have described serves to explain several phenomena which had hitherto been thought very perplexing. In the first place, it accounts for the small effect which the correction due to the solar motion has been found to have in diminishing the sums of the squares of the stellar proper motions. Again, it explains the fact that many double stars which have a common proper motion appear to have no motion of revolution around each other; for clearly two members of a drifting-system might appear to form a close double, and yet be in reality far apart and travelling not around each other, but more closely around the centre of gravity of the much larger system they form part of.

I may add that, while mapping the proper motions of the stars, I have been led to notice that the rich cluster around x Persei falls almost exactly on the intersection of the Milky Way with the great circle which

may be termed the equator of the solar motion; that is, the great circle having the apex of the sun's motion as a pole. This circumstance points

to that remarkable cluster, rather than to the Pleiades, as the centre of the sidereal system, if, indeed, that system have a centre cognizable by us. When we remember that for every fixed star in the Pleiades there are hundreds in the great cluster in Perseus, the latter will seem the worthier region to be the centre of motion. I should be disposed, however, to regard the cluster in Perseus as the centre of a portion of the sidereal system, rather than as the common centre of the Galaxy.

The peculiarities of the apparent proper motions of the stars seem to me to lend a new interest to the researches which Mr. Huggins is preparing to make into the stellar proper motions of recess or approach.

III. "On Jacobi's Theorem respecting the relative Equilibrium of a Revolving Ellipsoid of Fluid; and on Ivory's Discussion of the Theorem." By I. TODHUNTER, M.A., F.R.S., late Fellow of St. John's College, Cambridge. Received November 23, 1869.

(Abstract.)

Jacobi discovered the theorem that a fluid ellipsoid revolving with uniform angular velocity round its least axis might be in equilibrium. Ivory discussed the theorem, and made several statements regarding the limitations of the proportions of the axis. Ivory's statements contain various errors and truths based on erroneous reasoning. The object of the present memoir is to correct Ivory's errors, to supply his imperfections, and to add something to what is already known respecting the theorem.

January 27, 1870.

ARCHIBALD SMITH, M.A., Vice-President, in the Chair. Professor Wyville Thomson was admitted into the Society.

The Presents received were laid on the Table, and thanks ordered for them, as follows:

Transactions:—

Cambridge, Mass.:-Museum of Comparative Zoology. Bulletin. Nos. 8-13. 8vo. Cambridge 1869. The Museum. Copenhagen: Kongelige Danske Videnskabernes Selskab. Skrifter, Nat. og Math. Afd. Bd. VIII. 1, 3, 4, 5. 4to. Kjöbenhavn 1868–69. Oversigt, 1868, No. 5; 1869, No. 2. 8vo. Kjöbenhavn 1868–69. The Society.

Transactions (continued).

Frankfurt a. M.:-Senckenbergische Naturforschende Gesellschaft. Abhandlungen. Band VII. Hefte 1-2. 4to. Frankfurt 1869. Bericht von Juni 1868 bis Juni 1869. 8vo. The Society. Leipzig:-Astronomische Gesellschaft. Vierteljahrsschrift. IV. Jahrgang. Hefte 2-3. 8vo. Leipzig 1869. Publication IX. (Tafeln der Pomona.) 4to. Leipzig 1869. The Society. Neuchâtel:-Société des Sciences Naturelles. Bulletin. Tome VIII. cahier 1. 8vo. Neuchatel 1868. The Society. Philadelphia:-Franklin Institute. Journal. Third Series. Vol. LVIII. Nos. 1-6. 8vo. Philadelphia 1869. The Institute.

Agassiz (L., For. Mem. R.S.) Report upon Deep-Sea Dredgings. 8vo. Cambridge [Mass.]. Address delivered on the Centennial Anniversary of the birth of Alexander von Humboldt, under the auspices of the Boston Society of Natural History. 8vo. Boston 1869.

The Author. Campani (G.) Azione del Permanganato di Potassio sull Asparagina, 8vo. Siena 1869.

The Author.

Clark (F. Le Gros) Lectures on the Principles of Surgical Diagnosis, especially in relation to Shock and Visceral Lesions. 8vo. London 1870.

The Author.

Joly (N.) Haute Antiquité du Genre Humain. 8vo. Toulouse 1869.

The Author.

Pole (Dr., F.R.S.) On Probabilities as illustrated by events occurring in

Games with Cards. 12mo. London 1869.

The Author.

The Author.

Realis (S.) Note sur le Nombre e. 8vo. Paris 1869.
Rütimeyer (L.) Ueber Thal- und See-Bildung. 4to. Basel 1869.

Stainton (H. T., F.R.S.) The Tineina of Southern Europe. 1869. The Entomologist's Annual for 1870. 12mo.

The Author. 8vo. London London 1870.

The Author.

Sundby (Thor) Brunetto Latinos Levnet og Skrifter. 8vo. Kjobenhavn

1869.

The Author.

Catalogue of Books added to the Library of Congress, from Dec. 1, 1867 to Dec. 1, 1868. roy. 8vo. Washington 1869.

Statistics of New Zealand for 1868. fol. Wellington 1869.

The Library.

The Registrar-General of New Zealand.

Archivio per la Zoologia, l'Anatomia e la Fisiologia, pubblicato per cura dei Proff. S. Richiardi e G. Canestrini. Serie 2, Vol. I. 8vo. Torino 1869. The Editors.

Der Zoologische Garten, X, Jahrgang, No. 1-12. 8vo. Frankfurt a. M. The Zoological Society of Frankfort.

1869.

Melbourne-Flagstaff Observatory. Meteorological Observations, 1857 -58. 2 vols. sm. fol. Daily Meteorological Register, 1859-1863. 5 vols. fol. Original Observations on Atmospheric Electricity, 1858. sm. fol. Daily Electrical Register, 1860-63. 3 vols. 4to. Magnetical Observations, 1st May to 31st Dec. 1858. sm. fol. Romarks and Disturbance Observations during the year 1859. Daily Magnetical Register, 1860-62, and Jan. to Feb. 1863. 3 vols. sm. fol. MSS. Presented by the Observer, Dr. Neumayer.

The following communications were read :—

I. "Observations on the Temperature of the Strata taken during the sinking of the Rose Bridge Colliery, Wigan, Lancashire, 1868-69." By EDWARD HULL, M.A., F.R.S., Director of the Geological Survey of Ireland. Received November 27, 1869. In an elaborate paper by Mr. W. Hopkins, F.R.S., entitled "Experimental Researches on the Conductive Powers of various Substances," published in the Philosophical Transactions for 1857, an account is given of a series of experiments made under the general supervision of Mr. Hopkins himself and Mr. W. Fairbairn, F.R.S., during the sinking of the Astley Pit of Dukenfield Colliery in Cheshire*. At the time this paper was written the depth attained was only a little more than 1400 feet; and the rate of increase between the depths of 700 feet and 1330 feet was found to be 1° F. for about 65 feet. These observations were subsequently continued until the pits had attained their full depth of 717 yards from the surface. The last observation made was in the shale overlying the coal-seam, known as the "Black Mine," which it was the object of the proprietor, Mr. Astley, to reach, and the temperature was found to be 75° F. Assuming the "stratum of constant temperature," or, as it is also called by Humboldt, "the invariable stratum,' to be that which was reached at 16.5 feet with a temperature of 51° F., the total increase of temperature would amount to 24° F., giving as the rate of increase 1° F. for every 88.925 feet. This is much below the average rate of increase.

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During a part of the period above referred to (from 1854-56) another coal-pit was being sunk at Wigan, which reached the depth of 600 yards, down to the celebrated "Cannel Mine." At this pit similar observations on the temperature of the strata were made very carefully by the manager, Mr. Bryham, which were kindly communicated to myself for publication, and will be found in my work on the Coalfields of Great Britain.' The ultimate temperature attained in this pit at the depth from the surface of 600 yards was found to be 72° F.; and assuming the invariable stratum to be the same as that at Dukenfield Colliery, the resulting rate of increase would be 1° F. for every 61.5 feet, which accords very closely with the

The entire series of these interesting observations were kindly supplied to me by Mr. W. Fairbairn, and are published in 'The Coalfields of Great Britain,' 2nd edit. p. 226.

result obtained by Professor Phillips, F.R.S., at the Monkwearmouth Colliery.

Since the time above referred to, the proprietor of the Rose Bridge Colliery, Mr. J. Grant Morris, determined to carry down the shafts from the "Cannel" seam to the "Arley" seam of coal, which was known to lie more than 200 yards below it; and consequently in the spring of 1868 preparations were commenced for carrying out this project. In the incredibly short time of one year and two months the Arley coal was struck, and was found to be of good thickness and quality. The total depth reached was 808 yards, and the ultimate temperature in the coal itself was found to be 931° F. The manager of the colliery, Mr. Bryham, sensible of the value of observations on the temperature of the strata at such unusual depths (this being probably the deepest colliery in the world, certainly in Britain), made a series of observations with as much care as the circumstances would admit, and has entrusted them to me for publication.

The mode of taking the observations was as follows:-On a favourable stratum, such as shale, or even coal, having been reached, a hole was drilled with water in the solid strata to a depth of one yard from the bottom of the pit. A thermometer was then inserted, the hole having been sealed and made airtight with clay. At the expiration of half an hour the thermometer was taken up and the reading noted.

It might possibly be objected that the time allowed (thirty minutes) was insufficient for the imbedding of the thermometer, and that the readings are liable to error from this cause. I feel sure, however, that if any error has arisen it is inappreciable, and does not in the least invalidate the general result. In fact I am assured by Mr. Bryham that, from actual testing on several occasions, he found less than this time of thirty minutes sufficient for the purpose required.

While the temperatures of the strata were being measured, observations were also carried on pari passu on those of the open pit during the descent. These are given in the Table annexed. By a comparison of the results in the two columns, it will be observed that as the depth increased the differences between the corresponding temperatures in the pit and the strata tended to augment; in other words, the temperature of the strata was found to augment more rapidly than that of the open pit.

The effects of the high temperature and pressure on the strata at the depth of 2425 feet are, as I am informed by Mr. Bryham, making themselves felt, and cause an increase in the expense both of labour and timber for props. This colliery, in fact, will be in a position to put to the test our views and speculations on the effects of high temperature and pressure on mining operations.

In order to obtain the average rate of increase of heat, as shown by the experiments at Rose Bridge Colliery, we may assume (in the absence of direct observation) the position and temperature of the invariable stratum to be 50 feet from the surface and 50° F., which is probably nearly the

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