The application of this theorem to the division of an angle is obvious, and is illustrated by fig. 2, in which a portion of fig. 1 is reproduced with additions. The points 0, 1, 2, 3, 4, Fig. 1.

.5

are taken at equal distances along the perpendicular to OA; and the point 2 at a distance from O equal to the diagonal of a square whose side is the common distance. About each of these points a circular arc is described passing through O

and meeting the barycentride. Lines are drawn from 0 to the points of intersection, and the angles which they make with OA are inversely as the distances laid off from Ŏ along the perpendicular.

Suppose the largest of these angles (marked A01) to be given. The corresponding point 1 on the perpendicular to OA can be found by bisecting the radius vector 01 of the curve at right angles, and the figure can be completed in accordance with the above description. We thus obtain not. only the and of the given angle, but also an angle which is to the given angle as 1 to 2. The construction is extremely well conditioned.

The following values of sin 0/0 are useful for plotting the

and a check is furnished by the fact that the tangent to the curve at P (fig. 1) must pass through Q the extremity of the are AQ, of which P is the centroid.

=

When the tangent at P is parallel to AO we have OA sin 20 OP sin 0, OA cos 0=OP; hence OP is bisected at right angles by AH, and P and O are equidistant from A. The complete curve consists of an infinite series of convolutions, all touching OA at 0; and in each convolution the point furthest from OA lies on the circle described round A with radius AO.

IX. Notices respecting New Books.

CHARLES NORDMANN. Thèses présentées à la Faculté des Sciences de Paris. 1re Thèse: Essai sur le rôle des ondes Hertziennes en Astronomie Physique et sur diverses questions qui s'y rattachent. Paris: Gauthier Villars. 1903.

THIS

HIS thesis for the Paris Doctorate of Science was sustained on June 13th, 1903, the examiners being Profs. H. Poincaré, Pellat, and Moissan. It is well worth the attention of all interested in astrophysical speculations, if only for the wealth of references it contains. It treats of such varied subjects as the Solar Corona, Nebulæ, Nova Persei, Aurora, and Terrestrial Magnetism. The work is mainly devoted to the exposition of the author's theories as to the causes of the several phenomena discussed, and to destructive criticism of other theories. Older views, such as Faraday's on Terrestrial Magnetism, are not neglected, and a large number of recent writers (e. g. Arrhenius, Bigelow, Birkeland, Deslandres, Goldstein, Lockyer, and Schuster) will find something to interest them. Before passing to theory, the author deals slightly with two positive contributions to our stock of scientific facts. He tried but failed to detect Hertzian waves proceeding from the sun, the experiment being carried out on

Mont Blanc. He also made an investigation into the connexion between sun-spot frequency and mean annual temperature, employing records from a considerable number of tropical stations, extending over at least one sun-spot period. Only mean results from all the stations combined are given, so that the reader cannot judge fully the part played by chance. The author appears to confirm the result reached by Koppen in 1873, that in the Tropics mean temperature diminishes as sun-spots increase. Between years of absolute maximum and minimum of sun-spots Nordmann (p. 18) finds an average difference of 0°-26 C. Even supposing this small difference to be true for the whole surface of the earth, it would not necessarily follow, as the author seems to conclude, that the sun's thermal radiation diminishes as sunspots increase. It may also be noted in passing that it is open to doubt whether attention should not rather be given in this connexion to the mean diurnal range of temperature.

The future alone can show the real value of the theoretical part of the Thesis. The author displays a nimble mind, and his reading seems catholic and remarkably up to date. An English reference is as recent as March 1903, and one would infer a close study of the recent papers of Huggins, Ramsay, and others, especially of J. J. Thomson and his school. The free use of very recent results has its risks, even when guided by critical insight; and an intimate knowledge of all the subjects to which Nordmann applies his theories is perhaps rather too much to expect of any one man. As exemplifying the dangers to which too rapid speculation leads, reference may be made to p. 64. Values are there quoted for diurnal ranges of declination at Batavia in 1895. The figures given actually appear in the Batavia Observations (Table 26), but they have a totally different meaning from what the author supposes. The true ranges (obtainable from Table 18, 1. c.) are much smaller, being less than the values the author quotes for Nice. The mistake may mean undue haste in a single instance, but no expert in Terrestrial Magnetism is likely to retain undiminished confidence in a writer who follows this up by laying it down as a general law ("loi générale ") that the amplitude of the diurnal variation of magnetic declination diminishes as one retires from the equator! The eminent triumvirate to which the Thesis was submitted must surely have overlooked this statement. If the mathematical work on p. 115-in connexion with an estimate of auroral frequency-satisfied Prof. Poincaré, it presumably is correct, but the reviewer must confess to an inability to reconcile it with the physical problem proposed. The author is unusually successful in his spelling of English names, but he follows an American and erroneous authority when he talks-as he does repeatedly-of the "Addie" magnetograph; and when he locates this instrument at Greenwich, and describes Prof. Turner as "chef du service magnétique," he adds a little to the confusion. As the author is described as "Astronome a l'Observatoire de Nice," he is presumably more thoroughly at home with the astronomical subjects treated, and his discussions of the Corona, Nebulæ, and Nova Persei if slight are certainly suggestive.

The chief ingredients, so to speak, in Nordmann's theories are Hertzian waves (mainly from the sun), cathode rays excited by these waves (Ebert and Wiedemann), and gaseous lavers of critical density for maximum illumination (J. J. Thomson). There is also occasional use of the "Maxwell-Bartoli" pressure of light as opposing gravitation. Abstracts of theories are seldom satisfactory-at least to the propounder; and the reader who wishes particulars must be referred to the original Thesis.

X. Proceedings of Learned Societies.

GEOLOGICAL SOCIETY.

[Continued from vol. vi. p. 723.]

November 18th, 1903.-Sir Archibald Geikie, D.Sc., F. R.S.,
Vice-President, in the Chair.

HE following communications were read:

THE

C. C.

1. Notes on some Upper Jurassic Ammonites, with Special reference to Specimens in the University Museum, Oxford." By Miss Maud Healey.

6

2. On the Occurrence of Edestus in the Coal-Measures of Britain.' By Edwin Tulley Newton, Esq., F.R.S., V.P.G.S.

December 2nd.-Sir Archibald Geikie, D.C.L., D.Sc., Sec.R.S., Vice-President, in the Chair.

The following communications were read :—

1. Notes on the Garnet-bearing and Associated Rocks of the Borrowdale Volcanic Series.' By the late Edward Eaton Walker, Esq., B.A., B.Sc.

The first portion of the paper is occupied with an account of various intrusive rocks. A detailed description of sills and dykes of garnet-bearing rocks in the Langstrath Valley is given; and similar rocks are described, occurring as dykes and sills around the Eskdale granite and the Buttermere granophyre, and also in the Armboth-Helvellyn area. These rocks vary in degree of acidity. They consist of diabase, porphyrite, and granophyre. Evidence of their characters being dependent upon differentiation accompanied by some absorption is offered. They appear to be related to the Eskdale and Buttermere masses of intrusive rocks.

The volcanic rocks are next considered. Garnets are found in the Falcon-Crag Group, in a group of rocks below the great banded ashes and breccias of the Scawfell Group, and in the rocks of the Scawfell Group itself; but do not seem to occur, except as the result of contact-metamorphism, in the Eycott Group. The most interesting garnetiferous volcanic rocks are those which occur below the Scawfell ashes and breccias. These rocks often have a streaky structure which exhibits four distinct types: resulting from (a) infiltration along planes of weakness, (b) lamination of ash, (c) flow of igneous material, and (d) dynamic action on included fragments. The rocks are not intrusive, but consist of lavas and ashes, often exhibiting alternating bands of rhyolite and andesite. The banded ashes of the Scawfell Group also contain garnets.

In the Haweswater district there is an intercalation of rocks of the Eycott type with rocks possessing the streaky' structure. This intercalation appears to be original, and not the result of subsequent earth-movements.

The garnets are of the almandine-type. They often have a ring of felspar around them, which, when the intrusive rocks are studied, suggests that the mineral is original; but similar rings occur around garnets in the ashes, showing that the felspars may be formed in solid rock. In certain ashes of the Haweswater district, the existence of cavities in the garnets suggests a metamorphic origin for the mineral, but it is difficult to understand how the metamorphism has been produced.

The paper closes with a description of certain undoubted metamorphic changes.

2. A Contribution to the Glacial Geology of Tasmania. By Prof. J. Walter Gregory, D.Sc., F.R.S., F.G.S.

On reading the literature on the glaciation of Tasmania, the author came to the conclusion that, except for such traces of highlevel glacial action as those of Mount Sedgwick recorded by E. J. Dunn and T. B. Moore, and those near the summit of Mount Ida recorded by Officer, Balfour, and Hogg, the evidence consisted of material that was either not of glacial origin, or was due to glacial action at some Upper Palæozoic date. After giving a detailed analysis of the previous contributions to this subject, the author describes the evidence obtained by himself personally in the northern portion of the Island. The town of Gormanston stands on a glacial moraine of recent geological age, formed later than the excavation of the Linda Valley, and occurring as a bank projecting from the southern side of the valley, and nearly damming it across. The moraine is composed of typical boulder-clay, and behind it are bedded clays which probably accumulated in a glacier-lake above the moraine-dam. An erratic of fossiliferous limestone, 4 by 34 by 24 feet, scratched all over and partly polished, is mentioned, while the North Lyell Railway has cut through an enormous boulder of black Carboniferous Limestone at least 16 feet in length. The northern face of Mount Owen appears to be ice-worn to the height of about 1900 feet, while the base of the glacial deposits is not more than 700 feet above the sea. The general evidence suggests that the Eldon Range and the Central Plateau formed the gathering-ground of the ice which flowed westward and southwestward. A map is given to show the range of Pleistocene glaciation so far as it has been recorded, and also to indicate localities of the glacial deposition which probably dates from the Carboniferous Period. The lowest level at which evidence of Pleistocene glaciation has been found is 400 feet on the Pieman River. This latest glaciation is later than the formation of the peneplain of North-Western Tasmania, and occurred after the dissection of this peneplain had begun. Many of the deposits are little more altered than those of Northern England, despite the heavy rainfall; and the aspect of some of the rock-scoring is very recent.