In a Note published in the Annals of Botany for December 1899, I gave some account of the structure of two stems from the Lower Carboniferous of Scotland, provisionally named Araucarioxylon fasciculare, sp. nov., and A. antiquum, Kr. (Witham, sp.).

In the present paper these stems are described fully, with the help of illustrations, and others, presenting similar points of interest, are added. The species dealt with are the following:—

Calamopitys fascicularis (Araucarioxylon fasciculare of the Note).

Calamopitys beinertiana (Araucarioxylon beinertianum, Kr.), (Göpp., sp.).

Pitys antiqua, Witham (Araucarioxylon antiquum, Kr. of the Note).

Pitys Withami (Pinites Withami, Lindl. & Hutt.).

Pitys primœva, Witham.

Dadoxylon Spenceri, sp. nov.

§ 1. The shielding effect which exists within hollow iron spheres and cylinders, when placed in a uniform magnetic field, has been previously investigated. Poisson, Stefan, Maxwell, and among others, and more recently, Professors Rücker and Du Bois, have contributed to the subject. If

and the ratio of n to R be the order 1 to 100, it appears that the following expressions may be taken as sufficiently correct:

Since the publication of my “Report” in December 1899, Mr Tait, fossil collector to the Geological Survey of Scotland, has been successful in adding a number of specimens of great interest to the valuable series of Scottish Silurian Fishes which supplied the material for that memoir, and with the permission of the Director of the Survey, to whom my best thanks are due, I propose to give descriptions of them in the following Supplement. The search for these remarkable fishes has likewise been taken up by private collectors, and I have therefore pleasure in acknowledging my indebtedness to Messrs J. Young, of Lesmahagow, P. Macnair, of Glasgow, A. Whyte and F. White, of Muirkirk, and D. Nimmo, of Hamilton, for kindly submitting to me the material resulting from their own work in this field.

It is my intention in this, the second part of my memoir on the Craniology of the Races of India, to give the results of my examination of skulls obtained from the districts occupied by the aboriginal tribes in Chúta Nágpúr, the Central Provinces, the people in the province of Orissa, and to compare them with the skulls of some other aboriginal people.

The majority of the specimens described belong to the Indian Museum, Calcutta, and through the courtesy of the Trustees I was permitted to have them on loan for purposes of study. Many of these crania had been those of persons who had died in jail. The names, tribes, and castes, and not unfrequently the age, stature, and other physical characters, had been recorded in the prison books, and were embodied in the lists which were sent to me along with the skulls by the authorities of the museum. Several of these skulls were especially interesting, as having been presented to the museum by Colonel Dalton, the author of the valuable treatise on the Ethnology of Bengal, Other specimens in the museum had been obtained from the Medical College, Calcutta, and several were presented by Professor D. B. Smith; in all probability they were from bodies which had been used for anatomical purposes. Mr W. H. P. Driver also had presented a series of crania from Ranchi.

The vertical movements of the earth's atmosphere from which the energy is derived which causes the horizontal movements of the air which we call winds, and by means of which the moisture evaporated from the surface of land and water is collected and carried to the higher regions of the atmosphere, where it is condensed to cloud and again distributed in the form of rain over the earth's surface, are of great interest, and a thorough knowledge of the laws governing these vertical movements is necessary to enable us to arrive at a correct forecast of the coming weather over any area.

At the base of the wings of Anopheles maculipennis, Meig, is a small quadrilateral area (fig. 2, Plate) which has escaped the notice of the systematist, since the nervures in which he is interested lie almost entirely beyond the area in question, and which has escaped the notice of the morphologist, because it presents to him but a confused outline of meaningless ridges and intervening depressions of no structural importance. If, however, the well-preserved wing of a mosquito, whilst still attached to the thorax, be examined, a very curious apparatus can be made out, lying across the centre of the said quadrilateral area which is bounded posteriorly by the alula. This apparatus lies at about equal distances from the anterior and the posterior edge of the wing, and divides the base of the wings roughly into two halves.

The Duke of Richmond and Gordon's salmon fishings on the Spey extend on both sides of the river from the Boat o' Brig, where the Highland Railway crosses the stream between Keith and Elgin, to the sea, a distance of about nine miles.

The river here varies in breadth from 50 to 140 yards, and in depth from 2 feet, where the stream is broad, to about 10 or 12 in some of the pools. Its course is rapid, the fall being about 16 feet to the mile, and its volume is quickly increased when there is much rain, or when snow melts in the Monadhliadh and Grampian Mountains.

There are many excellent pools for salmon fishing with the rod on the Gordon Castle water, and in them large numbers of fish are usually taken with the fly every year during the month of September and the first half of October.

The district in which the city of Edinburgh is situated was one of the first in Britain from which fish-remains of Carboniferous age were collected. It is now sixty-seven years ago since Agassiz described the fossil fishes which were discovered by Lord Greenock at Wardie. Dr Hibbert at Burdiehouse, and Professor Jameson at Burntisland. The list given from this region in the “Tableau Générale” at the beginning of the Poissons Fossiles comprises twenty-nine names, of which eight were nomina nuda and are not now verifiable, the original specimens being lost; one, Diplodus minutus, was described, but insufficiently, and the original is also lost; six are synonyms of others in the list; leaving fourteen good species, of which one, Ptychacanthus sublævis, is a synonym of a Selachian spine (Tristychius arcuatus), described and figured from the Glasgow district.

The accompanying Tables I. and II. contain the readings from May 1888 to December 1899 of the new set of deep rook thermometers erected in June 1879 at the Calton Hill Observatory, to replace the old set which were destroyed in September 1876. The tables are in continuation of, and are similarly arranged to, those published by the Royal Society of Edinburgh in Vol. XXXV. part 3 of the Transactions, along with a paper by the late Prof. Piazzi Smyth. The tables published with Prof. Smyth's paper contain the observations made between October 1879 and April 1888, being the beginning of the series with the new set of thermometers.

The breeding habits of this asterid have been noted by M. Sars, who has described the external features of the developmental stages. He observed the peculiar habit of ‘brooding.’ In the spring of 1840 he found several of the parents at very low-tide-mark fixed to stones in their brooding position. The species he examined is described as Echinaster sanguinolentus, and is apparently the same species, though he speaks of the ‘blood-red’ embryo, whereas my specimens were a light orange. They conform exactly to the tint of the oral surface of the parent. The time of breeding of Cribrella oculata at St Andrews appears to extend from February to April inclusive, and throughout this period the parents are found fairly plentifully, adhering to the under surface of rocks, nursing the masses of eggs or young under their bodies. This habit of protecting its young is also pursued by an allied species, Asterias mütteri, which is equally abundant in the same locality, but the breeding of which is effected earlier, i.e., in November and December. I hope to proceed with the study of this species in the near future.

(l) Cayley in his paper entitled “Note sur l'addition des fonctions elliptiques” obtains among other similar things an expression for

in terms of

where

The form of the expression is the quotient of two determinants, and as the expression becomes useless for such cases as u = v, u = w, … on account of the simultaneous vanishing of numerator and denominator, he is led to seek a means of throwing out the common evanescent factors.

The study of lakes has received more attention on the Continent than it has in our own country. The inland waters of France and Switzerland have been most carefully surveyed, and in America accurate soundings of many of the lakes have been made by the Geological Surveys. But until recent years this work has been almost altogether neglected in Britain; the Government had considered it to be outside the function of the Ordnance Survey, and though of importance to geological research, it has not been undertaken by the Geological Survey. The absence of adequate knowledge concerning the forms of the basins occupied by the lakes has been a serious obstacle to the geological inquiry as to the mode of origin of these basins. But recently, in the English Lake District and in Scotland, this obstacle has been removed to a great extent through the work of geographers, who have carried out a very complete bathymetrical survey of many of the lakes of those regions; and the importance of this work has been recognised by geologists. But in North Wales not only had no attempt been made to ascertain the configuration of the lake-beds, but in many cases even the depths of the lakes remained unknown.

(1) There being n2 independent variables in a general n-line determinant, the Hessian of the determinant with respect to the said variables must be a determinant with n2 lines: and as a general n-line determinant has all its terms linear in the elements involved, it follows that each element of the Hessian being a second differential-quotient cannot be of a higher degree in the variables than the (n − 2)th, and that consequently the degree of the Hessian itself cannot exceed n2(n − 2). The object of the present short paper is to show that this degree is attained by the n(n − 2)th power of the given determinant being a factor of the Hessian.

(1) The continuant

is conveniently denoted by

and, when the elements b1, b2, b3 of the variable minor diagonal are each equal to 1, a further simplification is obtained by leaving them out;—thus,

stands fo