In my previous papers on “The Meteorology of Edinburgh” the data referring to local climate were reduced down to the end of 1896. In the time that has elapsed since their publication a number of memoirs from places on the Continent and elsewhere have appeared in which the data, mostly dealing with long periods, were brought down to the end of 1900. In order to facilitate the comparison of the Edinburgh record with those referred to, I have completed new monthly and annual averages for the ten years 1891–1900, the fifty years 1851–1900, and for longer periods, which embrace 137 years in the case of mean temperature, 131 years for mean barometric pressure, 130 years for the non-instrumental phenomena, and 124 years for rainfall (see Tables I. to IV.). The values previously published have been carefully examined, and a number of errors which escaped detection at the time eliminated. A Table of Errata (see Table XXIX.) is appended. Tables V. and VI. show respectively the mean monthly and annual departure from the normal of the mean maximum and minimum temperatures for the fifty years 1851–1900. A few of the values formerly published (see Table XVIIL, Trans., vol. xxxix. pp. 130–133) are about 0°·6 too high, but they have been corrected.

(1) The persymmetric determinant of the nth order

being such that in every case the element in the place r, s is the same as the element in the place r − 1, s + 1, and therefore having only 2n − 1 independent elements, viz., the elements a1, a2, …., a2n−1 forming the first row and last column, is conveniently denoted by

As it is a special form of axisymmetric determinant, any known relation between minors of the latter must of course hold in regard to the corresponding minors of the former.

Since Lord Kelvin showed that the resistance of the magnetic metals was influenced by the state of magnetisation of these substances, a good deal of work has been done in investigating more carefully the extent and nature of the relation. It does not appear, however, that any attempt has been made to discover how change of temperature affects this influence. Twelve years ago in Japan I set one of my Japanese students to the construction of an apparatus suitable for making this research. A few preliminary experiments were made; and leaving Japan shortly after, I brought the apparatus with me in the hope of continuing the work in this country. Not till this summer, however, did I find leisure to return to the problem. The results obtained I wish now to lay before the Society.

Up to the present time no systematic account of the cranial characters of the people of Scotland has been published. Incidental references to, and measurements of, a limited number of Scottish skulls may indeed be found in the writings of various authors, as in Sir Daniel Wilson's Prehistoric Annals of Scotland, in Drs Davis and Thurnam's Crania Britannica, and in Professor Cleland's Memoir on Variations in the Human Skull. Measurements of five Scottish crania are recorded by Sir W. H. Flower in the Osteological Catalogue (Man) of the Museum of the Royal College of Surgeons of England, four of which were found amongst the ruins of an ancient Culdee Monastery at St Andrews, and the fifth is said to be that of a Highlander. Dr Barnard Davis, in his Thesaurus Craniorum, gives the measurements of a somewhat larger number, six of which were from Caithness, and one is stated to be a Scottish Highlander. The same skulls have been remeasured and described by Dr J. G. Garson.

(1) This is a subject to which very little study has been directed. The first to enunciate any proposition regarding it was Jacobi; but the solitary result which he reached received no attention from mathematicians,—certainly no fruitful attention,—during seventy years following the publication of it.

Jacobi was concerned with a problem regarding the partition of a fraction with composite denominator (u1 − t1) (u2 − t2) … into other fractions whose denominators are factors of the original, where u1, u2, … are linear homogeneous functions of one and the same set of variables. The specific character of the partition was only definable by viewing the given fraction (u1−t1)−1 (u2−t2)−1…as expanded in series form, it being required that each partial fraction should be the aggregate of a certain set of terms in this series. Of course the question of the order of the terms in each factor of the original denominator had to be attended to at the outset, since the expansion for (a1x+b1y+c1z−t)−1 is not the same as for (b1y+c1z+a1x−t)−1. Now one general proposition to which Jacobi was led in the course of this investigation was that the coefficient ofx1−1x2−1x3−1…in the expansion ofy1−1u2−1u3−1…, where

is |a1b2c3…|−1, provided that in energy case the first term of uris that containing xr.

§ 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:

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.