The physical anthropology of the Faroes has recently been described in a very elaborate manner, as far as the island of Suderoe is concerned, by Dr F. Jørgensen (1), who was resident there as a medical man for some years. While pointing out, however, that the people of Suderoe differ considerably from those of the ‘northern islands,’ he only gives a comparatively small series of data regarding the latter, nor does he state to which of the northern islands the men he examined belonged, or even whether they came from one island or from several. Apart from Suderoe, there are sixteen inhabited islands (fig. 1) in the group, and between some of them very little communication exists even at the present day. In historical accounts of the Faroes the six following islands are usually called the ‘northern isles,’—viz., Kalsoe, Kunoe, Boroe, Wideroe, Fugloe, and Svinoe,—but I take it that Dr Jørgensen would include at least Osteroe, Stromoe, and “Waagoe also. His elaborate, laborious, and presumably accurate tables serve so well to point the moral that until a uniform method, a uniform standard, and a uniform set of anthropometrical instruments are adopted by anthropometrists of all nationalities final work in this branch of science will be impossible, that I have thought it well to put on record a small series of measurements taken by myself in the Faroes recently, and at the same time to point out wherein some of the data pretty generally adopted fail in accuracy, differing with the observer as well as the observed.

The first observations on seiches in Scotland were made last summer by members of the Lake Survey, the differences in level having been measured by a foot-rule. A Sarasin limnograph was procured by the Survey and was set up at Fort Augustus on Loch Ness in June of this year, and has been recording since then, with only a few stoppages. The biggest seiche so far recorded had an amplitude of about 9 cm. The boat-house of St Benedict's Abbey, kindly put at Sir John Murray's disposal by the Lord Abbot, gave shelter to the instrument both from wind and waves.

The particular bull trout with which I desire to deal in this paperare the important migratory fishes which are commonly referred to by this name in Scotland. I make no mention of more or less monstrous examples of the common brown trout, or even of those examples of S. fario which have assumed a semi-migratory habit, and have become much modified by reason of their life in the estuaries of our larger rivers.

Preliminary observations upon this subject, which were made by the author on behalf of a committee of the Royal Medical and Chirurgical Society of London, are published in a report presented by the committee and read on May 26th of this year before that Society.

Some time ago, while studying the chemical dynamics of the changes which occur in solutions of urea or carbamide, I came upon some rather unexpected results which led me to hope that investigations conducted on somewhat the same lines with other substances of the amide group might prove to yield results of some interest. The amides referred to are those derived from carboxylic acids. While proceeding to this investigation I noticed some measurements, obtained in connection with the viscosity of aqueous solutions of carbamide, which appeared of sufficient interest to demand an inquiry into the nature of solutions of this class of substances before proceeding further with the subject of inquiry in the manner at first intended.

Since the year 1889, when the last of a series of six papers with a title similar to the above appeared, further research has led to the discovery of a number of writings belonging to the period then dealt with, viz., 1693–1844. Of those an account is now given before proceeding to the papers of later date than 1844.

So long as Homo sapiens was believed to occupy a higher platform in the organic world than other animals by virtue of his special endowments, no one, apparently, thought of looking for evidence of his origin and history in the obscure vista of prehistoric times. The long cherished traditions and myths which had gathered around the inquiry left little room for any other hypothesis than that his apparition on the field of life was the last and crowning achievement of a long series of creative fiats which brought the present world-drama into existence. In the cosmogony thus conjured up, the multitudinous phenomena of the material world—animals and plants, the distribution of land and water, the recurrence of seasons, etc.—were regarded as having been specially designed and arranged to administer to the life-functions of this new being.

The more or less disguised use of continued fractions has been traced back to the publication of Bombelli's Algebra in 1572, eighty-four years, that is to say, before the publication of Wallis’ Arithmetica Infinitorum, in which Brouncker's discovery was announced and the fractions explicitly expressed. The study of the numerators and denominators of the convergents viewed as functions of the partial denominators was first seriously undertaken by Euler in his Specimen Algorithmi Singularis of the year 1764, in which denoting by

the convergents to

he established a long series of identities, such as

Till within recent years the epiphysis cerebri has been generally regarded as a mesial outgrowth from the roof of the thalamencephalon in Vertebrates. The researches of Béraneck (5), Dendy (11), Hill (17), and Locy (19), however, tend to demonstrate the fact that this structure arises in the form of two bilateral outgrowths; while Gaskell (12) has drawn attention to its bilateral nature in Ammocœtes. Some observations which the author made on the development of the epiphysis in Amphibia (8 and 9) were found to agree in the main with those of the above-mentioned workers. The present research was therefore undertaken with the view of corroborating the results which had been obtained in the Amphibia, and it was found that these received support in the case of the chick.

The theorem in question arises out of a consideration ol several passages in Jacobi's important memoir of 1833 or orthogonal transformation. Having determined the substitutior which simultaneously changes

and

Two years ago I communicated a short paper on Solar Radiation and Earth Temperatures (Proc, vol. xxiii., pp. 296–311). This paper had its origin in a critical discussion of certain results deduced by Dr Buchan from observations of Mediterranean temperatures which had been made by the staff of the Austrian warship Pola. The mathematical method by which I discussed the relation between the solar energy incident on the surface of earth or sea, and the corresponding fluctuations of temperature in the rock of the Calton Hill and the surface waters of the Mediterranean, has attracted some attention in America; and correspondence with Professor Cleveland Abbe has drawn my attention again to the subject. In this paper I propose to consider more carefully the significance of the observations made and published by the Austrians. These are contained in four quarto volumes, which Dr Buchan has kindly placed in my hands for the purposes of a thorough investigation from the point of view of solar radiation. Dr Buchan clearly saw that something might be made out of these; and the results he gave two and a half years ago before the Society indicated a penetration of solar heat every day to a depth of more than 100 feet. The results were based upon means of temperature at different depths grouped according to the time of day at which they were taken. As I showed in my former paper, the results so deduced indicated a daily penetration into the waters of the Mediterranean of an amount of heat greater than the sun could supply.

§ 1. Consider frictionless water in a straight canal, infinitely long and infinitely deep, with vertical sides. Let it be disturbed from rest by any change of pressure on the surface, uniform in every line perpendicular to the plane sides, and left to itself under constant air pressure. It is required to find the displacement and velocity of every particle of the water at any future time. Our initial condition will be fully specified by a given normal component velocity, and a normal component displacement, at every part of the surface.

It is commonly believed by geologists, as well as by coal miners, that the inner faces of the rocks which enclose intrusive masses were at one time in contact, and that each of these surfaces is the counterpart in form to the other, from which it has been severed by the forces to which the injection of the intrusive mass was due. In the case of a sill, for example, this belief implies that the rock floor below the sill and the roof above it were in unbroken contact at some time before the sill was intruded, and that the floor and the roof have been forced apart to a distance equal to the thickness of the intrusive mass.

The absolute viscosity calculated from the formula

(where p = the pressure, t the time, r the radius, l the length of capillary, and v the volume of liquid), which connects the viscosity of a liquid with the rate of flow through a long capillary tube, is not often made use of, mainly on account of the difficulty of accurately determining some of the constants (r in particular).

1. We have determined the relative viscosity of aqueous solutions of KCl, KBr, KI, HCl, HBr at 0°, 15°, and 25° C.; and at concentrations of 1 mol., 2 mol., and 3 mol. per litre. Also the equivalent conductivity of the same solutions at 0° C.

2. The change of viscosity with change of temperature diminishes from Cl-Br-I.

3. The effect of concentration on the viscosity depends on the temperature: it may affect the viscosity in opposite directions at different temperatures.

4. There are considerable differences in viscosity of chloride, bromide, and iodide, and especially in the effect of changes in concentration and temperature.

About forty-two years ago Mr Archibald Geikie (now Sir Archibald), then an energetic member on the staff of the Geological Survey, propounded and advocated the doctrine that the change in the relative level of sea and land, indicated by the 25-feet raised beaches which have been long known to geologists as fringing the winding shores of the firths of Central Scotland, took place subsequent to the occupation of the district by the Romans. Further researches, together with a more careful examination of the archaeological phenomena on which Sir Archibald mainly relied as evidence, convinced later observers that the facts did not justify this conclusion. Hence for some years I have been under the impression that the post-Roman theory was abandoned, not only by the general body of geologists and archaeologists, but, as I understood, by the author himself. The following statement of opinion on the subject, recently urged in the interests of the Trustees of the British Museum by a distinguished Professor of Geology, and one who has had exceptional opportunities of making himself conversant with all the factors of the problem, will, however, show how wide of the truth that impression must have been.

In connection with the function J[n], it may be of interest to give briefly the complete solution of the differential equation satisfied by the function J[n]. The method of Frobenius will be employed. Consider the differential equation

in which

It was pointed out to me a few months ago, by my friend Professor W. H. Heaton, that our knowledge of the laws of physical variations might be greatly increased if their study were facilitated by the invention of a machine which would automatically deduce the rate of change of a function from the curve representing that function. In cases where the physical law is already known, and is expressible in terms of known mathematical quantities, such a machine is not essential, though it provides an excellent illustration of mathematical laws; there is, however, a vast and ever-increasing mass of numerical results awaiting discussion and co-ordination, and it is in reducing these to law and order that the differentiator should prove a useful tool.

In a paper communicated to the Nova Scotian Institute of Natural Science,* Professor MacGregor has shown that in the case of weak aqueous solutions of certain hydroxides, the volume of a solution is less than the volume of water used in its preparation. At his suggestion I have investigated the hydroxides of sodium, barium, and strontium, to ascertain whether they exhibit this property, and how the excess of the volume of solution over the volume of constituent water varies with the temperature. From the observations made, I have also determined the thermal expansion coefficients, and found how they vary with temperature and with concentration.