These are stray notes on a few of the pelagic animals found in the Clyde. I noted down their occurrence whilst examining the plankton for medusæ. The records may be useful to students who intend working in the Laboratory at Millport, and should give them an idea as to the time of year at which these animals occur. They may also be useful for comparison with other years and other localities. Most of the species have been previously recorded for the Clyde, and the few which are not mentioned in the “Fauna of the Clyde,” are fairly common on the British coasts. As these notes form a kind of appendix to my Report on the Medusæ, I have curtailed this introduction to avoid repetition.

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

The material upon which this report is based was collected by Mr Alexander Gray, curator of the Biological Station at Millport. The tow-nettings were specially taken for Mr E. T. Browne, to aid his investigation of the Medusæ of the Firth of Clyde. After the material was examined by Mr Browne, all the Crustacea were forwarded to me for identification.

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.

The refraction equation sin i == μ sin r, though simple in itself, is apt to give rise, in problems connected with refraction, to formulæ too involved for arithmetical computation. In such cases it may be necessary to trace the course through the optical system in question of a certain number of arbitrarily chosen rays, and thence to find the course of the other rays by interpolation. The

linkage about to be described affords a rapid and accurate means of determining the paths of the rays through any optical system.

§ 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.

By the terms “ankylostomiasis,” “miners' anæmia,” and the “miners' worm disease,” is meant a malady due to the presence in the small intestine of numerous slender worms called Ankylostoma duodenale,—ἀγκύλος, crooked, στόμα, a mouth, and duodenale, because usually found in the upper part of the small intestine. Although the disease is known to have existed for long in Egyptian and Tropical countries, it was not until the huge mining engineering operations connected with the tunnelling of the Alps at Mont Cenis and St Gothard for railway extension were in progress that the disease attracted public attention in Europe. During the piercing of these Alpine heights the parasite was the cause of considerable ill-health and of loss of life among the miners, especially at the St Gothard. For a considerable length of time the true nature of the malady was not recognised. It was owing to the fact that as anæmia was one of the principal physical signs of the malady the disease came to be called miners' anæmia, and as the men worked in tunnels, the term “la maladie des tonnelles” was also given to it. After the discovery of the parasite in the small intestine of affected miners, the designation miners' worm disease came to be applied to it, and it is by this name that it is commonly known in this country.

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).

After a lecture on animal heat towards the end of last session, in which I described Langley's original form of bolometer, with its two iron gratings, and mentioned that Dr Stewart, of Philadelphia, had referred to the use of tinfoil and leadfoil gratings for physiological purposes in his text-book, I started to make a bolometer for our department. I should mention that some time ago Professor M'Kendrick, impressed by the probability of the bolometer being of use to physiologists, had communicated with Professor Langley, who kindly sent him, from Baltimore, literature dealing with the subject, and stated that the instrument was not made by an instrument-maker.

In the preparation of esters, one of the main difficulties is the removal of the water produced by the interaction of the acid and the alcohol. This difficulty is very pronounced in the case of those esters which are readily hydrolysed, e.g. oxalic and tartaric esters; the methods of preparation of such esters are long and troublesome, and the yields are not always satisfactory. The method described in this paper is rapid and easy, requires little attention, and gives satisfactory yields.

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.

It has been known for the last thirty-four years that when the fresh excised eyeball of a frog is connected by non-polarizable electrodes with a sensitive galvanometer, an electrical current (travelling through the eye from the retina to the cornea) may be detected, and that variations occur in this current, due solely to the action of light on the retina.

It is also well known that salts of radium are luminous in the dark, and that if a tube containing radium† is pressed against the closed lid of the eyeball, or even pressed against the temple, one has the consciousness of luminosity. This being so, it was of interest to ascertain whether this luminosity was due to the radium causing fluorescence of any of the structures of the eyeball, or whether it was due to the direct action of one or other of the emanations of radium on the retina itself.

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

In October 1894 a pair of Cape hunting dogs were acquired by the Royal Zoological Society of Ireland and added to their collection in Phœnix Park. They were purchased from Hagen-beck, in Hamburg, and at the time they came to Dublin they were not quite full grown. Although still existing in considerable numbers over a very wide area in Africa, the Lycaon is by no means a common specimen in Zoological Gardens, and it is rare to meet with it on the lists that are periodically issued by dealers in wild animals.

In a paper laid before this Society in July 1902, the magnetic æolotropy of iron demagnetised by decreasing reversals of co-directional and transverse magnetising forces, and also of iron left transversely magnetised, was established. In later communications (July 1903 and July 1904) it has further been shown that iron and nickel demagnetised by decreasing reversals of a directional force, develop an induction component at right angles to the subsequent magnetising force, which tends to disappear as saturation values are reached, when the angle between these two forces is other than 0° and 90°. In annealed iron this property is absent.

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.

1. Since a persymmetric determinant is a particular case of an axisymmetric determinant, it follows that every type of vanishing aggregate for axisymmetric determinants is also a vanishing aggregate for persymmetric determinants. The principal object of this paper is to give a series of theorems (I., II., III., IV., V.), by the application of which to any vanishing aggregate of minors of persymmetric determinants new vanishing aggregates are obtained (7–12), which, though true for persymmetric, are no longer true for axisymmetric determinants.

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.