Au mois d'Août dernier, Mr Scourfield eut l'obligeance de me remettre à Berne, lors du congrès de Zoologie, trois petits flacons, dont deux contenaient du détritus pris au fond du Loch Ness, et le troisième du plankton provenant du même lac; ces diverses récoltes dataient de 1903, et étaient conservées à l'alcool. Plus tard, en Novembre, Mr Scourfield m'adressa également trois tubes provenant de la même localité, et dont le contenu, récolté le 7 du même mois, était encore dans son eau d'origine, de sorte que beaucoup des organismes s'y trouvaient vivants et souvent en bonne santé.

Dr Penard has examined and reported upon the Rhizopods and Heliozoa collected in Loch Ness at depths exceeding 250 feet. No littoral samples were sent to him, as his object was to investigate the sarcodine fauna peculiar to deep lakes. The majority of the species found in the deep collections were recognised as belonging to the fauna of the littoral region, or of the adjacent moors, only some half a dozen species or varieties being regarded as peculiar to the abyssal region.

In order to complete the list of the Sarcodina of Loch Ness, in so far as this can be done from the observations made by the Lake Survey, I now add the names of several species which were not detected in any of the collections sent to Dr Penard. Nearly all are common bog species.

In 1895 the Edinburgh and District Water Trustees obtained an Act of Parliament for the introduction of a new water supply to the city of Edinburgh drawn from the Talla Water, one of the upper tributaries of the river Tweed.

The Bill as originally introduced contained provisions for giving off 4,000,000 gallons a day as compensation to the stream, and for appropriating the remainder of the water.

The Tweed Salmon Fisheries Commissioners and other proprietors interested were advised that the proposed amount of compensation was too small, and after various negotiations a clause was ultimately adjusted providing that rain gaugings should be taken over the drainage area for a period of seven years from the 1st January 1896 by the authors of this note (Mr Tait having been appointed in lieu of his predecessor), and that thereafter they should fix—taking all the circumstances into consideration—what was the available annual rainfall of the district.

A striking feature of the results obtained at the seven gauges in the drainage area is the divergence from the commonly accepted relation between rainfall and height above sea-level. The following table shows the “theoretical” amounts of rainfall, averaging 62·51 inches, that might have been expected at the several gauges, on the assumption that there was a uniform increase of 3 per cent. for every 100 feet of rise ; and in comparison with these, the amounts actually recorded, also averaging 62·51 inches.

§ 1. In the practical calculation of the periods and nodes of the lakes we have hitherto examined it has been found that the use of the Seiche Functions gives the best results. Indeed, as will appear from details presently to be submitted to the Society by Mr E. M. Wedderburn and myself, the agreement between theory and observation, so far as we have gone, is beyond what might reasonably have been expected. Also the phenomena of concave lakes, i.e. such as have no shallows or points of minimum depth, are easily deducible from the formulæ given in an abstract (Proc. R.S.E., vol. xxv. p. 328, 6th Oct. 1904) which I communicated to the Society on 18th July 1904. On the other hand, the theory of convex lakes is less easy of manipulation, chiefly owing to the difficulty in calculating the roots of the equations

The first of the writings dealt with in the present communication is of a considerably earlier date than the others: its proper place is immediately in front of Sylvester's paper of the same year. The account of it here given should therefore he found between pages 140 and 141 of this volume of the Proceedings.

In a paper read before the Royal Society of Edinburgh, on 6th January 1902, and printed in its “Proceedings,” I attempted to explain the constitution of matter by supposing the atoms of matter to be bubbles of ether.

In order to fully understand what follows it is absolutely necessary to read that paper in its entirety, but for the benefit of those who may not have access to it, or who do not care to enter deeply into the subject, I give a short synopsis of it.

1. Vanishing aggregates of determinant minors have of late received considerable attention and are now becoming well known. From aggregates for axisymmetric determinants of the form given by Kronecker,* Muir,† or the present writer‡ we may get other forms, and it is the object of this paper to consider some of these new forms, and in particular to show that the general theorem given by Professor Nanson § is readily obtained from the vanishing aggregates of the type given by the present writer.

In a recent communication I described how I had obtained crystals of potassium hydrogen succinate showing only curved faces, from an attempt, up to the present unsuccessful, to prepare complex derivatives of succinic acid corresponding to the chromoxalates. In searching the voluminous literature of the subject for particulars of such complex salts I especially noticed two things,—first, the frequent but hitherto scarcely noted parallelism exhibited by these compounds; and second, the noticeable lack of uniformity in the formulæ attributed to them.

Records relating to the occurrence of medusæ in the Firth of Clyde have not been numerous, though its waters have long been a noted resort for marine naturalists. Forbes, in his Monograph on the British Naked-eyed Medusæ, states that he paid special attention to the medusæ of the Clyde, and that those which he collected while on a yachting cruise in the autumn of 1839 were the foundation of his well-known monograph. Amongst those who have made additions to the list of species I may mention the names of Landsborough, Alder, Allman, Herdman, and two well-known foreigners, Claparède and Haeckel. In June 1902 Dr Clemens Hartlaub, of Heligoland, made a short stay at the Millport Biological Laboratory, solely for the purpose of collecting medusæ, but the complete results of his labours have not yet been published.

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 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.

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.

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.

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.

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.

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.

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.