In the determination of the effects of stress upon different materials, the investigator has several methods of attack open to him, each of which has its own particular advantages. In the great majority of cases the material under investigation obeys the generalised Hooke's law, and the effects of a stress are therefore most easily followed and measured by observations of the strains produced. The strains being usually exceedingly minute, it is necessary to magnify them sufficiently to allow of accurate measurement. To this end many instruments have been devised for measuring the strains obtained by the action of different stresses, and in fact the great majority of our experimental knowledge has been obtained in this way. The application of polarised light to the determination of stress was first suggested by Brewster, and he applied it to many problems, particularly the determination of the neutral axis of a glass beam. Neumann, with a full knowledge of the work of Brewster, developed a theory of the analysis of strain by polarised light, and Maxwell also independently developed a theory. A third method, which has assumed great prominence in recent years, is the microscopic examination of metals under stress, as developed by Ewing, and Rosenhain, and others.

The spectrum of the new star in Perseus, which Dr Anderson, of Edinburgh, discovered 1901 February 21, was photographed at the Glasgow Observatory from 1901 March 3 till 1903 January. From the early photographs one gains the impression that the spectrum consists of a number of bright bands of different lengths, fading towards the ends, and overlapping each other, thus producing a series of maxima and minima of brightness. Near wave-length 5000 the intensity rapidly falls off towards the less refrangible side, and the bands appear detached. The middle of each of the three most intense maxima approximately coincide with the hydrogen lines Hβ, Hγ, Hδ, and on two photo-plates, March 18 to 20 and March 25, each of the bands is crossed by a sharp Fraunhofer line. On the photo-plates taken after 1901 August 1 the bands are all detached; some, including the two bands whose middles approximately coincide with the principal nebular lines, have almost the same lengths, and suggest a line spectrum in which the lines have been broadened into bands, others are considerably longer and have pronounced maxima.

The material for the observations recorded in this paper has been kindly lent to me by Mr Graham Kerr, Professor of Zoology in the University of Glasgow. It consisted of some of his beautiful series of cut embryos, and of some freshly-sectioned material which I stained specially for the purposes of the research.

The blood corpuscles of the embryo Lepidosiren are exceptionally favourable objects for the study not only of the morphology of the blood, but also of cell structure. The karyokinesis in the red corpuscles presents features of considerable interest—and the phenomena are presented to the observer on such a scale as to render them almost diagrammatic.

In the present paper I shall deal with the structure of the corpuscles and the mitotic phases in the erythrocytes, reserving for a future communication the results of studies on the origin and histogenesis of the elements.

The original design of this research was to determine whether the extract of suprarenal medulla (or its active principle) has the power of antagonising the effects of an overdose of chloroform upon the heart and arterial system. Incidentally the research became extended so as to cover the action of certain other antagonising agents. It further appeared necessary, as the investigation proceeded, to subject the action of chloroform upon the vascular system to renewed study. For although, as the result of numerous recent researches, physiologists are in agreement regarding the general effect of the drug upon the heart, there yet remain various points requiring elucidation both as regards its effect on the heart and on the arteries.

(1) It is known that a continuant whose three diagonals are formed of certain equidifferent progressions is resolvable into linear factors, the earliest specimens placed on record being those of Sylvester and Painvin. The object of the present paper is to show that there are continuants of quite a different type which are also so resolvable, and to expound a general mode of investigating the subject.

The Bathgate and Linlithgow Hills occupy a well-defined belt of rising ground stretching S.S.W.–N.N.E. from Bathgate to Bo'ness, and included in the marginal portions of sheets 31 and 32 of the 1-in. maps of the Ordnance and Geological Surveys. Throughout the range the steeper slopes face the west, while the eastern flanks are deeply buried in drift. The glaciated contours are well seen from the east, and the sky-line is in several places deeply indented by glacial grooves. The physical geography is throughout intimately dependent upon the geological structure, but the latter is simplicity itself when contrasted with the complicated structure of the shale-fields to the east. Alternating zones of volcanic and sedimentary rocks strike parallel with the direction of elongation of the range from Bathgate to Bonnytoun Hill, and these are cut by a later connected series of dykes and sills of intrusive igneous rock. The latter, as a rule, are more resistant than the lavas, and form the more prominent features of the landscape, while the sedimentary intercalations may frequently be traced, even where no rock is visible, by the trough-like depressions which have been hollowed out of them between the zones of lava.

The new species here described were found in the course of the work of the Lake Survey on Loch Ness and other Highland Lochs. Half of the number were found in lakes, though they are not exclusively lacustrine, three in ponds, two from moss growing on the shores of Loch Ness, and one in a stream running into Loch Ness.

(41) The invariance of the equations

with regard to the group of cyclical substitutions,

and the consequent invariance of the eliminant with regard to the reduced group consisting of the last two substitutions, has been already referred to. When the eliminant is expressed in terms of the three-line determinants formable from the array of coefficients, the invariance in question is self-evident, as each of the twenty-eight parts composing the expression is invariant by itself. For convenience this form may be repeated from § 31 with a slightly improved notation.

The theory of the functions commonly known as q functions might perhaps be greatly developed, if investigators were to work on lines suggested by the functional notation of well-known analytie functions. For instance, the analysis connected with the circular functions sin x, cos x, …, might be regarded as the theory of certain infinite products without using any special functional notation. It need not be explained however, how great was the gain to elementary algebra by the introduction of the exponential function (regarded as the limit of a certain infinite product, or as the limit of a certain infinite series) denoted ex, with certain characteristic properties, enabling the worker to make transformations easily and quickly. Of course, the vast store of interesting and in many cases useful results connected with the elementary functions of analysis might have been obtained without the introduction of any notation capable of rapid and easy transformations, but I think it unlikely that they would have been obtained.

In September 1903 I received a bottle containing twelve specimens of a large parasite presented to me by Mr Chr. Castberg, the manager of a Norwegian whaling company which has established a fishing station at Ronasvoe in the north of Shetland. In his letters Mr Castberg stated that the parasites were attached to a Finner whale, which, from its size, the mottled character of the whalebone and the pointed head, was obviously a Razorback—Balænoptera musculus. The parasites were numerous, and were fixed to the back of the whale, and the attached end penetrated through the skin into the blubber. Although Mr Castberg had seen many hundred whales, this is the first occasion on which he had met with this form of parasite.

In the first part of this memoir I described the structure of the corpuscles at a stage of larval development when the red cells were actively dividing and the blood contained several varieties of white cells. During the course of these more strictly cytological observations, it was impressed upon me that the great size of the elements and their very marked histological characters, combined with the simple character of the organisation of the animal, made Lepidosiren a very favourable case for the study of the first principles of Hæmatogenesis. I was specially interested in what may be termed a middle phase in the history of the blood. I refer to a period after the primitive corpuscles have acquired haemoglobin and there are leucocytes present, but before the blood-forming organs are unfolded. This stage lasts a relatively long time in Lepidosiren up to the differentiation of the spleen, as the liver takes no part in blood-formation at any period.

Since the publication, about a year ago, in the Transactions of this Society, of my paper on the Lower Devonian Fishes of Gemünden, a review of it has appeared in the pages of Science by Professor Bashford Dean, of New York. In this review Professor Dean endeavoured to throw doubts on the correctness of my orientation of the elements of the dermal skeleton of Drepanaspis Gemündenensis, in the following words:—

“Thus, his grounds seem inadequate for distinguishing dorsal and ventral sides. In no specimen figured is the relation of the dorsal lobe of the tail shown convincingly to be continuous with the so-called dorsal aspect; moreover, the eyes occur on the side which Traquair regards as ventral. Unless additional evidence is forthcoming, it would accordingly seem to me more probable that the ‘labial’ of Traquair was the ‘rostral’ plate, a structure which appears constant in Heterostracans.