Some time ago, at the request of Professor Ewart, I undertook an examination of the skull and visceral skeleton of the Greenland shark, Læmargus microcephalus. This I readily consented to do, not only because no attempt had yet been made to describe these structures in this shark, but because they claim careful consideration in view of the recent work by Professor Ewart on the cranial nerves of Elasmobranchs.

In this paper I shall endeavour, without entering into too much detail, to point out some of the more salient features of the skull and visceral skeleton of Læmargus, and to compare them with those of other Elasmobranchs where that seems necessary.

I have made preparations of the above-named structures from the heads of several specimens of Læmargus. The sharks from which the heads were taken were of various sizes, the smallest being about six feet in length, and the largest twelve. As might have been expected, the skeletal parts of these heads are very similar to each other, but I have noticed among the few specimens I have examined points of difference, which make me wish I had a larger number of preparations at my disposal, to enable me to decide the more usual conditions.

The tract of land embraced in the area from which the fossils have been derived, that form the subject of the present Memoir, extends in an easterly direction from Saltcoats to Newmilns, a distance of about 19 miles. At both extremities, the Coal Measures narrow down to under half a mile wide at Saltcoats, and about a mile broad at Newmilns. The greatest width is found towards the centre of the field, where in a northeast and south-west direction it is over 12 miles broad.

In our former paper we described the results obtained by electrolysing concentrated aqueous solutions of the ethyl-potassium salts of normal saturated dibasic acids. The chief products were shown to be diethyl compound ethers of the same homologous series, and the formation of these compound ethers was shown to occur in accordance with the equation: 2C2H5·O·ĊO·R˝·CO·O- = C2H5·O·CO·R˝R˝CO·O·C2H5 + 2CO2. We now find that precisely similar results are obtained by electrolysing the corresponding compounds derived from saturated dibasic acids with side chains. We have thus been able to effect the synthesis of acids of the succinic acid series, in which hydrogen is symmetrically replaced by alcohol radicals of the form CnH2n+1.

[Since this second instalment of my paper was read to the Society my attention has been called to a remarkable investigation by Hertz; in which the circumstances of collision of two elastic spheres are fully worked out, under the special limitations that both are smooth, and that their deformations are exceedingly small. This forms a mere episode in the paper, which is devoted mainly to the statical form of the problem of deformation; as, for instance, the case of the ordinary apparatus for the production of Newton's rings. But it contains a definite numerical result; giving for the duration of impact between two iron spheres of 50mm diameter, which encounter one another directly with a relative speed of 10mm per second, the value 0s·00038. This seems to be the earliest reckoning of the time of collision. The experimental verification of Hertz' formulæ was undertaken with success by Schneebeli, who obtained results in close accordance with them. His mode of measuring the duration of impact was defective, though ingenious.

In the course of investigations that I have lately been making into the transformation of permutations, I have found it convenient to employ several new symbols of operation, which combine with each other according to laws that differ materially from the ordinary algebraical laws; and it is my object in this paper to explain those laws, and give a few examples of the manner in which various propositions relating to permutations may be demonstrated by means of my symbols.

In May 1891 I communicated a paper to this Society “On a Method of Observing and Counting the Number of Water Particles in a Fog,” and in July of the same year a paper “On the Solid and Liquid Particles in Clouds.” One conclusion to which the observations contained in these papers pointed was, that there existed a relation between the thickness or density in clouds and fogs and the number of water particles present. Though the figures did not show that this relation was very close, yet in all the fogs and clouds tested there was a rough relation between the thickness of the air and the number of water particles observed.

The curious effects of rotation upon the path of a spherical projectile have been investigated experimentally by Robins and many others, of whom Magnus is one of the more recent. They have also been the subject of elaborate mathematical investigation, especially by Poisson, who has published a large treatise on the question. For all that, we know as yet very little more about them than Newton did in 1666, when he made his famous experiments on what we now call dispersion.

At the meeting of the British Association in Edinburgh, in August 1892, the President of the Biological Section, Professor W. Rutherford, M.D., F.R.S., F.R.S.E., gave an able opening address on “The Colour-Sense,” in which he took occasion to speak at some length on that remarkable defect of vision called Colour-Blindness. After alluding to the large share of public attention it had lately attracted, both on scientific and popular grounds, he pointed out the unsatisfactory nature of certain statements lately put forward, and gave good reasons why the views still largely held on it in this country required revision.

The numerous analyses of sea-water by Forchhammer previous to 1865, and the later analyses by Dittmar, from samples collected during the “Challenger” Expedition, show that while the salinity—i.e., the amount of dissolved salts contained in 100 parts of seawater—varies greatly in different regions of the ocean, still the composition of these dissolved salts—i.e., the ratio of the constituents of sea-salts—remains practically the same in all the superficial waters of the ocean. Consequently, it is only necessary to determine the chlorine in a definite weight of water to ascertain at once the respective quantities of the other salts present in the sample. Dittmar's examination of the “Challenger” waters has, however, shown that lime is slightly, although distinctly, more abundant in samples of sea-water collected in greater depths than in those samples collected nearer the surface of the ocean, and Dittmar's tables showing the difference between the chlorine calculated from the specific gravity and the chlorine found by analysis point to differences in the composition of the sea-salts, but the observations are relatively so few, these differences so slight, so mixed up with observational errors, and so irregular in their geographical and bathymetrical distribution, that they cannot be said to indicate any general law other than a greater quantity of lime in deep water.

Though a great deal has been written on the Eurypteridæ, and many points of their anatomy elucidated in the brilliant memoirs of Huxley and Salter, Hall, Woodward, Schmidt, &c, nevertheless many points of morphological importance remain obscure. This is perhaps to be attributed to the fact that nearly all the writers on this group have treated them rather from the systematic than the morphological standpoint. In dealing with remains so fragmentary and obscure as the majority of these fossils are, the value of some theory as to their relations among recent forms is enormous, both as suggesting points to be looked for and aiding in the interpretation of structures observed. The greater part of the work on this group was done before the arachnid relationship of Limulus was fully appreciated, and it is in the light of a possible relationship to this form, and also to the lower orders of terrestrial Arachnida, that it seemed to me to be worth while to revise the anatomy of the group. It has been necessary to include a certain amount of what is already well known in the description of the different genera, and I have taken special care to confirm, as far as possible, points which seemed to me to rest on insufficient grounds.