A few years ago the late Sir C. Wyville Thomson gave me for examination some specimens of Ascidians which had been obtained during the cruises of the “Porcupine” and “Lightning,” and last summer I received from Mr John Murray the remainder of the Ascidiæ Simplices and two species of the Ascidiæ Compositæ from the same deep-sea dredging expeditions. Some additional specimens of the “Porcupine” Ascidiæ Compositæ have been placed in my hands during the last few days (January 1, 1884). The present paper contains a detailed account of the Simple Ascidians alone; the Compound forms will be worked up along with the “Challenger” Ascidiæ Compositæ, and will be described and figured in the second part of my Report upon the Tunicata of the “Challenger” Expedition. It may, however, be useful to state here that the “Porcupine” Compound Ascidians include:—

Of all known examples in physical science, of simplifying, and at the same time “precisionising” some of its fundamental data, which might otherwise fall to be entangled in high numbers, none has been happier than Fraunhofer's application of the letters of the alphabet to certain chief lines in the solar spectrum. Happy both in its conception by the inventor, and its universal acceptance since then by the world. Whence it comes to pass now, that in every country, whoever observes the solar spectrum at all, with whatever instrument, large or small, diffracting or refracting, and whether he holds to the undulatory, or any other theory of light, and catalogues spectral lines either in Wave-lengths or Wave-numbers, or merely in terms of the brass scale screwed to his instrument by a maker,—yet whenever he speaks of the line A, or B, or C, or any other so named by Fraunhofer, he singles out thereby from among thousands, exactly the same identical line which any and every other spectroscopist alludes to under the same simple letter.

The dust particles floating in our atmosphere are every day demanding more and more attention. As our knowledge of these unseen particles increases, our interest deepens, and I might almost say gives place to anxiety, when we realise the vast importance these dust particles have on life, whether it be those inorganic ones so small as to be beyond the powers of the microscope, or those larger organic ones which float unseen through our atmosphere, and which, though invisible, are yet the messengers of sickness and of death to many—messengers far more real and certain than poet or painter has ever conceived.

The Norway lobster, Nephrops norvegicus, on account of its abundance in the Firth of Forth, and the consequent ease with which it can be obtained from the Newhaven market, is given to the practical classes in the Natural History Laboratory of Edinburgh University for dissection, as an example of the decapodous Crustacea. One day in December last, while I was superintending the work of a class engaged in the study of this animal, one of the students, whose name I have unfortunately forgotten, called my attention to some globular protuberances on the intestine of the specimen he was dissecting. At the time I was unable to answer his questions any further than to say that the protuberances were the cysts of a parasite, and I put the specimen by for subsequent examination. On opening the cysts afterwards I found in them a small white worm, which proved to be a Trematode possessing novel characteristics. In the following paper I shall describe this parasite, and show that it is so distinct from all Trematodes hitherto known as to constitute a new genus. On several occasions I had the pleasure of examining the animal in the company of my friend and former colleague, Mr Duncan Matthews, and some of the points in its structure were first noticed by him.

1. By a knot of n crossings, I understand a reticulation of any number of meshes of two or more edges, whose summits, all tessaraces (ἀκή), are each a single crossing, as when you cross your forefingers straight or slightly curved, so as not to link them, and such meshes that every thread is either seen, when the projection of the knot with its n crossings and no more is drawn in double lines, or conceived by the reader of its course when drawn in single line, to pass alternately under and over the threads to which it comes at successive crossings.

In the twenty-ninth volume of the Society's Transactions, at page 59, Lord Brouncker's process for finding the ratio of two quantities (commonly known as the method of continued fractions) is extended to the comparison of three or more magnitudes. It is there shown that recurrence, which was believed to belong exclusively to equations of the second degree, extends to those of higher orders, and examples of this extension are given in determining the proportions of the heptagon and enneagon.

One main object of the present brief paper is to take advantage of the results obtained by Kirkman, and thus to extend my census of distinct forms to knottiness of the 8th and 9th orders; for the carrying out of which, by my own methods, I could not find time. But I employ the opportunity to give, in a more extended form than that in the short abstract in the Proceedings, some results connected with the general subject of knots, which were communicated to the Society on January 6, 1879, as well as others communicated at a later date, but not yet printed even in abstract.

The Universe, as we have it, is an organised system of rational or reasonable forces and forms; of which the former are the product of the plastic, self-energising, productive power within, the latter the external presentation or manifestation of that power.

Perhaps the most interesting feature connected with the Old Red Sandstone formation in Shetland is the evidence of prolonged volcanic activity in those northern isles. The great development of contemporaneous and intrusive igneous rocks, which gives rise to some of the most striking scenery in Shetland, is all the more important when compared with the meagre records in the Lower Old Red Sandstone of Orkney and the Moray Firth basin. Not till we pass to the south of the Grampians do we find evidence of a far grander display of volcanic action during this period, in the sheets of lava and tuff in the Sidlaws and Ochils and in the great belt stretching from the Pentlands south-westwards into Ayrshire. The relations of the Shetland igneous rocks are admirably displayed in the various coast sections, especially in the mural cliffs of Northmavine and some of the Western Islands. From these records, though they have been subjected to much denudation, it is possible to construct a tolerably complete sketch of the volcanic history of this formation, as developed in that region.

The appearance of a green or blue sun, though not unknown, is of sufficiently rare occurrence to make a full investigation of all the phenomena connected with it highly desirable. I have therefore tried to obtain as accurate and complete information as possible concerning the appearance of a green sun in India during several days in September 1883.

Let there be given, in a plane π, six (fundamental) points 1, 2, 3, 4, 5, 6, of which neither any three lie in a right line, nor all in a conic; and consider the six conics [1] ≡ 23456, [2] ≡ 13456, [3] ≡ 12456, [4] ≡ 12356, [5] ≡ 12346, [6] ≡ 12345, and the fifteen right lines 12, 13,…, 16, 23,…, 56.

There is a pencil of cubics 1223456 (curves of the third order, having a node at 1 and passing through the other fundamental points); their tangents at the common node form an involution, viz., they are harmonically conjugate with regard to two fixed rays. Five pairs of conjugate rays of this involution are already known; for instance, the line 12 and the conic [2] have conjugate directions at the point 1, for, they make up a cubic 1223456.