Some time since I published in the Transactions of this Society a paper upon Phreoryctes; the present paper is the second of what I hope will be a series of memoirs upon the structure of the Oligochæta Limicolæ; this will be a parallel series to that upon the Oligochæta Terricolæ, which is being published by me in the Quarterly Journal of Microscopical Science. As I took pains in my paper upon Phreoryctes to point out, in accordance with views previously expressed by myself and by others, that it is impossible to draw a hard and fast line between those two groups of Claparède, it may seem rather illogical to retain this classification—if only in the title of a paper; I do so simply as a matter of convenience, and without in the least desiring to revive these old divisions of the Oligochæta; indeed the genus Moniligaster, which is treated of in the present communication, is by most naturalists regarded as an earthworm; in many points it does undoubtedly agree with certain terricolous genera; but as its affinities, into the discussion of which I shall enter later, seem to me to be more with the Lumbriculidæ, I put it into the Limicoline series; it is useful to have a name corresponding to “earthworm” for those Oligochæta which are not earthworms, and are for the most part aquatic, and I therefore use that term.

The development of the inverse square root

into a series

gives rise to the coefficients Zn, which have been called “Laplace's Coefficients” If in Zn we substitute for z the expression

where

then the function of ψ, which Zn will represent, can most appropriately be expressed by

The object of this paper is to show, by actual calculation, that the coefficients Ns, (functions of x, x′, y, y′) can be worked out by elementary algebraical processes, the only auxiliary taken from higher analysis being the expression of the powers of cos ψ in function of the cosines of the multiples of ψ.

As to our notations, we shall observe throughout the following restrictions:—

1. The function Π(x) shall not be employed otherwise than for integer positive values of x, so that

2. The factorial

will be made use of for integer values only of r (as, for example, r = + 1, or r = − 1, or r = + 2, &c., the exponent t being integer positive.

I will commence by stating that three reasons have moved me to bring this subject before the Society—(1) Because I found everywhere loose and even altogether false ideas possessing the public mind on the subject; (2) because I much fear that we, the academical teachers of the Greek language, are chiefly to blame for the currency of these false ideas; and (3) because, if Greek is a living and uncorrupted language, and dominating large districts of Europe and the Mediterranean, as influentially as French on the banks of the Seine and German on the Rhine, it follows that a radical reform must take place in our received methods of teaching this noble and most useful language. Now that the current language of the Greeks in Athens and elsewhere is not, in any sense, a new or a corrupt language, as Italian is a melodious and French a glittering corruption of Latin, may be gathered even a priori; for languages are slow to die, and the time that elapsed from the taking of Constantinople by the Turks in 1453 and the establishment of the Venetian power in the Morea in 1204, to the resurrection of Greek political life in 1822, was not long enough to cause such a fusion of contrary elements as produced the English language from the permanent occupation of the British Isles by the Normans.

The appearance of a learned and exhaustive work on the life and labours of Koraes, by a native Greek of great ability, naturally invites the scholars of Western Europe to a grateful acknowledgment of the obligation of the Greek language to this most distinguished of its modern exponents. The fact, indeed, that Greek in this country is popularly talked of as a dead language, and as such taught from books through the eye and the understanding, rather than by living converse with those who speak it, may serve as an apology for the general ignorance that prevails, even in professional circles, with regard to the scholarly achievements of this remarkable man; but the appearance of works of such mark in the living literature of Greece as those of Thereianos, Paspates, Bikellas, Polylas, and others, warns us that it is high time to take note of living Greece as living Greece again, and give to the learned Grecians of the present day their proper share in that homage which we pay so liberally to the great masters of Greek wisdom in the past.

Adamantios Koraes was born at Smyrna in 1748, the son of a Chiote merchant who had removed from the island to the great centre of commerce on the Continent. As a boy young Koraes was remarkable for his love of learning and his hatred of the Turks as the enslavers and debasers of his people; and having inherited a valuable library from one of his maternal relatives, he found it necessary to acquire the Latin language, in which all the famous commentaries on the great Greek classics had been composed.

The present paper is the second of the series dealing with the Fossil Flora of the Staffordshire Coal Fields. As in previous memoirs, I give a short sketch of the Geology of the coal field, merely for the purpose of indicating the relationship of the beds to each other, from which the fossils have been derived.

Various memoirs dealing with the geological structure and resources of the Potteries Coal Field have already appeared, but in these the names applied to the different groups of strata which compose the Potteries Coal Field have generally special application to the local geological features, and do not treat of the Coal Field in its wider relationship, when considered as only forming a part of the Coal Measures as developed in Britain. A similar course has usually been taken in the published memoirs of other British Coal Fields, which makes a comparison of their relative ages, from the data given, very difficult.

Although the Mollusea have usually been collected and examined, from their great vertical distribution—in some cases extending throughout the whole range of carboniferous rocks—they as a whole afford little data for the determination of the divisions of the Coal Measures, and unfortunately the fossil plants appear to have received little attention when the memoirs of the various coal fields were being prepared.

At the end of 1886 a method occurred to me of rapidly recording the positions of the lines of the solar spectrum, which I thought might be used with advantage for determining the faint “Telluric dry-gas lines” near D, mentioned in Professor Piazzi Smyth's maps of The Visual Solar Spectrum in 1884. The fundamental idea of the recording apparatus is that of magnifying by some mechanical means the motion of the grating, or prism, to such an extent that it can be recorded on a continuous fillet of paper. The viewing telescope being then firmly clamped, the exact positions of the grating can be pricked off on the strip of paper as the lines are successively brought to the fixed cross in the field of view.

For the satisfactory use of the method two conditions suggest themselves as desirable. First, the punctures should not be less than a good-sized pin hole, and the interval between the closest lines, which the spectroscope is able to separate, should be represented on the paper strip by a space of several tenths of an inch.

Forty years ago Kolbe showed that a strong aqueous solution of potassium acetate, when subjected to the influence of the electric current, is decomposed with formation of the following products. At the anode a gaseous mixture is evolved which consists chiefly of carbonic acid and ethan; while at the cathode hydrogen escapes, and potassium hydrate is formed in the solution. When dilute solutions of the same substance are electrolysed under similar conditions, the decomposition products at the cathode are the same as in the previous case, but at the anode the gas evolved is now oxygen, and free acetic acid makes its appearance in the solution. The difference between the two cases must, on modern views of electrolysis, be attributed to the occurrence of secondary reactions. The primary process is in all cases the transference of the electrically-charged submolecules or ions to the corresponding poles, where they lose their charges, and thereby become capable of reacting with one another or with neighbouring molecules. As a general rule they are, when discharged, themselves incapable of independent existence.

The present inquiry is closely connected with some of the phenomena presented in golf:—especially the fact that a ball can be “jerked” nearly as far as it can be “driven.” For this, in itself, furnishes a complete proof that the duration of the impact is exceedingly short. But it does not appear that any accurate determination of the duration can be made in this way. Measurements, even of a rude kind, are impracticable under the circumstances.

In 1887 I made a number of preliminary experiments with the view of devising a form of apparatus which should trace a permanent record of the circumstances of impact. I found that it was necessary that one of the two impinging bodies should be fixed:—at least if the apparatus were to be at once simple and manageable. This arrangement gives, of course, a result not directly comparable with the behaviour of a golf-ball. For pressure is applied to one side only, both of ball and of club; but when one of two impinging bodies is fixed it is virtually struck simultaneously on both sides.