VI. Researches on myohamatin and the histohæmatins

In a short paper read before the Physiological Society, in 1884 I gave a preliminary account of a new colouring matter which I had discovered in muscle by means of the spectroscope; also of a class of colouring matters found in the tissues and organs of invertebrate and vertebrate animals to which the former pigment evidently belongs, and which I named histohæmatins from their occurrence in the animal tissues. The name myohæmatin was proposed for the muscle pigment for reasons which will be given further on. Since the publication of that paper I have been engaged in working out the distri­bution of these pigments in the Animal Kingdom, and have tried to find out their relationship to other colouring matters and the changes produced in them by reagents.

III. On evaporation and dissociation.—Part II. A study of the thermal properties of alcohol

1. The density of gases is found to increase as the temperature falls towards their condensing point. This may be explained by one of two theories:— (1) That complex gaseous molecules are formed in increasing numbers as the temperature falls; these complex molecules consisting of congeries of the simpler molecules known to exist in gases (see Playfair and Wanklyn, Trans. Roy. Soc. Edin., xxii., (3), p. 441, and ‘Annalen,’ 122, p. 245; also Naumann, ‘Annalen,’ 155, p. 325, and ‘Thermochemie.' pp. 86 et seq .).

II. On evaporation and dissociation. —Part I

1. The phenomena exhibited by gases when exposed to varying temperatures and pressures have been shown by many eminent observers to be explicable by an extension to molecules of the laws of motion of matter which are known to be true in the case of large bodies. Such molecules of gas are supposed to be in a state of very rapid motion, the free path of each molecule bearing a very large ratio to the diameter of the molecule. As a liquid is formed by the condensation of a gas, it is clear that its molecules are in closer proximity to each other, and that the average free path of each molecule in the liquid state cannot be nearly so great as in the gaseous state. It was pointed out by Naumann (Ann. d. Chem. u. Pharm., 1870, 155, 325; see also Ramsay, Proc. Roy. Soc., 1880, April 22 and December 16) that it is conceivable that an explanation of the closer proximity of molecules in a liquid than in a gas may be that two or more gaseous molecules have united to form complex molecular groups, analogous to those complex molecules which are known as chemical compounds, in which two or more elements exist in combination. On the other hand, it is held by some that the difference between gas and liquid is due solely to the greater proximity of the molecules in the liquid state, by reason of which they come within the sphere of mutual attraction, but do not necessarily coalesce to form groups of molecules analogous to the group of atoms in the molecule of a compound.

IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil

1. Lubrication, or the action of oils and other viscous fluids to diminish friction and wear between solid surfaces, does not appear to have hitherto formed a subject for theoretical treatment. Such treatment may have been prevented by the obscurity of the physical actions involved, which belong to a class as yet but little known, namely, the boundary or surface actions of fluids; but the absence of such treatment has also been owing to the want of any general laws discovered by experiment. The subject is of such fundamental importance in practical mechanics, and the opportunities for observation are so frequent, that it may well be a matter of surprise that any general laws should have for so long escaped detection.

XVII. On the blood-vessels of mustelus antarcticus: a contribution to the morphology of the vascular system in the vertebrata

The present inquiry was undertaken with a view of settling, if possible, one or two doubtful points in our knowledge of the vascular system of Fishes, and of giving, in an accessible form, a fairly complete account of the blood-vessels of a typical Selachian, since, as far as I am aware, this has not yet been done. The arteries and veins of the Skate are figured, for the most part very accurately, by Monro (16); the arteries of Raja and Torpedo are described and figured in detail by Hyrtl (11), and there are good general accounts of the vascular system in both orders of Plagiostomi in the works of Müller (17), Stannius (25), and Milne Edwards (14). By all these authors, however, several points of considerable importance are either missed or but slightly referred to, while others are more or less inaccurately described. In all the more modern text-books of comparative anatomy to which I have had access the vascular system of Fishes is very meagrely treated, the manuals of Owen (19), Huxley (10), Claus (4), Gegenbaur (7), Rolleston (24), Macalister (13), Günther (8), and Wiedersheim (26), adding little or nothing to the excellent though brief account in Stannius’s handbook just referred to. Indeed, the only general work I have seen which gives any important information not to be found in Stannius is Milne Edwards’s ‘Leçons,' in which the description of the vascular system, and especially of the arteries of Fishes, is full, and, like everything else in that invaluable book, admirably clear.

XV. On systems of circles and spheres

This Memoir is divided into three Parts: Part I. treats of systems of circles in one plane; Part II. treats of systems of circles on the surface of a sphere; and Part III. of systems of spheres; the method of treatment being that indicated in two papers among Clifford’s ‘Mathematical Papers,ʼ viz., “On Power-Coordinates” (pp. 546—555) and “On the Powers of Spheres” (pp. 332-336). These two papers probably contain the notes of a paper which was read by Clifford to the London Mathematical Society, Feb. 27, 1868, “On Circles and Spheres,” which was not published (‘Lond. Math. Soc. Proc.,ʼ vol. 2, p. 61). The method of treatment indicated in these papers of Clifford’s was successfully applied by the author to prove some theorems given by him in a paper “On the Properties of a Triangle formed by Coplanar Circles” (1885) (‘Quarterly Journal of Mathematics,ʼ vol. 21), and then to the extension of those theorems to the case of spheres. But as Clifford’s papers contained some suggestions as to the application of the same method to the treatment of Bi-circular Quartics, he was induced to develop these ideas and extend the results to the case of the analogous curves on spheres—called by Professor Cayley Spheri-quadrics—and also of cyclides. It is impossible to say whether, if at all, Clifford was indebted to Darboux for any of the ideas contained in the two papers cited above; but it is noticeable that they coincide in a great measure with those expressed by Darboux in several papers published during the years 1869‒1872. In Part I. (§§ 1—124) of this Memoir a general relation is first shown to subsist between the powers of any two groups of five circles; the definition of the power of two circles, as the extension of Steiner’s “power of a point and a circle,” being due to Darboux, but the definition is here slightly modified so as to include the case when the radius of either (or each) circle is infinite. In Chapter II. an extension of the definition so as to apply to a certain system of conics is given; this is practically adapted from Chapter II. in Professor Casey’s Memoir “On Bicircular Quartics” (1867) (‘Irish Acad. Trans.,’ vol. 24). In Chapter III. the general theorem is applied to several interesting cases of circles; some of the results of this chapter are believed to be new. In Chapter IV. the problem of drawing a circle to cut three given circles at given angles is considered, and the circles connected with a triangle formed by three circles, which are analogous to the circumcircle, the inscribed and escribed, and the nine-points circle of an ordinary triangle are discussed. The results are the same, with one or two exceptions which may be new, as arrived at, but in a different manner, in the paper by the author in the ‘Quarterly Journal’ (vol. 21). In Chapter V. the power-coordinates of a point (or circle) are defined, and the equations of circles, &c., discussed; and it is shown that there are two simple coordinate systems of reference; one consisting of four orthogonal circles, mentioned by Clifford (Casey and Darboux consider five orthogonal spheres), the other consisting of two orthogonal circles and their two points of intersection, which seems to have been indicated for the first time by Mr. Homersham Cox in a paper “On Systems of Circles and Bicircular Quartics” (‘Quarterly Journal,’ vol. 19, 1883). In Chapter VI. the general equation of the second degree in power-coordinates is discussed, and in Chapter VII. Bi-circular Quartics are classified according to the number of principal circles which they possess. In Chapter VIII. the connexion between Bi-circular Quartics and their focal conics is briefly indicated, the circle of curvature is found, and an expression for the radius of curvature at any point of a bi-circular quartic is investigated. In these last three chapters the results are probably all old, but as the method employed is different from any previously used to discuss these curves in detail, it may not be without interest.

XIV. Description of fossil remains of two species of a genus (Meiolania) from "Lord Howe's Island."

In 1884 I was favoured by Dr. Woodward, F. R. S., F. G. S., with the inspection of a series of fossil remains from “Lord Howe’s Island,” which had been transmitted by the Government of New South Wales (Department of Mines) to the Department of Geology in the British Museum of Natural History. These fossils indicated a Saurian Reptile allied to the genus, characters of which are described and figured in the 'Philosophical Transactions of the Royal Society’ for the years 1858, 1880, and 1881.

XIII. The solar spectrum, from λ 7150 to λ 10,000

The accompanying map of the solar spectrum between the limits of λ 7150 and λ 10,000 is made from photographs taken with the diffraction gratings, and is more complete in every respect than the map from λ 7600 to λ 10,000 which appeared in the Phil. Trans, for 1880, under the title of “The Method of Mapping the Least Refrangible End of the Spectrum.” In the map which accompanied the paper above referred to the scale numbers attached to the different lines have more accuracy than the wave numbers, and it was to correct the latter that the new series of photographs have been taken. It is my intention at some future and indeterminate time to publish the photographs of this region in connexion with Professor Rowland’s new photographic spectrum which he has in hand, and these will show the minute features of the spectrum down to a wave-length of nearly double that shown; but as the wave-lengths adopted for the visible spectrum by Professor Rowland differ slightly from those given by Ångström, I Lave thought it better to publish the part which, is to supersede the map of 1880 on the latter scale, leaving the discussion of the true wave-numbers to a later period. It must be recollected at the time the first map of this region was made that the photographic process employed was comparatively new—that is to say, it had been brought to its true state of perfection but a short time. Four years have elapsed since then, and much experimental work has been undertaken in connexion with it; and moreover the instrumental defects which were then present have been remedied to a large extent, new apparatus having been procured and finer gratings having been employed.

I. A memoir on the theory of mathematical form

1. My object in this memoir is to separate the necessary matter of exact or mathematical thought from the accidental clothing—geometrical, algebraical, logical, &c.—in which it is usually presented for consideration; and to indicate wherein consists the infinite variety which that necessary m atter exhibits. 2. The memoir is confined to the exposition of fundamental principles, to their elementary developments, to their application to such a variety of cases as will vindicate their value, and to a description of some simple and uniform modes of putting the necessary matter in evidence. I have been unable to ascertain that the principles here set forth have been previously formulated.

V. Further observations on enterochlorophyll, and allied pigments

In a paper, read before the Royal Society in 1883, I described the results of an examination of the so-called “bile” of invertebrates, and proved that the alcohol extracts of the “liver,” or other appendage of the intestine answering to it, showed a spectrum so like that of vegetable chlorophyll as to have led me to conclude that no essential difference exists between the spectrum of enterochlorophyll and plant chlorophyll. At that time I could not decide the points which are now considered.