(1) It is well known that if equations of the type referred to in the title be dealt with like ordinary quadrics, the eliminant obtained is marred by association with an irrelevant factor. Thus, to take the simplest case, viz.

the left-hand member of which contains the irrelevant factor |α2β2|, being readily shown to be equal to

The object of the present short paper is to draw attention to other modes of procedure, and to formulate the results for n variables.

There are few organs which have engaged the attention of the topographical anatomist more than the stomach, and few which have yielded him so small a reward as the result of his labours. The changes which so rapidly set in after death through relaxation of its muscular wall, combined with the many different forms which the organ may assume during life, make the investigation one of great difficulty. Improved methods, and more especially the introduction of formalin as a hardening and preserving agent, have, however, placed the modern anatomist in a much more favourable position than his predecessor for attacking problems of this nature, and have enabled him to do justice to many views which have been more or less tentatively put forward by the earlier observers in this branch of study.

The material for this work was that collected and prepared by Professor J. Graham Kerr in the Chaco (Lepidosiren), and by Budgett from the Gambia (Protopterus). The process of development follows nearly the same course in the two genera, and where differences occur they are mainly such as are to be expected from a comparison of the adult skulls. While the series of stages of Lepidosiren left no unfilled gaps, the material was scantier in the case of Protopterus. Except where otherwise stated, the detailed descriptions were worked out in Lepidosiren, but whenever I was unable to verify that the process was substantially the same in the other genus, the fact has been mentioned. The stages are numbered in correspondence with the stages figured by Graham Kerr (Phil. Trans. Roy. Soc, B., vol. cxcii.). The Protopterus stages are numbered the same as the corresponding ones in the other genus. As far as possible, the nomenclature adopted by Gaupp* has been adhered to.

The observations recorded in the following pages were begun upwards of four years ago. In the course of an investigation into the anatomy and physiology of the central nervous system of the monkey, it was deemed necessary, amongst other things, to note whether the lesions established had influenced the temperature of the affected limbs. On consulting the chapter on “Animal Heat” by Pembrey in Schäfer's Text-booh of Physiology, and Richet's article “Chaleur,” in the Dictionnaire de Physiologie to find what the normal temperature of the monkey was, it was discovered that very few observations on the temperature of this animal had been made. Considering the high position which the monkey occupies in the animal scale, it seemed to us that this was an omission which we might with advantage do something to remedy; we decided therefore to avail ourselves of the material at our disposal, and to record the temperature of such healthy monkeys as should come into the laboratory from time to time.

The term intermedio-lateral tract was introduced in 1859 (Phil. Trans., 1859, p. 445) by Lockhart Clarke to designate a tract or column of nerve cells in the spinal cord, which he had previously described in 1851 (Phil. Trans., 1851, ii. p. 613) as occupying that portion of the lateral margin of the grey matter which is intermediate between the anterior and posterior cornua. According to Clarke's original account, the column in question was very transparent in appearance, and resembled somewhat the substantia gelatinosa of the posterior horn. It was found in the upper part of the lumbar enlargement, extended upwards through the dorsal region, where it distinctly increased in size, to the lower part of the cervical enlargement. Here it disappeared almost entirely. In the upper cervical region it was again seen, and could be traced upwards into the medulla oblongata, where, in the space immediately behind the central canal, it blended with its fellow of the opposite side. In the more complete account of the tract published in 1859 (p. 446), its component cells are described as in part oval, fusiform, pyriform, or triangular, and as being smaller and more uniform in size than those of the anterior cornua. In the mid-dorsal region, where they are least numerous, they are found only near the lateral margin of the grey matter, with the exception of some cells which lie among the white fibres beyond the margin of the grey substance. In the upper dorsal region the tract is larger, and not only projects further outwards into the lateral column of the white fibres, but also tapers inwards across the grey substance, almost to the front of Clarke's column. In the cervical enlargement it gradually disappears, although it seems to contain, in part at least, a few scattered cells resembling those of the intermedio-lateral tract of the dorsal region. In the upper cervical region, as already stated, it is again seen occupying a lateral horn similar to that found in the dorsal region. It is composed of the same kind of cells, and can be followed up into the medulla, where it is said to give origin to some of the fibres of the vagus and the spinal accessory.

The lavas of the Bathgate and Linlithgow Hills occur, as already described, in a series of zones alternating with sedimentary deposits. So far as their field characters are concerned they may be grouped with convenience into two classes: fine-grained, columnar, basaltic types, usually porphyritic with augite and olivine, rarely with felspar, and coarser-grained, doleritic types, usually much decomposed, not evidently porphyritic or porphyritic with olivine alone. The yellow crusts of the compact lavas are minutely vesicular and pumiceous, while steam-cavities are rare in the interior. The doleritic lavas on the other hand are coarsely vesicular and amygdaloidal above and below, and frequently also throughout. The blue basaltic types are relatively very fresh; the doleritic types are frequently entirely decomposed into a whitish, earthy material, with knots of limonite, calcite, and quartz, similar in many respects to the white trap of the coal-fields. Good examples of this mode of weathering may be found in the Riccarton Burn. The differences in texture are probably to be referred not so much to differences in chemical composition as to the effect of variation in the quantity of water vapour contained in the successive flows. The coarse and open structure of the dolerites has evidently also given freer scope to the action of decomposing influences than the more compact structure of the basalts. Both types are much veined by such secondary minerals as calcite, siderite, limonite, quartz, chalcedony, and various zeolites. Frequently cavities in the veins, steam-holes in the pumiceous crusts, and even vesicles within the solid rocks, are found filled with brown viscous pitch or black lustrous asphalt. Such occurrences undoubtedly indicate that these rocks have been subjected to some slight extent to post-volcanic pneumatolytic action.

A necessary preliminary to the study of the complex problems involved in the biology of lakes is to ascertain the facts. The collection of the bathymetrical data was begun many years ago by Sir John Murray and Mr Pullar, and is nearing completion under the Lake Survey. The next thing is to take a census of the inhabitants. This we are now trying to do by compiling lists of the animals and plants living in the lakes. The study of the problems after the data are collected falls outside the province of a lake survey, and within that of some permanent biological station. This present compilation is one step in the accumulation of the facts.

It has been known for a length of time that the presence of a non-volatile substance diminishes the vapour pressure of the solvent in which it is placed, and as the boiling point of a solvent or a solution is the temperature at which the vapour pressure is just equal to, or overcomes the pressure of the atmosphere, it follows that a solution has a higher boiling point than the solvent. Amongst the first experimenters in this field were Faraday, Legrand, Griffiths, and Raoult. TO Raoult we owe much for his development of the subject.

Although great advances have been made during the last thirty years in our knowledge of dilute solutions, there has been no corresponding advance in respect of concentrated solutions. This is primarily due to the fact that hitherto no simple and general relationship has been discovered between the conductivity and the concentration of concentrated solutions of electrolytes. Ostwald's law of dilution holds only for dilute solutions of weak electrolytes, and the formulæ of Rudolphi and Van T'Hoff are applicable only to dilute solutions of good electrolytes. It seems therefore important to inquire whether the difficulty may not be to some extent overcome by an alteration in the mode of representing the facts.