Most individuals consume daily nearly a pound of carbohydrate food in the form of starch or sugar.

The cheapness of sugar in recent times has led to its increased consumption. In 1891 the annual consumpt of cane sugar alone per head of the population was estimated at 80 lbs.

There can be no doubt that the increased consumption of sugar has been followed by an increase in the number of cases of acid dyspepsia, which may in some individuals become so troublesome that they are obliged to abandon saccharine articles of diet as much as possible.

In the following pages we propose to obtain expressions for the several parts of a parabola (axis, focus, vertex, directrix, tangent at vertex, and parameter), whose equation is expressed in the most general form in Cartesian co-ordinates.

Some of the results obtained have already appeared, in which cases we shall supply alternative proofs. We shall also endeavour to complete the investigation of the whole subject.

The object of the work was—

1st, To determine the mean solar horizontal parallax.

2nd, To compare the tabular and observed motion of the planet, with a view to ascertain whether any periodic perturbations of short period occur,—such, for example, as would be accounted for by an error in the adopted value of the lunar equation.

The results depend on the following series of observations :—

A. Meridian observations of the comparison stars and of the planet made at twenty-one different observatories during the opposition of 1889.

This history presents many points of interest to the naturalist, the antiquary, and the historian. The paper is a plea for a wider, yet reliable, record and characterisation of these mammals and birds than we have at present. All zoologists are familiar with them, but the information consists mainly of details which none but specialists can appreciate. General readers look for more science, suggestive of habits and habitats. They wish to know something of the number of species recorded at different periods, their gradational relations, their geographical distribution, and the opinions of early observers as to them. Do their remains throw any light on their physical environments, or on man's condition at the time, as in touch with them, as influenced by them—the living among the living? In tracing the history of beast or bird, we meet with many collateral subjects of importance—such, for example, as climatal changes, alterations of surface over wide areas, links dropped out of gradational rank, and thereby the realisation of new conditions of existence by the removal of one old species or the introduction of one new species.

Lakes whose causal conditions are due to the direct interposition of glaciers, may be formed in one or other of the two following ways. First, when a glacier descending a lateral valley protrudes so far as to dam up a river in the main valley, the obstructing element being either the actual ice or the morainic débris deposited from it. Or, secondly, when a glacier occupying a main valley blocks up the outlet of some tributary stream. In both instances the water accumulates behind the obstruction and so forms a lake, varying in size according to the height of the barrier and the surface configuration of the district immediately above it.

That liquids, if finitely compressible, must (at any one temperature) become steadily less compressible as the pressure is raised, seems to be obvious without any attempt at proof. Yet the assertion is even now generally made, mainly in consequence of an erroneous statement of Örsted, which has been supported by some comparatively recent investigations of Cailletet and others, that the compressibility of water (at any one temperature) is practically the same at all pressures not exceeding a few hundred atmospheres.

Coal, we are all aware, is a remnant of the organic matter of plants which flourished long ago. Owing to the length of time that has elapsed since the remains were entombed, and the pressure the material has been subjected to by overlying strata of great thickness, coal now presents to the unaided eye little or no evidence of organic structure, but is a lustrous black product not at all like wood in appearance.

There was considerable difficulty in selecting a proper title for this paper. It may appear to some, after reading it, that a shorter and better title would have been, “On the Hazing Effects of Smoke.” But as smoke particles generally reflect a reddish-brown light, they do not therefore seem to be the cause of the whitish light which we call haze; and further, smoke particles generally condense into little masses of such a size that they fall to the ground before they are carried to any great distance. It was thought that as this paper is a continuation of previous work, and is founded on results already communicated to this Society, it would be better to keep to the use of the same terms, and as usual, under the name of “dust particles,” to include all the solid and liquid products of combustion, of whatever size or colour they may be.

These well-known figures are generally produced by placing a coin on one side of a piece of glass, and on the other side opposite it another coin or small plate of metal. The coin and the plate are then strongly electrified—the one positively, the other negatively. When the coin is afterwards removed, and the surface of the glass on which it rested is breathed on, there is developed an image of the coin, showing many of the details of the engraving. The image is produced by the condensed moisture being deposited in different-sized patches at different places.

The Insecta are dioecious Invertebrates, and the rudiments of the sexual organs exist in the larvæ, but are chiefly developed during the pupal stage. These organs present such wide and manifold variations, that even those of individuals belonging to the same genus are so widely different in structure, &c., that it is only by a systematic study of each species that the student of nature is capable of arriving at correct conclusions concerning the reproductive organs of any particular species.

In the course of an investigation into the “Present State of Knowledge and Opinion in regard to Colour-blindness,” it was found necessary to search for many data illustrative of various matters connected with the phenomena of the defect. These were obtained from a great variety of sources, chiefly from foreign publications not easily accessible; and as it was highly desirable to bring them forward in evidence, showing their bearing on difficult and controverted points, the plan has been adopted of collecting in this place the most important extracts, and of arranging them in a convenient manner for reference.

The experiments referred to in my paper of March 6th (anté, p. 65) have been completed, but the results are by no means so exact as I hoped to make them. There was great difficulty in procuring the small bore tubes for the piezometers, and thus I had to employ them without previous calibration, as the solutions to be experimented on had already been prepared, and their densities determined at definite temperatures. Delay might have led to evaporation. When I proceeded to the calibration, after completing a large series of experiments, I was greatly annoyed to find that the bores of many of the tubes were by no means uniform. This accounts for the fact that my experiments, though fairly concordant, are not sufficiently so to afford more than a very strong probability in favour of the general result of the inquiry. For this reason I have described my paper as a Preliminary Note.

This paper is an extension to higher powers of the process which I applied to the elimination of θ from the equations of the Ellipse-Glissette (Proc. Roy. Soc. Edin., xix. p. 89). It depends on the principle that where the highest power or powers of one of the variables are awanting, derived equations can always be formed by eliminating a power of each of the other variables between the two primitives.

[In February 1892, by the kindness of Messrs David Bruce & Co., Dundee, my assistant, Mr Alexander Rodger, obtained a berth on board the whaler “Esquimaux,” and proceeded with her on her usual sealing and whaling voyage. Mr Rodger was provided with dredges, tow-nets, and other appliances, and was instructed to use all diligence in the collection of Natural History specimens, both vertebrate and invertebrate. The course of the ship and the business of her people could not be interfered with for such a purpose, but, by his own industry and the great kindness of the master, Captain Jeffery Phillips, Mr Rodger's results have proved very considerable, and compare well with those of some more costly expeditions.—D. W. T.]

Most of the sugars undergo certain fermentations, the chief of these being the lactic, butyric, and the alcoholic or vinous.

To determine the rate at which fermentation occurs in the commoner varieties of sugar, I performed the following experiments.

In September 1892 I sailed from Dundee on board the s.s. “Active,” which, with three other ships, was sent out to discover, if possible, a whale fishery among the Antarctic ice. The general record of my voyage will be published elsewhere, as will also sundry other observations in natural history. The present note is concerned solely with the species of penguin met with to the south of the Falklands.

The present communication consists of a description of the apparatus and methods employed in a series of hygrometric experiments recently made at the Ben Nevis High-Level Observatory, and a very brief notice of some of the results obtained. The investigation here outlined is a necessary preliminary to a more elaborate one, which, it is hoped, may be carried out this summer.

During the last fifty years not a few familiar and apparently quite uninteresting structures have all at once assumed unusual importance and arrested the attention of naturalists in all parts of the world. This is especially true of what used to be known as rudiments, of what we nowadays generally designate vestiges. Of all the known vestiges, the most familiar are perhaps the “splint” bones of the horse. For long the interest in these splints was extremely limited, but since it was shown that they correspond to the functional second and fourth metacarpals and metatarsals of other vertebrates they have attracted the notice of both comparative anatomists and palæozoologists, and are now invariably looked upon as affording strong evidence in support of the view that the horse has descended from polydaetylous ancestors.

The ophthalmic surgeon has frequently to prescribe convex lenses of less than four inches focus for the correction of the optical defect in the eye left by removal of the intransparent crystalline lens in the operation for cataract. Occasionally, too, equally strong concave lenses are required to correct high degrees of short sight.

In 1892, I suggested that communication could be established between ship and ship by means of coils, and as a trial of the system on a large scale has recently been made with the view of establishing communication between North Unst lighthouse, situated on Muckle Flugga, and the mainland (fig. 1), thence to the lighthouse station at Burrafiord, a distance of two miles, a record of the trials may be of interest to the Society.