1. This paper consists of two parts, the first of which is confined to describing the experiments performed; while in the second it is attempted to connect these with certain theoretical views regarding Radiant Heat.

2. The experiments were made with a fourfold object; at least, for the sake of clearness, it is well to class them into four distinct groups:—

Group I. Contains those experiments in which the quantities of heat radiated from polished plates of different substances, at a given temperature, are compared with the quantity radiated from a similar surface of lamp-black, at the same temperature.

II. Those in which the quantities of heat radiated at the same temperature, from polished plates of the same substance, but of different thicknesses, are compared with one another.

III. Those in which the radiations, from polished plates of different substances at any temperature, are compared with that from lampblack at the same temperature, with regard to the quality or nature of the heat radiated.

IV. Those in which the same comparison is made between the radiations from polished plates of the same substance, but of different thicknesses.

If we examine the flame arising from the combustion of any of the hydrocarbons, such as that of coal-gas, or of a common candle, it will be found to consist of several portions easily distinguishable by the eye, and in which the matter composing the flame exists in very different conditions. There is, first, a central non-luminous region, in which the gases are not yet ignited; secondly, a blue conoidal envelope, extending from the wick or burner, and gradually thinning out towards the top of the flame; thirdly, a more or less luminous conoid, thin towards the bottom of the flame, where it is enveloped by the blue conoid, but thicker towards the top. And fourthly, a faintly luminous outer envelope, completely surrounding the other portions of the flame, and greatly developed towards the top.

In 1849 I presented to the Royal Society of Edinburgh a paper “On the Gradual Production of Luminous Impressions on the Eye.” The object of that communication was to investigate the laws of the production of visual impressions. The subject was then new; for although the fact that light requires a certain time to produce its full effect on the eye had been noticed at comparatively early periods, yet no one, so far as I am aware, had attempted to measure that time; and the whole subject of the production of visual impressions, regarded as a branch of experimental science, was quite untouched. I have frequently wished to resume a subject of inquiry which seems to me to merit more attention than it has hitherto received, and which I have not as yet been able to discuss so completely as I could have desired. Various portions of it demand more extended experiments. Among these may be specified, the examination of isolated impressions of shorter duration than my limited instrumental means had enabled me to observe; a more careful determination of the time required for light to produce its complete effect on the eye; and a series of observations on the eyes of various individuals, so that any personal peculiarity of vision, which might affect results derived exclusively from experiments on my own eye, might be eliminated. These, and other subjects of inquiry, I hope sooner or later to overtake; and, indeed, I had anticipated before the end of the present session of the Society to have been able to obtain some experimental results. In this I have been disappointed, owing to the instruments required for my observations having taken a much longer time to make than I had expected.

The rain experienced in January of this year has so much exceeded the average quantity, considerable as that is in the Lake District, that I have been led to consider it worthy of record, especially keeping in mind, that as regards risks from floods, it is not the ordinary, but the extraordinary that is to be guarded against in the construction of all works with which water is concerned as an element of danger.

It may not be amiss to premise, that the year preceding, as to weather, was chiefly remarkable for the mildness of the first quarter, for its high summer temperature, for the unusual cold experienced in November, and this succeeded by a mild December. January set in with weather of the same character, and was without any marked peculiarity, excepting its mildness, till the 9th, when rain commenced, and, with the exception of two or three days, continued to fall more or less heavily till the end of the month.

In a recent work of an elaborate kind, displaying much ability, its author, Dr Richardson, has endeavoured to prove that the cause of the coagulation of the blood is of a chemical nature, and referable to the escape of a volatile matter, and that the volatile matter is ammonia.

It is not my intention at present to consider the various circumstances which he brings forward in favour of his conclusion. I shall restrict myself to a few observations which I have made, the results chiefly of trials instituted for the purpose of testing his speculations, and of satisfying myself, if possible, on the subject.

1. The first part of this paper describes the following groups of experiments:—

Group I. On the effect which roughening the surface of a body produces upon its radiation.

II. On the nature of that heat which is radiated by rock-salt, at 212°F.

III. On the radiation of glass and mica, at high temperatures.

The second, or theoretical portion, of the paper, has reference to the law which connects the radiation of a particle with its temperature, and to Dulong and Petit's experiments on this subject.

There is also an addition of a later date than the rest of the paper on General Diathermancy.

1. To find the numerical law according to which the temperature of a place varies with its latitude, is an empirical problem which has, since the middle of the last century, from time to time engaged attention.

2. Lambert, Mayer, and Kirwan in the last century, De Humboldt, Brewster, Kämtz, and Dove in the present, may be cited amongst those who have investigated formulæ which express, with more or less accuracy, the mean temperature of a place in terms of its latitude.

3. The formulæ proposed are mostly reducible to two types—a variation depending upon the cosine of the latitude simply (that of Sir D. Brewster), and one depending on the square of the same quantity (that of Mayer).

The following Memoir contains the results of researches made during the last three years. My investigations were originally directed to British lichens only, but they have subsequently and gradually embraced lichens from all parts of the world. The majority of Scotch species examined were collected by myself while on botanical tours in various parts of Scotland during the last ten years. Lowland species were collected chiefly in the counties of Perth, Edinburgh, and Dumfries; but also in Forfar, Fife, and others of the midland counties. In order to study alpine species I made a special tour among the highest of our Scotch mountains in the summer of 1856. I then visited the Braemar Highlands, Ben Lawers, Ben Nevis, and the Coollin Hills, in Skye. I have likewise studied the lichens of Don, now in the possession of Mr M'Nab, of the Ptoyal Botanic Garden, Edinburgh; the lichens collected by Maughan, M'Millan, and others, in the Herbarium of the Botanical Society of Edinburgh; those collected by the late Alexander Menzies, in the Menziesian Herbarium belonging to the Botanic Garden of Edinburgh; those collected by Borrer, Hooker, Carmichael, Gardiner, and others, in the magnificent Hookerian Herbarium at Kew; and I have also examined the valuable herbarium of the University of Edinburgh, under the care of Professor Balfour, and the herbarium of Dr Greville.