The mineral, of which I have the honour to lay an account before the Society, was brought to Edinburgh in considerable quantity about six years ago by a dealer in fossils, though indeed it had found its way, long before this period, into one or two collections.

By some it was mistaken for fluor. Its great specific gravity, its fibrous appearance, and its quality of forming an insoluble substance with sulphuric acid, made it generally be received as the native carbonate of barytes. From a few experiments, I was led at that time to entertain some doubt of its being any form of barytes ; and for several years, when I filled the chemical chair in the University of Glasgow, I used, when I exhibited the mineral itself, to mention in my lectures such of its properties as I had discovered, and which indicated that it did not belong to the barytic genus.

Dear Sir,

Allow me at present to trouble you with a few general observations on natural history, which I had an opportunity of making while on a botanical excursion, with my friend Mr Anderson, to the Dutch colony of Demerary. Guiana is a country but little known in Europe, though its animals and vegetables have added considerably to the catalogue of natural productions. It is not however the organic kingdom which I mean at present to touch upon; all I aim at is to give you some idea of the face of the country, as leading to the knowledge of its formation and present state. It is not a field for the mineralogist, as its interior is unexplored. But to the geologist, who wishes to trace revolutions of the latest date, it is not uninteresting to contemplate such a recent and singular country as Guiana.

Several of my friends have suggested to me the propriety of publishing something of the kind now offered to the Society, observing, that the great brevity with which the Antecedental Calculus is written, and the very concise form in which it is delivered to the public, may lead some to form erroneous opinions respecting the principles on which it is founded. In compliance partly with their request, I have drawn up this short paper, which I hope will remove even the possibility of misconception on that head, and convince every intelligent reader, that the antecedental calculus has the same geometrical principles for its ground-work, that the formulæ in the Universal Comparison themselves have, from which I originally derived it more than twenty years ago.

In the second volume of the Asiatic Researches, an extract is given from the Surya Siddhanta, the ancient book which has been long, though obscurely, pointed out as the source of the astronomical knowledge of the Brahmins. The Surya Siddhanta is in the Sanscrit language: It is one of the Sastras, or inspired writings of the Hindoos, and is called the Jyotish, or Astronomical, Sastra. It professes, as we learn from Mr Davis, the ingenious translator, to be a revelation from heaven, communicated to Meya, a man of great fanctity, about four millions of years ago, toward the close of the Satya Jug, or of the Golden Age of the Indian mythologists; a period at which man is said to have been incomparably better than he is at present; when his stature exceeded twenty-one cubits, and his life extended to ten thousand years.

The nature of those mathematical propositions, which were called Porisms by the ancient geometers, is now no longer a matter of uncertainty. The relation which they bear to other mathematical truths, the way in which they may at first have been observed, the kind of analysis to be employed in their investigation, their application to the solution of problems, have all been considered by some eminent mathematicians of the present age.

Dear Sir,

Some time ago I promised to send you the result of a series of observations, made to determine the situation of this place. Having, however, been much hurried of late, I am only able at present to transmit you the determination of the latitude, deduced from a series of observations of the sun's meridian zenith distances. With respect to the longitude, as soon as it is in my power, I will reduce some observations of occultations, and of the late solar eclipse, and send you the results.

Dear Sir,

I now sit down to give you some account of the little hydrostatical lamp, which I so briefly mentioned to you in a former letter. As I am far from being fure whether what I have to offer upon this subject may be entitled to the notice of the Edinburgh Royal Society, so I will refer this point to your determination, after you have had leisure to consider the contents.

Dear Sir James,

I Send under cover the representation of a very singular Halo of the Moon, (See Pl. V,), seen here on the night of the 18th of February last, about 10 o'clock, and this I have hitherto delayed, in order, if possible, to gain farther information in the neighbourhood concerning it.

During the short continuance of the small halo, which did not exceed 10 minutes after I got notice of it, I could not lay my hands on any other instrument to take the angles, but a Sisson's theodolite, which, unluckily, having been constructed so as not to admit of a vertical angle so great as the moon's altitude then was, I laid it aside, not recollecting that it might have measured several of the smaller angles. But I observed sundry marks, from which I took the angles as exactly as I could next day.

Dear Sir,

Having, as you know, bestowed a good deal of time and attention on the study of that part of physical astronomy which relates to the mutual disturbances of the planets, I have, naturally, been led to consider the various methods of resolving the formula (a2 + b2 − 2ab cos θ)2 into infinite series of the form A + B cos θ + C cos 2θ + &c. In the course of these investigations, a series for the rectification of the ellipsis occurred to me, remarkable for its simplicity, as well as its rapid convergency. As I believe it to be new, I send it you, inclosed, together with some remarks on the evolution of the formula just mentioned, which, if you think proper, you may submit to the consideration of the Royal Society.

The mountain of Gibraltar is situated in 36° 9' north latitude, and in 5° east longitude from Greenwich. It is the promontory which, with that of Ceuta upon the opposite Coast of Barbary, forms the entrance of the Straits of Gibraltar from the Mediterranean; and Europa Point, which is the part of the mountain that advances most towards Africa, is generally regarded as the most southern promontory in Europe. The form of this mountain is oblong; its summit a sharp craggy ridge; its direction is nearly from north to south; and its greatest length, in that direction, falls very little short of three miles. Its breadth varies with the indentations of the shore, but it no where exceeds three quarters of mile. The line of its ridge is undulated, and the two extremes are somewhat higher than its centre.