The common series for the rectification of the ellipse is

where p represents the semicircumference of the circle, and e the excentricity of the ellipse. The series which this author has invented, and which has the advantage of a quicker convergency, is

:

The first step to obtain this series is made by supposing the quantity (a+b2-2ab. cos. z)" A+B cos z+C cos 2% + &c. and thence deducing the values of A and B if the semitransverse of the ellipse is 1, and z be the arc of the corresponding circle, then the fluxion of the arc of the ellipse is Z√1—1 cos1z or =√1—2—2 cos 2 z which, compared

-ε 2

with za+b-2ab cos 2z, gives the value of a and b ; and then, taking the whole fluent while z from becomes p, the length of the same ellipse is obtained.

The latter part of the memoir is concerning the evolution of the fraction (a2+b2-2ab cos q)-2 which occurs in computing the planetary disturbances.

A short mineralogical Description of the Mountain of Gibraltar. By Major Imrie.

We wish that this description had been given in simpler language. Many of the words appear to us to be exotics.-The remarks concerning the fossil bones, however, are worthy of notice :

It only now remains for me to mention what are generally called the fossil bones, found in the rock of Gibraltar. These have been much talked of, and by some looked upon as a phænomenon beyond the power of explanation. The general idea, which exists concerning them, is, that they are found in a petrified state, and inclosed in the solid calcareous rock; but these are mistakes, which could only arise from inaccurate observation and false description.

In the perpendicular fissures of the rock, and in some of the caverns of the mountain, (all of which afford evident proofs of their former communication with the surface,) a calcareous concretion is found, of a reddish brown ferruginous colour, with an earthy fracture, and considerable induration, inclosing the bones of various animals, some of which have the appearance of being human. These bones are of various sizes, and lie in all directions, intermixed with shells

of

of snails, fragments of the calcareous rock, and particles of spar; all of which materials are still to be seen in their natural uncombined states, partially scattered over the surface of the mountain. These having been swept, by heavy rains at different periods, from the surface into the situations above described, and having remained for a long series of years in those places of rest, exposed to the permeating action of water, having become enveloped in, and cemented by, the calcareous matter which it deposits.

The bones, in this composition, have not the smallest appearance of being petrified; and if they have undergone any change, it is more like that of calcination than that of petrifaction, as the most solid parts of them generally admit of being cut and scraped down with the same ease as chalk.

• Bones combined in such concretions are not peculiar to Gibraltar: they are found in such large quantities in the country of Dalmatia, and upon coasts in the islands of Cherso and Osero, that some naturalists have been induced to go so far as to assert, that there has been a regular stratum of such matter in that country, and that its present broken and interrupted appearance has been caused by earthquakes, or other convulsions, experienced in that part of the globe. But, of late years, a traveller, (Abbé ALBERTO FORTIS,) has given a minute description of the concretion in which the bones are found in that country: and by his account it appears, that with regard to situation, composition and colour, it is perfectly similar to that found at Gibraltar. By his description it also appears, that the two mountain rocks of Gibraltar and Dalmatia consist of the same species of calcareous stone; from which it is to be presumed, that the concretions in both have been formed in the same manner and about the same periods.

Perhaps if the fissures and caves of the rock of Dalmatia were still more minutely examined, their former communications with the surface might yet be traced, as in those described above; and, in that case, there would be at least a strong probability, that the materials of the concretions of that country have been brought together by the same accidental cause, which, in my opinion, has collected those found in the caverns of Gibraltar. I have traced, in Gibraltar, this concretion, from the lowest part of a deep perpendicular fissure, up to the surface of the mountain. the concretion became less firmly combined, and, when it had no As it approached to the surface, covering of the calcareous rock, a small degree of adhesion only remained, which was evidently produced by the argillaceous earth, in its composition, having been moistened by rain and baked by the

sun.'

Description of a Thermometer, which marks the greatest Degree of Heat and Cold, from one Time of Observation to another, and may also register its own Height at every Instant, By Alexander Keith, Esq. F. R. S. & F. A. S. Edin.

This thermometer is intended as an improvement on the one which was invented by Mr. Six, which shews the greatest rise or fall from one period of observation to another. The invention

II

invention of Mr. Keith appears to be a very ingenious one, and adequate to the end proposed. Is it not, however, liable to the objection under which that of Mr. Six has fallen, that it requires too delicate workmanship to be fit for common use?

Description of a Barometer, which marks the Rise and Fall of the Mercury from two different Times of Observation. By

the Same.

The contrivance for indicating the greatest rise or fall is the same as in the thermometer.

Meteorological Abstract for the Years 1794, 5, and 6.-The mean temperature of 1794 was greater than in ordinary seasons by almost 2°: but, falling chiefly in the winter months, it was not attended with any particular advantage. The rain that fell was 28.73 inches.The commencement of 1795 was remarkable for severe and continued cold: the thermometer being at 8 P. M. 22d Jan. at 141: but the medium, during 52 or 53 days, was 29° 6. with remarkable fluctuations: the rain amounted to 35.729 inches.-The winter of 1796 was peculiarly mild; the thermometer standing, for 10 days in the middle of January, above 50° day and night. The whole year was remarkable for dryness, the fall of rain being only 19.395 inches.

LITERARY CLASS.

On the Origin and Principles of Gothic Architecture. By Sir James Hall, Bart. F. R. & A. S. S. Edin.

This essay is the precursor of a more comprehensive one which the author destines to the same subject; in this, however, are contained his fundamental principles of the theory of Gothic Architecture. Of the origin of this style of building, formerly despised from wrong motives, and since commended inconsiderately and beyond its deserts, whose beauties must be felt, and whose conveniences cannot be demonstrated, we have small and imperfect knowlege :-but, in the free and wide field of conjecture, many theories have been advanced, all resting on a very small basis of acknowleged truth, yet more or less supported by facts and rational hypothesis. In such theories, the object has been to deduce the pecuKarities of the Gothic architecture from some simple principle; and to shew the idea which so predominates, as to make that a regular system, which might otherwise appear to be a mass of parts and ornaments, fancifully and capriciously formed and put together.

The prominent characteristics of the Gothic style are the clustered pillar and the pointed arch. The origin of the latter

has

has been differently assigned: it has been referred to the form which the tops of an alley of trees assume; to the shape of the whale's jaw-bone; and to the intersection of circular arches. The origin discovered by the present writer, and the circumstances which led to it, are thus related:

I was first led by Mr. Byres, a very respectable member of this Society, to observe, among the remains of antiquity at Rome, many beautiful examples of the application of these principles by the ancients; and though my view of the subject was then very obscure, the theoretical solution of the question not having occurred till long after, I was fully aware of the very great practical advantages which they had derived from the employment of the principle of imitation.

Occupied with this view of ancient art, as I was travelling through the western provinces of France, in my return from Italy, in the end of 1785, I was struck with the beauty of many Gothic edifices, which, far from appearing contemptible, after the masterpieces of art I had seen in Italy and Sicily, now pleased me more than ever. I was thus induced to believe, that those extensive works, possessed throughout of so peculiar a character, and so eminent for unity of style, could not have been carried on, unless the architects who built them, like those of ancient Greece, had been guided in their execution, by some peculiar principle; and being dissatisfied with all the theories of the art which I had heard of, Ï undertook the investigation, which has given rise to the following Essay *.

Conceiving that some rustic building, differing widely from the Grecian original, might have suggested the Gothic forms, I had made it my business to search for such a one, when the following accidental circumstance greatly assisted my speculations.

It happened that the peasants of the country through which I was travelling were then employed in collecting and carrying home the long rods or poles which they make use of to support their vines, or to split into hoops; and these were to be seen, in every village, standing in bundles, or waving, partly loose, upon carts. It occurred to me, that a rustic dwelling might be constructed of such rods, bearing a resemblance to works of Gothic architecture, and from which the peculiar forms of that style might have been derived t.

This

After stating my own views at full length, I shall enumerate and examine the various opinions of others on the subject of Gothic architecture, no less than five in number. At the time here alluded to, 1 was acquainted with an opinion, which I have since found to have originated with Dr. Warburton, that the Gothic style was copied from an alley of trees. I was aware of the advantages of this theory in some essential points, yet it always appeared to me unsatisfactory in many others; and I conceive it to be at best far too vague to serve as a guide to the artist.

This resemblance, though very obvious in many cases, has not, to my knowledge, been observed by any one but the late Mr. Grose;

This conjecture was at first employed to account for the main parts of the structure, and for its general appearance only; but after an investigation carried on, at different intervals, during the course of these eleven years, with the assistance of some friends, both in the collection of materials, and in the solution of difficulties, I have been enabled to reduce even the most intricate forms of this elaborate style to the same simple origin.

In the present state of the question, the following inquiry must be considered as falling under the denomination of, what is called by Mr. Stewart," Theoretical History," and by some French authors, "Histoire raisonée;" being an attempt to trace by conjecture, the steps through which an art has passed, in attaining the state in which we observe it. Indeed it is probable, that few investigations have been undertaken, which more completely correspond to that definition, since, in most subjects of this kind, many steps of the progress are known, and nothing is required but to fill up, by theory, the interval between them; whereas, in the present case, as all direct testimony is wanting, and as no steps of the actual progress of the art have come to our knowledge, our opinions on the subject, hitherto, can only amount to presumptions, founded upon the correspondence of the theory with the monuments of the art now in existence; and, the more numerous and complicated the cases are, in which this coincidence takes place, the greater probability there is in favour of the system.

But, though such be the actual situation of the inquiry, we may hope to see it, hereafter, assume a different form; for, should the conjecture, brought forward in the following Essay, carry with it sufficient plausibility to excite a spirit of research among persons best qualified to pursue the subject, there is reason to expect, that discoveries may be made, of a literary or architectural nature, by which its truth or falsehood will be established beyond dispute.

What has just been said will, it is hoped, serve as my apology for having advanced a system, which, strictly speaking, is founded on conjecture alone; and, on the other hand, for having enumerated a multitude of particulars, many of which might justly be considered as superfluous, were the theory supported by direct testimony."

Without the aid of plates, we are unable to follow the author in the farther illustration of his theory. His readers, according

to whom it seems to have occurred in a transient way. He makes use of the shape of a bower to assist his description of a Gothic roof, (Antiquities of England and Wales, p. 75.); but he does not go so far as to ascribe the architectonic forms to this origin; a view which, probably, would not have escaped him, had he not been preoccupied with a different one; for he considers the rudiments of a Gothic arch as formed" of two flat stones with their tops inclined to each other, and touching." I did not meet with this passage till several years after I had undertaken the present inquiry, and had carried it a considerable length.'

Biographical Account of Mr. Smith.'

to