be considered a symbolical representation of that species of proportion.

Of quadrilateral superfices, the most simple is, the square formed by uniting the hypothenuse or side subtending to the right angle of two right angled Isosceles triangles, containing equal. It is also most perfect on account of the equality of its relations in

the same manner.

The rectangular parallelogram is founded by the similar union of two scaleni triangles of the same description.

A rhomb is the union of two equilateral triangles. A rhomboid of two right angled triangles, conjoined by the larger of those sides which contain the right angle; but in an inverted position.

Oi trilateral and quadrilateral figures, it is to be observed, that none are admissible into symbolical geometry, but those which in their respective lines and angles, bear the relation of equality or such integral proportions, as may be adequately expressed by some of the numerical terms of the tetractys, i. e. the numbers 1, 2, 3, 4.

We next proceed to the construction of multilateral figures. Having their sides and angles equal, these are invariably formed by the combination of as many acute angled triangles, as the figure has sides.-This class of forms, may be sufficiently illustrated by the pentagon, which resolves itself into five isosceles acute angled triangles; but there is one which requires particular notice; I mean the hexagon, which, being composed of six equilateral triangles, is equal, in all its relations, and retains the quality of being infinitely divisible into similar triangles, according to the geometrical projection observed in the divisions of that trilateral figure, and may, therefore, be considered as the most perfect of all multilateral forms.

From this enquiry, it results, that the three most perfect of all geometrical diagrams are the equilateral triangle, the square and the equal hexagon. To this we may add an observation, for which we are indebted to our grand master Pythagoras, that there exists no other regular equilateral forms, whose multiples are competent to fill up and occupy the whole space about a given centre which can only be effected by six equilateral triangles, four squares, and three equal hexagons. There are but five regular solids contained under a certain number of equal and similar superfices, which, from the use made of them in the Platonic philosophy, are usually denominated the five Platonic bodies. Those are,

A Tetracdron, or pyramid, contained under four equal and equilateral triangles, representing, according to the Platonists, the element of fire.

An Octaedron, contained under eight such triangles, repre

sents air.

An Aosaedron, under twenty such triangles, representing

water.

An Hexaedron, or cube, contained under six squares, and representing the earth.

A Dodehaedron, under twelve equal and equilateral pentagons, representing the whole system of the universe.

There remains yet another geometrical emblem to be explained which is the diagram of the 47th proposition of the first book of Euclid by the assistance of which, we prove that the square of the hypothenuse of a right angled triangle, that is, the opposite to right angle, is equal to the sum of the square of the sides which contain the right angle. For this discovery, we are likewise indebted to the great Master of the Pythagorean school. who is said to have offered a hecatomb, or sacrifice, of a hundred oxen, to express his joy and gratitude to heaven, on account of this discovery. And, indeed well might he estimate its value so highly, when we reflect, that, upon this principle, depends the solution of the great principles in the mathematical, mechanical and philosophical knowledge, and that it is the true key to the doctrine of the proportions and powers of all quantities, arithmetical, geometrical and algebraical. By it, we may prove any multiple of a given square, as we have only to construct an isosceles right angled triangles, of which one of the sides including the triangle shall be equal to the sides of such square. And in the same manner, it may be applied to form squares and other figures of duplicate ratios to others which are given. Accordingly, he was accustomed to distinguish this proposition by the appellation EUREKA, which signifies I have found it. Thereby, denoting the superior importance of this over all other discoveries. As, therefore, the letter G denotes to us the science of symbolical geometry, and the Pythagorean tetractys the mysterious powers of numbers, so is this symbol the representation of all mechanical and physical science.

But whilst each of those our symbols reciprocally serves to illustrate the rest, there is one sense, in which they yield to the de cided preeminence of the great central emblem, whose sacred initial character, surrounded by a blaze of eternal glory, recalls our minds, from the work to the architect, from the science to its mystery. This brings us to the moral advantages to be derived from Geometry.

Geometry is the first and noblest of sciences, and the basis on which the superstructure of Freemasonry is erected.

The contemplation of this science, in a moral and comprehensive view, fills the mind with rapture. To the true Geometrician, the regions of matter, with which he is surrounded, afford ample scope for his admiration, while they open a sublime field for his enquiry and disquisition.

Every blade of grass which covers the field, every flower which

blows, and every insect which wings its way in the bounds of expanded space, proves the existence of a first cause* and yields pleasure to the intelligent mind. The symmetry, beauty and order displayed in the various parts of animate and inanimate creation are pleasing und delightful themes, and naturally lead to the source. whence the whole is derivedt. When we bring, within the focus of the eye, the variegated carpet of the terrestial creation, and survey the progress of the vegetative system, our admiration is justly excited. Every plant which grows, every flower that displays its beauties or breathes its sweets, affords instruction and delight. When we extend our views to the animal creation and contemplate the varied clothing of every species, we are equally. struck with astonishment! and when we trace the lines of Geometry, drawn by the divine pencil, in the beautiful plumage of the feathered tribe, how exalted is our conception of the heavenly work! The admirable structure of plants and animals, and the infinite number of fibres and vessels which runs through the whole, with the apt disposition of one part to another, is a perpetual subject of study to the true geometrician, who, while he adverts to all the changes, which all undergo in their progress to maturity, is lost in rapture and veneration of the great cause which produced the whole, and governs the sytsem. When he descends into the bowels of the earth, and explores the kingdom of ores, minerals and fossils, he finds the same instances of divine wisdom and goodness displayed in their formation and structure; every gem and pebble proclaims the handy work of an almighty creator.

When he surveys the watery element, and directs his attention to the wonders of the deep, with all the inhabitants of the mighty ocean, he perceives emblems of the same supreme intelligence The scales of the largest whale, as well as the pencilled shell of the most diminutive fish, equally yield a theme for his contemplation, on which he fondly dwells, while the symmetry of their formation, and the delicacy of tints, evince, to his discerning eye, the wisdom of the divine artist. When he exalts his view to the more noble and elevated parts of nature, and surveys the celestial orbs, how much greater is his astonishment! If, on the principles of geometry and true philosophy, he contemplates the sun, the moon. the stars, the whole conclave of heaven, his pride is humbled, and he is lost in awful admiration. The immense magnitude of those bodies, the regularity and rapidity of their motions, and the vast extent of space through which they move, are equally inconceivable; and as far as they exceed human comOf a cause, but why a first? R. C.

To matter, its motions, its varieties, its composition of varieties and its alternate decomposition. That is all, first, last, beginning, end, succession and samenes. R. C. Yes, but it is utterly, contrary to all experience to suppose that creating power to be intelligent, or a designing, thing like man. R. C.

prehension, baffle his most daring ambition, till lost in the immensity of the theme, he sinks into his primitive insignificance.

By Geometry, then, we curiously trace Nature through her various windings, to her most concealed recesses. By it, we discover the power, the wisdom and the goodness of the Grand Artificer of the universe, and view with delight the proportions which connect this vast machine. By it, we discover how the planets move in their different orbits and demonstrate their various revolutions. By it, we account for the return of the seasons and the variety of scenes which each season displays to the discerning eye. Numberless worlds are around us, all framed by the same divine artist, which roll through the vast expanse and are all conducted by the same unerring law.

A survey of nature and the observation of her beautiful proportions, first determined man to imitate the divine plan and study symmetry and order. This gave rise to societies and birth to every useful art. The architect began to design and the plans which he laid down, improved by experience and time, produced works which have been the admiration of every age.

To him, the great Geometrician of the universe, the father of light and life, the fountain of eternal wisdom let us humbly dedicate our labourers, imploring him to bless and prosper the work of our hands to his own glory and the good of mankind and the salvation of our immortal souls.

As far as I can perceive, it is rare, that such a lecture as I have copied is given in a masons lodge; but as I found it among my collection, under the head of lectures &c. for the second degree, and as it is all that is really good in masonry, I have copied at large. I am of opinion that one half of the masons in this Island could not give the most simple definition of the word geometry. I have now hardly space to introduce the form of closing the lodge and must defer further comment until the master's degree has been described.

FORM OF CLOSING A LODGE IN THE SECOND DEGREE.

The master knocks to order which is echoed by the two wardens. W. M. Brethren, assist me to close this Fellow Craft's Lodge. Brother Junior Warden, what is the constant care of every Fellow Craft Freemason?

J. W. To prove the lodge close tiled.

W. M. Direct that duty to be done.

J. W. Brother Inner Guard, you will prove the lodge close tiled. (The Inner Guard and the Tiler both give the Fellow Craft's three knocks.)

1. G. Brother Junior Warden, the lodge is close tiled.

J. W. (knocks and makes the sign.) Worshipful Master the lodge is close tiled.

W. M. Brother Senior Warden, the next care?

S. W. To see the brethren appear to order as Craftsmen.

W. M. To order brethren as Craftsmen.-Brother Junior Warden, in this character what have you discovered?

J. W. A sacred symbol.

W. M. Brother Senior Warden, where is it fixed?

S. W. In the centre of the building.

W. M. Brother Junior Warden, to what does it allude?`

J, W. To God the grand Geometrician of the universe.

W. M. Brethren, let us remember wherever we are and whatever we do, his all seeing eye beholds us and while we continue to act as faithful Fellow Craft Masons, let us never fail to discharge our duties towards him with fervency and zeal.-P. M. So mote it be.

1

W. M. Brother Senior Warden, our labours being closed in this degree, you have my command to close this Fellow Craft's Lodge (Gives the three knocks.)

S. W. In the name of the Grand Geometrician of the Universe and by the command of the Worshipful Master I declare this Lodge of Fellow Crafts duly closed. (Gives the knocks)

J. W. And it is accordingly so done. (With the knocks)

This, Sir, you will readily admit forms a fair and complete description of the Fellow Craft's, or second, degree in masonry. It is more free from frivolity and offensiveness than any other degree and though not wholly free, it has less of fable attached to it than any other degree.

I hope you will give me credit for the honesty of this revelation of the mysteries of masonry, and acknowledge, that, if man could not reveal to more good effect that a God, me should all have remained in a lamentable state of ignorance: we of the human race should have been beasts of the field and forest.

Yours in masonic instruction,
RICHARD CARLILE.

TO WILLIAM WILLIAMS, ESQ., M. P. PROVINCIAL GRAND MASTER OF THE ASSOCIATION OF FREEMASONS FOR THE COUNTY OF DORSET.

LETTER IV.

SIR,

Dorchester Gaol, July 21, Anno tenebræ 1825.

WE come now to a revelation of the ceremonies, &c., of the third degree of Freemasonry, which, in point of fact, is the last. All others, by whatever names or means supported, must be looked