will be unable to appreciate their merit, even with the help of the 'plates which accompany them.

We are lastly, in this class, presented with a communication from Mr Prior of Nessfield, near Skipton in Craven, Yorkshire, giving an account of a Larum applicable to Pocket Watches. It requires some little knowlege of the construction of a watch to employ this machine, though, as Mr. P. remarks, it has but one wheel in it:-the main spring is wound up and stopped by a method entirely new; and it will be very useful to watch-makers, clock-makers, and others.

COLONIES AND TRADE.

A Letter from Dr. Roxburgh, of Calcutta, the well known corresponding member of the Society, accompanied Specimens of the Aldacay or Caducay Galls, with which the yellow colour in the Indian Chintzes is formed. We shall extract from this paper the author's account of these Galls, and his subsequent hints on other unknown treasures of the East:

The tree which produces the yellow my rabolans, mentioned in the foregoing passage, also yields a species of galls, of a very irregular shape and yellowish colour. When fresh they are lighter coloured, and darken by age, until they become dark brown, or nearly black. On the coast of Coromandel, where they seem to be better known than in Bengal, they are called Aldacay by the Telingas, and by the Tamuls, Caducay. I have never ventured so far in amongst the mountains as where the galls are found; but, from the information I have been able to collect, it seems that an insect punctures and deposits its eggs in the young tender leaves of the tree, which causes them to swell into the various forms the galls assume.

They are sold in every market, being one of the most useful dying drugs the natives know. Their best and most durable yellow is dyed with them, and fixed with alum. With ferruginous mud they are used to dye black. They are also the chintz painters best yellow. Their astringency seems to be greater than that of the fruit, as an ink made with them resisted the weather longer than that which was made with the pulp which covers the nuts. I am inclined to think they are the Faba Bengalensis of our old Materia Medica writers.

Upon the leaves of this tree I have found an insect, which I take to be the larva of a coccus, or chermes; they are about three eighths of an inch long, and a quarter of an inch broad; flat below, convex above, and composed of twelve annular segments. The whole insect is replete with a bright yellow juice, which stains paper of a very deep and rich yellow colour. Could these insects be collected in any quantity, I am inclined to think they might prove as valuable a yel low dye as the cochineal is a red.

I beg, Sir, you will inform the Members of the Society, that it will yield me particular pleasure, to be in any shape instrumental in bringing under their notice as many, as in my power, of the numerous treasures, yet little known, with which this extensive empire

abounds;

abounds; which, through their means, must essentially conduce to the advancement of arts, manufactures, and commerce; and, in the mean time, I beg leave to draw the attention of the Society to the following objects:

First.-Resins, commonly called dammer in India. They are the produce of various trees, and, when boiled up with oil, are used instead of pitch, in the marine yards throughout India.

Second. A drying oil, or very thin balsam, extracted, by incision, from the trunk of a large tree, which I have called Oleoxylon Bal samifera. It grows abundantly in Chittagong, and is chiefly used in painting.

Third.-Vegetable substances, and their extracts containing the tanning and astringent principles, abound in India, probably more than in any other country in the world.

Fourth.-Substitutes for hemp and flax are numerous over Asia. In my essay on these, above twenty are already enumerated. If found to answer, of which there is little doubt if put to the test of fair experiment, they might soon form a considerable addition to the export trade of these countries, and of use to the manufactures of the mother country. This appears to be a most important object, deserving the greatest encouragement, even when on the best of terms with Russia.

Fifth. The coarse silks, spun by the wild tussah and domestieated Berinda worms. The latter is soft as shawl wool, and incre. dibly durable.

Sixth. The very fine, delicate, silky wool, the produce of the two trees, bombax pentandria and heptaphylla, if still found unfit for the loom, might answer for hats, or some other such purpose, where the very softest hair of animals is employed.'

This industrious naturalist is intitled to the thanks of his country.

From Upper Canada, a letter was received from Mr. Hughes, giving an account of the Culture of Hemp in that province. It is stated that two acrcs and half of a black loamy clay soil, after two ploughings, was sown broadcast with hemp seed about the middle of May 1803; that the hemp produced on this piece of ground was plucked about the middle of August; and that the produce amounted to 1843 pounds avoirdupoise weight.

The concluding paper contains a letter from Mr. Vondenwelden of Quebec, containing a brief description of the Cotonnier or cotton plant; and a suggestion that the silky substance, which it produces, may be profitably employed in the manufacture of writing-paper, by being mixed with linen or other rags. The remainder of the volume consists, as usual, of Lists of the Rewards bestowed by the Society, of presents received in books and models, of the officers, and of the subscribing members.

Facing the title, is placed a portrait of Thomas Hollis, Esq. of Corscombe in the County of Dorset; and the preface commences with a brief notice of this respectable character. At the end, equally concise mention is made of that ingenious and truly classical artist James Barry, Esq. who died on the 26th of February, 1806, in the 65th year of his age; whose remains lay in state in the Society's great room, decorated by his immortal labours, and were interred in St. Paul's Cathedral between those of Sir Chistopher Wren and Sir Joshua Reynolds.

These volumes of Transactions certainly include a great variety of useful matter: but if the Society were disposed, it might be easily exhibited in a more compressed form.

ART. III. A Treatise on the Teeth of Wheels, Pinions, &c. demonstrating the best Forms which can be given to them for the various Purposes of Machinery: such as Mill-work, Clock-work, &c. and the Art of finding their Numbers. Translated from the French of M. Camus, with Additions. Illustrated by fifteen Plates. 8vo. 10s. 6d. Boards. Taylor.

THE

"HE translator has deemed it proper to usher in the treatise of his author with a preface, which, if it reminds us of the importance of the subject, does not convince us of the mathematical competency of the writer: for he says that the perfection of the most simple as well as the most complicated. engines, depends almost entirely upon the due action of the teeth of the wheels with each other; or in other words, on the best form for ensuring their proper action with the least friction, and of course with the least wear and loss of power.' Now if we understand the work before us, the least friction is not the circumstance either accomplished or attempted in the epicycloidal form of teeth, but equable angular motion. No form can be given to teeth, so that both these advantages shall be obtained; and therefore, if we wish to investigate the form by which friction shall be avoided, we must suppose the angular motion to vary not uniformly: which uniformity, however, is preserved in De la Hire's and Camus's constructions. That it is an equable or uniform angular motion which is sought in M. Camus's investigations, one of the first passages in the work will prove: We may consider as the best form that can be given to the teeth of the wheels of any machine, that which will cause these teeth to be always, in regard to each other, in situations equally favourable; and which consequently will give the machine the property of being moved uniformly by a power constantly equal.'

After

After having premised the definition of certain technical terms, the author proceeds to shew what will be the ratio of the forces, when the wheels act on each other by means of their teeth, with the forces when the wheels act by contact, or by teeth infinitely small. This ratio, assuming a general form for the teeth, is variable; and the inquiry is to be directed towards that form with which this ratio shall be constant.

If we join the centres C, O, of the two wheels A, B, and divide the line joining the centres, in the ratio which the number of teeth in wheel A ought to have to the number in the wheel B, and call the point of division D, then a line drawn perpendi'cularly to the common tangent of two teeth in contact will intersect the line of the centres in some point, E; and the forces, of which we have spoken, will be to each other as CD. EO: OD EC.

The best form of teeth being that in which the perpendicular to the parts of the teeth in contact passes through the same point E, the inquiries of M. Camus in the 22d page are directed towards such form; and he accordingly explains the manner in which Epicycloids and Hypocycloids may be generated for in these curves a perpendicular to the tangent at the point of contact will always pass through the same point in the line of the centres, the generating circle being the same for the two basis circles, the radii of which circles are proportional to the angular velocities of the wheels. If the two basis circles remain the same, and the generating circle vary, different epicycloidal curves will be generated; all (under certain limitations) producing equable motion. In a certain value of the radius of the generating circle, (when it is equal to half the radius of the circle within which it revolves,) the hypocycloid becomes a right line tending to the centre of the wheel. In another case, the hypocycloid becomes nearly a point; that is, when the radius of the basis circle becomes nearly equal to the radius of the wheel. It is easy to see to what cases, in practice, these two forms will apply.

M. De la Hire preceded M. Camus in his reasonings and demonstrations; and in his tract De l'Usage des Epicycloides dans les Méchaniques, he taught that the teeth of wheels for the production of equable motion should possess an epicycloidal form. The demonstrations of De la Hire are by no means concise, nor very perspicuous; and M. Camus has not much improved on his model.-Neither of these gentlemen, indeed, has considered the subject in all its extent and variety. Epicycloidal curves possess not solely the property of imparting equable motion: equable motion may be effected in an infinite number of ways; " et quoniam," says Euler, " hoc infinitis modis prastari

præstari poterit, inde quovis casu eum, qui ad praxin maxime accommodatum videbitur, eligere licebit."

The investigation of the form that shall be most commodious for practice is of no small consequence; and although Euler distinctly perceived the proper and legitimate object of inquiry, yet he failed (except in one instance) in deducing from his analytical conclusions, simple and commodious constructions. Towards the end of his memoir, he shews, but not as a deduction from his differential formulæ, that the involute of a circle is a proper form for the tooth of a wheel: with such a figure, equable motion would be obtained; and such a figure admits of an easy mechanical description.

Euler's investigations are far more profound and scientific than those of either Camus or De la Hire: but they are more interesting to the analyst than useful to the mechanic; and their great author, probably passing on to other inquiries, has not derived from his formulæ all the advantages which may be obtained. Ought they not to comprehend all that Camus and De la Hire have done?

M. Camus has paid much attention to the interests of the practical mechanic; and if sufficient time be given to his descriptions and demonstrations,, he cannot fail to be understood but to the mathematician who is only slightly and moderately versed in the practice of demonstration, this author's reasonings and deductions will appear tediously dilated. In proving a simple case of equilibrium from the property of the lever, and in shewing that the virtual velocities of the weight and power are inversely as the weight and power, he consumes twenty pages. This is very unnecessary; for though every thing should be made clear, and no important step omitted, yet, after these conditions are observed, brevity becomes an excellence.-The description of the manner of generating epicycloids is sufficiently well executed: but we by no means are inclined to commend the transition from the preceding matter to these curves. The author no where distinctly states by what peculiar property these curves are subservient to the end which is to be attempted in the formation of the teeth of wheels.

In passing these censures, it is, however, our duty not to forget that the original of the present work was written fifty years ago. Since that time, mathematical science has been much extended and improved: authors now write with enlarged views, and aided by more powerful instruments of calculation; and as they address more enlightened readers, if they do not labour to be brief, they may yet be concise, and still

avoid