As a simple case of entire transfer of force from A to B, it is evident that if A were allowed to ascend to the height due to its velocity, and if by any mechanical contrivance, of lever or otherwise, the body B were to be raised by the descent of A, their heights of ascent would be reciprocally as the bodies; consequently, that the square of the velocity to be acquired by the free descent of B, would be, to that of A, in the above-mentioned ratio, and the quantity of mechanic force so estimated would be preserved unaltered.

But, on the contrary, the momentum, which is in the simple reciprocal ratio of the bodies, would be increased by such means in the subduplicate ratio of the bodies that might be employed; and if momentum were really a force efficient in proportion to its estimated magnitude, it should not only be capable of reproducing the original quantity, but the additional force, thus acquired, might be employed for counteracting the usual resistances, and perpetual motion would be easily produced. But since the impetus, or mechanic force, remains unaltered, it is evident that the utmost that B could effect, in return, would be the reproduction of A's velocity, and restitution of its former force, neither increased nor diminished, excepting by the necessary imperfection of machinery.

The possibility of perpetual motion is consequently inconsistent with those principles which measure the quantity of force by the quantity of its extended effects, or by the square of the velocity which it can produce.

Since we can, at pleasure, by means of any mechanic force, consisting of a vis motrix extended through a given space, give motion to a body for the purpose of employing its impetus in the production of any sudden effect, or can, on the contrary, occasion a moving body to ascend, and thus resolve its impetus into a moving force ready to exert itself through a determinate space of descent, capable of producing precisely the same quantity of mechanic effect; the force depending on impetus may justly be said to be a force of the same kind as any other mechanic force, and may be strictly compared with them as to quantity.

In this manner, the author says, we may even compare the force of a body in motion, with the same kind of force contained in a given quantity of gunpowder, and may say that we have the same quantity of mechanic force at command, whether we have one pound of gunpowder, or the weight which it would raise to the height of 30 feet, actually raised to that height, and ready to be let down gradually; or the same weight possessing its original velocity of ascent, to be employed in any sudden exertion.

By employing the same measure, we have a distinct expression for the quantity of mechanic force given to a steam-engine by a peck or by a bushel of coals; and are enabled to compare its effect with the quantity of work which one or more horses may have performed in a day. In short, whether we are considering the sources of extended exertion, or of accumulated energy,-whether we compare the accumulated forces themselves by their gradual or their sudden effects,

the idea of mechanic force, in practice, is always the same, and is proportional to the space through which any moving force is exerted, or to the square of the velocity of a body in which such force is accumulated.

Mémoire sur les Quantités imaginaires. Par M. Buée. Communicated by William Morgan, Esq. F.R.S. Read June 20, 1805. [Phil. Trans. 1806, p. 23.]

Chemical Experiments on Guaiacum. By Mr. William Brande. Communicated by Charles Hatchett, Esq. F.R.S. Read December 19, 1805. [Phil. Trans. 1806, p. 89.]

No one of the resins, Mr. Brande observes, possesses so many curious properties as that called Guaiacum; and he thinks it remarkable, that although many of the alterations it undergoes, when heated with different solvents, have been mentioned by various authors, it has not excited a more particular attention.

After noticing its more obvious properties, of which we shall only repeat, that when pulverized, it is of a gray colour, but gradually becomes greenish by exposure to the air, he proceeds to examine the action of various solvents upon it.

The first solvent tried by Mr. Brande was water; about 9 per cent. of extractive matter was taken up, and the solution appeared also to contain a small portion of lime. Alcohol, which was next tried, dissolved nearly the whole of the guaiacum, leaving only about 5 per cent. of extraneous matter. The effects of water, of various acids, and of alkalies, upon this solution, are then noticed. Water forms a milky fluid, which passes the filter. Muriatic acid throws down an ash-coloured precipitate. Liquid oxymuriatic acid forms a precipitate of a pale blue colour. Sulphuric acid forms one of a pale green. Acetic acid does not form any precipitate; nor does nitric acid until after the expiration of some hours, unless water be added, in which case a precipitate may be sooner obtained. This precipitate is of a green or a blue colour; whereas that which forms spontaneously is brown. Alkalies do not form any precipitate when added to the solution of guaiacum in alcohol.

Guaiacum is less soluble in sulphuric ether than in alcohol, but the properties of the two solutions are nearly similar.

Muriatic acid dissolves only a small portion of guaiacum. Sulphuric acid forms with that substance a deep red liquid, which, when fresh prepared, deposits a lilac-coloured precipitate on the addition of water. The effects of nitric acid on guaiacum are minutely examined, of which we shall only mention, that this acid, when its specific gravity was 139, completely dissolved guaiacum, which solution, after standing some hours, deposited a quantity of crystallized oxalic acid; but when the nitric acid was diluted, a slight effervescence took place, and a part only of the resin was dissolved, the remainder being converted into a brown substance, which was similar

to the brown precipitate obtained, by nitric acid, from the solution of guaiacum in alcohol, and possessed the properties of a resin in greater perfection than guaiacum itself. If successive portions of nitric acid be added to the above-mentioned residuum, or if a large quantity of that acid is employed so as to form a complete solution, a product may be obtained, by evaporation, which is equally soluble in water and in alcohol; both which solutions have an astringent bitter taste.

Guaiacum is soluble in the pure and in the carbonated alkalies. The precipitates formed from these solutions, by dilute sulphuric acid and by muriatic acid, were of a flesh colour, and approached to the nature of extract; being less acted upon by sulphuric ether, but more soluble in boiling water than guaiacum.

Mr. Brande now proceeds to the analysis, by distillation, of the substance here treated of. By this method he obtained, from 100 grains, the following products:

Acidulated water..

Thick brown oil, becoming turbid on cooling

Thin empyreumatic oil

Coal remaining in the retort

Mixed gases, chiefly carbonic acid and carbonated
hydrogen....

The coal, on incineration, yielded four grains of lime, but no alkali could be discovered.

From the foregoing experiments it appears, that although guaiacum possesses many of the properties common to resins, it differs from them in the following circumstances.

1. By affording a portion of vegetable extract.

2. By the alterations which take place in it when submitted to the action of bodies which readily communicate oxygen, such as nitric and oxymuriatic acids, and by the rapidity with which it is dissolved in the former.

3. By being capable of being converted into a more perfect resin, in which it resembles the green resin that constitutes the colouring matter of leaves.

4. By yielding oxalic acid.

5. By the quantity of charcoal and lime obtained from it by distillation.

These circumstances, the author says, shows that guaiacum differs not only from the substances denominated resins, but also that it differs from those which are called balsams, gum-resins, gums, and extracts; and he thinks we may, for the present, consider guaiacum as composed of a resin, modified by the vegetable extractive principle, so that it may perhaps, without impropriety, be defined by the term Extracto-resin.

In a postscript Mr. Brande observes, that the action of oxygen on some other resinous bodies is very remarkable. By digesting mastic

in alcohol, a partial solution is formed, leaving an elastic substance, which is said to possess the properties of caoutchouc, but which becomes hard by exposure to the air.

The author has remarked, that the portion of mastic dissolved in the alcohol may be precipitated from it by water, and that this precipitate possesses the properties of a pure resin; but when a stream of oxymuriatic acid gas was passed through the solution, a tough elastic substance was thrown down, which became brittle when dry: this precipitate was soluble in boiling alcohol, but separated from it as the solution became cool. Its properties, therefore, approached in some measure to those of the original insoluble part.

On the Direction of the Radicle and Germen during the Vegetation of Seeds. By Thomas Andrew Knight, Esq. F.R.S. In a Letter to the Right Hon. Sir Joseph Banks, K.B. P.R.S. Read January 9, 1806. [Phil. Trans. 1806, p. 99.]

It is, Mr. Knight observes, very well known, that in whatever position a seed is placed to germinate, its radicle always makes an effort to descend towards the centre of the earth, whilst the elongated germen takes a precisely opposite direction: and it has been proved by Du Hamel, that if a seed, during its germination, be frequently inverted, the points, both of the radicle and germen, will return to their first direction. These opposite effects have, by some naturalists, been attributed to gravitation; and Mr. Knight conceived, that if they really proceeded from that cause, those effects would take place only whilst the seed remained at rest, in the same position with respect to the attraction of the earth, and that the operation of gravitation would be suspended by a constant and rapid change of position in the germinating seed, and might be counteracted by the agency of centrifugal force. In order to determine how far the above opinion was well founded, he made the following experiments :

Having a strong rill of water passing through his garden, he contrived, by its means, to give motion, vertically, to a wheel of eleven inches diameter. Round the circumference of this wheel, several seeds of the garden-bean, which had been previously soaked in water, were bound in such a manner that their radicles were made to point in every direction. The wheel made rather more than 150 revolu

tions in a minute.

In a few days the seeds began to germinate, and Mr. Knight had the pleasure to see that the radicles, in whatever direction they were protruded, turned their points outwards from the circumference of the wheel, and in their subsequent growth receded still further from it. The germens, on the contrary, took the opposite direction; and in a few days their points met at the centre of the wheel. Three of these plants were suffered to remain on the wheel; their stems soon extended beyond its centre, but their points returned, and met again at the centre.

As Mr. Knight conceived that some slight objections might be urged against the conclusions he was inclined to draw from the above experiment, he repeated it in a different manner, by adding to his former apparatus another wheel, also of eleven inches diameter, which moved horizontally, and to which he could give different degrees of velocity. Round the circumference of this horizontal wheel, seeds of the garden-bean were bound, as in the former experiment, and the wheel was made to perform 250 revolutions in a minute. The effect produced by this motion soon became obvious; for the radicles now pointed downwards about ten degrees below the horizontal line of the wheel's motion, whilst the germens pointed the same number of degrees above it: but when the motion of the wheel was diminished to 80 revolutions in a minute, the radicles pointed about 45 degrees below the horizontal line, and the germen as much above it; the one always receding from the axis of the wheel, the other approaching to it.

The foregoing experiments, the author thinks, prove that the radicles of the germinating seeds are made to descend, and the germens to ascend, by some external cause, and not by any power inherent in vegetable life; and he sees little reason to doubt that gravitation is the principal if not the only agent employed in this case by nature. The radicle, he says, is increased in length only by parts successively added to its point; whereas the germen, on the contrary, is elongated by a general extension of its parts previously organized; and its vessels and fibres appear to extend themselves in proportion to the quantity of nutriment they receive. When the germen deviates from a perpendicular direction, the sap accumulates on its under side; and consequently, as the vessels and fibres on that side elongate more rapidly than those of the upper side, the point of the germen must always turn upwards. This increased elongation of the vessels and fibres of the under side produces also the most extensive effects in the subsequent growth of the trunks and branches of trees. The immediate effect of gravitation, Mr. Knight says, is to occasion the depression of the branches; but, by the above-mentioned increased longitudinal extension of the under side, their depression is prevented, and they are even enabled to raise themselves above their natural level.

The

It has, however, been objected by Du Hamel, that gravitation can have little influence on the germen when it points perpendicularly downwards. To obviate this objection, Mr. Knight made many experiments on the seeds of the horse-chestnut and of the bean. result was, that the radicle of the bean, when made to point perpendicularly upwards, formed a considerable curvature in the course of a few hours. The germen was more sluggish; but, in spite of any efforts made by the author to prevent it, constantly changed its direction in less than twenty-four hours.

It may also, Mr. Knight says, be objected, that few of the branches of trees rise perpendicularly upwards, and that their roots always spread horizontally. Respecting the first of these objections, he ob