of the contraction of the arms, as was said concerning the body. The body and the arms admit of inflexions in all their parts; and that in all manner of ways. From the different degrees of extension, contraction, and inflexion, which the body and the arms of the polypus admit of, result a great variety of figures, which they can form themselves into.

These animals do not swim; they crawl upon all the bodies they meet with in the water; or on the ground, on plants, on pieces of wood, &c. Their most common position is, to fix themselves by their posterior end B, to something, and so stretch their body and arms forwards into the water.

They make use of their progressive motion, to place themselves conveniently, so as to catch their prey. They are voracious animals: their arms extended into the water, are so many snares which they set for numbers of small insects that are swimming there. As soon as any of them touches one of the arms, it is caught. The polypus then conveys the prey to its mouth, by contracting or bending its arm. If the prey be strong enough to make resistance, he makes use of several arms. A polypus can master a worm twice or thrice as long as himself. He seizes it, he draws it to his mouth, and so swallows it whole. If the worm come endways to the mouth, he swallows it by that end; if not, he makes it enter double into his stomach, and the skin of the polypus gives way. The size of the stomach extends itself, so as to take in a much larger bulk than that of the polypus itself, before it swallowed the worm. The worm is forced to make several windings and folds in the stomach, but does not keep there long alive; the polypus sucks it, and after having drawn from it what serves for his nourishment, he voids the remainder by his mouth, and these are his excrements. According as the weather is more or less hot, the polypus eats more or less, oftener or otherwise.

They grow in proportion to what they eat; they can bear to be whole months without eating, but then they waste in proportion to their fasting.

The observations in the Philos. Trans. principally concern the manner in which these polypi multiply. What is there said of them is true and exact. The more we search into the manner how a polypus comes from the body of its parent,. the more we are persuaded that it is done by a true vegetation. There is not on the body of a polypus any distinguished place, by which they bring forth their young. M. T. had some of them, that greatly multiplied under his eyes,

and of which he can almost say, that they have produced young ones from all the exterior parts of their body.

A polypus does not always put forth a single young one at a time; it is a common thing to find those which produce five or six: he had some which put forth nine or 10 at the same time, and when one dropped off, another came in its place. These animals seem so many stems, from which issue many branches. He learned by a continual attention to two species of them, that all the individuals of these species produce young ones.

He next proceeds to the singularities resulting from the operations he tried upon them. If the body of a polypus be cut into two parts transversely, each of those parts becomes a complete polypus. On the very day of the operation, the first part, or anterior end of the polypus, that is, the head, the mouth, and the arms, lengthens itself, it creeps and eats.

The second part, which has no head, gets one: a mouth forms itself, at the anterior end, and shoots forth arms. This reproduction comes about more or less quickly according as the weather is more or less warm. In summer, he has seen arms begin to sprout out 24 hours after the operation, and the new head perfected in every respect in a few days. Each of those parts thus becomes a perfect polypus, performs absolutely all its functions. It creeps, it eats, it grows, and it multiplies; and all that, as much as a polypus which never had been cut.

In whatever place the body of a polypus is cut, whether in the middle, or more or less near the head, or the posterior part, the experiment has always the same success. If a po Typus be cut transversely, at the same moment, into three or four parts, they all equally become so many complete ones.

The animal is too small to be cut at the same time into a great number of parts; he therefore did it successively. He first cut a polypus into four parts, and let them grow; next he cut those quarters again; and at this rate he proceeded, till he had made 50 out of one single one; and here he stopped, for there would have been no end of the experiment. He has several parts of the same polypus, cut into pieces about a year before; since which time they have produced a great number of young ones.

A polypus may also be cut in two lengthways. Beginning by the head, one first splits the head, and afterwards the stomach the polypus being in the form of a pipe, each half of what is thus cut lengthways forms a half-pipe; the anterior extremity of which is terminated by the half of the head, the

half of the mouth, and part of the arms. It is not long before the two edges of those half-pipes close, after the operation. They generally begin at the posterior part, and close up by degrees to the anterior part. Then each half-pipe becomes a whole one, complete: a stomach is formed in which nothing is wanting, and out of each half-mouth a whole one is formed also..

He has seen all this done in less than an hour; and that the polypus, produced from each of those halves, at the end of that time did not differ from the whole ones, except that it had fewer arms; but in a few days more grew out. He has cut a polypus lengthways, between seven and eight in the morning, and between two and three in the afternoon each of the parts has been able to eat a worm as long as itself..

If a polypus be cut lengthways, beginning at the head, and the section be not carried quite through, the result is, a polypus with two bodies, two heads, and one tail. Some of those bodies and heads may again be cut lengthways, soon after. In this manner he has produced a polypus that had seven bodies, as many heads, and one tail. He afterwards at once cut off the seven heads of this new hydra: seven others grew again; and the heads that were cut off became each a complete polypus.

He cut a polypus transversely, into two parts: he put these two parts close to each other again, and they re-united where they had been cut. The polypus, thus re-united, ate the day after it had undergone this operation: it afterwards grew, and multiplied.

He took the posterior part of one polypus, and the anterior of another, and brought them to re-unite in the same manner as the foregoing: next day, the polypus that resulted, ate⚫ it had continued well two months after the operation; grew, and put forth young ones, from each of the parts of which it was formed. The two foregoing experiments do not always succeed: it often happens that the two parts will not join again.

To comprehend the following experiment, we should recollect, that the whole body of a polypus forms only one pipe, a sort of gut, or pouch. He has been able to turn that pouch, that body of the polypus, inside outwards; as one may turn a stocking. He had several by him, that have remained turned in this manner: their inside is become their outside, and their outside their inside: they eat, they grow, and they multiply, as if they had never been turned.

Concerning the wonderful Increase of the Seeds of Plants, e. g. of the Upright Mallow. By JOSEPH HOBSON of Macclesfield. In the upright mallow, the seeds being disposed in rings, Mr. H. counted those which were on the principal stems, and found them as follows:

He then counted the seeds in several particular rings, and found them commonly 14 in each, but has confined himself to multiply the rings by 12, which is moderate, yet makes the number of seeds amount to 130,000, allowing 7612 seeds for two large stems cut down and destroyed; a moderate allowance, considering two of the stems alone contain each above 1000 rings: some of these stems were above two yards and a half high. This plant was a seedling last year, transplanted out of the fields on the end of a sloping strawberry-bed; and he counted the rings in the middle of July, when it had thousands of flowers upon it, which, with thousands that must still succeed, might very probably produce at least 50,000 seeds more, even supposing many of the flowers to produce no seed, considering 1000 rings contain 12,000 seeds and more; and if we multiply the number of rings actually counted by 14, the number of seeds contained in one ring, instead of 12, we shall have an addition of 20,000 seeds, all which, added together, amount to 200,000, the possible increase of one seed.

On the Method of Fluxions. By COLIN MACLAURIN.

THE grounds of the method of fluxions are as follows:Magnitudes are conceived to be generated by motion; and the velocity of the generating motion is the fluxion of the magnitude.

Lines are supposed to be generated by the motion of points. The velocity of the point that describes the line is its fluxion, and measures the rate of its increase or decrease.

Other magnitudes may be represented by lines that increase or decrease in the same proportion with them; and

their fluxions will be in the same proportion as the fluxions of those lines, or the velocities of the points that describe them.

When the motion of a POINT is uniform, its velocity is constant, and is measured by the space which is described by it in a given time. When the motion varies, the velocity at any term of the time is measured by the space which would be described in a given time, if the motion was to be continued uniformly from that term without any variation.

In order to determine that space, and consequently the velocity which is measured by it, four axioms are proposed concerning variable motions, two concerning motions that are accelerated, and two concerning such as are retarded.

The first is, that the space described by an accelerated motion is greater than the space which would have been described in the same time, if it had not been accelerated, but had continued uniform from the beginning of the time.

The second is, that the space which is described by an accelerated motion is less than the space which is described in an equal time by the motion which is acquired by that acceleration continued afterwards uniformly. By these, and two similar axioms concerning retarded motions, the theory of motion is rendered applicable to this doctrine with the greatest evidence, without supposing quantities infinitely little, or having recourse to prime or ultimate ratios.

The author first demonstrates from them all the general theorems concerning motion, that are of use in this doctrine; as, that when the spaces described by two variable motions are always equal, or in a given ratio, the velocities are always equal, or in the same given ratio; and conversely, when the velocities of two motions are always equal to each other, or in a given ratio, the spaces described by those motions in the same time are always equal, or in that given ratio; that when a space is always equal to the sum or difference of the spaces described by two other motions, the velocity of the first motion is always equal to the sum or difference of the velocities of the other motions; and conversely, that when a velocity is always equal to the sum or difference of two other velocities, the space described by the first motion is always equal to the sum or difference of the spaces described by these two other

motions.

In comparing motions in this doctrine, it is convenient and usual to suppose one of them uniform; and it is here demonstrated, that if the relation of the quantities be always