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bodies will be but one half of the velocity of the moving body before the stroke.
As to the second general case, where both the bodies are in motion before the stroke, and move one and the same way. In order to find their common velocity after impact, let the sum of their motions before the stroke be divided by the sum of the bodies, and the quotient will express the common velocity.
As to the third general case, where the bodies move in direct opposition to each other, if they have equal quantities of motion, they will upon the stroke lose all their motion, and continue at rest; for, by the proposition, the bodies after impact will be carried with the difference of their motions before the stroke; which difference, in such a case, is nothing.
When two bodies meet with unequal quantities of mo: tion, if the difference of their motions be divided by the sum of the bodies, the quotient will express their common velocity after the stroke; for, by the proposition, the difference of their motions before the stroke is equal to the sum of their motions after the stroke; consequently, that difference divided by the sum of the bodies must give the velocity.
Such are the principal laws which govern the collision of bodies devoid of elasticity. The motions of elastic bodies are determined by different rules; for when they are perfectly elastic the velocity gained by the body struck, and the velocity lost by the striking body, will be twice as great as if the bodies were perfectly inelastic. In estimating, therefore, the motions of such bodies, we may first consider what they would have been, after impact, had they been inelastic, and thence deduce the desired conclusion. See Helsham's Lectures, a work in which the subject appears to be very clearly treated.
NOTE 2. p. 32.
We are indebted to Sir Everard Home for a description of that peculiar structure, by which several species of animals are enabled to sustain their bodies in opposition to the force of gravity. His first paper upon this subject is published in the 106th volume of the Philosophical Transactions, in which he says, he was not aware that any animal, larger than the house-fly, was endowed by nature with such a power, so as to admit of examination, until Sir Joseph Banks mentioned that the lacerta gecko, a species of lizard, which is a native of the island of Java, comes out of an evening from the roofs of the houses, and walks down the smooth, hard, and polished chinam walls, in search of the flies which settle upon them, and which are its natural food, and then runs up again to the roof of the house. Sir Joseph, while at Batavia, amused himself with catching this animal, by standing close to the wall, at some distance from the lizard, with a long flattened pole, which being made suddenly to scrape the surface of the wall, knocked the animal down. He pre. sented Sir Everard with a specimen weighing five ounces and three quarters, avoirdupois, which enabled him to ascertain the peculiar mechanism by which the feet of this animal can keep their hold of a smooth, hard, perpendicular wall, and carry up so large a weight as that of its body.
The foot has five toes, at the end of each of which, except that of the thumb, is a very sharp and much curved claw; on the under surface of each toe are sixteen transverse slits, leading to so many cavities or pockets, the depth of which is nearly equal to the length of the slit that forms the orifice; they all
forwards, and the external edge of each opening is serrated, like the teeth of a small-toothed comb. The cavities, or pockets, are lined with a cuticle, and the serrated edges are also covered with it. The structure just described is supplied with various muscles whose action is to draw down the claw, open the orifices of the pockets, and turn down the serrated edges upon the surface on which the animal stands. Upon examining attentively the under surfaces of the toes, when the pockets are closed, Sir Everard Home was struck with their resemblance to the surface of that portion of the echineis remora, or sucking fish, by which it attaches itself to the shark, or to the bottom of ships; and it consequently suggested the probability of obtaining, from an examination of this latter apparatus, much useful information which might be applicable to the subject of the lizard; more especially as the parts of which it is composed are so much larger in size, and more within the reach of anatomical examination.
The surface on the top of the head of this fish, fitted for adhesion, is of an oval form, and bears a considerable proportion to the size of the whole animal; it is surrounded by a broad, loose, movable edge, capable of
applying itself closely to the surface on which it is placed; and it is evident that when the external edge is so applied, and the cartilaginous plates are raised up, the interstices must become so many vacua, and the serrated edge of each plate will keep a sufficient hold of the substance on which it rests to retain it in that position, assisted by the pressure of the surrounding water, without a continuance of muscular exertion. It thus the adhesion of the sucking fish is produced by so many vacua being formed through an apparatus worked by the voluntary muscles of the animal, and the pressure of the surrounding water.
From the similarity of the mechanism of the under surface of the toes of the lacerta gecko, there can be no doubt that the purpose to which it is applied is the same: but as in the one case the adhesion is to take place under water, and is to continue for longer periods, the means are more simple; in the other, where the mechanism is to be employed in air, under greater disadvantages with respect to gravity, and is to last for very short periods, and then immediately afterwards be renewed, a more delicate structure of parts, a greater proportional depth of cavities, and more complex muscular structure become necessary.
Having ascertained the principle on which an animal of so large a size as the lacerta gecko is enabled to support itself in its progressive motion against gravity, Sir E. Home felt himself more competent to enquire into the mechanism by which the common fly is enabled, with so much facility, to support itself in still more disadvantageous situations. In the natural size, the feet of
the fly are so small, that nothing can be determined respecting them; Keller was the first person who made a drawing of the fly's foot in a highly magnified state, in which the concave surfaces are visible, and which, no doubt, like those of the lizard above described, are employed to form vacua, which enable the fly to move under such disadvantageous circumstances. Mr. Bauer, who has so greatly distinguished himself in microscopic researches, was judiciously enlisted into the service of Sir E. Home upon this occasion; and he has shown that this principle, on which progressive motion against gravity depends, is very extensively employed by nature in the structure of the feet of insects; and Sir Everard observes, that now this structure is known, it can be readily demonstrated by looking at the movement of the feet of any insect upon the inside of a glass tumbler, through a common magnifying glass; the different suckers are readily seen separately to be pulled off from the surface of the glass, and reapplied to another part.
In consequence of the expedition to the polar regions, Sir E. Home was enabled to obtain and examine the foot of the walrus, in which he detected a resemblance in structure to that of the fly; and it is not a little curious that two animals so different in size should have feet so similar in their use. In the fly, the parts require to be magnified one hundred times to render the structure distinctly visible; and in the walrus the parts are so large, as to require being reduced four diameters, to bring them within the size of a quarto page.
Nor is progressive motion, the only function in which nature avails herself of the pressure of the atmosphere