reverse the operation by multiplying by that number. Thus, we see that “ton," "hundred-weight," and "pound," are only so many different expressions for the same unit-namely, the pound either singly or collectively, and that, therefore, for practical purposes, we may say that a pound weight is the "unit of force."

But we cannot leave this subject without determining the relation between this unit and the very small one of which I first made mention. I have asked you to take it on credit that the latter is nearly eight grains. The more correct value involves decimals, and is 7.85 grains nearly, that is, seven grains and eighty-five parts out of a hundred of one grain. Hence, since there are 7,000 grains in an avoirdupois pound, if we divide this number by 7.85, we shall have the number of these small units (which henceforth we shall call the dynamical unit), to which one pound weight is equal. The division gives 892 nearly for the quotient; and thus we learn how we may pass from dynamical units to pounds, or from pounds to these units. The result may be summed up in the following table :7-85 Grains make nearly one Dynamical Unit. 892 Dynamical Units make nearly one Pound. 112 Pounds make one Hundred-weight. 20 Hundreds make one Ton.

Forces applied to a Point.-When a single force is applied to any point of a body, if the latter be free, motion will ensue, and the question belongs to Dynamics. If it be not free, but fastened in any way to fixed objects, the force will be communicated through its substance to the points of support or connection, which will resist, and by resisting cause the body to sustain strain. For example, suppose a beam of wood is fixed at one point, round which, as on a pivot, it can turn in any direction, and that a force is applied to it at some other point. It is clear that this force will pull the beam round towards itself so far as it can go, that is, until the line of direction of the force passes through the fixed point. Then this point will resist, and equilibrium will be produced. The case thus becomes one of two forces-namely, that applied and the resistance produced; and we see thus that a single force can never in Statics be the subject of study, without involving the consideration of other forces which it calls into existence. A statical problem must be concerned about at least two forces.

If two forces be applied to a point in the same direction, we assume in Mechanics, as a self-evident truth, the result of experience, that their joint effect is the same as that which would be produced by a single force equal to their sum. If two men of unequal strength pull on a rope against another man stronger than either, who succeeds in balancing their united strength, we say, without hesitation, that his force is equal to the sum of those put forth by the two. When two forces thus act separately at a point, the single force to which their joint power is equal is called the "resultant" of these forces. We therefore say, if two forces act on a point in the same direction, their resultant is the sum of these forces. If three act on it, since two of them are equivalent to one equal to their sum, this one with the third must be equivalent to a single force equal to the sum of the three. And so on, as to more than three, we may lay it down as a general rule that

The resultant of any number of forces acting on a point in the same direction, is a single force equal to the sum of the separate forces.

When two forces act in opposite directions on a point, for the same reason as in the former case, we assume that the resultant is the difference of the two. And this leads us to the most general case that can occur of such forces-namely, that in which any number of them are applied to a body along the same line, some in one direction and others in the opposite direction. To determine the resultant of all, it is evident that it is sufficient to take the separate resultants of the opposing seta, then take the difference of these resultants, and that this difference will be the required resultant of all, and its direction that of the greater of the two separate resultants. Hence the following rule:

If any number of forces be applied to a body along the same line, their resultant is the difference between the sums of those which act in the opposite direction, and its direction is the same as that of the greater sum.

For example, if fifteen men pull on a rope against eleven, and drag them along a road, the resultant of the twenty-six

forces applied to the rope along its length is the difference between the united powers of the fifteen and of the eleven, whatever be the particular strength of each man, and its direction is that in which the fifteen pull.

But suppose now that two forces only are employed, and that they are equal and in opposite directions; what will be the result? They will balance, or be in equilibrium. Now it is sometimes said that the body to which two such forces are applied at one of its points is in the same condition as if no force had been applied to it. This is not true, strictly. It is in the same condition so far as equilibrium is concerned, but not otherwise. It is not in the same condition as to pressure or strain. The rope, which at one moment is lying stretched on the ground, is not in the same condition it was in a few minutes before, when two strong men were pulling at opposite ends of it with balanced strength. In the latter case it is strained along its whole length-every thread on the stretch, ready to snap. Its condition is very different on the two occasions-different in every circumstance, except that of there being no motion. So, also, if two equal and opposite pressures are applied to a round ball, it will be an equilibrium, but the condition of its substance will be changed. Its particles will be pressed towards one another inwards; and, if it be made of soft or elastic material, its form will be altered by the flattening effect of the opposing forces. And this is true, whatever be the magnitude of the ball. It may be as small as we please, even so small as an atom, or what is called a "material particle," and yet there will be this internal compression or straining. Thus we see that even the "material particle," acted on by two equal and opposite forces, cannot be said to be in the same condition before and after their application,

The case of equal and opposite forces presents some other points of interest, which may well occupy your attention in this lesson. Suppose, for example, two men pull against each other with equal strength at the opposite ends of a rope. What will be the strain on the rope? What will be its amount, considering that both are pulling? Most persons at first incline to say that it is strained by the united strength of both, or by double the strength of either man. Such is not the case; the strain is only equal to the strength of one of the men. What is the reason of this ? A moment's reflection makes it evident. Suppose one man only to pull; the rope follows him, and there is no strain on it. But the instant the other seizes his end and pulls, strain begins, caused by his resistance. If he gives a strong pull, it is great; if a weak, it is slight. But, to put this in another way, suppose the first man leads, pulling with all his might, while the other, holding on with less strength, is dragged after. The rope is strained in this case also. By how much? By the less of the two forces. The stronger pull becomes divided into two parts, one putting both the rope and the second man in motion, and the other balancing the latter's pull. It is this second portion which strains the rope, and must be equal to the strength of the hinder man, while the other, which causes motion, is the difference of the two pulls or forces. Suppose, lastly, that the two pulls become equal, their differenco becomes nothing, motion ceases, and the men come to a standstill. But the strain remains, as before, equal to the hinder force, which, being equal to that of the leading man, we can say it is equal to either of the forces.

Let us next suppose that for one of the men an iron ring, fastened on a wall, is substituted, to which one end of the rope is attached. So long as the rope hangs loosely from the ring there is no strain on it. Let the other man now pull at the far end, the rope at once is strained, evidently not by the wall, but by the man's pull. The wall puts forth no more effort to strain it than it did before; but simply resists the force communicated to it through the rope. It is, in fact, a case of a force applied to the wall through the rope, every point of which may be considered a point of its application.

Again, take two equal weights attached to the ends of a cord which passes over a pulley. The strain on the cord which hangs down at either side is evidently equal to the weight on that side; and, since the weights are equal, the strains on both sides, and therefore all through the cord, are equal to that weight.

If two bullocks raise water from a pond in a large bucket by a rope which passes over a pulley, as the bucket ascends two forces are acting at the ends of the rope The stronger pull of

the bullocks overcomes the weight of the water and bucket, and an amount of motion results, due to the difference of the two forces. The rope, however, is strained only by the weaker force, evidently so in the part which descends from the pulley to the bucket, and therefore also in the remainder, since the strain must be uniform along its whole length.

In all these cases the forces were of the nature of a pull, causing a stretching strain. But the conclusions hold equally good of pushing forces. If two such, equal to each other, be applied to a ball at opposite sides in opposite directions, the compressing strain within the ball will be equal to only one of the forces. Or if the ball be pushed against a wall by only one of them, though the wall resists, the strain will still be the same equal to the single force. The resistance counts for nothing. Also, when the two forces are unequal, and motion ensues, there is a compressing strain equal to the smaller force, while the motion produced is due to the difference of the forces. When a man ascends a ladder with a hod of mortar, there are two such compressing forces acting on his shoulder at the spot on which the hod rests-namely, his own muscular power pushing his shoulder up

wards, and the weight of the hod and mortar pushing it down. His ascent is effected by the difference of these forces, the muscular being the greater; while the compressing strain is evidently the weight of the loaded hod. These examples will make clear to you the principle I have been explaining; and you will find no difficulty in multiplying them by thinking of others yourselves.

We now pass to the case of three forces, whose directions are all different, applied to a point, and producing equilibrium. Now it is evident, first of all, that the three must pull or push in the same plane or flat, such as, for instance, the flat surface

other, and therefore could not make equilibrium. In the case of the ring on the table, to which the three strings are attached, if the direction of the effect of the pulls on two of the strings were not opposite to that of the third pull, the three would make the ring move to the side of the table, towards which these two directions incline. And, furthermore, even if the directions were opposite, the ring would move, if the effect of the two, o their resultant, were not equal to the third force. These two principles may be definitely stated as follows:1. When three forces applied to a point are in equilibrium, they are in the same plane.

2. The resultant of any two of three forces in equilibrium at a point is equal and opposite to the third force. From these principles it is evident that in order to ascer

of a table; for if two of them pulled along that surface, while the third pulled in a slanting direction upwards, this latter force should lift the body off the table. Try the experiment with three strings attached to a ring which lies flat on a table, two of which are pulled horizontally along the table, and the third in any direction upwards. The ring will be lifted, and soon the three strings will come into one plane. I am not here taking into account the weight of the ring and strings, which are a fourth force applied to the body. For the sake of simplification, to enable you to understand the principle, I suppose these to be so small in comparison to the others as to count for nothing. Secondly, when three forces applied to a point are in equilibrium, the resultant of any two of them is equal and opposite to the third force. This is also evident; for, if it were not, the resultant of the two and the third force, to which the three are equivalent, would not be two forces equal, and opposite to each

to hang down in the middle, we shall have a case of three equal forces applied to a point. There are the two outside weights acting over the pulley, and drawing the knot ob liquely to either side, and the middle weight pulling it downwards. What position will the strings settle themselves into? Evidently so that the angles all round between the strings may be equal; for no reason in the world can be given why they should be unequal. Whatever reason could be assigned for supposing one of these angles greater than the other, since the forces are equal all round and all the other circumstances the same, that same reason should make that other angle greater than the first. The angles, therefore, must be equal. Let any one of you make the experiment, and measure the angles, and he will find the result to be as I have stated. But you will find this same conclusion arrived at in the next lesson in another and more satisfactory manner, by the Parallelogram of Forces.

ANIMAL PHYSIOLOGY.-II.

THE EYE (Continued).

THROUGHOUT those classes of animals which are called vertebrate, because they have an internal skeleton, the main central portion of which consists of a back-bone of pieces jointed to one another in a long row stretching from one end of the body to the other, the eye is essentially of the same structure as in man. It is true there are differences in the proportion and shape of the parts, and in some cases additional parts are found, while in others the eye is so reduced and degraded as to be of little

VERTICAL SECTION OF THE EYE OF A SOARING BIRD.

1, Sclerotic; 2, Choroid; 3, Retina; b, Pecten; 4, Vitreous humour; 5, Bony support of sclerotic or hard coat; 6, Iris; 7. Cornea; 8, Lens; 9, Aqueous humour; 10, Lens ligament; 11, Ciliary processes; 12, Optic nerve.

or no use; but in the majority of cases in brutes, reptiles, and fishes, and in all birds, the eye is well developed, and even where it can be of no use, still indications of it are found.

Our English mole is an instance of an animal with a degraded condition of eye. It is in this animal smaller than a pin's head, and has to be looked for carefully in the midst of the velvet fur. Of course, to an animal which lives underground, burrowing continually in soft earth, an eye would be useless, and even inconvenient; yet the rudiment of an eye is found.

Besides man, only apes (and some lizards, such as the chameleca, and perhaps some fish) have the yellow spot of distinct vision. Vision in some apes must be very powerful, for it is said a gentleman who owned a baboon used to ride away across the plain until he could only just see his dog-ape with the naked eye; then using his telescope, he made a number of gestures, which were immediately mimicked with precision by the animal. In looking into the open eye the white is part of the opaque sclerotic. The coloured part is the iris seen through the transparent cornea and vitreous humour, while the pupil is the hole through the middle of this, which seems black because of the dark non-reflecting choroid at the back of the eye.

place in the choroid of pigment of metallic brilliancy. This may be well seen at the bottom of the eye of the ox inside; in others, the sclerotic is coloured, as any visitor at the Zoological Gardens may see to be the case in the eye of the chimpanzee.

These diversities, with many others, such as the contraction of the iris of the cat, so as to leave a slit instead of a circular opening, are interesting, but by no means so functionally important as others to be mentioned hereafter, when we describe eyes suited to conditions altogether different, such, for instance, as the fish's eye, which is constructed to see in water.

Birds, some of which are almost exclusively denizens of the air, and most of which have the power of betaking themselves to flight occasionally to escape pursuit, to hunt active prey, to search for new feeding-grounds, or to select a more genial climate at the change of the seasons, must have eyes suited to distant vision. Hence the lens is of a very flattened form, and does not increase in density from the outside to the inside as it does in mammalia, and more strikingly in fish. The distance from the lens to the back part of the eye is small, and to the cornea large relatively; in other words, they have a larger amount of aqueous and a smaller amount of vitreous humour than brutes have. The back part of the eye too is flatter, and is a portion of a larger sphere in relation to the rest of the eye than in animals. The shape will be best seen by the aid of the diagram of the vertical section of the eye of a soaring bird.

When the eye is spherical and distended with fluid, as in Iman, there is no tendency of the pressure within to alter the shape of the ball; but when, as in the case of birds, it has any other form, the internal pressure would strain the elastic capsule of the eye in some parts more than in others. This strain can only be prevented by rendering those parts of the capsule which are exposed to the extra pressure more solid. In the case of the bird, this is effected by means of a series of bony plates which encircle the sclerotic, bedded in its substance, and stretching from the rim of the cornea to the circumference of the large segment of the eye, on the inside of which the retina is spread out.

The structures described above, conducive to long sight in a thin medium, are more especially to be remarked in soaring, raptorial birds, like the eagles, vultures, and hawks. These, as they wheel round at a great height, survey a large extent of

VOL. L.

VERTICAL SECTION OF THE EYE OF A FISH.

Sclerotic; 2, Choroid, 2, Inner layer of Choroid; 3, Retina; o, Choroid gland; 4, Vitreous humour; 5, Bony support of sclerotic or hard coat; 6, Iris; 7. Cornea; 8, Lens; 9, Aqueous humour; 10, Lens ligament; 11, Ciliary processes; 12, Optic nerve. country; yet their sight is so keen at that elevation that no young unprotected animal, or maimed and disabled prey, escapes their sight. So keen is the sight of the condor of the Andes, that if a carcase be exposed where the naked eye can detect none of these creatures in the horizon, yet in a few minutes they are seen streaming in from all directions straight towards their hoped-for meal.

But though birds be long-sighted, it is also highly necessary that they should see minute objects at a short distance. No entomologist will deny that an insectivorous bird must have keen eyes for short distances, if it is to get its living with ease. A microscopic sight is scarcely less requisite for a grain 5