so found, which evidently will be the middle of c x, is the centre of the three. Now join Y with D, and divide Y D into ten parts (the sum of 1, 2, 3, and 4), and take four next Y and six next D. This last point, z, is the centre of all the given forces. Try your own hands now on the following Examples, and in the next lesson we shall have for subject the centre of gravity, which is a centre of parallel forces.

Examples.

1. Three equal parallel forces act at the corners of a triangle; find the centre through which their resultant passes.

2. A force of a pound is applied to one end of a beam, of three at the other, and of two at the middle; find the centre of these forces, they being parallel to each other.

3. A weight of one pound and three-quarters hangs from one end of a rod which is two feet in length, and of three and a-half from the other; find the magnitude of the resultant, and the centre of parallel forces.

4. A door is seven feet high and three feet wide, and the centres of its hinges are distant one foot from its ends. A force of twenty-three pounds is applied along its upper edge, pulling it off its hinges, and one of thirty-seven along the lower. Find the strains on the hinges.

LESSONS IN ARITHMETIC.-VIII.
GREATEST COMMON MEASURE.

1. A composite number, as already defined (see Lesson VI., Art. 2), is one which is produced by multiplying two or more numbers or factors together.

A prime number is one which cannot be produced by multiplying two or more numbers together; it cannot, therefore, be exactly divided by any whole number except unity and itself. Thus 1, 2, 3, 5, 17, 31, etc., are prime numbers, or primes, as they are sometimes called.

A measure of any given number is a number which will divide the given number exactly without a remainder. Thus, 3 is a measure of 9, 25 is a measure of 75.

A common measure of two or more numbers is a number which will divide each of them without a remainder. Thus, 2 is a common measure of 6, 8, 12, 18, 30, etc.

The greatest common measure of two or more numbers is the greatest number which will divide them all without a remainder. Thus, 9 is the greatest common measure (or, as it is sometimes written for shortness, the G. C. M.) of 18, 27, 36, and 45.

2. To find the greatest common measure of two given numbers. RULE.-Divide the greater by the less, then the preceding divisor by the remainder, and so on, until there is no remainder. The last divisor will be the greatest common measure required.

RULE. Find the greatest common measure of two of them; then find that of the common measure thus obtained and of the third; then that of this common measure and the fourth, and so on. The last obtained will be the greatest commor. measure of the given numbers.

EXAMPLE. Find the greatest common measure of 204, 357, 204) 357 (1

and 935.

First, we find the greatest common measure of 204 and 357 to be 51, by the rule given for two numbers.

Next, we find the greatest common measure of 51 and 935, which we see to be 17.

Hence, according to the rule, 17 is the greatest common measure of 204, 357, and 935.

We do not give the reasons for the truth of the foregoing rules, as they cannot be satisfactorily established without the aid of algebra.

4. The above rules are infallible methods for finding the greatest common measure of two or more numbers. In practice, however, we can frequently dispense with these operations, and determine the greatest common measure by inspection, or by splitting up the numbers into their elementary cr prime factors. It is evident that if two or more numbers have a common measure at all, they must be composite numbers, i.e., capable of being separated into factors. If any given numbers be separated into prime factors, the greatest common measure will evidently be the product of all the factors which are common to each of the given numbers.

Thus, 75, 135, and 300, when separated into their prime factors, are respectively

3 x 5 x 5, 3 × 5 × 9, and 2 × 2×3×5×5

Now, the factors which are common to all of these are 3 and 5, and therefore 3 × 5-that is, 15-is the greatest common measure of 75, 135, and 300.

5. We subjoin a

Rule for dividing a composite number into its prime factors. Divide the given number by the smaller number, which will divide it without a remainder; then divide the quotient in the same way, and continue the operation until the quotient is unity. The divisors will be the prime factors of the given

532) 1274 (2

1064

210) 532 (2

420

112) 210 (1 112

98) 112 (1

98

14) 98 (7

98

The reason of the truth of the above rule may be thus explained:

Every division of a number, where there is no remainder, resolves it into two factors-namely, the divisor and quotient. But in the above rule the divisors in each case are the smallest numbers which will divide the given number and the successive quotients without a remainder hence they are all prime numbers, and the division is continued until the quotient is unity. Hence, clearly, the product of all these divisors (which are all primes) will be equal to the original number. In other words, these divisors are the prime factors of the given composite number.

EXAMPLE.-Resolve 16170 into its prime factors. Arrange the process thus

..

Here, in accordance with the rule, we divide 1274 by 532, which gives a remainder 210; then 532 (the preceding divisor) by 210, giving a remainder 112; again 210 (the preceding divisor) by 112, which gives a remainder 98; then 112 (the preceding divisor) by 98, which leaves a remainder 14; and lastly, 98 by 14, which gives no remainder. 14, therefore, according to the rule, is the greatest common measure of 532 and 1274. 3. To find the greatest common measure of three or more given numbers.

Hence the prime factors of which 16170 is composed are 2, 3, 5, 7, 7, 11; or, 16170 = 2 x 3 x 5 x 7 x 7 x 11.

EXERCISE 19.

1. Find the greatest common zumbers:

1. 285 and 465.

2, 532 and 1274.

3, 888 and 2775.

5. 1879 and 2425.

6. 75, 125, and 60.

7. 183, 3996, and 108.

1. 42634 x 63. 2. 50035 × 56. 3. 72156 × 1000. 4. 42000 x 40000. 5. 80000 × 25000. 6. 2567345 × 17. 7. 4300450 × 19. 8. 9803404 x 41. 9. 6710045 × 71.

1. 856783 x 999.

2. 5878065 × 99999.

3. 34567 x 22.

4. 94200 × 38.

5. 210354 × 46.

6. 149681 x 52.

7. 89567 × 85. 8. 3567 x 284. 9. 293621 × 546. 10. 149628 × 246. 11. 274032 × 9612.

13. 107206 × 486819. 14. 59634231 x 5432. 15. 62327453 × 90091. 16. 49532816 × 58673. 17. 101299867 × 14059. 12. 1429461 × 10812. 18. 637589931 × 98765.

9. Divide one thousand billions by 81 and 729.

10. Divide a thousand thousand millions by 111. 11. Divide a thousand millions of millions by 1111. 12. Divide 908070605040302010 by 654321. 13. Divide 4678179387300 by the following divisors, separately, 2100, 36500, 8760, 957000, 87700, 1360000, and 87000. 14. If the annual revenue of a nobleman be £37960, how much is that per day, the year being supposed to be exactly

365 days.

15. What is the nearest number to one thousand billions that can be divided by 11111 without a remainder?

11. 7000541 × 91. 12. 4102034 × 99. 13. 42304 × 999.

14. 50421 x 9999. 15. 67243 × 99999. 16. 78563 × 93. 17. 34054 × 639. 18. 52156 × 756. 19. 41907 x 54486. 20. 26397 × 24618 21. 12900 × 14000 22. 64172 × 42132. 23. 26815678 × 81 21. 85 x 85. 25. 256 × 256. 26. 322 × 325.

20. Work the following examples:

1. 1188 33.

2. 3128

3. 2516

4. 7125

86. 37. 95.

27. 5231 x 2435. 28. 48743000 × 637. 29. 31890420 x 85672. 30. 80460000 × 2763. 31. 2364793 × 8485672. 32. 1256702 × 999999. 33. 6840005 × 91 x 61. 34. 45067034 x 17 x 51. 35. 788031245 x 81 x 16. 36. 61800000 × 23000. 37. 12563000 × 4800000. 38. 91300233 × 1000000. 99. 680010000 × 1000000.

17. 3562189 ÷ 225. 18. 685726 + 32000. 19. 723564175. 20. 892565225. 21. 456212 + 275. 22, 925673 ÷ 125. 23. 763421 + 175. 24. 876240 ÷ 275.

5. 568210 42. 6. 785372 ÷ 63. 7. 896736 ÷ 72. 8. 67234568 + 5. 21. How long would it take a vessel sailing 100 miles per day to circumnavigate the earth, whose circumference is 25000 miles ?

22. The distance of the earth from the sun is 95000000 of miles: how long would it take a balloon, going at the rate of 100000 miles a year, to reach the sun?

23. Divide 467000000000 by 25000000000.

LESSONS IN BOTANY.—IV.

SECTION VI.-LEAVES CONSIDERED AS TO THEIR

FUNCTIONS.

ALTHOUGH leaves have a great variety of uses, yet the principal is that of respiration or breathing. In this manner they become the representatives of lungs in animal beings. But though plants breathe, the vegetable function of respiration in them is not to be considered as similar to that function in animals. On the contrary, it is directly the reverse: the very gas which animals expel from their lungs as useless or injurious, plants receive through the medium of their leaves, take out of it that which is suitable to their wants, then exhale the portion which is refuse to them, but which is necessary to the existence of animals. What a train of reflections does the contemplation of this beautiful provision call forth! Not only are vegetables useful in supplying us with food and timber, not only do they beautify the landscape with their waving branches and picturesque forms, but they are absolutely necessary to the existence of animal life as a means of purifying the atmosphere!

The breathing function of leaves is far too important to admit of being lightly passed over with these few remarks, yet a difficulty occurs in pursuing it further, inasmuch as to understand the precise theory of vegetable respiration the reader must be acquainted with certain facts in chemistry. readers, doubtless, are acquainted with these chemical facts, others are not; consequently, the best plan will be to present a slight outline of these facts at once.

Some

To begin, then: did the reader ever set fire to a bit of stick or a little charcoal ? No doubt he has. What does the reader think becomes of this stick or charcoal ? Is it lost, destroyed? Oh no, there is no such thing as destruction in all nature; substances, even when they appear to be destroyed, only change their form. What, then, becomes of a piece of stick or a piece of charcoal when we burn either in the fire? Now, whenever philosophers desire to study the conditions of an experiment, and the choice of more than one set of conditions stands before them, they very properly take the simplest. We have here two sets of conditions; the burning of a stick is one, the burning of a piece of charcoal is the other. The latter being the simpler of the two, we will take it, and use it for our purposes; moreover, we

will assume the charcoal employed to be absolutely pure. We burn, then, an absolutely pure bit of charcoal in atmospheric air, and it totally disappears; nothing remains; not the smallest trace of ashes; all is gone. What, then, has become of the charcoal? This is not a chemical book, therefore we have not space to go into the matter in all its chemical relations. We must, therefore, content ourselves by saying that the charcoal, by burning, is converted into a gas termed the carbonic acid gas. This carbonic acid gas is quite invisible, therefore one might look for it in vain; but it has a smell and a taste, therefore we might be conscious of its existence, even though we had no means of catching it. But we have such means. If this gas comes in contact with lime, or potash, or soda, either of these substances lays hold of it, combines with it, or, if we may be pardoned the expression, licks it up. Therefore, by setting a little quicklime in places where carbonic acid gas exists, we may catch it just as readily as we can catch a mouse in a trap-ay, more readily, because a mouse may at least choose whether he go into the trap or stay out of it; but the carbonic acid gas has no such choice; if it comes in contact with the trap of lime, in it must go without fail. Now, what we want to come at is this. Although a a piece of charcoal when burnt goes away in an invisible form, it nevertheless only makes a new acquaintance and puts on a mask. We can catch it, can unmask it, and get the charcoal out of it once more.

Carbonic acid gas is a poison, as, we dare say, most of our readers know; hence the danger of sitting near a pan of burning charcoal.

Proceeding with our chemical remarks, we must now go on to say that combustion is far from being the only source of carbonic acid gas: thus it is given off during fermentation, is given off from effervescent wines, such as champagne and sparkling moselle, is given off from ginger beer and soda water, and, what is far more to our purpose, is given off from the lungs of animals by the act of respiration. Indeed, the functions of animal digestion and respiration taken together may be considered as a sort of combustion, and are actually termed combustion by some authors. The similarity is indeed striking, as a little contemplation will serve to demonstrate. Thus, if we throw a lump of coal into a fire-place, heat is given out, and gaseous matter

we should be if we were always puffing out charcoal dust with every expiration! We do not expire a small quantity either, no less than thirteen ounces of charcoal being evolved during twenty-four hours from each human individual. Had not some provision been adopted for enabling carbon to be thus evolved in a gaseous form, we should all have been blacker than chimney-sweeps. What a miserable state of things would this have been!

Respiration, then, is the chief function of leaves, but it is not the only function; they also serve as evaporative organs, by means of which the plant gets rid of excessive moisture; and in this respect, again, they present a striking analogy to animal lungs. Who amongst us is not aware that our breath contains moisture?

SECTION VII.-ON THE FORM AND MODIFICATIONS OF LEAVES.

Having described the general functions of leaves, we must now proceed to examine their forms, and to learn the terms by which those forms are designated, otherwise we should not be able to

describe a plant in such a manner that a person would understand our description. As in many other parts of Botany, the student will here encounter some long names; they are very useful names, nevertheless, and require to be understood.

In the first place, taking a general review of the aspect of leaves, it I will be evident to the reader that their form is exceedingly varied, as is also their manner of attachment to the stem, to say nothing of such characteristics as softness, hardness, thickness, thinness, and so forth. As regards their attachment to the vegetable, some leaves grow directly out of the stem, or, in figurative language, may be said to sit upon the stem. Such leaves are termed by botanists sessile, from the Latin word sessum, a part of the verb sedeo, to sit. Others are attached to the parent stem by a little stem of their own. Now, this leafstem, or foot-stalk of a leaf, botanists denominate a petiole, from the Latin petiolus, a little foot, and leaves thus supplied with a petiole are said to be petiolate. Again, some leaves are attached to the parent stem exactly opposite each other, consequently they are said from this circumstance to be opposite or opposed. Others are alternately attached, from which circumstance the denomination alternate is given to them. All these characteristics are very important, not only in enabling a botanist to describe the configuration of plants in the fewest possible words, but in enabling him at the same time to separate plants into natural groups and alliances.

(chiefly carbonic acid) escapes. If we swallow a morsel of food, it is digested, heat is given out, and carbonic acid escapes. In the former case carbonic acid escapes by the chimney, in the latter case by the lungs. One chemical point yet remains to be explained before the student will be in a position to understand the functions of a vegetable leaf. The carbonic acid, of which we have been speaking, is a gaseous compound of charcoal, termed by chemists carbon and something; that something is oxygen, the vital principle of the air. Now, the bulk of vegetable bodies is made up of carbon, otherwise how could we get charcoal in the ordinary way? And this bulk, this carbon, is got out of the air. Yes, the largest tree, whatever its size, is for the most part formed of carbon, and all this carbon once existed in the gaseous form. Philosophers have made calculations, from which it appears that the total amount of carbonic acid thus floating about in the atmosphere amounts to the enormous quantity of many tons, and that tons of carbonic acid hover over each acre of ground, ready to give up its carbon to vegetables which require this substance. Before quitting this subject, we must not forget to direct the reader's attention to the beautiful provision by means of which the amount of n necessary to be got rid of from the animal economy is in the particular form of gas. Even supposing no ary to result, yet just think how dirty and begrimed

Again, some leaves are single in themselves, as is the case with those of the apple-tree; whilst others are made up of several little leaflets, as we see, for example, in the ash. Hence arises the very natural distinction of leaves into simple and compound.

The forms which leaves assume are so very numerous, that botanists are accustomed to indicate them by the similarities which they manifest to natural objects. Some are like shields, for which reason they are termed peltiform (Latin, pelta, & shield); others are like hearts, whence they are termed cordiform or cordate (Latin, cor, cordis, a heart). Some resemble feathers, others are jagged like a saw, whence arise the denominations penniform (Latin, penna, a feather or wing), serrate or serra. tiform (Latin, serra, a saw), and so forth; but we shall give in our next lesson dra ings of the chief varieties of leaves, from an inspection of which the various names respectively applied to them will be rendered more evident.

ANIMAL PHYSIOLOGY.-IV.

THE EAR.

A MAN who had been born blind, when asked what he supposed scarlet was like, replied, "Like the sound of a trumpet." The reply is startling, because it shows how dependent the mind is upon the senses for its ideas. No one who could both see and hear would ever think of comparing sound with light, or tone with colour.

But though the sensations conveyed to the brain by the eyenerve and the ear-nerve are so different as to be incomparable, there is much resemblance between sound and light. They obey the same laws. Sound can be absorbed, reflected, and refracted at the surface of bodies, as we have seen light is; and, moreover, it is probable that both consist of rapid vibrations, or waves, succeeding one another at regular intervals, like the enlarging circles which follow one another and break upon the banks when a stone is thrown into the middle of a still pond, and disturbs the glassy surface of the water.

the cry of the partridge, and it be not repeated so often as to let us try experiments on it, by turning the head this way and that, it is very difficult to tell from whence the sound comes, even to the extent of a whole quadrant of the horizon. Upon this fact ventriloquism depends for its success. The idea of the direction of sound being inferential, and not much dependent upon the sense-being, in fact, owing to the operation of the mind, and not to that of the ear-the ventriloquist has only to direct the mind where to expect the sound, and then to make a sound of just such a pitch of intensity, and just such a tone, as the sound would have if it came from that quarter, to completely impose on the ear of the listener as to the direction from which it comes.

But although the ear is at fault as regards direction, the accuracy of some of its other notifications is wonderful in the extreme. It can note not only the likeness and difference of musical sounds, but of their harmonies when many are sounded together, and a fine ear will detect an erring note when a thousand instruments are sounded. The recognition of slight

V. STAPES.

Though there are these points of similarity as to the essential nature and qualities of light and sound, there are also great differences. Light travels with a rapidity which, for all appre ciable distances that is, for all earthly objects-is instan taneous; while sound travels, relatively, very slowly, and, when common air carries it, it goes only 1,093 feet during each second of time. Again, while the vibrations of light are so rapid that it is impossible to know them to be vibrations but by reasoning apon its effects, the waves of sound may be often observed by the eye when they are propagated through, or originated from, a solid body, as when we see a cord or glass vessel respond to a musical note, or give out a sound when struck. Sound, too, 18 the vibration of the substances themselves-which substance we can feel, or see, or know by means of other senses-while light is supposed to be the vibration of some fluid which is imponderable, or, in other words, has no weight, and of which we know nothing except by the eye.

The waves of sound, then, being coarser and more liable to interference than the waves of light, it follows that the ear cannot be so good an indicator of the direction of sound as the eye is of the direction of a luminous object. Indeed, the ear Can of itself scarcely give us any idea of direction. If the sound be short and sharp, like the piercing shriek of the bat, or even

VOL. I.

differences is truly wonderful when we consider that not only can the ear know when the same note is sounded by instruments of different kinds (though physicists are unable to tell us how there can be any difference, the number of vibrations in a second being the same, and the medium identical), but very slight differences in the same kind of instruments, such as whether there is one per cent. more or less of a metal in an alloy of which an organ-pipe is made, or of which a bell is cast, are observed so shrewdly, that these matters have to be attended to with the nicest care. A violin must not only be of a certain shape, but the wood of which it is composed must be of a certain age, to produce the best instrument; and these observed differences are carried to such a nicety that fiddles made in a certain part of Germany, in a certain year, are considered the best, and will command almost fabulous sums. Yet all this depends upon what is called timbre, a word which gives a name to a something which is entirely dependent on the delicacy of our sense of hearing, but which has not received any other explanation.

Though we cannot directly connect these niceties of sense with the intricacies of complication in the organ of hearing, these latter will be seen to be so numerous and peculiar when we describe the ear, that one is not surprised that much con

9

nected with sound is unexplained, because there are so many structures connected with the organ which has been given us as the recipient and interpreter of sound, at the use of which we can hardly guess.

That which is usually called the ear is familiar to every one as the external semi-circular cartilage, closely invested with skin, and ending below in a soft lobule, which is sometimes the support of barbarous pendants. This structure, which, when well formed, has a beauty of its own that needs no supplement or advertisement, is but a remote appendage to the true ear. Though it in some sort collects sound, and protects the orifice which leads down towards, not to the true ear, it is non-essential, and can be dispensed with without much inconvenience; so that some of our poor ancestors, who found that they could not retain both good external ears and good consciences, like William Prynne in the time of Charles I. and the Star Chamber, suffered less real loss than might have been anticipated.

The external gristly ear is called the pinna, and though flattened as to its general surface, is somewhat folded into ridges and furrows, there being a rim round the outside and a channel within this, which deepens and widens as it runs first upward, along the back part, then downward along the fore part to a central crypt. From this crypt the passage becomes narrower as it runs forward and inward to the pit of the ear. Sound, no doubt, is conveyed along this canal in the same direction as we have described its course. If the pinna were quite flat, sound would rebound from it; but as it is so shaped, sound is caught and reflected round the canal from point to point, as it is reflected round the Whispering Gallery of St. Paul's, and finally delivered down the tube of the ear.

The tube is an inch and a half deep, and its innermost half enters one of the bones of the head, called the temporal bone, and in this bone all the other parts of the ear are enclosed and protected. At the bottom of the tube is an oval membrane stretched across the passage, and barring the entrance to all external objects. Behind this is a roundish, irregular cavity, filled with air. This stretched fibrous membrane bounding the air cavity, naturally suggests the idea of a drum, shaped like a kettle-drum; and hence the cavity is called the tympanum, from a Latin word meaning drum, and the parchment-like tissue the membrane of the drum. It differs, however, from a kettle-drum in that several orifices open into it, and it contains structures to be described presently.

On the further side of the drum is the true car, completely encased in bone, except at two very small holes, which are closed with membrane. The larger and upper aperture is called the oval hole, and the smaller and lower the round hole. From the membrane of the tympanum to the membrane of the oval hole stretches a chain of bones, whose shape is best seen in the engraving. The outer one, next the parchment of the drum, is called the hammer. It has three processes, or projections, two of which are long; so that, rather than hammer, it might be called a woodcutter's beetle. One of these processes, called the handle, is attached to the centre of the membrane, which it makes tight when pulled inward by a small muscle, and lax when another muscle acts on it.

The former operation is probably the action which we uncon sciously cause when we consciously listen. The head of the hammer is applied to another bone called the anvil (incus). It has two processes, one for its suspension to the wall of the tympanic cavity, and the other to connect it with the third or stirrup-bone (stapes). This bone is more like the article it is named from than the others are, and the foot-part of the stirrup is applied to the oval membrane, which it nearly covers. These bones can move a little in relation to one another, and their actions are limited by small muscles, but they usually act together as if in one piece, playing round an axis which runs through the heads of the hammer and anvil, so that when the tympanic membrane is thrust in and out by vibration, the membrane of the oval hole is made to vibrate correspondingly. The round hole is open to the influence of sound conveyed through the air of the tympanum; but whether this be its function, or merely to allow the fluid of the internal car to be more readily thrown into vibration in the passage it fills-in other words, whether it be a hole for the entrance or exit of vibrations-seems hard to tell.

The fore-part of the drum cavity is connected with the throat by a passage, which runs forward and downwards to open in the

gullet behind the nose and mouth. Through this passage the cavity is kept supplied with renewed air at the same pressure as the external air. The reader may be conscious of the existence of these passages to the ears from the throat by preventing the air from rushing out of the mouth and nose, while he forces it up from his lungs. The cavity of the drum will then be dis tended with air; hearing will be less perfect, by the unnatural tension of the membranes, and there is a slight singing in the ear. With a little practice, air may be conveyed through the mouth to the drum, without entering the lungs, and thus gases have been applied as remedies to diseases of the ear. But the exclusion of these from the lungs is difficult, and cannot be relied One of our greatest aurists, when pursuing his philan thropic and scientific investigations on the effect of chloroform and prussic acid applied thus, died, because he could not exclude the latter deadly poison from his lungs as he had supposed he could. The proper, or essential ear, consists of a chamber longer than broad, communicating on its upper and outer side with three semi-circular canals, and at its front inner end with a cavity shaped like a snail-shell.

on.

The chamber is called the vestibule; this and the semi-cir cular canals are called together the labyrinth; and the hollow, like that of a snail-shell, the cochlea. They are all channelled out of the substance of the skull-bone before named as the temporal. The part of this bone which lodges them juts inwards, so as to lie at the base of the brain, and is so strong and thick as to be called the petrous or stony part of the bone. Accurately resembling the bony labyrinth in shape, but a little smaller in its dimensions, so as to allow a little liquid to lie between it and the bone, is a membranous labyrinth. That part of the membrane which is on the floor of the vestibule leaves its proximity to the bone at the entrance of the cochlea, and forms a horizontal stage across the widest part of the spiral passage, and so mounts round the three whorls of the spire, dividing it into two parts; so that, if we may imagine a small insect exploring these regions, it could mount to the apex of the spire by either of two spiral staircases, the roof of the lower one being the floor of the upper. These circular staircases only commu. nicate with one another at the point of the shell. The lower one at its foot communicates with the tympanum by the round hole, while the vestibule communicates with the chain of bones by the oval hole. Hence, if our imaginary insect could gain access to the cochlea through the membrane of the round hole, it must first mount to the top of the lower staircase, and then descend all the way down the upper one, before it could explore the labyrinth.

All the cavities are filled with fluid, by whose agency the vibrations are conveyed along its walls; and in these walls, especially at certain parts, are distributed the nerve-fibres of the nerve of hearing. It would seem, however, as though the vibrations of the liquid are not enough to impress the nerve, and there are found small, hard structures wherever the nervethreads are most thickly placed, and at two places in the floor of the vestibule are found collections of small, hard, marble stones, held in a mesh of fibres; so that, as the waves sweep by in the liquid, these are made to strike and rebound against the nerves. The spiral sheet of membrane which divides the cochlea receives the nerves from a main nerve which runs up the central pillar, and it has in its substance fibrous bars, which radiate outwards at regular intervals, like the key-notes of a piano, and, like these, each is supposed to receive and transmit to the nerve at its root a separate note. Thus the spiral sheet of the cochlea is supposed to be able to appreciate difference in tone, and the labyrinth differences in the amount of sound. The nerves from all parts are collected into one bundle, but, as is usual with nerves wherever they may be found, the strands remain distinct.

To assist the reader in his conception of the ear, we may compare it to a house of business. The pinna is the house-front; the tube is the porch; the drum-membrane the front door (closed); the drum is the hall; a few steps, the ossicles, lead to an office, round which are convenient counters, closets, and passages, at which clerks enter business transactions; while, directly communicating with this large office, cognisant of all proceedings, but reserving to himself any special business, sits the general manager, who has also a door direct to the hall; whilst, at the back of the premises, telegraph wires run to the London agent.