« ZurückWeiter »
so found, which evidently will be the middle of c x, is the centre RULE.—Find the greatest common measure of two of them; of the three. Now join y with D, and divide y d into ten parts then find that of the common measure thus obtained and of the (the sum of 1, 2, 3, and 4), and take four next y and six next third;
then that of this common measure and the fourth, and so This last point, z, is the centre of all the given forces. Try on. The last obtained will be the greatest commor measure of your own hands now on the following Examples, and in the next the given numbers. lesson we shall have for subject the centre of gravity, which is EXAMPLE.—Find the greatest common measure of 204, 357, a centre of parallel forces.
and 935. Examples.
First, we find the greatest common 204 ) 357 (1
measure of 204 and 357 to be 51, by the 1. Three equal parallel forces act at the comers of a triangle; find rule given for two numbers. the centre through which their resultant passes.
153 ) 204 (1 2. A force of a pound is applied to one end of a beam, of three at
153 the other, and of two at the middle; find the centre of these forces, they being parallel to each other.
51 ) 1533 3. A weight of one pound and three-quarters hangs from one end of
153 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 Next, we find the greatest common measure of 51 51 ) 935 ( 18 its hinges are distant one foot from its ends. A force of twenty-three and 935, which we see to be 17. pounds is applied along its upper edge, pulling it off its hinges, and
425 one of thirty-seven along the lower. Find the strains on the hinges. Hence, according to the rule, 17 is the greatest
408 common measure of 204, 357, and 935.
17) 51 (0
We do not give the reasons for the truth of the LESSONS IN ARITHMETIC.–VIII.
foregoing rules, as they cannot be satisfactorily GREATEST COMMON MEASURE.
established without the aid of algebra. 1. A composite number, as already defined (see Lesson VI., 4. The above rules are infallible methods for finding the Art. 2), is one which is produced by multiplying two or more greatest common measure of two or more numbers. In practice
, numbers or factors together.
however, we can frequently dispense with these operations, and A prime number is one which cannot be produced by multi- determine the greatest common measure by inspection, or by plying two or more numbers together; it cannot, therefore, be splitting up the numbers into their elementary cr prime exactly divided by any whole number except unity and itself. factors. Thus 1, 2, 3, 5, 17, 31, etc., are prime numbers, or primes, as
It is evident that if two or more numbers have a common they are sometimes called.
measure at all, they must be composite numbers, i.e., capable of A measure of any given number is a number which will divide being separated into factors. If any given numbers be sepathe given number exactly without a remainder. Thus, 3 is a rated into prime factors, the greatest common measure will measure of 9, 25 is a measure of 75.
evidently be the product of all the factors which are common to A common measure of two or more numbers is a number which each of the given numbers. will divide each of them without a remainder. Thus, 2 is a Thus, 75, 135, and 300, when separated into their prime common measure of 6, 8, 12, 18, 30, etc.
factors, are respectively The greatest common measure of two or more numbers is
3 * 5 * 5, 3 x 5 x 9, and 2 * 2 * 3 * 5 * 5 the greatest number which will divide them all without a remainder. Thus, 9 is the greatest common measure (or, as it Now, the factors which are common to all of these are 3 and 5, is sometimes written for shortness, the G. C. M.) of 18, 27, 36, and therefore 3 x 5—that is, 15—is the greatest common and 45.
measure of 75, 135, and 300. 2. To find the greatest common measure of two given numbers.
5. We subjoin a
Rule for dividing a composite number into its prime factors. RULE.-Divide the greater by the less, then the preced- Divide the given number by the smaller number, which will ing divisor by the remainder, and so on, until there is no divide it without a remainder ; then divide the quotient in the remainder. The last divisor will be the greatest common mea- same way, and continue the operation until the quotient is sure required.
unity. The divisors will be the prime factors of the given EXAMPLE.-To find the greatest common measure of 532 and number. 1274. Arrange the process thus :
The reason of the truth of the above rule may be thus ex
plained :532) 1274 (2
Every division of a number, where there is no remainder, 1064
resolves it into two factors-namely, the divisor and quotient.
But in the above rule the divisors in each case are the smallest 210 ) 532 (2 420
numbers which will divide the given number and the successive
quotients without a remainder : hence they are all prime num112) 210 (1
bers, 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, 98 ) 112 (1
these divisors are the prime factors of the given composite number.
EXAMPLE.—Resolve 16170 into its prime factors. Arrange 14 ) 98 (7 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 nurabers,
Hence the prime factors of which 16170 is composed are 2, 3, 5, 16. How often could 43046721 be subtracted from 7, 7, 11; or, 16170 = 2 X 3 X 5 X 7 X 7x11.
22876792454961, and at last leave no remainder ?
17. How many times does 310314420 contain 39390 ? EXERCISE 19.
18. What number is that which divided by 123456 would 1. Find the greatest common measure of the following give a quotient of 826451, and a remainder of 70404 ? numbers :
19. Work the following examples in multiplication :1. 285 and 465. 5. 1879 and 2425.
1. 42631 X 63. 14. 50421 x 9999. 27. 5231 X 2435. 2. 532 and 1274. 6. 75, 125, and 60.
2. 50035 X 56. 15. 67243 X 99999. 28. 48743000 X 637. 3. 889 and 2775. 7. 183, 3996, and 108. 3. 72156 X 1000. 16. 78563 x 93.
29, 31890120 x 85672. 4. 2145 and 3471. 8. 672, 1440, and 3472.
4. 42000 X 40000. 17. 31054 x 639. 30. 80 460000 * 2763, 2. Resolve all the composite numbers from 9 to 108 into their 5. 80000 X 25000. 18. 52156 X 756.
31. 2364793 X 8185672.
6. 2567345 X 17. 19. 41907 x 54486. 32. 1256702 X 999999. prime factors.
7. 4300450 X 19. 3. Resolve into their prime factors 180, 420, 714, 836, 2898,
20. 26397 X 24648 33, 6840005 X 91 X 61.
8. 9803404 x 41. 21. 12900 X 14000 81. 45067034 X 17 X 51. 11492, 1728, 1492, 8032, 71640, 92352, 81660.
9. 6710045 x 71. 22. 64172 x 42132. 35. 788031215 x 81 x 16. 4. Find the greatest common measure of the following 10. 3150701 * 18. 23. 26815678 X 81 36. 61800000 X 23000. Inmbers by resolving them into factors :
11. 7000541 X 91. 21. 85 X 85.
37. 12563000 x 4800000. 12. 4102034 X 99. 25. 256 X 256.
38. 91300233 X 1000000. 1. 36, 60, and 108. 1 2. 56, 84, 140, and 168. 13. 42304 X 999. 26. 322 x 325.
89. 680040000 x 1000000. 3. 5355, 6545, 17017, 36465, 91385. 5. Find the greatest common measure of the following
20. Work the following examples :numbers:
1. 1188 33.
9. 31256726 15. 17. 3562189 – 225. 1. 105 and 165. 3. 140, 210, and 315.
2. 3128 + 86.
10. 42367581 - 45. 18. 685726 - 32000. 2. 108, 126, and 162. 4. 24, 42, 54, and 60.
3. 2516 - 37.
11. 16753672 · 35. 19. 723564 + 175. 4. 7125 – 95.
12. 3256385 + 55. 20. 892565 225. 6. Find all the divisors common to the following numbers:- 5. 568210 42. 13. 45672400 – 25. 21, 456212 + 275, 1. 15, 18, 21, and 36.
4. 82, 118, and 146.
6. 785372 + 63.
14. 6245634 * 45. 22. 925673 + 125. 2. 11, 23, 42, and 35.
5. 42 and 66.
7. 896736 + 72.
15, 8215623 + 125. 23, 763421 + 175. 3. 10, 35, 50, 75, and 60.
8. 6723-1568 + 5. 16. 462156 + 75. 24. 876240 • 275. 7. Resolve the following numbers into their prime factors :- 21. How long would it take a vessel sailing 100 miles per 1. 120 apd 144.
7. 1492 and 8032.
day to circumnavigate the earth, whose circumference is 25000 2. 180 and 420.
8. 4604 and 16806.
miles ? 3. 714 and 836.
9. 71640 and 20780,
22. The distance of the earth from the sun is 95000000 of 4. 574 and 2898.
10. 81570 and 65480.
miles : how long would it take a balloon, going at the rate of 5. 11492 and 980.
11, 92352 and 1660.
100000 miles a year, to reach the sun ? 6. 650 and 1728.
23. Divide 467000000000 by 25000000000.
That our readers may have sufficient practice in multiplication and division, we give in this lesson upwards of one hundred
LESSONS IN BOTANY.-IV. examples in these rules. The operations should be contracted SECTION VI.-LEAVES CONSIDERED AS TO THEIR when practicable, and the correctness of every result should be
FUNCTIONS. tested by the methods given in our Lessons on Multiplication ALTHOUGH leaves have a great variety of uses, yet the principal and Division.
is that of respiration or breathing. In this manner they become EXERCISE 20.
the representatives of lungs in animal beings. But though 1. Find the product 678954 X 72, by multiplying by succes- plants breathe, the vegetable function of respiration in them is sive factors.
not to be considered as similar to that function in animals. On 2. Find in the same way the product 78530700 x 1250. the contrary, it is directly the reverse : the very gas which 3. Find the product of the following by dividing by succes- animals expel from their lungs as useless or injurious, plants aire factors :
receive through the medium of their leaves, take out of it that
which is suitable to their wants, then exhale the portion which 1. 16128 • 24. 3. 91080 • 72. 5. 142857 • 112. 2. 25760 • 56.
is refuse to them, but which is necessary to the existence of 4, 123456 - 168,
animals. What a train of reflections does the contemplation of 4. Divide 9643 by 30, by 300, and by 3000.
this beautiful provision call forth! Not only are vegetables 5. Divide 3360000 by 17000.
useful in supplying us with food and timber, not only do they 6. Divide 123456789 by 290000.
beautify the landscape with their waving branches and pic7. Multiply and also divide :
turesque forms, but they are absolutely necessary to the exist1. 98734 by 5. 4. 103561203 by 15. 7. 25426 by 125.
ence of animal life as a means of purifying the atmosphere ! 2. 53960201 by 5. 5. 1125 by 75.
8. 237135 by 75.
The breathing function of leaves is far too important to 3. 1256 by 15. 6. 5093123 by 75. 9. 3929764 by 125, admit of being lightly passed over with these few remarks, yet
a difficulty occurs in pursuing it further, inasmuch as to under8. Work the following examples in multiplication :
stand the precise theory of vegetable respiration the reader 1 86783 x 999.
7. 39567 X 85. 13. 107206 x 486819. must be acquainted with certain facts in chemistry. Some 2. 5978065 x 99999. 8. 3567 X 284. 14. 59634281 5432.
readers, doubtless, are acquainted with these chemical facts, 3. $4567 x 22. 9. 293621 x 546. 15, 62327453 X 90091.
others are not; consequently, the best plan will be to present a 4, 942200 X 38. 10. 149628 X 246. 16. 4953281ộ x 58673.
slight outline of these facts at once. 5. 210054 X 46.
11. 274032 x 9612. 17. 101299867 x 14059. 6. 149681 X 52.
To begin, then : did the reader ever set fire to a bit of stick 12. 1429461 X 10812. 18. 637589931 x 98765.
or a little charcoal? No doubt he has. What does the reader 9. Divide one thousand billions by 81 and 729.
think becomes of this stick or charcoal? Is it lost, destroyed ? 10. Divide a thousand thousand millions by 111.
Oh no, there is no such thing as destruction in all nature; 11. Divide a thousand millions of millions by 1111.
substances, even when they appear to be destroyed, only change 12. Divide 908070605040302010 by 654321.
their form. What, then, becomes of a piece of stick or a piece 13. Divide 4678179387300 by the following divisors, sepa- of charcoal when we burn either in the fire ? Now, whenever rately, 2100, 36500, 8760, 957000, 87700, 1360000, and 87000. philosophers desire to study the conditions of an experiment,
14. I the annual revenue of a nobleman be £37960, how and the choice of more than one set of conditions stands before much is that per day, the year being supposed to be exactly them, they very properly take the simplest. We have here two 365 days.
sets of conditions; the burning of a stick is one, the burning of 15. What is the nearest number to one thousand billions that a piece of charcoal is the other. The latter being the simpler of can be divided by 11111 without a remainder ?
the two, we will take it, and use it for our purposes; moreover, we will assume the charcoal employed to be absolutely pure. We we should be if we were always puffing out charcoal dust with burn, then, an absolutely pure bit of charcoal in atmospheric air, every expiration! We do not expire a small quantity either, no and it totally disappears; nothing remains; not the smallest trace less than thirteen ounces of charcoal being evolved during of ashes; all is gone. What, then, has become of the charcoal ? twenty-four hours from each human individual. Had not some This is not a chemical book, therefore we have not space to go provision been adopted for enabling carbon to be thus evolved into the matter in all its chemical relations. We must, there in a gaseous form, we should all have been blacker than fore, content ourselves by saying that the charcoal, by burning, chimney-sweeps. What a miserable state of things would this is converted into a gas termed the carbonic acid gas. This have been ! carbonic acid gas is quite invisible, therefore one might look for Respiration, then, is the chief function of leaves, but it is not it in vain ; but it has a smell and a taste, therefore we might be the only function; they also serve as evaporative organs, by conscious of its existence, even though we had no means of means of which the plant gets rid of excessive moisture; and in catching it. But we have such means. If this gas comes in this respect, again, they present a striking analogy to animal contact with lime, or potash, or soda, either of these substances lungs. Who amongst us is not aware that our breath contains lays hold of it, combines with it, or, if we may be pardoned the moisture ? expression, licks it up. Therefore, by setting a little quicklime in places where carbonic acid gas exists, we may catch it just as
SECTION VII.-ON THE FORM AND MODIFICATIONS OF readily as we can catch a mouse in a trap-ay, more readily,
LEAVES. because a mouse may at least choose whether he go into the Having described the general functions of leaves, we must now trap or stay out of it; but the carbonic acid gas has no such proceed to examine their forms, and to learn the terms by which choice; if it comes in contact with the trap of lime, in it must go those forms are designated, otherwise we should not be able to without fail. Now, what we want
describe a plant in such a manner to come at is this. Although a
that a person would understand a piece of charcoal when burnt goes
our description. As in many other away in an invisible form, it never
parts of Botany, the student will theless only makes a new acquaint
here encounter some long names; ance and puts on a mask. We can
they are very useful names, never. catch it, can unmask it, and get the
theless, and require to be undercharcoal out of it once more.
stood. Carbonic acid gas is a poison, as,
In the first place, taking a general we dare say, most of our readers
review of the aspect of leaves, it know; hence the danger of sitting
will be evident to the reader that near a pan of burning charcoal.
their form is exceedingly varied, Proceeding with our chemical re
as is also their manner of attachmarks, we must now go on to say
ment to the stem, to say nothing of that combustion is far from being
such characteristics as softness, the only source of carbonic acid gas:
hardness, thickness, thinness, and thus it is given off during fermen
so forth. As regards their attachtation, is given off from effervescent
ment to the vegetable, some leaves wines, such as champagne and
grow directly out of the stem, or, sparkling moselle, is given off from
in figurative language, may be said ginger beer and soda water, and,
to sit upon the stem. Such leaves what is far more to our purpose, is
are termed by botanists sessile, from given off from the lungs of animals
the Latin word sessum, a part of the by the act of respiration. Indeed,
verb sedeo, to sit. Others are atthe functions of animal digestion
tached to the parent stem by a little and respiration taken together may
stem of their own. Now, this leaf. be considered as a sort of combus.
stem, or foot-stalk of a leaf, botation, and are actually termed com
nists denominate a petiole, from the bustion by some authors. The simi.
Latin petiolus, a little foot, and larity is indeed striking, as a little
leaves thus supplied with a petiole contemplation will serve to demon
are said to be petiolate.
Again, strate. Thus, if we throw a lump
some leaves are attached to the of coal into a fire-place, heat is
parent stem exactly opposite each given out, and gaseous matter
other, consequently they are said (chiefly carbonic acid) escapes. If we swallow a morsel of food, from this circumstance to be opposite or opposed. Others are it is digested, heat is given out, and carbonic acid escapes. In alternately attached, from which circumstance the denomination the former caso carbonic acid escapes by the chimney, in the alternate is given to them. All these characteristics are very latter case by the lungs. One chemical point yet remains to be important, not only in enabling a botanist to describe the con: explained before the student will be in a position to understand figuration of plants in the fewest possible words, but in the functions of a vegetable leaf. The carbonic acid, of which enabling him at the same time to separate plants into natural we have been speaking, is a gaseous compound of charcoal, groups and alliances. termed by chemists carbon and something; that something is Again, some leaves are single in themselves, as is the case oxygen, the vital principle of the air. Now, the bulk of with those of the apple-tree; whilst others are made up of vegetable bodies is made up of carbon, otherwise how could we several little leaflets, as we see, for example, in the ash. Hence get charcoal in the ordinary way? And this bulk, this carbon, arises the very natural distinction of leaves into simple and is got out of the air. Yes, the largest tree, whatever its size, is compound. for the most part formed of carbon, and all this carbon once The forms which leaves assume are so very numerous, that existed in the gaseous form. Philosophers have made calcu. botanists are accustomed to indicate them by the similarities lations, from which it appears that the total amount of carbonic which they manifest to natural objects. Some are like shields, acid thus floating about in the atmosphere amounts to the for which reason they are termed peltiform (Latin, pelta, & enormous quantity of many tons, and that tons of carbonic shield); others are like hearts, whence they are termed cordiform acid hover over each acre of ground, ready to give up its carbon or cordate (Latin, cor, cordis, a heart). Some resemble feathers, to vegetables which require this substance. Before quitting others are jagged like a saw, whence arise the denominations this subject, we must not forget to direct the reader's attention penniform (Latin, penna, a feather or wing), serrate or serra: to the beautiful provision by means of which the amount of tiform (Latin, serra, a saw), and so forth; but we shall give in carbon necessary to be got rid of from the animal economy is our next lesson dra ings of the chief varieties of leaves, from an
- in the particular form of gas. Even supposing no inspection of which the various names respectively applied to
'jury to result, yet just think how dirty and begrimed them will be rendered more evident.
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 THE EAR.
that, it is very difficult to tell from whence the sound comes, A MAN who had been born blind, when asked what he supposed even to the extent of a whole quadrant of the horizon. Upon scarlet was like, replied, “Like the sound of a trumpet.” The this fact ventriloquism depends for its success. The idea of reply is startling, because it shows how dependent the mind is the direction of sound being inferential, and not much dependent upon the senses for its ideas. No one who could both see and upon the sense-being, in fact, owing to the operation of the bear wonld ever think of comparing sound with light, or tone mind, and not to that of the ear—the ventriloquist has only to with colour.
direct the mind where to expect the sound, and then to make a But though the sensations conveyed to the brain by the eye. sound of just such a pitch of intensity, and just such a tone, as nerve and the ear-nerve are so different as to be incomparable, the sound would have if it came from that quarter, to comthere is much resemblance between sound and light. They pletely impose on the ear of the listener as to the direction from obey the same laws. Sound can be absorbed, reflected, and which it comes. refracted at the surface of bodies, as we have seen light is; But although the ear is at fault as regards direction, the and, moreover, it is probable that both consist of rapid vibra- accuracy of some of its other notifications is wonderful in the tions, or waves, succeeding one another at regular intervals, extreme. It can note not only the likeness and difference of like the enlarging circles which follow one another and break musical sounds, but of their harmonies when many are sounded upon the banks when a stone is thrown into the middle of a together, and a fine ear will detect an erring note when a still pond, and disturbs the glassy surface of the water.
thousand instruments are sounded. The recognition of slight
I. THE HUMAN EAR. II. SECTION SHOWING THE HOLLOW OF THE COCHLEA. III. MALLEUS. IV. INCUS. V. STAPES. Reference to Nos, in Fig. I.-1, pinna ; 2, lobule; 3, tube ; 4, tympanic membrane ; 5, incus, or anvil ; 6, malleus, or hammer; 7, eustachian
tube; 8, semi-circular canals ; 9, vestibule; 10, cochlea.-I., II., III., and IV. enlarged.
Though there are these points of similarity as to the essential | differences is truly wonderful when we consider that not only nature and qualities of light and sound, there are also great can the ear know when the same note is sounded by instruments differences. Light travels with a rapidity which, for all appre- of different kinds (though physicists are unable to tell us how ciable distances—that is, for all earthly objects—is instan. there can be any difference, the number of vibrations in a second taneous ; while sound travels, relatively, very slowly, and, when being the same, and the medium identical), but very slight comidon air carries it, it goes only 1,093 feet during each second differences in the same kind of instruments, such as whether of time. Again, while the vibrations of light are so rapid that there is one per cent. more or less of a metal in an alloy of it is impossible to know them to be vibrations but by reasoning which an organ-pipe is made, or of which a bell is cast, are obtapon its effects, the waves of sound may be often observed by served so shrewdly, that these matters have to be attended to the eye when they are propagated through, or originated from, with the nicest care. A violin must not only be of a certain a solid body, as when we see a cord or glass vessel respond to i shape, but the wood of which it is composed must be of a certain a musical note, or give out a sound when struck. Sound, too, age, to produce the best instrument; and these observed dif. is the vibration of the substances themselves—which substance ferences are carried to such a nicety that fiddles made in a we can feel, or see, or know by means of other senses—while certain part of Germany, in a certain year, are considered the light is supposed to be the vibration of some fluid which is im. best, and will command almost fabulous sums. Yet all this ponderable, or, in other words, has no weight, and of which we depends upon what is called timbre, a word which gives a name know nothing except by the eye.
to a something which is entirely dependent on the delicacy of The waves of sound, then, being coarser and more liable to our sense of hearing, but which has not received any other interference than the waves of light, it follows that the ear explanation. esanot be so good an indicator of the direction of sound as the Though we cannot directly connect these niceties of sense Eye is of the direction of a luminous object. Indeed, the ear with the intricacies of complication in the organ of hearing, can of itself scarcely give us any idea of direction. If the sound these latter will be seen to be so numerous and peculiar when be short and sharp, like the piercing shriek of the bat, or even we describe the ear, that one is not surprised that much con.
nected with sound is unexplained, because there are so many gullet behind the nose and mouth. Through this passage the structures connected with the organ which has been given us as cavity is kept supplied with renewed air at the same pressure the recipient and interpreter of sound, at the use of which we as the external air. The reader may be conscious of the existence can hardly guess.
of these passages to the ears from the throat by preventing the That which is usually called the ear is familiar to every one air from rushing out of the mouth and nose, while he forces it as the external semi-circular cartilage, closely invested with up from his lungs. The cavity of the drum will then be disskin, and ending below in a soft lobule, which is sometimes the tended with air; hearing will be less perfect, by the unnatural support of barbarous pendants. This structure, which, when tension of the membranes, and there is a slight singing in the well formed, has a beauty of its own that needs no supplement ear. With a little practice, air may be conveyed through the or advertisement, is but a remote appendage to the true ear. mouth to the drum, without entering the lungs, and thus gases Though it in some sort collects sound, and protects the orifice have been applied as remedies to diseases of the ear. But the which leads down towards, not to the true ear, it is non-essential, exclusion of these from the lungs is difficult, and cannot be relied and can be dispensed with without much inconvenience ; so One of our greatest aurists, when pursuing his philan. that some of our poor ancestors, who found that they could not thropic and scientific investigations on the effect of chloroform retain both good external ears and good consciences, like and prussic acid applied thus, died, because he could not exclude William Prynne in the time of Charles I. and the Star Chamber, the latter deadly poison from his lungs as he had supposed he suffered less real loss than might have been anticipated. could. The proper, or essential ear, consists of a chamber longer
The external gristly ear is called the pinna, and though flat- than broad, communicating on its upper and outer side with tened as to its general surface, is somewhat folded into ridges three semi-circular canals, and at its front inner end with a And furrows, there being a rim round the outside and a channel cavity shaped like a snail-shell. within this, which deepens and widens as it runs first upward, The chamber is called the vestibule; this and the semi-cir. along the back part, then downward along the fore part to a cular canals are called together the labyrinth; and the hollow, central crypt. From this crypt the passage becomes narrower like that of a snail-shell, the cochlea. They are all channelled as it runs forward and inward to the pit of the ear. Sound, no out of the substance of the skull-bone before named as the temdoubt, is conveyed along this canal in the same direction as we poral. The part of this bone which lodges them juts inwards, have described its course. If the pinna were quite flat, sound so as to lie at the base of the brain, and is so strong and thick would rebound from it; but as it is so shaped, sound is caught as to be called the petrous or stony part of the bone. Accurately and reflected round the canal from point to point, as it is reflected resembling the bony labyrinth in shape, but a little smaller in round the Whispering Gallery of St. Paul's, and finally delivered its dimensions, so as to allow a little liquid to lie between it down the tube of the ear.
and the bone, is a membranous labyrinth. That part of the The tube is an inch and a half deep, and its innermost half membrane which is on the floor of the vestibule leaves its enters one of the bones of the head, called the temporal bone, proximity to the bone at the entrance of the cochlea, and forms and in this bone all the other parts of the ear are enclosed and a horizontal stage across the widest part of the spiral passage, protected. At the bottom of the tube is an oval membrane and so mounts round the three whorls of the spire, dividing it stretched across the passage, and barring the entrance to all into two parts; so that, if we may imagine a small insect ex. external objects. Behind this is a roundish, irregular cavity, ploring these regions, it could mount to the apex of the spire filled with air. This stretched fibrous membrane bounding the by either of two spiral staircases, the roof of the lower one being air cavity, naturally suggests the idea of a drum, shaped like a the floor of the upper. These circular staircases only commukettle-drum; and hence the cavity is called the tympanum, from nicate with one another at the point of the shell. The lower a Latin word meaning drum, and the parchment-like tissue the one at its foot communicates with the tympanum by the round membrane of the drum. It differs, however, from a kettle-drum hole, while the vestibule communicates with the chain of bones in that several orifices open into it, and it contains structures to by the oval hole. Hence, if our imaginary insect could gain be described presently.
access to the cochlea through the membrane of the round hole, On the further side of the drum is the true car, completely it must first mount to the top of the lower staircase, and then encased in bone, except at two very small holes, which are closed descend all the way down the upper one, before it could explore with membrane. The larger and upper aperture is called the the labyrinth. oval hole, and the smaller and lower the round hole. From the All the cavities are filled with Auid, by whose agency the membrane of the tympanum to the membrane of the oval hole vibrations are conveyed along its walls; and in these walls, stretches a chain of bones, whose shape is best seen in the en especially at certain parts, are distributed the nerve-fibres of graving. The outer one, next the parchment of the drum, is the nerve of hearing. It would seem, however, as though the called the hammer. It has three processes, or projections, two vibrations of the liquid are not enough to impress the nerve, of which are long; so that, rather than hammer, it might be and there are found small, hard structures wherever the nervecalled a woodcutter's beetle. One of these processes, called the threads are most thickly placed, and at two places in the floor handle, is attached to the centre of the membrane, which it of the vestibule are found collections of small, hard, marble makes tight when pulled inward by a small muscle, and lax stones, held in a mesh of fibres ; so that, as the waves sweep when another muscle acts on it.
by in the liquid, these are made to strike and rebound against The former operation is probably the action which we uncon. the nerves. The spiral sheet of membrane which divides the sciously cause when we consciously listen. The head of the cochlea receives the nerves from a main nerve which runs up bammer is applied to another bone called the anvil (incus). It the central pillar, and it has in its substance fibrous bars, which has two processes, one for its suspension to the wall of the radiate outwards at regular intervals, like the key.notes of a tympanic cavity, and the other to connect it with the third or piano, and, like these, each is supposed to receive and transmit stirrup-bone (stapes). This bone is more like the article it is to the nerve at its root a separate note. Thus the spiral sheet named from than the others are, and the foot-part of the stirrup of the cochlea is supposed to be able to appreciate difference in is applied to the oval membrane, which it nearly covers. These tone, and the labyrinth differences in the amount of sound. bones can move a little in relation to one another, and their The nerves from all parts are collected into one bundle, but, as actions are imited by small muscles, but they usually act to is usual with nerves wherever they may be found, the strands gether as if in one piece, playing round an axis which runs remain distinct. through the heads of the hammer and anvil, so that when the To assist the reader in his conception of the car, we may tympanic membrane is thrust in and out by vibration, the mem compare it to a house of business. The pinna is the house-front; brane of the oval hole is made to vibrate correspondingly. The the tube is the porch ; the drum-membrane the front door round hole is open to the influence of sound conveyed through (closed); the drum is the hall; a few steps, the cssicles, lead the air of the tympanum; but whether this be its function, or to an office, round which are convenient counters, closets, and merely to allow the fluid of the internal ear to be more readily passages, at which clerks enter business transactions; while, thrown into vibration in the passage it fills—in other words, directly communicating with this large office, cognisant of all whether it be a hole for the entrance or exit of vibrations-seems proceedings, but reserving to himself any special business, sits hard to tell.
the general manager, who has also a door direct to the hall; The fore-part of the drum cavity is connected with the throat whilst, at the back of the premises, telegraph wires run to the by a passage, which runs forward and downwards to open in the London agent.