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LESSONS IN PHYSIOLOGY.-No. II.

MAN.

This

You remember what we said in our first lesson about the
little germ, from which all animal substance comes.
germ is surrounded by a fluid in which it floats, and from
which it draws those elements which are necessary for its
growth and enlargement. It then becomes a cell, including
within itself other little germs, which, on the bursting of this
parent-cell, are set free to perpetuate themselves from genera-
tion to generation.

In a vegetable, as we find, all that is required for the growth of such a cell, is a supply of water and carbonic acid; because the acid being the product of carbon and oxygen, and the water of oxygen and hydrogen, the water and the acid supply the three elements-oxygen, hydrogen, and carbon-which enter into the composition of the plant. Now it is so arranged that the vegetable kingdom supplies all that is required for the growth and increase of the germ in the animal economy. In other words :-if a vegetable needs nothing more than a supply of water and carbonic acid for its maintenance and reproduction, then, to sustain life, an animal needs only a corresponding supply of vegetable substance. So with the little germ. By the principle of life within itself, it can take up and appropriate from the elements which surround it whatever is suited to its own nature, make it a part of itself, and impart to it its own vitality. It is in connexion with this principle of life that we must seek for those wondrous changes which all matter undergoes in the act of being taken up and assimilated to any living thing. For example:-The food which we take into our stomach, goes through a wonderful process before it is in a state to become a part of ourselves; and this process could never be effected but for the principle of life in the human body. It could not be done either by chemical action or by mechanical force. It is not only something different from these and from all other known physical causes, but that which rises above them-that which includes them and controls them-that to which they are subject, and by virtue of which, each particle takes on all the characteristic properties and attributes which belong to the body itself.

To the question:-What is this vital action ?-we can give no other answer, than that it is one of those terms which man has invented to conceal his ignorance of those profounder laws which pervade the whole organic world. This, however, we can say, that in proportion to the vital activity of any organised structure, the shorter will be the term of its life. Increase the activity, and existence is shortened. On the other hand, diminish the activity, and life is prolonged. Take the following example :-Put a corn-seed in a place in which it will be impossible for the hidden life within it to be developed, and in this state it may remain for ages multiplied by ages. This suspended vital action is not to be looked upon as death, which implies a total loss of vital properties; but only as a dormant vitality. Let us suppose that the cornseed had been deposited in an Egyptian mummy, and that it had been there for thousands of years, but that we take it out, and so change the conditions of its being as to subject it to the influence of soil, and rain, and light, and heat, and it will soon take root, spring up, bear fruit, and go through the whole vital operations, as if those operations had never been sus pended. But mark-the seed which existed for thousands on thousands of years in one condition, in the possession of a hidden life, when that life becomes developed soon ceases to be. How is this? Because by putting the seed in the ground, and so bringing it under all those outward influences which favour vegetation and growth, we have increased the vital activity, and so shortened its life.

To take another illustration. Bring up nearer to the surface some of the deeper soil of a field, and seeds which had been long embedded in that soil, will come up in the form of flowers and plants. But how soon do these flowers wither, and these plants die? Raspberry trees have been raised from seeds taken from the stomach of a man whose skeleton was found thirty feet below the surface of the earth. Nor is it possible to say how long this vital action might be suspended without in the least degree impairing the vitality itself. Life is something which cannot be destroyed. We may damage and

render useless the mechanism through which life manifests
itself, but life we cannot touch. As all organised being has
its origin or commencement in a single germ, it follows that
and this principle it is which in every organised being chal-
in that germ there must be a vital and imperishable principle;
lenges all the changes of time, and all the force of created and
finite power to destroy.
rived the substance called cartilage or
From these little germs and cells (fig. 1.), we have seen, is de-
gristle, and out of this gristle or cartilage
Fig. 1.
is bone developed. Of bones we have

found that there are in the human
body one hundred and ninety-eight,
exclusive of the teeth. Of this number
thirty-four are single bones, and all
the rest go in pairs. The bones are
the same in each arm and hand, in
each leg and foot, on each side of the
head, and the ribs are the same on each side of the trunk. We
have seen what a beautiful structure these bones make in the
human skeleton; how exquisitely they are fitted the one to
the other; how firmly they are attached and held together by
cartilage and ligament; and how easily and harmoniously
they move upon each other by means of the synovial fluid
which is found between these joints. The bones being the
hardest parts of our bodies, they form a frame-work for
protecting the vital organs, as the heart or lungs; they make
complete cases where the more delicate textures, as the brain
and spinal marrow, are securely lodged; they constitute also
a firm basis on which the moving powers are fixed; a series of
levers, by means of which, through the agency of the muscles,
locomotion and all the various offices of life are performed.
The bones, then, would be of no use without the muscles.
If the muscles need a lever, or a firm and inflexible body with
which to act, this lever or inflexible body would be more than
useless without the muscles as agents to move and work it.
Now, whence is muscle derived, and how is it formed? To
again go back to the little
answer this question, we must
Fig. 2.
germ. When the germ has
grown into a cell, from the cell
there comes a further develop-
ment in the shape of filaments
or threads (fig. 2.), of such ex-
ceeding fineness as in some in-
stances not to exceed the 20-
thousandth part of an inch.
Larger than these, but of es-
sentially the same character,
are those fibres which enter
into the formation of the mus-
cles. These fibres consist of
a series of filaments, and take
the form of a tube, with a pecu-
liar enlargement at frequent
intervals. They are arranged
in parallel lines, and present
the appearance of bands or
little bundles. Look at this
mass of fibres as it exists in the
larger muscles of the chest in a
baby just before birth. You
see how these fibres resemble
so many small tubes, while the
little bodies or enlargements
which you observe upon them
are centres of nutrition, from
which come the cells that com-
pose these fibres. In the adult,
the diameter of these fibres is
three times larger than it is
in the infant, as you may
see by looking at figure 3,
which represents organic mus-
cular fibres magnified three
hundred and fifty times. And even this does not much ex-
ceed one fifteen-hundredth part of an inch.

[graphic]

vessels, but the vessels run in parallel lines in the minute spaces between the fibres, so that each fibre is in close relation with a blood-vessel, from which it draws materials for its growth and renovation (fig. 4). These vessels are very minute and very numerous; and as they convey thither the blood after

Fig. 4.

length, but increased their diameter, as they bulge out in the centre. Or take a still simpler experiment. When you undress on going to bed, make naked your arm, then bend it, and you will see how much thicker it appears than when you extend it, or hold it down. It is the position of the muscles which is altered, not their bulk.

In cold-blooded animals this power of contraction is found to remain for some considerable time after death. For example:-the heart of a frog will go on beating for many hours after it has been taken from the body; and so the heart of a sturgeon which had been first filled with air, and then hung up to dry, has been seen to continue beating until it became so dry as to rustle with every successive movement. In the case of men who have been executed, the heart has been known to contract even sixteen hours after death.

This power of contraction depends on the health and notrishment of the muscles. Being nourished by a due supply of blood, the flow of blood increases with the use that is made of the muscles themselves. What would be sufficient for an individual leading an inactive life, would be far too little for another individual who is continually exercising his muscular power. The nourishment is in proportion to the flow of pure blood; and in proportion to the nutrition is the power of the muscle. Hence it is, that the more a muscle is exerted it has passed through the lungs, and been purified by coming or exercised, the more powerful and the more bulky does it into contact with the oxygen of the air which we breathe, become. For example:-look at the arm of a blacksmith, this accounts for that beautiful bright red colour which dis-or at the leg of an opera dancer, and what a difference do they tinguishes the muscle or flesh of animals. Without such a present in bulk and strength to the leg and arm of persons supply of blood the muscles would be wholly unfit for action. whose muscles are never called into such active and healthful They would lose their power of contracting, and thus become play. Fig. 6 gives a view of the form and arrangement of a useless in the animal economy. number of the principal muscles in the human body. Fig. 6.

Not only is the substance of muscle full of these capillaries, or hair-like blood-vessels, but, next to the skin, the muscles are most copiously supplied with nerves. These nerves form a series of loops, and seldom, if ever, terminate in the substance of the muscle itself (fig. 5). They possess the power or property of convey

ing impressions to th brain, the brain communicates with the mind, and the mind expresses itself through the will. The mind has not only the consciousness of power, but can express that power in its will and determination. If I

wish to raise my hand

Fig. 5.

or to extend my arm, I will it, and I do it. My will to do it, is my power to do it. If the structure of my body be perfect, my will acts on the nervous system, the nerves act as a medium of conveying an impression or stimulus to the particular muscles, and no sooner is the stimulus felt, than the hand is raised, or the arm is extended.

But the most wonderful thing in the muscles is their power of contracting, or shortening themselves, on the application of any external stimulus. Something of the same kind we find in the vegetable kingdom. Touch ever so gently the leaf of the Sensitive Plant, and it will immediately contract, or draw itself in, or close. Stimulate the muscle itself, or convey the stimulus through the nerves which go to the muscle, and immediately the contraction takes place. We do not mean that there can be no contraction without nervous action. The contrary of this is true. But, wherever a nervous system exists, the nerves have to do more or less with the contraction of the muscles. This contraction will take place under the influence of heat, or cold, or electricity. If you plunge your hand into an alkaline or acid fluid, you will have the feeling of contraction in the muscles of the hand. This contraction does not affect the bulk of the muscle. As you make its two ends approach each other, you indeed shorten it in the direction of its fibres, but its diameter enlarges in the same proportion. This you may prove by a very simple experiment. Take a skein of thread or worsted in loose threads, fasten both ends to a piece of whalebone or hoop: bring these two ends to approach each other by bending the hoop or whalebone, and you will find that you have shortened the threads in their

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BIOGRAPHY.

are those which are under the influence and government of the will-such as the muscles of locomotion. If I wish to move from one place to another, I have but to will it, and at once all the muscles needful for motion are called into exercise. But the involuntary muscles are those over which the will has no power. Over the movements of such vital organs as the heart, stomach, and intestines, we have no control. Cases have been reported of individuals having the power of determining the action of the heart, but it may be questioned whether such cases have ever been fully established.

In addition to these two divisions, there is the class of MIXED MUSCLES, as the diaphragm and other organs of respiration, certain muscles of the eye, and some others, of the action of which we are not sensible, unless the mind be directed specially to them, and yet we have the power of increasing or suspending their action for a longer or shorter length of time.

There is part of the muscles called TENDONS, which present the appearance of a fibrous cord, and conduct the motions of the muscles to the bone. They are made up of small white fibres, closely united to each other, and have a beautiful shining silvery appearance. This appearance is owing to the fact, that they are not, like the body of a muscle, supplied with blood-vessels. Into one of these tendons all the fibres, and consequently all the strength of one of the largest and most powerful muscles, may be seen to concentrate and become fixed on a small bony surface, where there would not be room for the insertion of all the muscular fibres. These tendons, again, are protected by sheaths, which are composed of close and strong fibres; while some of them, as those of the wrist and in the instep, contain the united tendons of several muscles. An arrangement this, which, like all the other arrangements in the human body, sets forth the wisdom and the goodness of that God all whose works are perfect, and whose infinite and unchangeable mind delights in the happiness of all his

creatures.

The form and arrangement of the muscles are such as we might expect from a Being of supreme goodness. These muscles are the instruments or active agents in performing the various movements of the body. It is in connexion with them that we are endowed with the power of moving from place to place, and of performing every manual exercise and every bodily exertion. Deprive us of this muscular system, alter even its beautiful arrangement, and how do we know that we could either walk or speak? Speech we should have none. The blood would cease to circulate. The stomach and the intestines could no longer urge on their contents. The fluids tould no longer move forward in their appointed channels.

Of these muscles there are not fewer in the human subject than five hundred and twenty-seven, of which two hundred and fifty-seven are pairs, and lie on either side of the body; and with the exception of four single muscles situated on the middle line of the body, all the rest are internal, and are connected with the vital functions.

What a world do we each carry about with us! How sublime are its wonders! KNOW THYSELF, is a sentiment which was deemed worthy of a divine origin and a heavenly descent. And yet how little does man study himself-his own nature body, soul, and spirit! Familiar with the world without, how little does he know of the world within! While throwing back fold after fold of the veil from the face of external nature, and inquiring into its hidden secrets, how forgetful is he that there is the temple of his own humanity still to enter, with its deeper veil to lift, and its grander mysteries to explore! Let it not be so with us! Let us give ourselves to diligent study, and just as we advance step by step-just as we come to know more and understand more of the curious structure of our own bodies, the more inclined shall we be to take up the sentiment of the inspired writer, and with the same loving and adoring feelings to exclaim-"I am fearfully and wonderfully made; marvellous are thy works, and that my soul knoweth right well."

QUESTIONS FOR EXAMINATION.

Whence does the vegetable get its supply of materials?
What provision exists for the growth of the animal economy?
What is that substance called in which the bones are formed?

How and from what is the muscle formed?
What gives to the muscles their beautifully bright red colour?
In connexion with what are these little hair-like blood vessels
found?

Are the muscles largely supplied with nerves?
What office do the nerves fulfil in connexion with the muscles
What is the grand distinguishing property of a muscle?
In contracting, does the muscle lose any of its bulk?
Explain by some example how the bulk remains the same.
Does this power of contracting depend on the nerves?
Can muscle contract after death?

Give an example in proof of this fact.

On what does the nourishment of a muscle depend?
Does a muscle increase by exercise?

Give an example of this increase in some well-known cases.
Into how many classes do the muscles divide themselves?
What do you mean by the involuntary muscles?
What examples have we of involuntary muscles?
Are there any mixed muscles? Name one or two.
What is a tendon?

What purpose do tendons serve?

What would occur if the muscular system was changed? What does the present arrangement prove in relation to God as the Creator?

BIOGRAPHY.-No. I.

ALEXANDER MURRAY.

IN bringing before our readers occasional biographical notices, we shall endeavour to select such examples-like that of Stone in our first number, and that of Murray in our present number-as will tend to excite in all, but especially in the young, a laudable desire to imitate their indomitable industry and their noble self-denial, in the acquisition of the various branches of knowledge, or walks of art, which have made their names remarkable. Every individual who allows the faculties of his mind a fair degree of scope and exercise, some peculiar walk of life, in which he is more likely than in any will sooner or later discover that there is some art or science, or other to rise to excellence; and that if he follows the real bent of his genius in an honest and honourable manner, he will be sure to meet with success, not only in the superiority to which he will attain in his own peculiar department, but in the high reward with which his labours will ultimately be crowned.

Alexander Murray was the son of a shepherd who lived in the his letters by writing them on a board with a burnt stick, for shire of Kircudbright. At the age of 76, his father taught him want of book and slate.

There was, indeed, a "Shorter Catechism" in that humble dwelling, which in Scotland is generally printed with a copy of the alphabet, in a large type; it was bought by the old man expressly for his little son, but then it was deemed "too good a book" to be plements for acquiring knowledge had fully answered their purpose. commonly handled, and was therefore locked up till these rude imThen only was the catechism presented, and in a month or two, Sandy could read the easier parts of it; and with the board and the brand, he still daily amused himself with copying the printed Not long after, his father gave him a small psalm book letters. for which he totally abandoned the catechism-a book which he seemed never to have liked; and this cannot be much wondered at; for it contained such an abstract and condensed view of the Scriptures, as was only adapted for the hardest headed Calvinistic theologian. He soon committed many psalms to memory, and longed for a new book. books were likely to be found in a Galloway shepherd's hut seventy years ago? The Bible, indeed was used every night in the family; but the Bible appropriated to these exercises of domestic religion, Sandy was not permitted either to open or touch. The rest of the books were put up in chests. At length, however, he obtained a New Testament, and read the historical portions with great curiosity and ardour; but he longed to read the Old Testament, and actually went to where he knew an old loose-leaved Bible lay, and carried it away piece-meal. He pored over these pieces of the Bible in secret for many months, but durst not show them openly; and as he read constantly and remembered well, he soon astonished all the neighbours by the large passages of Scripture he was able to repeat.

But here difficulties arose; for what

Two or three scores of sheep, with four muirland cows, were the whole property of his father. No sooner, therefore, was he

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seven or eight years of age, than he was sent to the hills with the sheep. But he was not robust, and consequently not so agile as those who were so; and he was short-sighted, which his father did not know; his own account is, "I was sedentary, indolent, and given to books, and writing on boards with coals.' Sandy's father was too poor to send him to school, but on one of his uncles coming to pay the family a visit, he heard such accounts of the genius of his nephew, whose abilities and knowledge were the discourse of the whole glen, that he offered to support him for a short time at a school in New Galloway. Here Sandy made, at first, only an awkward figure. "My pronunciation," he says, “was laughed at, and my whole speech was a subject of fun. But I soon gained impudence; and before the vacation, I often stood dux of the bible class. I was in the meantime taught to write copies, and use paper and ink. But I both wrote and printed, that is, imitated printed letters, when out of school."

Scarcely, however, had three months elapsed, when illness compelled him to return home; and for nearly five years he was left again to be his own instructor. As soon as he became sufficiently well, he was once more a shepherd's boy. He now spent every sixpence that friends or strangers gave him, on ballads and penny histories, bundles of which he carried in his pockets, and read them when sent to look for cattle on the banks of Lake Loch, Greenock, and on the wild hills of its neighbourhood. Still he excited much astonishment by his attainments, and many said he was a living miracle." When about twelve years old, he borrowed from a friend, a translation of the works of Josephus, the Jewish historian, and Salmon's Geographical Grammar. From the latter he derived "immense benefit;" it gave him an idea of geography and universal history, and many years after he arrived at manhood, he says, “I actually recollect at this day almost everything it contains." He learned to copy the maps which he found in this volume; he even made similar delineations of his native glen and its neighbourhood; and the grammar of geography had no little share in determining the direction and character of his future life.

He now went as a teacher into the families of two of the neighbouring farmers, and received for his labours during the winter, the sum of sixteen shillings. He immediately laid out a part of it in books; one of which was "Cocker's Arithmetic," and in two or three months, advanced to the rule of three, with no other assistance except the use of an old copy-book of examples made by some boy at school, and a few verbal directions from his brother Robert.

At school, during three months and a half, when he was about fifteen years of age, he seems to have imbibed his taste for learning foreign languages, about which Salmon's Grammar had previously awakened much interest. Observing that the divisions of the 119th Psalm were marked by the letters of the Hebrew alphabet, he printed them off in his usual way and kept them, and began the study of the French language. But, an interesting incident occurred; one of his class-mates told him that he had once studied Latin for a fortnight, but had not liked it, and that he still had "the Rudiments" by him. The results of this conversation he thus describes :-" I said, Do lend it me; I wish to see what the nouns and verbs are like, and whether they resemble French. He gave me the book. I examined it for four or five days, and found that the nouns had changes on the last syllables, and looked very singular. I used to repeat a lesson from the French Rudiments every forenoon at school." Accidentally putting his Latin Rudiments in his pocket by mistake, and pulling it out, his master said, "Sandy, I shall try thee with Latin; and accordingly, he read over to me no less than two of the declensions. It was his custom to permit me to get as long lessons as I pleased, and never to fetter me by joining me to a class. There was at that time in the school a class of four boys, advanced as far as the pronouns in Latin grammar. They ridiculed me on account of my separated condition. But before the vacation, I had reached the end of the Rudiments, knew a good deal more than they did, by reading at home the notes at the foot of each page, and was so greatly improved in French, that I could read almost any French book at the opening of it. I compared French and Latin, and rivetted the words of both in my memory by this practice. When proceeding with the Latin verbs, I often sat in the school during play-hours, and pored on the first page of a schoolfellow's Greek Grammar-the only one I had ever seen. He was then reading Livy and learning Greek. By help of his book I mastered the letters, but I saw the sense of the Latin rules in a very indistinct manner.' Murray now obtained two or

three Latin books from a friend and some of his school-fellows, end was much aided by one that had a literal interpretation. "When my lesson was prepared," he says, "I always made an excursion into the rest of every book; and my books were not, like those of other schoolboys, opened only in one place, and where the lesson lay." In the following winter he was, as usual, occupied in teaching; but he continued to pursue his studies in private. Having bought an old copy of Ainsworth's Latin Dictionary, he says—“ I literally read the dictionary throughout. My method was to resolve the leaves of the letter A, to notice all the principal words and their Greek synonymes, not omitting a glance at the Hebrew; to do the same by B, and so on through the book. I then returned from X and Z to A; and in these winter months, I collected a large stock of Latin and Greek vocables."

He was now sixteen years of age, and he devoted the summer at this time, to hard and continued reading. He had, in fact, and that chiefly by his own unassisted exertions, made himself familiar with the French, Latin, Greek, and Hebrew languages. and perused several of the principal authors in all of them, within about a year and a half from the period when they were all entirely unknown to him-a most extraordinary instance of youthful ardour and perseverance.

It was not long before an event occurred to him, of signal importance. Mr. Kinnear, a journeyman printer in the King's Printing-office at Edinburgh, urged him to send an account of himself and his attainments to that city, with a promise to bring it before some of its literary characters; the result was, that mensures were taken to have the classes of the university thrown open to him, and his maintenance secured during his time of attendance. Passing on through the course of education necessary to qualify him for the ministry in the Scottish church, he continued to pursue, with his former enthusiasm, the study of languages. He devoted his leisure moments, while minister of Uir, in Dumfriesshire, for six years, to the composition of his stupendous work on the languages of Europe.

On the professorship of oriental languages, in the university of Edinburgh, becoming vacant in 1812, he was most warmly recommended to become a candidate to fill this chair. Among his testimonials was that of Mr. Salt, so eminent as an orientalist :-" My acquaintance with Mr. Murray," he wrote, "originated in my admiration of the deep erudition and extensive research displayed in his edition of Bruce's 'Abyssinia.' Having twice visited that country, I was led to pay particular attention to its history and literature, and in these pursuits I received so much assistance from Mr. Murray's labours, that I took an early opportunity, on my return to England, in February, 1811, from the mission to Abyssinia in which I had been engaged, to recommend him to the Marquis Wellesley as the only person in the British dominions, in my opinion, adequate to translate an Ethiopic letter which I had brought from Ras Willida Selasé, addressed to the king. My recommendation was attended to, and Mr. Murray finished the translation in the most satisfactory way."

He was elected to the vacant office, and received from the senate of the university the degree of doctor of divinity. His health was, unhappily, but weak; in a few months illness seriously increased. To the last, however, he was surrounded by his books and papers, and dictated to an amanuensis; but Dr. Murray died in his thirtyeighth year, having prosecuted, during his short life, the study of languages with a zeal and success rarely approached, and probably never surpassed.

ANSWERS TO CORRESPONDENTS.

The suggestions of our correspondents at Leicester aud Brighton shall receive our serious consideration. PARLEZ VOUS FRANCAIS.-As we stated, in reply to a correspondent, in our last number, the "Series of Lessons in French," reprinted from the Working Man's Friend (which contains Twenty-five Lessons and an Appendix), will, by special permission of her Majesty's PostmasterGeneral," be transmitted free to any person's address on the receipt of

Seven Penny Stamps, at this office,

W. W.-The WORKING MAN'S FRIEND, New Series, is now issued

in half-yearly volumes, neatly bound and lettered, price 38. 6d-Vol. 1. is now ready, containing the HISTORY of CHINA and the CHINESE, and also the HISTORY of HUNGARY complete. The volume contains nearly two hundred engravings.

Other Answers and Solutions in our next number.

Printed and Published by JOHN CASSELL, 335, Strand, and Ludgate-hill, London.-April 17, 1852.

LESSONS IN GEOMETRY.-No. II.

INSTRUMENTS USED IN PRACTICAL GEOMETRY.

In the operations of practical geometry, a case of mathematical instruments must be considered as an essential requisite. These instruments vary in number and quality, according to their price. Some are made of wood, bone, and ivory-as rulers and scales; others are made of brass and steel, German silver, and other compound metals, such as compasses, drawing pens, and protractors. We shall proceed to describe the most useful, and afterwards to show their application.

The Common Ruler or Straight-edge.-This instrument generally consists of the bevelled edge of the plane or diagonal scale, of the common Gunter's scale, of an ordinary foot rule, or of a plain flat rule, made with a fine straight edge, for the sole purpose of drawing straight lines from Fig 1. one point to another, or through any two points. It is sometimes made in the form of a right-angled triangle (fig. 1), with a similar edge, to serve the various purposes of drawing straight lines, perpendiculars, right-angled triangles, and parallel straight lines. In the mechanical arts, a straight line is most readily obtained by fixing a well-chalked string firmly at both ends over the place where it is wanted, on a board or stone, raising it, when tense (i.e. stretched), above the same, and then letting it drop suddenly, when the white or chalky trace of the string will be marked on the board or stone as a straight line. The Parallel Ruler.-This very useful instrument is constructed in a variety of forms. Those represented in figs. 2, 3, and 4, are the most common, and the cheapest. Fig. 2. Fig. 3.

Fig. 4.

The

departure from the straight line will then become visible. A good ruler, besides having a straight edge, must be per fectly flat and even, flexible, and made of well-seasoned wood. Some are made of ivory, bone, and metal; these are less liable to be affected by changes in temperature, or by the humidity of the atmosphere. Parallel straight lines are most easily drawn by artists and mechanics, with an F or a T square, of which the form is distinctly noted by the name.

The Compasses, of which there are several kinds. This instrument, which usually consists of two equal legs jointed at one Fig. 6. extremity, is employed for measuring the lengths of

straight lines, measuring and laying off distances, and describing circles or arcs of circles in general. The Dividers, or compasses with dry points, represented in fig. 6, are chiefly used for dividing straight lines into equal parts, or into parts having any other proportion to each other. The best kind are furnished with a turnscrew for tightening the screw-axle at the joint. Others are furnished with an arc and tangent screw, to fix the legs at any required distance apart.

The Socket Compasses, represented in fig. 7, is furnished with moveable points, or pieces, which can be inserted in the socket at pleasure, according to the use which is to be made of them. It is chiefly employed in describing, that is, drawing circles, in ink, or in pencil, or in mere trace. in order to keep it perpendicular to the paper when the legs The tracing-point in fig. 7 is furnished with a joint and a screw, are stretched to a great length. The ink-point, represented in fig. 8, is furnished with a screw, to admit more or less ink at pleasure, with a joint for the same purpose as the tracer, and with a joint in one of the leaves of the point to admit of its being cleaned. The pencil or crayon-point, represented in fig. 9, is furnished with a joint for keeping the pencil or crayon perpendicular to the paper, and a socket or case for holding it. The socket compasses are also furnished with a lengthening bar, represented in fig. 10, which is furnished with a socket exactly the same as that of the leg, in order to admit of the description, that is, the drawing of larger circles than those which can be drawn only by the use of the moveable points and legs of the compasses. Fig. 7.

Fig. S.

Fig. 9.

Fig. 10.

defect of the construction in fig. 2 is, that in drawing a parallel to a straight line through a given point, if the latter be at a considerable distance from the former, the ruler may, from its lateral motion, pass the point altogether, and render the problem nugatory. This defect is obviated by the constructions in figs. 3 and 4, provided they be properly managed; but this management is the result of a little practice.

Fig. 5.

The triangular ruler represented in fig. 1 being made to slide against a fixed ruler or straight-edge, as represented in fig. 5, is frequently employed for the purpose of drawing parallel straight lines. In many cases, this apparatus will be found even more handy for this purpose than the parallel rulers represented above. Fig. 5 represents the same triangle in two different positions, and not two separate triangles.

In order to test the accuracy of a ruler, let it be applied to one eye, and

The Bow Compasses, so called because in their first construction they could be shut up into a hoop, which served as a handle to them or the Plug Compasses, represented in fig. 11, and so called because the stationary leg screws out and in like a plug, are only Fig. 11. used for describing circles of a very small size. Such compasses are of the greatest utility to draughtsmen and engineers in drawing their plans. The plug construction seems to present some advantages over the old bows.

Beam Compasses are employed for describing circles of very large radius, and such as are far beyond the reach of a case of mathematical instruments. They consist of a long beam or bar, carrying two brass cursors, that is, pieces on which it runs. One of these is fixed

at one end, and the other slides along the beam, and is fur

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viewed along its edge from one end to the other; the slightest nished with a screw to fix it at any required distance. To the

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