observations made on young dragon-trees, the growth of which is remarkably slow. What grand, what stupendous thoughts does a contemplation of this fact awaken! When did this monster first begin to grow? How many thousand years have rolled over its weather-beaten head? We are afraid to speculate on these points, but will content ourselves by saying that, according to the most reasonable evidence which can be adduced, this great dragon-tree began to grow long, very long, before the creation of man. Yet this monster is a lily!

The student will admit that, supposing our previous remarks to be correct, our ordinary notions concerning the similarities or dissimilarities of vegetables-in other words, their alliances, and as a consequence their classification—are very incorrect. Not less incorrect are some of our common ideas regarding the similarities and dissimilarities, or the alliances, of the parts of which vegetables are composed. For example, do we not commonly speak of onions and potatoes as roots? Yet they are not roots, nor are they similar, far less identical, in character. The onion is a bulb, or underground bud, and the potato is a tuber or knotty excrescence developed underground, from which the roots and stems of the potato plant respectively spring. Why are they not roots? the learner may ask. The reason why will appear by-and-by: to explain these reasons is an object, and one of the main objects, of botany. We merely cite the example now for the purpose of making known in a striking manner the incorrectness of many notions we are in the habit of entertaining.

Again, do we not in ordinary language term the strawberry and the fig fruits? Yet neither is a fruit.

"Not a fruit!" the learner exclaims, "do we not eat them?" Well, surely, our reader would not limit the term fruit to something which grows on a vegetable, and which is good to eat. We think he will admit that the bunches of apples, as they are called, which grow on potato stems, are the fruits of the potato plart; yet potato apples are not good to eat. He will admit that the bunches which grow on ash-trees are the fruits of those trees, yet they are not good to eat. Finally, not to multiply examples unnecessarily, he will admit that acorns are the fruits of the oak-tree; and although our ancestors, the ancient Britons, are known to have eaten them, yet all we can say upon that point is, that one pities the bad taste or the hard fortune, as the case may be, of our forefathers.

If strawberries, then, and figs are not fruits, what are they? Why, the fig is to all intents and purposes a compound flower, as much as the dandelion is a compound flower; and a strawberry is something like a fig turned inside out; but the learner shall judge for himself.

The strawberry plant bears, as we all know, a very evident, a very pretty flower, the petals or flower-leaves of which dropping of, we ultimately get something which is good to eat, and which we term the strawberry fruit.

Why, then, is it not a fruit? We will see. If it be a fruit, it should contain seeds; but on cutting it open we cannot find any. Here, then, the learner would be puzzled if botany did not cone to his aid. General principles have to be appealed to, and the appeal will not be made in vain. Whilst conjecturing within ourselves the botanical nature of the strawberry, and trying to find out the freak which Nature has been playing in order to lead us astray, we all at once bethink ourselves of the little hard protuberances on the outside of the strawberry. What are they ?-of what do they consist ?-what is their function ?

A learner, if he had not been rendered cautious by previous experience, might all at once arrive at the conclusion that the strawberry is a fruit turned inside out, having consequently its seeds externally; and amazingly 1. TORUS OF THE MARIGOLD. like seeds do these little protuberances appear. They are not seeds, nevertheless: they are fruits, the real strawberry fruits; but so little adapted or eating are they that the lover of strawberries wishes them very far away. Then what is the edible portion of the strawbery? Botany answers this question satisfactorily, and makes al clear. It is the juicy torus of the plant. The reader

gains little knowledge from this remark beyond the knowledge of an, at present, unmeaning name; and as we do not intend that any names in this series of papers on the Science of Botany shall be unmeaning, we will at once proceed to explain what a torus is.

Torus, then, is the Latin word for bed, and signifies that portion of certain flowers upon which the flower itself reposes or grows. Take, for example, the marigold, and strip off all its floral parts; there will then remain underneath a flat, fleshy expansion, called the torus. In the case of the marigold the torus is flat; but the reader may easily conceive that it might have been round or approaching to rotundity. In the marigold it is leathery and nauseous, but the reader will as easily conceive that it might have been fleshy and delicious, as indeed we find it to be in the strawberry. Analysed thus, we find a similarity between the strawberry and the marigold that the non-botanical reader would have little suspected. Nor is the similarity forced; it is natural, and loses nothing by the fullest investigation which the learner can devote to it. Thus, we dare say, the reader has watched the progress of a marigold to maturity; has noticed the flowers blown away, one by one, and nothing but the stem, the torus, and the little seed-like things embedded upon the torus remain. These little things, like the hard excrescences on the strawberry, look so much like seeds, that they might be taken for such. However, we are never to assume because a thing is small that it is imperfect. If these so-called seeds be dissected and examined, they will be found to be real fruits, as much as the apple or the pear, and so contain seeds internally.

2. LONGITUDINAL SECTION OF A FIG.

What is the fig? Nature here, if we different from those Let us cut open a

And now for our other example, the fig. Not a fruit certainly, although the freak of may without disrespect use such a term, is which have come under our notice hitherto. fig; what then do we see? Why, little things very similar in appearance to flowers, at the base of each of which there is a hard nut-like thing which cracks between the teeth. Flowers indeed they are, and the nut-like things are fruits, the edible portion of the fig being a torus; so that if we assume the strawberry to have had a flat torus instead of a knob-like one, and that the flat torus had been turned outside in, in such a manner as to form a bottle with a very narrow mouth, we should have had a result very much resembling a fig in structure and general appearance.

Even the delicious pine-apple can hardly be termed a fruit. Each pine-apple certainly contains many fruits, one corresponding with each lozenge-like marking; but the main bulk of the pine-apple, that which we find so delicious to eat, is only an assemblage of juicy fructs, as botanists call them, the exact counterpart of those little scales which, when tightly compressed together, form the cup of the acorn.

We are sure, then, that sufficient has been stated to make apparent to the reader the necessity of abandoning many common notions he may have previously entertained in relation to the similarities and dissimilarities of vegetables, and the parts of which they are made up.

LESSONS IN GERMAN.—I.

THE object of the author of these Lessons in German is to unite theory and practice; to introduce, one by one, the easier forms and usages of the language; and to direct the student's attention to the more obvious differences between the German and English languages. The learner will be supplied, throughout the various exercises, with the materials necessary for their due performance. Every section is headed with the statement and illustration of all new principles involved, with an explanation of words and phrases, and a vocabulary alphabetically arranged. To render these lessons complete, there will be given at the end a series of reading lessons, each accompanied by a full vocabulary. The whole is specially intended for those

preceded by a, o, or u, as will be perceived by experiment, a slight hissing sound of 8 or ich naturally attaches to the d, as in recht, reich, ich, Grieche, etc. EXERCISE 1.

i.

C.

Altar, altar; Baar, pair; Ahle, awl; Balsam, balsam; baten,
to bathe; Pfalm, psalm.

Heer, host; mehr, more; edel, noble; Ente, end; Letter, letter;
Herbft, autumn.

Trinken, to drink; finden, to find; Biber, beaver; hier, here;
Rint, child.

Beet, boat; hohl, hollow; oft, often; Hobel, plane; Roller,
collar; Koffer, trunk.

Fuß, foot; gut, good; unten, below; Putel, poodle; Kudud, cuckoo; Muth, courage.

Nymphe, nymph; Rhythmus, rhythm; Sylbe, syllable; synonym, synonym; Syrup, syrup.

si, ei. Main, Maine; mein, my; Laib, loaf; Leib, body; Rain, Cain;

3.

R.

T

3.

Achre, ear (of corn); Männer, men; leben, to live; Krähe, crow; nämlich, namely; nehmen, to take.

Löffel, spoon; Deffnung, opening; öfters, oftener; röthlich, reddish.

lebel, evil; fünf, five; Rüssel, proboscis; Krüppel, cripple; Jünger, disciple.

EXERCISE 2.

Glasse, class; Greatur, creature; Criminal, criminal; Lection, lesson; Galcutta, Calcutta ; Contract, contract; Gur, cure; Gement, cement; Giter, cider; Cylinder, cylinder. Gabe, gift; geben, to go; Giraffe, giraffe; geben, to give; Goit, gold; groß, large; Ring, ring; bringen, to bring; grün, green; grau, grey; ruhig, quiet; ewig, eternal; Berg,

mountain.

Hase, hare; hart, hard; Hunger, hunger; Horizont, horizon;
Mebl, flour; mehr, more.
Jüngling, youth; Sute, Jew; ja, yes; Joseph, Joseph; Juli,
July; Jurist, jurist.

Reif, ripe; reich, rich; Rest, rest; rar, rare; Rücksicht, regard;
Ferm, form; Räthsel, enigma.

Sattel, saddle; Segel, sail; Speer, spear; Sprofi, sprout;
starf, strong; Strumpf, stocking; Güt, south; Reis, rice;
Straße, street; wissen, to know.

Tisch, table; Tarif, tariff; Tempel, temple; Truppe, troop;
Titel, title; Devastation, devastation.
Vampyr, vampire; Base, vase; Vers, verse; Violine, violin;
Visite, visit; Valuation, valuation.

Bert, word; Wurm, worm; Wunter, wonder; Wille, will;

Wagen, wagon; Wanderer, wanderer.

3inf, zine; 3ahl, number; zahm, tame; 3eit, time; 3entner, hundred-weight; Holz, wood.

Ch. Flachs, flax; sprechen, to speak; wachsam, watchful; Chor, choir; Ghauffee, turnpike-road.

Sch. Schaft, shaft; Schatten, shadow; Schnee, snow; frisch, fresh ; Schilt, shield, sign.

f. Fleis, diligence; Flicß, fleece; lassen, to let; haffen, to hate; Haß, hatred; häßlich, ugly.

* 3 Size, heat; Klos, log; fibeln, to tickle; schwagen, to prattle; schwigen, to perspire; furz, short; schwarz, black.

honest voice to the closing strain. In public worship, too, no frowns or dissuasives could hinder him from "doing his best" to join in the praises of God. He often wondered how it was that he came to be born with "no voice," especially when he observed that the infants of the present day are so much more highly endowed, every one of them who attends an infant-school apparently taking for granted that he "has a voice," and using it accordingly. As a religious man, also, he could not help noticing that one whole book of the Scriptures was written for the promotion of public vocal praise, and that it abounded in such expressions as this: "Let the people praise thee, O God: let ALL the people praise thee." The example of Christ and the precepts of his apostles seemed also to set forth the same duty. "It cannot be," he sometimes reflected, "that the Father of all should command us to sing,' in addition to making melody with our hearts,' and yet give to so many of his children no voice!" Such thoughts as these led him to the conclusion that it is " no practice and no cultivation," rather than "no voice" and no ear," with which the majority of men are afflicted. In consequence of this, to the no small amusement of his musical acquaintance, our friend was soon found to have become an attentive and painstaking member of a singing class. He was soon deep in "thirds" and "fifths" and "sevenths," toiling at a series of the most unmusical exercises that could well be invented. But hope sweetens toil, and the expectation of conquering at last gave to our friend courage and long patience. When sixty laborious lessons, relieved by an occa sional song, were over, he made the discovery that he had learnt "a system," that he had gained also some confidence and much command of the organs of voice. But what did he know of music? Could he take the plainest psalm tune (not in the key of C), unseen before, and sing it? Alas! no. His labour had not been lost, but it had produced small fruit. He could follow the "leader" more promptly and easily, but he could not go about his endeavours. He could seldom be sure whether he without him. There was still an indecision and uncertainty not a few tune-books, which he had purchased in his hopeful was right or not by half a tone. And many a choice song, and days, lay on his table unenjoyed because of this musical uncertainty in which he was left. Once more, however, our friend has "taken heart," and has promised to follow the course of effort which we shall prescribe; we, on our part, undertaking that he shall in that case be enabled to sing at first sight by himself, and to make good use of the books on his table. We shall begin at the beginning, however, for your sake, gentle road" to music. No worthy attainment is won without labour. reader, if you will join him in his efforts. We have no royal advantage when the common road is very circuitous, and But we have a straight and clear road, and that is a great

66

to ask of you: the first, that you will be content to learn one thing at a time, instead of being impatient for knowledge not at the moment helpful-perhaps, just then, only confusing to you; the second, that when something is set before you to be done, you will really do it, instead of supposing it to be done, and going on; for only "by doing we truly understand."

abounding with needless hindrances. We have only two things

FIRST PRINCIPLES OF MUSIC.

You must allow us to lay before you certain fundamental method of teaching or of writing it-principles which would be principles of music itself-of music considered apart from any

66

true of music if Guido had never invented the "staff," and if "crotchet" and "quaver," flat" and "sharp," had never been heard of. You know what is the difference between "high" and "low" in music. The "squeak" is high, the "growl" is low. Recognise this difference to yourself now by singing first a high and then a low note. Between the highest and the lowest sounds which the human ear can appreciate, an indefinite number of other sounds may be produced. But how, out of this vast chaos of possible sounds, are the distinct and choice notes of a TUNE to start into life and power? The question is thus answered. Before a TUNE can be created, a certain sound, whether high or low in pitch, must be chosen and fixed as the KEY-NOTE (sometimes called the governing note, and in books of science the tonic) of the coming tune. Immediately, according to those laws of nature by which God has tuned our ears and souls, six other notes spring forth, at measured distances from the key-note,

claiming the sole right of attendance upon it.

Let this be clearly understood. Any sound may be taken for the KEYNOTE; and that being fixed, the places of the six other notes are known.

The common human ear throughout the world is pleased when these sounds attend that key-note, and is displeased when other sounds, not holding the same relation to the key-note, and not standing at precisely the same relative pitch, are used in their stead; for even an uncultivated ear would promptly mark the difference between the accurate singer and the inaccurate, between the singer in tune and the singer out of tune.

This distinct arrangement of six sounds around a key-note is called the musical "scale." It may be high in pitch in one tune, and low in another, but the relative position of its notes remains unchanged. These notes may be reproduced in replicates or "octaves of higher or lower pitch, but they still retain the same relation. Transition or "modulation" (which will be afterwards explained) may change the key-note in the course of a tune, but the new key-note governs its dependents exactly as the old one did. Every apparent exception only proves the rule. This one scale is the foundation of all music. Some speak of this scale as though it were of human invention; but if so, how is it that every newly-discovered nation is found either using it (if they are musical at all), or possessed of ears which readily approve it? How is it that the Chinese or Indians have not "invented" some other scale? The truth is, some of these nations do omit a note or two, but they do not alter the rest; and when the question is fairly examined, it is found the omissions were caused by their rude and incomplete instruments, rather than by defective ears. Again, let me ask, going back to the time of the ancient Greeks, of whose musical notation there is not a remnant from which we could have copied, how is it that we learn, from their philosophical treatises, that the scale which the people used was the same as ours? Could not that refined people have "invented" something better? Are we not right, then, in calling it the scale of all nations and of all times, the scale to which the ear and soul of man are tuned by the all-wise Creator ?

DOH'

5

TE

9

LAH

When we examine its structure more closely, we find other proofs that it comes from the hand of God. Like many of his works-the rainbow, for instance-it seems to the careless observer irregular, but discloses a beautiful harmony and purpose to him who is more thoughtful. The distances in pitch (that is, highness or lowness of sound), or, in other words, the intervals between the notes of this scale, are very delicately arranged. In another lesson we shall be able to describe its structure more minutely; but let it suffice for the present to say, that the simplest measurement of the scale in plain figures is that which divides it into fifty-three degrees. Such a division is only inaccurate to the extent of being about one-third of a degree too large. If you will make use of the sol-fa syllables to represent the notes of this scale, DOH standing for THE KEY-NOTE OF A TUNE, at whatever pitch it is taken, then the number of such degrees between each couple of notes may be set forth by the figures at the side. Why the scale of music found most acceptable to human ears should be thus curiously and delicately formed, and why it does not exhibit a greater apparent uniformity, we cannot tell. It is an "ultimate fact" of philosophy, like the structure of the rainbow. We must take it as it is, and reverently study the laws of its structure. Sir Isaac Newton's division of the spectrum into seven colours bore some analogy to these seven notes; and in a large work written by Mr. Hay, of Edinburgh, a clear relationship has been established between the principles of beauty in the human form, and certain angles founded on the proportions of the musical scale. Doubtless there are in the various departments of Nature certain uniting principles, certain secret affinities of things, which shall prove them all to have sprung from one creating Hand.

8

SOH

9 FAH 5

ME

8

RAY

9

DOH

It may, however, be noticed here, that every note of the scale sounds pleasantly, when heard at the same time with the key. note, excepting only RAY and TE; and of these, the most difficult notes of the scale, more will be said when our lessons are further advanced.

For the present, we wish your attention confined to the three notes, Dон, ME, and Soн, the first, the third, and the fifth. They are the strong notes of the scale, on which, as you will afterwards learn, the others lean. We may call them "the framework of the building." When sounded together they are commonly called the "chord of the tonic," tonic being the scientific name for key-note. Chiefly by these notes your voice must be tuned. Take, then, some low sound of your voice for the key-note, or Doн, and try to sing the following exercises, pointing to the notes on the scale given above, as you sing. This pointing on the scale is more important than you would at first imagine. In no other way can you obtain so clear a notion of the relative position of notes. If previously uninstructed, you must ask some musical friend to sing these notes to you, or play them on an instrument for a pattern. Do not, on any account, however, sing with him or let him sing with you. Remember that you are learning to sing alone. Your friend will know what notes to play when you tell him D, F sharp, A, and upper D'; or, if he prefers it, C, E, G, and upper C1. You will notice that when a note is repeated in a higher pitch, we put this mark (1) above it: thus, Doн1. You need not trouble yourself with the "staff" of five lines at present, except to notice that DOH is printed as a square note.

SOH

ME

Дон

DOH1 Note.-Sing these notes first slowly, then quickly, and again with a sound "long drawn out." Do not be disappointed if your friend pronounces you inaccurate in the first and second notes, though they are the easiest. Let him patiently set the "pattern "of those two notes again, and, if need be, many times again. Master one note at a time. Some pupils require several lessons, with much patient "patterning" of the teacher, and much careful listening, followed by vocal effort of the learner, before this exercise is perfectly done. EXERCISE 2.

LESSONS IN GEOMETRY.-I.

THE term Geometry, which comes from two Greek words, yn, the earth, and perpe, to measure (pronounced ghee, and met-rine), literally signifies land-measuring, and was originally applied to the practical purpose which its name signifies, in the land of Egypt, the cradle of the arts and sciences. Herodotus, the oldest historian, with the exception of Moses, whose works have reached us, gives the following account of its origin :-"I was informed by the priests at Thebes, that King Sesostris made a distribution of the territory of Egypt among all his subjects, assigning to each an equal portion of land, in the form of a quadrangle, and that from these allotments he used to derive his revenue, by exacting every year a certain tax. In cases, however, where a part of the land was washed away by the annual inundations of the Nile, the proprietor was permitted to present himself before the king, and signify what had happened. The king then used to send proper officers to examine and ascertain, by admeasurement, how much of the land had been washed away, in order that the amount of the tax to be paid for the future might be proportional to the land which remained. From this circumstance I am of opinion that geometry derived its origin; and from hence it was transmitted into Greece." The existence of the pyramids, the ruins of the temples, and the other architectural remains of ancient Egypt, supply evidence that its inhabitants possessed some knowledge of geometry, even in the higher sense in which we now use the term; although it is possible that the geometrical properties of figures necessary for the construction of such works might have been known only in the form of practical rules, without any scientific arrangement of geometrical truths, such as are presented to us in the Elements of Euclid.

The word "geometry," used in its highest and most extensive meaning, signifies the science of space; or that science which investigates and treats of the properties of, and relations existing among, definite portions of space, under the abstract division of lines, angles, surfaces, and volumes, without any regard to the physical properties of the bodies to which they belong. In this sense, it appears to be very doubtful whether the Egyptians or Chaldeans knew anything of the science. It is to the Greeks, therefore, that we must look for the real origin of geometry, as an abstract science. Thales, the Greek philosopher, born 640 B.C., is reported, by ancient historians, to have astonished even the Egyptians by his knowledge of this science. The founder of scientific geometry in Greece, however, appears to have been Pythagoras, who was born about 568 B.C. He discovered the celebrated 47th proposition of the first book of Euclid's Elements, and various other valuable and important theorems. He was great also in astronomy, having anticipated the Copernican system of the universe. Plato, another great geometrician, and founder of the academy at Athens, who was born 429 B.C., was the first who made some advances into what is called the higher geometry. The next name super-eminent in the science of geometry is that of Euclid, whose "Elements" has been the principal text-book for learners during a period of more than 2,000 years. He flourished at Alexandria, in Egypt, about 300 B.C., during the reign of Ptolemy Lagus, who was one of his pupils, and to whom he made the celebrated reply, when asked if there was a shorter way to geometry than by studying his Elements:-"No, sire, there is no royal road to geometry."

become a "household word." Scarcely less celebrated was the famous Apollonius of Perga, in Pamphylia, who flourished from B.c. 247 to 222, at Alexandria, in the reign of Ptolemy Euergetes, another king of the same Ptolemaic dynasty, and who was called by his contemporaries the "Great Geometer." He wrote several books, full of discoveries, on the higher geometry, and greatly extended the domains of the plane geometry. Other geometricians of eminence arose in the school of Alexandria, and bequeathed the precious remains of their genius to happier times. Claudius Ptolemæus, the author of the great work on astronomy called Megale Syntaxis, the Great Construction, or Almagest; Pappus, the author of the Mathematical Collections; and others, including Theon and his daughter Hypatia, bring us down to the period when the second Alexandrian library was burnt by command of the Mohammedan barbarian, the Saracen Caliph Omar, in 640, and the labour and learning of ages were irrevocably destroyed. The dark ages supervened, and little was done in the advancement of science until the glorious invention of printing, and the general revival of literature about the middle of the fifteenth century. The ancient Greek geometry was speedily made known to the moderns through the medium of translations of, and commentaries upon, the writings of the great masters. The Elements of Euclid, indeed, were reckoned so perfect, that no attempt was made to supersede them; and the only object of writers on geometry in general was to explain his works, and to make what additions they could to the science, in the same masterly style of composition. A host of names of eminent authors might be mentioned, who succeeded in establishing the Greek geometry, and in extending its domains. The principal of these, however, was Dr. Robert Simson, Professor of Mathematics in the University of Glasgow, who flourished in the middle of the last century. His grand endeavour was to present to modern Europe the Elements of Euclid as they originally appeared in ancient Greece. In this he succeeded to admiration, and his edition of this great work maintains its reputation to the present moment.

In giving our first lessons on geometry, we think it advisable to follow what seems to have been the natural course of events in the history of this science. The present advanced state of our geometrical knowledge was preceded in early times by a species of practical geometry gathered from experience, and suited to the wants of those who required its application, before any attempt was made to enter very deeply into the study of the theory. The latter was left to the schools of the philosophers and the academy of Plato. Accordingly, we shall precede our disquisitions on the Elements of Euclid and other geometers, both ancient and modern, by a short system of practical rules and easy explanations in this important science; and we shall endeavour to make the subject both simple and clear by plain definitions, suitable diagrams, and palpable demonstrations, after the manner of the French writers on this subject, who have even in their more elaborate treatises to a great extent abandoned the system of Euclid.

DEFINITIONS.

has three dimensions, viz., length, breadth, and thickness. 1. Extension, or the space which any body in nature occupies, This is Euclid's definition of a geometrical solid.

2. A point is the beginning of extension, but no part of it; hence it is said to have position in space, but no magnitude. to have length without breadth. Hence, also, the extremities 3. A line is extension in one direction only; hence, it is said of a line are points; and lines intersect or cross each other only in points.

5. A crooked line is one composed of straight lines joined at

*The first library, which was founded by Ptolemy Soter, and which was said to have contained 400,000 manuscripts, was accidentally burnt 47 B.C., when Alexandria was taken by Julius Cæsar. second library is supposed to have contained 700,000 volumes.

The