hended the raceme, the panicle, the corymb, the umbel, the spike, the capitulum, and the cyme, all of which we shall now proceed to describe.

or stem.

The raceme, from the Latin racemus, a cluster, is that kind of inflorescence in which the pedicels or secondary axes are almost equal in length, and arise immediately from the primary axis Of this kind of inflorescence the black, white, and red currant-trees offer familiar examples (Fig. 62). The panicle (from the Latin panicula, anything of a little round swollen figure, the diminutive of panus, a woof about the quill in a shuttle), sometimes called a compound raceme, is a form of inflorescence in which the secondary axes or pedicels, springing from the primary axis or stem, do not at once bear each a terminal flower, but ramify a third, and sometimes even a fourth time. Of this description is the inflorescence of the horse-chestnut (Fig. 63).

The corymb, from the Greek Kоруμßоs (pronounced kor-um'-bos), a branch, is that kind of inflorescence in which the lower pedicels, much longer than the upper ones, terminate, in consequence of this difference of length, at the same level, or nearly so, as the latter. An example of this is afforded by the Mahaleb cherry, of whose inflorescence a diagram is appended (Fig. 64).

The umbel, from the Latin umbella, a little shade, the diminutive of umbra, a shade, is an inflorescence in which the pedicels or secondary axes, being equal in length amongst themselves, spring from the same level, rise to the same height, and diverge like the ribs of an umbrella or parasol. An umbel is simple when each pedicel terminates at once in a flower, as, for example, in the common cherry (Fig. 65); and compound when the pedicels, instead of terminating at once each in its own flower, severally give off other pedicels on which the flowers are arranged. An example of this is seen in the common fennel (Fig. 66).

The spike, from the Latin spica, a point, may be either simple or compound. The compound spike is that form of inflorescence in which the pedicels are completely, or almost completely wanting, and the flowers accordingly are sessile, as may be seen in the vervain (Fig. 70). The compound spike is that form in which the secondary axes, instead of terminating in a flower, emit each a little flower-bearing pedicel. Of this description is the inflorescence of wheat (Fig. 69).

The capitulum, from the Latin caput, a head, is the form of inflorescence in which sessile flowers are collected upon the thickened head, called torus, of a peduncle. This torus may be flat, as we see it in the marigold and the scabious (Fig. 71), or concave, as in the fig. It appears, then, that the capitulum is that form of inflorescence to which the fig belongs.

The cyme, from the Greek kuua (pronounced ku'-ma), a wave, is a definite inflorescence which imitates by turns several of the indefinite kinds of inflorescence, from all of which it essentially differs in the circumstance that the primary axis is itself terminated by a flower which appears before the others; each of the subsidiary axes also terminates in a flower, but the secondary axes flourish before the tertiary ones, tertiary axes before quaternary ones, and so on in iike manner for the rest. The chief varieties of the cyme are the racemous cyme, as in the campanula or blue-bell; the dichotomous, or divided, cyme (Fig. 67), from the Greek dixa, apart, and reμvw (pronounced tem-no), to cut; the corymbous cyme (Fig. 72); the umbellar cyme (Fig. 74); the scorpioidal, or scorpion-like, cyme, as in the myosotis or forget-me-not; and the contracted cyme, in which the flowers are crowded together through the extreme shortness of the axes. The fascicule, from the Latin fasciculus, a little bundle, is an inflorescence in which the axes preserve a certain length and an irregular distribution, as in the sweet-william.

Mixed inflorescence is that which partakes of the characters of both definite and indefinite inflorescence. In the dead-nettle the general inflorescence is indefinite, whilst the partial inflorescence consists of true cymes or fascicules. In the mallow there is a similar arrangement (Fig. 73). In the groundsel (Fig. 68) and the chrysanthemum the general inflorescence is a definite corymb, but the partial inflorescences are capitulous. In the family of plants called umbelliferous. and to which the carrot, the fennel, angelica, etc., belong, each umbel in itself is indefinite, but the aggregate of umbels is definite; frequently, indeed, the axis of an umbel bears a little central umbel of

its own.

Banished from Rome! what's banished, but set free from daily contact of the things I loathe ? "Tried and convicted traitor"Who says this? Who'll prove it, at his peril, on my head? "Banished?"-I thank you for 't. It breaks my chain! I beld some slack allegiance till this hour-but now my sword's my own. Your consul's merciful. For this all thanks. He dares not touch a hair of Catiline. "Traitor!" I go - but I return. This trial! Here I devote your senate! I've had wrongs to stir a fever in the blood of age. This day is the birth of sorrows. The eye could at once command a long-stretching vista, seemingly closed and shut up at both extremities by the coalescing cliffs. It seemed like Laocoon struggling ineffectually in the hideous coils of the monster Python.

In those mournful months, when vegetables and animals are alike coërced by cold, man is tributary to the howling storm and the sullen sky; and is, in the pathetic phrase of Johnson, a "slave to gloom."

I would call upon all the true sons of humanity to cooperate with the laws of man and the justice of Heaven in abolishing this "cursed traffic."

Come, faith, and people these deserts! Come and reänimate these regions of forgetfulness.

I am a professed lucubrator; and who so well qualified to delineate the sable hours, as

A meagre, muse-rid mope, adjust and thin ?" He forsook, therefore, the bustling tents of his father, the pleasant "south country" and the "well Lahai-roi;" he went out and pen

sively meditated at the eventide (see Genesis xxiv. 62).

The Grecian and Roman philosophers firmly believed that "the dead of midnight is the noon of thought."

Young observes, with much energy, that "an undevout astronomer is mad."

Young Blount his armour did unlace, and, gazing on his ghastly face, said "By Saint George, he's gone! that spear-wound has our master sped; and see the deep cut on his head! Good night to Marmion!"-" Unnurtured Blount! thy brawling cease; 66 peace!" eyes," said Eustace, A celebrated modern writer says, "Take care of the minutes, and

he opes

hic

* In this lesson, as well as in some of the preceding lessons, there are several sentences of poetry, which are not divided into poetical division, was to prevent the student from falling into that "sing song" lines. The object of printing these lines without regard to this utterance, into which he is too apt to fall in reading verse. remains to be observed here, that abbreviations and contractions, such as occur in poetical sentences in this lesson and others, which appear in the form of prose, are not allowable in prose itself.

It

in Fig. 27 above, or are some in that plane, some above, and some below. Let them be four in number and on the same plane, their centres being A, B, C, D; then four parallel forces, the weights, act at these centres: what has to be done? Join first A with B, and cut the joining line at x inversely as the weights at these points. Next connect x and c, and cut cx at Y inversely as the two first weights to that at c. Lastly, Y being joined to D, divide D Y at z inversely, as the weights of the three balls already used are to that of the fourth, D. This last point, z, is the required common centre of gravity.

You observe that the joining and cutting of the lines is in no way influenced by, or dependent on, the bodies being on the same or in different planes, or of their number. How many soever they be, the operation is the same. Note, also, that a common centre of gravity can be outside the bodies of which it is the centre.

2. To find the Centre of Gravity of a Right Line.-A mechanical right line being, as we have agreed, a line of atoms of equal size and weight, the case is that which we have considered in Lesson IV., of a number of equal parallel forces acting at equal distances from each other, along a right line. The resultant passes through the middle point of that line; hence the centre of gravity of a right line is its middle point.

This enables us to find the centre of gravity of a uniform rod. By "uniform," I mean such that the cross sections are of the same size and form throughout its length. Such a body may be considered a collection of equal mechanical right lines placed side by side, their ends being made flat or level. As the centre of each line is in its middle, the centre of the whole bundle is in the cross section at the rod's middle. And observe that this holds good of all other bodies, besides mere rods, which can be considered made up of equal parallel lines, such as of a cylinder or uniform pillar, or of a beam of timber, a cubical block of stone; the centres of gravity will be in the cross sections at their middle points. And it makes no difference whether the flat ends of the cylinder, pillar, beam, or block are perpendicular to the lines of which it is supposed to be composed, as in c and e (Fig. 28), or oblique to them, as at d and f (Fig. 29); the centre of gravity is still in the middle cross section parallel to

Fig. 28.

the flat ends. Moreover, as all bodies so shaped may be considered a collection of areas, one atom thick, piled on top of each other, either perpendicularly or with a slope, like cards, or a pile of sovereigns, the centre of gravity of each must lie also on the line joining the centres of gravity of the two areas which form their ends. The centre itself, therefore, is the point in which this line pierces the middle cross section, as at c and e, Fig. 28, in the cylinder and cube. But this requires us to be able to find the centre of gravity of such areas, of which take first the triangle.

3. To find the Centre of Gravity of a Triangle.-This we do by considering the triangle made up, as in the triangle a, in Fig. 30, of lines an atom thick, all parallel to the side A B. The centre of gravity of each line is at its middle point. If, therefore, I can satisfy you that the middles of all the lines are on the line CM, which joins the vertex c with the middle м of AB, the centre for the whole triangle is somewhere on that line. I have, then, to prove that Cм bisects, or divides into two equal parts, every line parallel to A B. Suppose, now, that I cut cM into three equal parts, cx, xy, y M, as in the triangle b, in Fig. 30, and draw parallels to A B at the two points of section inside, meeting AC and B C each in two points from which parallels to c M are drawn, meeting A B in four points, two on each side of M. Now, since c M is equally divided, and the white figures inside are parallelograms, it is evident that the line parallel to c м marked a, b, on each side, are equal to each other, and to cx, the third part of c M. Hence the three small shaded triangles next to AC are equal to each other, and have equal angles. Their three sides parallel to AB are therefore equal, which shows that A M is cut by the parallels to c M into three equal parts. For the same reason в M is cut into three equal parts; and since AM is equal to в M, the six parts into which AB is divided are equal to each other. You thus see that the first parallel above AB is made of parts, two on either side of c M, equal to the parts below, and is therefore bisected by c M. The next above is also evidently bisected, being composed of two parts, one on either side. Now, if I divide cм into five parts instead of three, I have four other parallels also bisected by CM; if into 7 or any other number, it is the same-I can fill the whole triangle with parallels to AB bisected each by the line c M. The centre of gravity of the triangle is therefore on C M.

044

Fig. 29.

But by a similar reasoning it can be shown that this centre of gravity must be in A L (in triangle a, Fig. 30) bisecting A C. Hence we have for rule that, in order to find the centre of gravity of a triangle, we must join any two of its vertices with the middle points of the sides opposite to them, and that the intersection G of the joining lines is the required point. This centre G is distant from M one-third of c M, and from L one-third of A L.

AA

Fig. 30.

с

The centre of gravity of a parallelogram can now be shown to be the intersecting of its diagonals A C, BD (see c, Fig. 30); for, since the diagonals bisect each other, the line B D is the bisector of the common side A c of both the triangles, A B C and AC D. The centre of each, therefore, is on that line, and therefore the common centre of both-that is, the centre of the parallelogram. But, by the same reason, considering the parallelogram made of the two triangles on BD, the centre is on A c. Being thus on both diagonals, it is at their intersection.

4. To find the Centre of Gravity of a Polygon.-Let ABCDE (Fig. 31) be the polygon, and from the angle a draw the dotted lines A C, A D to the remote angles c and D. The polygon is thus cut up into three triangles. Let G, H, and K be the centres of gravity of these latter figures; there are thus three bodies whose centres, G, H, and K, are known, and whose masses are the three areas of the three triangles. Suppose now that you had calculated these areas, and had them written down in numbers. Then join G with H and cut G H at x inversely as the numbers expressing the areas of the triangles A B C, AD C. Connect x now with K, and cut K X at y inversely, as the quadrilateral A B C D to the triangle AED; the point Y is the required centre. If the polygon had more sides than are in Fig. 31, the process is the same, and must be continued until all the triangles into which it is necessary to divide the polygon have been gone over.

Fig. 31.

H

E

5. To find the Centre of Gravity of the Circumference of a Circle.-Let the circumference be taken to be a curved line of atoms, as in a, in Fig. 32, to the right; and through the centre of the circle let any line, A G B, be drawn passing through two of them, one on either side. Since these two are of equal

weight, and equally distant from G, their common centre of gravity is the middle of A B, that is, the point G. So, likewise, going round the figure, the centre of gravity of every opposite pair of atoms is G, and therefore a is the common centre of all, or of the circumference.

The centre of gravity of a ring is thus seen to be the centre of the circle in which it is formed, for the ring may be considered a bundle of circles an atom thick, bound together, one above and around the other, so as to have for common centre of gravity the centre of the central circle.

LESSONS IN PENMANSHIP.-XIV.

Is Copy-slip No. 46 (page 196), an example was given of the letter x. This letter is formed of the letter c twice repeated; the first, or the one to the left, being turned upside down, while the second, or the one to the right, is formed in the ordinary way. The left half of the letter is commenced on the line c c with a hair-line which is turned at the top to the right, and brought downwards without being thickened by pressure on the pen. The hair-line is turned to the left as it approaches the line bb, carried round, and terminated in a dot about midway between the lines b b, c c. The right half is then added. It is made in precisely the same way as the letter C, the thick down-stroke touching the thin down-stroke of the turned C, and forming the thickened centre of the letter.

In Copy-slip No. 48 the learner will find an example of the letter e, which is commenced on the central line, c c, by a hairstroke carried up in a slanting direction to the right. This hair-line is then turned at the top line, a a, and carried to the left, and the letter is finished in the same manner as the letter Cor the right half of the letter x; but in making the thick down-stroke care must be taken to let it pass over the point in

the line c c, at which the up-stroke forming the loop or bow of the letter e was commenced.

Copy-slips Nos. 47 and 49, comprising the words tax and axe, are given to show the learner how the letters x and e are connected with letters that precede or follow them.

In the last lesson it was said that the letters C, X, and e are modifications of the letter o. The learner may prove this in a practical manner for his own satisfaction, if he will take the trouble to make the letter o in pencil, on a piece of ruled paper, and then trace the letter cor e over it in ink; or otherwise, by making the letters C and e, and then adding to them the fine hair-stroke on the right side that is required to form the complete oval of the letter O. To show that x is a modification of o it will be necessary to make the letter O twice over, so that the right side of the first touches the right side of the second, and then trace the letter X over the double o thus formed; or, as in the case of C and e, the hair-stroke that is necessary to complete the oval of o may be added on the right and left of the letter X. In the letters C, X, and e, the bottom-turn is carried to the right, beyond the limit of the bottom-turn of the letter O, in order to join them the more readily to any letter that may follow them.