Abbildungen der Seite



and B


point n. From the point B as centre, with the distance B N, straight lines K M, L N, parallel to A o or B P, and along Ku draw arcs cutting the circumference of the circle A c E set off K Q, equal to A B, and along L n set off L R, also equal in c and n. Join C B, B H. These straight lines are sides to A B. Then from the points Q and e as centres, with a of a heptagon inscribed in the circle A C E, and the heptagon radius equal to A B, draw arcs cutting the perpendiculars a 0, itself may be completed by applying B P, in s and T.

Join QS, ST,
the compasses, with an opening equal T R. The figure A BLRT SQK
to B N or NM, round the circum- is an octagon, and it is described
ference of the circle A CE, as may on the given straight line A B as
be needful. The triangle A BL is an required.
equilateral triangle (see Problem Next, let A B (Fig. 77) be the
XVII., Vol. I., page 209), and A B is given straight line on which it is
the side of a hexagon that may be required to construct an octagon.
inscribed in the circle A C E, in which Produce A B indefinitely both
the heptagon B C D E F G H has already ways to x and y, and through
been inscribed.

the points A and B draw the
PROBLEM LIII.--To construct a straight lines A O, BP, perpen-
Fig. 74.

heptagon on any given straight line. dicular to A B or x y, and set off Let A B (Fig. 75) be the given straight line on which it is along A o and B P the straight

Fig. 77. required to construct a heptagon. Produce a B indefinitely both lines A C, B D, each equal to ways to x and y. Bisect A B in c, and again bisect c b in d. From A B. Join A D, B C, and produce them indefinitely to B along the straight line B y set off E equal to five times BD, respectively; and long D Q, CR, set off D E, C F, each equal to and from a along the straight line A F set off a x equal to B E, A B. Through E and F draw the straight lines EG, FH, meeting or five times BD. Then from the points A and B as centres, xy in G and h; and along E G, FH, set off E L and F K, each equal with the distances A E, B F, respectively, describe the arcs E G, to A B. Through k draw ku parallel to a Q, and cutting B P in FG, cutting one another in the point G; and from g as centre, M; and through draw L n parallel to B R, and cutting A o in n.

with a radius Join A K, BL, E M, MN, NF. The figure A BLENN FK is an
equal to A B, de- octagon, and it is described on the given straight line A B, as
scribe the arc u K, required. If it be required to cut off the corners of a square
cutting the arcs piece of wood or pasteboard as A BCD in Fig. 78, so as to form
F G, E , in the an octagon, first draw the diagonals a C,
points 1 and K. BD, intersecting each other at right
Join G I and G K, angles in E, and then from the points
and bisect them A, B, C, D in succession, with the distances
respectively in the A E, B E, C E, D Е, describe the arcs
points, L, M; and FEG, H E K, L E M, and NEO, having
join A M, BL, their terminations in the sides of the

intersecting each square. Then join 0 H, GL, K N, and XF

other in the point MF. The figure M F O IGL K N is an Fig. 75.

N, which is the octagon.

centre of the circle PROBLEM LV.-To inscribe a nona. Á circumscribing the required heptagon. From the centre n, at gon in a given circle.

Fig. 78. the distance n A or N B, describe the circle A B K G H. Bisect Let A B C (Fig. 79) be the given circle the arcs A A, B K, in the points 0, P, and join a 0, 0 A, B P, P K. in which it is required to inscribe a nonagon. Draw any diameter, The figure A B PKG 1 0 is a heptagon, and it is described on C E passing through the centre d of the circle A B C, and produce the given straight line A B, as required.

it indefinitely towards F. From the point E as centre, with the PROBLEM LIV.-To construct an octagon on a given straight distance Ed, describe the aro A D B, cutting the circumference of line.

the circle A b c in the points A and B. Join A B, and proAs it has been remarked in a former lesson (see page 192), it duce it indefinitely both ways towards G and , and let it is easy to inscribe a hexagon in a given circle when we can place cut c at right angles in the point k. Then from K an equilateral triangle within it, as the process is merely to as centre, with a radius equal to D Е, describe the semicircle bisect the arcs intercepted between the ends of the sides of the LM N, having its terminations L, n, in the straight line GB; triangle, and to form the hexagon by joining the six points thus and from L and N as centres, with the radi L K, N K respecobtained in the circumference of the circle. By a similar pro- tively, describe the arcs K 0, K P, meeting the semicircle LYN cess of bisection, an octagon may be inscribed in a given circle in the points o, P. Join DO, DP, cutting the circumference of when we have once placed a square within it; while the bisec- the circle A B C in the points Q, R. Join A Q, Q R, R B. These tion of the arcs intercepted between the ends of the sides of a three straight lines are the sides of a nonagon inscribed in the pentagon and hexagon will similarly produce a decagon and a circle A B C, which may be

dodecagon. There are, how completed by following the
ever, one or two processes of same process with the arcs
constructing an octagon on a A C, C B, or, applying the
given straight line which we compasses round the cir.
give here, as they may be of cumference of the circle
use to the learner in cutting with an opening equal to
out an octagon in timber, or an A Q, Q R, or r B, and join-
octagonal flower-bed in turf. ing the points taus ob-
First, let A B (Fig. 76) be the tained. The straight line
given straight line on which it A B is manifestly the side
is required to construct an oota-of an equilateral triangle

gon. Produce A B indefinitely inscribed in the circle A B C,
Fig. 76.
both ways to x and y, and at the and the process which has

Fig. 79. points A and B draw the straight been gone through is simply lines A 0, B P, perpendicular to A B or x Y. From a as centre, the trisection of the arc A B, or, what is virtually the same thing, with the distance A B, describe the arc B C D, cutting A o in c, the trisection of the angle A D B..

d from B, as centre, with the distance B A, PROBLEM LVI. - To construct a nonagon on any given straight

F, cutting B p in E, and x y in F. Join line.
em in G and respectively. Join a G, Let A B (Fig. 80) be the given straight line on which it is
to meet the arc B C D in K, and B r to required to construct a nonagon. Produce A B indefinitely
L. Through the points K, L draw the both ways to x and y, and on the straight line x I, with




line A B.

do so.

the points A and B as centres, and the radii A B and B A the point mas centre, with the distance A or M B, describe respectively, describe the semicircles A C D, B C E, intersecting the circle A B F. This circle passes through A, B, F, G, H, the each other in the point c. Bisect A B in F, and through the extremities of three sides of the required undecagon that have point c draw F G perpendicular to A B or x y. Next trisect the been already determined, and the vertices of the remaining arc A c in the points 1 and K, and the arc Bc in the points angles of the polygon will be found in its circumference. To L and m; and from the point a, through the points M, L, and c in the arc B C, draw the straight lines AN, AO, AP of indefinite length; and from B, through the points H, K, and c, in the arc A.C, draw the straight lines B S, B R, and B Q, also of indefinite length. From the points a and B draw the straight lines A T, Bu to the points, T, U, in which the straight lines B S, AN cut the semicircles B C E, A CD; bisect A T, BU in the points V and w respectively, and through the points v and w draw the perpendicular lines V I, w z of indefinite length, intersecting each other and the straight line f g in the point a. This point is the centre of a circle circumscribing the required nonagon. From the point a as centre, with the distance a A or a B, describe the circle Ad B. This circle passes through the extremi. ties of the given straight line A B, the points T and u in which the straight lines B S, A N respectively intersect the semicircles BCE, A C D, and the points c and e in which the straight lines BQ, w z and A P, v I intersect each other: it also cuts the

Fig. 81. straight lines B R, F G, and A o in the points b, d, and f. Join Tb, bc, cd, de, ef, and f u: the figure Atb c d e f u B is a determine them, with an opening of the compasses equal to a B, nonagon, and it is described, as required, upon the given straight set off from A, along the arc A G, the arcs a N, NO, O P, and

along the arc B H, from B, set off the arcs B Q, Q R, R 8. Join The construction of the uneven-sided polygons, the heptagon the chords A N, NO, OP, PG, BQ, Q R, RS, s H.

The figure and nonagon, by the aid of the ruler and compasses, have been A B QR SHF GPON is an undecagon, and it is described on given to show the learner that there is no regular polygon of any the given straight line A B, as required. number of sides that could not be constructed without having The reader will have noticed, doubtless, that the method of recourse to the measurement of the angle of the polygon or the constructing an undecagon on a given straight line by a purely angle at the centre of the circumscribing circle. The construction geometrical process, as given above, is similar in all essential of the decagon and dodecagon on any given line by the ruler and details to the process used for constructing a heptagon on a compasses alone we do not give, because either figure may be con- given straight line, and it is based in both cases on the structed by learners, if they will exercise a little thought, and it numerical relation of the straight line on which either is to be

will afford them two constructed, to the sides of an isosceles triangle whose vertex is useful exercises to the apex of the polygon, and whose base is the given straight

We shall line. In the case of the heptagon, the proportion of the base to therefore conclude the sides of the isosceles, whose vertex is the apex of the polygon, our problems on the is as 1 to 2 or 2-25; and to construct a heptagon on any given construction of the straight line, we have only to produce it indefinitely both ways, regular polygons and find points on either side of each extremity at a distance with the method of equal to 11 of the given line, or to bisect the given line and set constructing an un- off on either side of the perpendicular section straight lines decagon or eleven- equal to 1 of the given line. In the case of the undecagon, sided figure on a the proportion of the base to the side of the isosceles triangle, given straight line, whose apex is the vertex of the polygon, is as 1 to 3 or 3.5; and and then bring our to construct an undecagon on any given straight line, we have Lessons on Geome- only to produce the given straight line indefinitely both ways, try to an end with and set off from either extremity lines equal to 2, of the given

a brief description straight line, or to bisect the given line, and from the point of

Y of the methods used bisection to set off on either side of it, along the given line proFig. 80.

for drawing the el. duced indefinitely, lines equal to 3 times the given straight line.

lipse, parabola, and We have added these remarks on the geometrical constructions hyperbola, curves made by the section of a right cone in parti- that we have given of the heptagon and undecagon, in the hope cular directions; the mode of tracing a spiral; and one or two that they may give the student a clue to other geometrical conother things, such as the connection of two curves by a straight structions of a similar character. We also recommend to his line, etc., which may be of practical use to our students. notice the geometrical construction of the nonagon, based on the

PROBLEM LVII.—To construct an undecagon on any given preliminary construction of an equilateral triangle on the given straight line.

straight line on which it is required to construct the nonagon, Let A B (Fig. 81) be the given straight line on which it is re- and the trisection of the angles on either side of the base, or quired to construct an undecagon. First bisect A B in c, and pro- the arcs that are described opposite to them by drawing semiduce A B indefinitely both ways to x and y. Then along cx set circles from either extremity of the base as centres, with a radius off a line, C D, equal to three times A B, or six times CA, and equal to the base. along'c y set off a line, C E, equal to c D. From the point A as In drawing figures to exhibit the methods of constructing the centre, with the distance A E, describe the arc E T, and from the different polygons, from the pentagon to the undecagon, that point B as centre, with the distance B D, describe the arc D z, have been given in detail in this and preceding lessons, the and let the arcs E T, D z intersect each other in the point F. student is advised, for the sake of accuracy, to make them on This point is the apex of the undecagon, the straight line A B on a large scale; as, if he attempt to construct his figures in the which it is constructed being considered as its base. From the limited space in which are drawn the figures that are used to point f as centre, with a radius equal to A B, draw small arcs illustrate our Lessons in Geometry, he may fail to complete cutting the larger arcs D 2, E T in G and h, and draw the chords them to his satisfaction, in consequence of not being able to FG, FH. Join CF: the straight line drawn from c, through F, is draw the straight lines and arcs, of which the figures are com. perpendicular to A B, and the centre of the circle circumscribing posed, of suitable fineness, and to subdivide the arcs, whenever the required undecagon will be in CF. To find the centre, bisect it is necessary to do so, with sufficient acouracy. In all cases, FG, FH in the points K and L, and join A L, B K. The straight for the sake of good practice, the straight line on which a polylines A L, B K intersect each other and the straight line C F in the gon is to be constructed, should never be taken less than an ipoint M, which is the centre of the circumscribing circle. From in length.



life with unvaried liberality; and, perhaps, his character may receive

some illustration, if he be compared with his master. PROMISCUOUS EXERCISES (continued).

Integrity of understanding, and nicety of discernment, were not 11.-THE PURITANS.

allotted in a less proportion to Dry'den than to Pòpe. The rectitude [Marked for Inflections.]

of Dryden's mind was sufficiently shown by the dismission of his

poetical préjudices, and the rejection of unnatural thoughts and Tue Puritans were men whose minds had derived a peculiar character rugged numbers. But Dryden never desired to apply all the judgment from the daily contemplation of superior beings and eternal interests. that he had. He wrote, and professed to write, merely for the Not content with acknowledging, in general terms, an overruling Pró- poople; and when he pleased others, he contented himself. He spent vidence, they habitually ascribed every event to the will of the Great

no time in struggles to rouse latent powers; he never attempted to Being, for whose power nothing was too vást, for whose inspection make that better which was already good, nor often to ménd what he nothing was too minute. To know Him, to serve Him, to enjóy Him, must have known to be faulty. He wrote, as he tells us, with very was with them the great end of existence. Théy rejected with con- little consideration : when occasion or necessity called upon him, he tèmpt the ceremonious homage which other sects substituted for the poured out what the present moment happened to supply, and, when pùre worship of the soul. Instead of catching occasional glímpaes of once it had passed the préss, ejected it from his mind; for when he the Deity through an obscuring véil, they aspired to gaze füll on the had no pecuniary interest, he had no further solicitude. intolerable brightness, and to commune with Him fáce to fàce.

Pope was not content to sátisfy; he desired to excèl, and therefore Hence originated their contempt for terrestrial distinctions. The always endeavoured to do his bèst; he did not court the cándour, but diffərence between the greatest and méanest of mankind seemed to dared the judgment of his reader, and, expecting no indulgence from vànish, when compared with the boundless interval which separated others, he showed none to himself. He examined lines and words the whole race from Him on whom their own eyes were constantly with minute and punctilious observation, and retouched every part fixed. They recognised no title to superiority but His fàvour; and, with indefatigable diligence, till he had left nothing to be forgiven. cónfident of that favour, they despised all the accomplishments and all

For this reason he kept his pieces very long in his hands, while he the dignities of the world. If they were unacquainted with the works considered and reconsidered them. The only poems which can be of philosophers and poets, they were deeply read in the oracles of God. supposed to have been written with such regard to the times as might If their names were not found in the règisters of héralds, they felt hasten their publicátion, were the two satires of Thirty-èight: of which assured that they were recorded in the Book of Life. If their stops Dodsley told me, that they were brought to him by the author, that were not accompanied by a splendid train of ménials, legions of minis. they might be fairly còpied. “Every line," said he," was then tering angels had charge over them. Their pálaces were houses not written twice over; I gave him a clean trànscript, which he sent soma made with hånds; their diadems, crowns of glory which should never time afterwards to me for the press, with every line written twice over fade away!

a second time." On the rich and the èloquent, on nòbles and priests, they looked down

His declaration, that his care for his works ceased at their publiwith contempt; for they esteemed themselves rich in a more precious cátion, was not strictly true. His parental attention never abandoned treasure, and eloquent in a more sublime language ; nobles by the right them; what he found amiss in the first edition, he silently corrected of an earlier creation, and priests by the imposition of a mightier in those that followed. He appears to have revised the Niad, and hànd. The very meanest of them was a being to whose fate a mys- freed it from some of its imperfections; and the Essay on Criticism terious and térrible importance belonged, -on whose slightest action received many improvements, after its first appearance. It will seldom the spirits of light and darkness looked with anxious interest; who be found that he altered without adding clèarness, élegance, or vigour. had been destined, before heaven and earth were created, to enjoy a Pope had, perhaps, the judgment of Dry'den; but Drydeu certainly felicity which should continue, when heaven and earth should have wanted the diligence of Pope. passed away.

In acquired knowledge, the superiority must be allowed to Dry den, Events which shortsighted politicians ascribed to earthly causes, whose education was more scholastic, and who, before he became at had been ordained on his account. For his sake, èmpires had rìsen, author, had been allowed more time for stúdy, with better means of and Alburished, and decayed. For his sake, the Almighty had pro information. His mind has a larger ránge, and he collects his images claimed his will by the pen of the evångelist and the harp of the prò and illustrations from a more extensive circumference of science, phet. He had been rescued by nó còmmon deliverer, from the grasp Dryden knew more of man in his general náture, and Pope in his local of no cómmon fòe. He had been ransomed by the sweat of nó manners. The notions of Dryden were formed by comprehensive vulgar ágony, by the blood of nò earthly sàcrifice. It was for him speculátion, and those of Pope by minute attention. There is more that the sun bad been dàrkened,* that the ròcks had been rènt, that diguity in the knowledge of Dry'den, and more certainty in that of the dead had arisen, that áll nature had shuddered at the sufferings of

Pope. her expíring God.

Poetry was not the sole praise of either : for both excelled likewise Thus the Puritan was made up of two different mòn, the one all in pròse : but Pope did not borrow his prose from his predecessor. self-abåsement, penitence, gratitude, pássion; the other proud, càlm, The style of Dryden is capricious and váried; that of Pope is cautious infléxible, sagacious. He próstrated himself in the dust before his and uniform. Dryden obeys the motions of his own mind; Pope Máker; but he set his foot on the néck of the king. In his devotional constrains his mind to his own rules of composition. Dryden is some. retirement, he prayed with convulsions, and gróans, and tears. He times vehement and rápid; Pope is always smooth, uniform, and was half-maddened by glorious or térrible illusions. He heard the gentle. Dryden's page is a natural field, rising into inequalities, and ly'res of ángels, or the tèmpting whispers of fiends. He caught a gleam diversified by the varied exuberance of abundant vegetation ; Pope's is of the beatific vision, or woke screaming from dreams of everlásting a velvet làwn, shaven by the scythe and levelled by the roller. fire. Like Váne, he thought himself entrusted with the scèptre of the

of génius, that power which constitutes a poet ; that quality withmillónnial year. Like Fleetwood, he cried in the bitterness of his out which judgment is cold, and knowledge is inert; that energy sóul, that God had híd his face from him. But when he took his séat which collects, combines, àmplifies, and animates; the superiority in the council, or girt on his sword for war, these tempestuous work must, with some hesitation, be allowed to Dryden. It is not to be ings of the soul had left nò perceptible trace behind them. People inferred, that of this poetical vigour Pope had only a little, because who saw nothing of the godly but their uncóuth visages, and heard Dryden had more; for every other writer since Milton must give place nothing from them but their groans and their hy'mns, might laugh at to Pope ; and even of Dry'den it must be said, that if he has brighter them. But those had little reason to laugh, who encountered them in paragraphs, he has not better poems. Dryden's performances were the håll of debáte, or in the field of battle.

always hasty, either excited by some external occasion, or extorted by The Puritans brought to civil and military affairs a coolness of domestic necessity; he composed without consideration, and published judgment, and an immutability of púrpose, which some writers have without correction. What his mind could supply at cal, or gather in thought inconsistent with their religious zéal, but which were in fact one excursion, was all that he sought, and all that he gave. The the necessary effects of it. The intensity of their feelings on óne dilatory caution of Pope enabled him to condénse his sentiments, to subject made thom trànquil on évery other. One overpowering sen múltiply his images, and to accumulate all that study might produce, timent had subjected to itself pity and hátred, ambition and fear.

or chánoe might supply'. If the flights of Dryden, therefore, are Death had lost its tórrors, and pleasure its chàrms. They had their higher, Pope continues longer on the wing. If of Dryden's fire the smiles and their tears, their ráptures and their sòrrows, but not for the blaze is brighter, of Pope's the heat is more regular and constant. things of this world.' Enthusiasm had made them stòics, had cleared Dry'den often surpásses expectation, and Pópe never falls belòw it, their minds from every valgar passion and préjudice, and raised them Dry den is read with frequent astónishment, and Pope with perpétual above the influence of dánger and of corruption.-Macaulay.

delight.-Johnson, III.--POPE AND DRYDEN.

IV._UNIVERSAL DECAY. [This piece is marked in application of the rules of Inflection.] [Marked for Rhetorical Pauses, Emphasis, and Inflections.]*

Pope professed to have learnt his poetry from Dry'den, whom, We receive such repeated intimations of decay l in the world through whenever an opportunity was presented, he praised through his whole

The learner having been conducted through the application of the an emphatic series causes, thus, a succession of falling rules for Pauses, Emphasis, and Inflections separately, will now be "he second one in each clause falls lower than the first. prepared to study and apply them in conjunction,

which we are passing ;- decline | and change and loss, follow ' decline | With regard to the English association not much is to be and change | and loss || in such rapid succession, that we can almost said, because, while the human urchin is actively mischievous, catch the sound of universal wasting, and hear the work of desolation !

and often made to smart for it, passively, the other urching going on busily around us. “ The mountain / falling || cometh to

are very harmless except in passive self-defence. The other nought, and the rock | is removed out of his place. The waters I wear the stones, the things which grow out of the dust of the earth || are washed resemblance, though misleading anatomically, is very marked, on cváy, and the hope of man | is destròyed.” Conscious of our own insta- account of the dense covering of sharp spines sticking out in all bility, we look about ' for something to rèst on; but we look ' in vain. directions, matted and crossing one another like the spines The heavens ' and the earth | had a beginning, and they will have an of the thistle leaf; and also on account of the globular form, end. The face of the world | is changing, dáily and hourly. All' ani- which, though temporary in the land urchin, is permanent in the mated things I grow old and die. The rocks crumble, the treos | fall, echinus. the leares | fade, and the grass | vithers. The clouds | aro flying, and the The shell of a typical echinus, upon which the spines are set, waters | are flowing away from us.

is a round box of very complex and beautiful structure. It The firmest works of min, too, are gradually giving wày: the ivy 1, consists of plates of carbonate of lime so closely and accurately clings to the mouldering tower, the brier 1 hangs out from the shattered fitted together, that, even after the spinos have been stripped off, windoro, and the wall-flortor / springs from the disjointed stones. The founders of these perishable works || have shared the same fato I long it requires minute examination to discover the lines of division ago. If we look back to the days of our ancestors, to the men | as well between them. The box has the form of a more or less de. as the dwellings of former times, they become immediately associated pressed sphere, varying from the shape of a true globe to that in our imaginations, and only make the feeling of instability strònger and of a Turkish turban. At the two poles of the box are two holes : deeper than before. In the spacious domes, which once held our fathers, that which opens on the under side of the animal is the mouth, the serpent | hisses, and the wild bird | scrèams. The halls, which once while that which is found at the centre of the top side is thi were crowded I with all that taste and science | and labour | could pro- other end of the food canal. A further examination reveal3 cure,--which resounded with melody, and were lighted up with beauty, are buried by their own rùins, mocked by their own desolation. The voice

that the shell is made up of five similar radial divisions, which of merriment, and of wailing, the steps of the bùsy' and

the idle || have stretch from pole to pole, and may be thus described :--The ceased in the deserted courts, and the weeds I choke the entrances, and the central zigzag line, running from mouth to anus, has on either long grass I waves upon the hearth-stone. The works of art, the forming side of it a row of small plates alternating with one another; and hand, the tombs, the very ashes they contained, are all gòne.

on the outer side of each of these rows of plates is a row of small While we thus walk! among the ruins of the past, a sad feeling of holes. There are six of these boles in each plate. Externally insecurity I comes over us; and that feeling' is by no means diminished to these perforated plates are situated two other rows of larger when we arrive at home. If we turn to our friends, we can hardly plates, one on each side, and these are united at their external speak to them || before they bid us farewell. We see them for a few edges to the next radial division of the box by a zigzag line. niments, and in a few moments more their countenances are chànged, The outer

side of both the perforated plates and the plates and they are sent away. It matters not how néar i and dear they are. The ties which bind us together || are never too close ' to be parted, or

without holes are covered with bosses, each of which has a more · too strong 'to be broken. Tears I were never known to move the king of prominent rounded knob projecting from the top of it, which terrors ; neither is it enough ' that we are compelled to surrender ons, knob has a pit in its centre. These knobs bear the spines. or trcó, or many of those we love ; for though the price is so great, we They are of various sizes, but so arranged as to form a beautibuy no favour with it, and our bold' on those who remain | is as slight fully regular pattern; for each plate has at its centre a large as ever. The shadows || all | elude our gråsp, and follow one another boss, and, as the plates are regularly placed one above the down the valley. We gain no confidence, then, no feeling of security, by other, there are, on the whole shell, twenty rows of these turning to our contemporaries and kindred. We know that the forms tubercles running from top to bottom, set on lines which correwhich are breathing around us, are as shortlived ' and feeling' as

spond to the meridians of a globe. Yet, if the reader has those were, which have been dúst' for centuries. The sensation of tiguity, uncertainty, and rúin, is equally stròng, whether we muse on

followed the description, he will see that these rows are not all what has long been pròstrate, or gaze on what is falling now, or will fall'

at equal distances from one another, for those on the smaller so soon.

perforated plates are approximated, while those of the larger If everything | which comes under our notice || has endured for so plates are removed from one another; nor are the tubercles short a time, and ' in so short a time I will be no more, we cannot say of the several rows all at the same distance from each other. that we receive the last assurance || by thinking on ourselves. When a Besides these tubercles, a great many others of very various few more friends have léft, a few more hopes | deceived, and a few more sizes lie between the rows. The whole effect of the pattern is changes | mócked us, "we shall be brought to the grave, and shall remain in the tomb : the clods of the valley shall be sweet unto us, and

very beautiful, and shows that symmetry without sameness, every man shall follow us, as there are innumerable ' before us."

that unity in variety, with which all the works of God abound,

ALL power' will have forsaken the stròngest, and the loftiest I will be laid low, and which the architect and the designer are so perpetually and every eye' will be closed, and every voice' húshed, and every heart !

striving after, but to which they so seldom attain. will have ceased its beating. And when we have gone ' ourselves, even our The ten perforated tracts which, being arranged in pairs, form memories' will not stay behind us long. A few of the near and dear || five double bands or courses, converge towards the mouth and will bear oar likeness in their bosoms, till they' too ' have arrived ' at anus. The regularity of these tracts, converging at both ends the end of their journey, and entered the dark dwelling of unconsciousness. and leaving between them a solid tract, has suggested a fanciful In the thoughts of others || we shall live only till the last sound of analogy. They were thought to resemble the gravel walks of the bell, which informs them of our departure, has ceased to vibrate in their ears. A stone, perhaps, may tell some wanderer where we lie, when and so were called ambulacra; ambulacrum being a post-classical

our gardens, with their borders or avenues of trees on each side, we came here, and when we went away; but even that I will soon refuse Latin word, mea to bear us rècord; "timo's effacing fingers" | will be busy on its surface,

a garden walk. At the point where the two and | at length 'will wear it smooth; and then the stone itself will converging perforated tracts unite, is a single six-sided solid plate, sink, or crumble, and the wanderer of another age will pass, without a

which has at its side nearest the ambulacra a hole from which single call' upon his sympathy, over our unheeded gràves.--Greenwood. the ambulacral holes seem to diverge. The five perforated hexa

gonal plates which thus stand at the end of the ambulacral

avenues, are separated from one another and from the top openCOMPARATIVE ANATOMY.-VI. ing by five other irregularly eight-sided plates which surround ECHINODERMATA (HEDGEHOG-SKINNED ANIMALS.)

the small movable scales which cover in the anus. As far as

our previous description has gone, the reader will perceive that From the earliest times, before Aristotle wrote of animals, the all the parts are perfectly radial. The five segments are absogreat similarity in outward appearance between the hedgehog, lutely alike; but one of the eight-sided plates has, between the when rolled up in self-defence, and the sea-egg, or echinus, has large pore and the anus, a space which is full of a great been so recognised as to cause them to be called by the same multitude of holes, and in this respect it differs from all the

In Greek, echinus (exivos) means both the one and the other five plates of the series, and is called the madreporio other. In English, we have expanded this superficial association plate. At the other pole of the body there is a large opening to include the young of our own species when they have arrived covered by a leathery membrane, in the centre of which is the at that age when they are always in mischief, and when, ac- mouth. Placing the animal with its mouth downwards, which cording to the notions of a past generation, they were always to is the position it usually occupies, and looking at it from above, be cuffed, because, if they did not deserve it at the time of let us enumerate the perforations which we have described, the infliction, they soon would do so.

beginning from the centre at top, and proceeding outward and


downward, so that all confusion may be avoided. We have the while the ridges between the grooves, stretching further in. following different series :

ward than the furrows, form saw-like edges, so that after the 1. The central round opening, which is covered by small food, mixed with hard particles, has passed the tips of the movable calcareous pieces, called the apical hole.

teeth, it can be ground down to a fine pulp by these triturating 2. On one side of this are the minute crowded holes of the edges and surfaces. madreporic plate.

The food canal does not run in a straight line from month to 3. In the five plates which surround the apical hole are the anus, but, after proceeding a short way as a contracted throat, five holes, each of which occupies the external angle of its plate; opens sideways into a wider canal, which, after winding once these are called the generative pores.

round the inside of the shell, is bent on itself, and winds round 4. In the five plates which are intermediate to and outside back again, and then delivers at the apical hole. This winding these the oenlar holes are seen.

enables the food to undergo a more thorough digestion, while the 5. Stretching away in five double tracts are the ambulacral nutritive parts of the food are dissolved, and either pass into holes.

the blood vessels, which are found in the walls of the intestines, 6. The large opening below for the mouth and its membrane. or into the surrounding cavity. It must not be supposed that

We are now in a position to indicate the relation of the soft this long alimentary canal is loose in the box, only attached by its parts of the animal to this protective box. All the above- two extremities. If so, it would be liable to become entangled. named perforations have their uses; and a study of these will It is attached by a membrane which lines the inner surface of teach us almost the whole anatomy of the animal.

the shell, and then passes off from this round the alimentary The alimentary canal connects the two largest holes which lie tube, so as to hold it in a loop, or rather fold. This arrangein the vertical axis of the body. The entrance, or mouth, is in ment is very general, not only in these, but in the higher the centre of the wide orifice in the under side, which is covered animals. in by a leathery membrane, with the exception of where the The holes in the five larger plates surrounding the anal opening pointed teeth project. The curious beak, composed of five are those through which the eggs are extruded (in the case of the sharp teeth, forms a very effective instrument wherewith the female) into the sea-water, so to renew the round of life. They animal can scrape away the soft, calcareous rocks in which so farnish the exits for five separate organs situated just below many worms and sea-animalcules bore and hide themselves. them. The holes in the alternate plates are called ocular It is supposed that the animal swallows chalk and animals holes, because, through them, a nerve passes to an organ, suptogether, and lives on the nutritive, organic substances, while posed to be an eye. The ambulacral holes and the madreporic the chalk, etc., are passed out again, just as in the case of the holes need a further explanation, which will lead to a description earth-worm, great quantities of soft vegetable mould are swal of the locomotive organs of the animal. The locomotive organs lowed for the sake of the nutriment it contains in the shape of of the echinus are of two kinds—the soft for pulling, and the particles of leaves, etc. The protruded part of the beak, how hard for pushing. The hard-pushing organs are the spines. ever, gives no idea of the very complex machinery by which These are, no doubt, defensive organs, but they also unite with these teeth are worked from within. If the leathery membrane this function that of locomotion. The spines are, as we have be cut round close to the shell and pulled out, it brings with said, set upon the knobs of the outside of the shell. They are, it, or allows to be abstracted, a large and complicated hard however, movable upon these, so that they can be turned in all framework in the form of a five-sided pyramid, with its base up- directions. To effect this movement without destroying the ward, and its apex formed by the teeth. This pyramid consists of solidity of their attachment, there is a curious contrivance. At five jaws, each of which is a frame which sustains the tooth, and the centre of the concave base of the spine, there is (at least has attached to it the muscles which move this tooth in all re- in the purple-tipped sea-urchin) a pit corresponding to the pit in quired directions. The jaw being hollow allows the tooth to enter the centre of the tubercle on which it is set. A ligament at its upper broader side, and to pass down in a groove which be- runs from one pit to the other, and so prevents the spine from comes closely applied to the tooth on all sides at the lower end, slipping off its support, while from the edges of the base of and so holds it in a kind of socket, in which, however, it can the spine muscular fibres run to the membrane which clothes the move downward, as the tooth is worn away below, and is sup- shell. It will be seen from this that the shell is not naked, but plied from above. The tooth consists of a curved and flattened covered with irritable and live membrane, which membrane bar, ending in a point, and having on its inner side a flange passes down between each plate, and, no doubt, subserves the to strengthen it, which flange stands out at right angles to the function of secreting fresh matter round the edges of these flattened inner surface of the tooth. The tip of the tooth is plates as the animal grows. How far the spines may aid the of enamel-like hardness, but as you trace it up through the jaw, animal in progression may be a matter of question; but those it becomes softer and softer, until it is found to be quite who have observed its motion believe they are concerned in without hard deposit at the part where it protrudes above the it. By far the most efficient organs of locomotion are the jaw. This shows that there is a process of continual renewal, little tubular feet ending in discs, which are protruded through the tooth being laid down as a gelatinous substance in which the ambulacral holes. These feet act like suckers, when ap. more and more hard, earthy salts are deposited as it is pushed plied to the rock on which the animal moves. The coatings of forward, until it consists almost wholly of these, and is fitted to circular and longitudinal muscles which enclose the hollow tubes cope with the hard material to the rasping of which the animal are sufficient to move the animal when a multitude of these discs applies it.

have been extended and attached; but the question arises, how Round the base of the pyramid runs a pentangular muscle, are they protruded ? This is done by a curious contrivance. which binds the jaws together. From the outer side of the base Each little tube, after traversing the shell and arriving at the of each jaw run muscles to the shell at the sides of the orifice interior, expands into a muscular bag. Both bag and tube conof the mouth. These, when contracted, protrude the teeth all tain liquid. All the little bags, set on each line of ambutogether from the mouth. Other muscles unite the sides of the lacra, communicate with a vessel, which stretches from mouth jaws to one another, and these, when contracted, bring the to anus, and these ten vessels all communicate with a ring round teeth together. A series of long pieces attached to the centre the mouth, which ring has, opening into it, some larger bladders of the base of the pyramid, gives attachment to muscles, which, to contain a reservoir of water, and

it also communicates with running to the shell, have the function of approximating the tips the madreporic holes by a tube, which is filled with fine sand. of the teeth. In order to retract the whole apparatus when the method of protruding the tubular feet is supposed to be acting together

, or to pull away each separate tooth from the the following: sea-water is filtered through the madreporic rest when acting separately, a number of muscles (two for each plate and sand canal to the ring round the mouth. tooth) run from the lower end of the jaw to some calcareous animal is in a lively state and inclined for locomotion, the loops or arches, which, standing on the sides of the oral hole, bladders force the water into the rows of little bags, and these rise up within the shell.

being muscular, can, by contracting, force out any or all of the The jaws, however, are not solely devoted to the sustaining sucking feet at pleasure. When, on the other hand, the animal and of the teeth, but are themselves employed to wishes to retract all its feet, the bags, distended by receiving d, for on the sides of each jaw which are op all the water which

was in the tubes when extended, would be of the next jaws on either hand, are found in an awkward state of tension, unless the fluid were allowed to hich transform the surfaces into fine files, pass back into the ring and bladders.


When the

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