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#796.]

Monocotyledonous and Dicotyledonous Vegetables.

layers are to be discovered, nor central pith, nor medullary proceffes; the ligneous fibres, placed by the fide of each other, are envelopped in pith filling up the interftices; as they approach the circumference, they are brought nearer together, grow more compact, and, therefore, are more flender: fo that the trunk is ftronger, and more denfe, at its circumference than its centre, directly con trary, in this refpect, to the dicotyledo. nous plants.

When a palm nut begins to vegetate, it throws out fucceffively, for the four or five first years, a number of leaves, which, by the union of their footftalks, form a bulb juft above the root fibres; this bulb increafes, by degrees, in fize and folidity, and at length rifes through the ground, forming the trunk, being, at its first appearance, as denfe and thick as it ever will be. The figure, therefore, is that of an exact cylinder, whofe diameter is always the fame, though its axis is continually increasing.

It happens, however, fometimes, that the trunk does not preferve a regular cylinder throughout this irregularity takes place on account of the greater or lefs abforption of nutrition by the roots; thus, if a young plant be moved from a very dry to a moift fituation, the nutritive juices being more abundant, the upper part of the trunk will be thicker than the lower, and vice versa. Of this variation, a cycas, in the National Garden, furnishes a remarkable example. This plant was tranfplanted from the Ifle of France, in a tub, in the year 1789; when arrived at Paris, it languished for a long time, during which its ftem, however, increafed in length a few inches; but the whole of this elongation was much less in diameter than the reft of the trunk. By flow degree, the tree recovered; the fhoots became more vigorous and larger, but the ftrangulated part continued, and ftill continues, of its former dimenfions. That portion of trunk which was produced in its native country, is 23 inches in circumference, the ftrangulated part 14 inches; the upper part is 19 inches, and the inferiority in fize of this, to the lower part of the ftem, may be fairly attributed to the deteriorating influence of a foreign climate. The fame caufe could never produce the fame effect in a tree with two feminal leaves, because, its increafe in bulk being owing to the fucceffive application of concentric cylinders, extending from its bafe to its fum

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mit, it preferves its original form and proportions, whether the new cylinder of wood be greater or lefs. It has been mentioned, in the former part of this paper, that the inner bark of bicotyledonous trees is renewed every foring, and, therefore, that the number of concentric cylinders is greateft at the foot of the tree, the branches of a year's growth poffeffiug only a fingle layer of wood. Nothing fimilar takes place, with refpect to the bark of the palm, that being merely an expanfion of the fibres at the base of the leaf-ftalks, covering the trunk with a coarse imbricated kind of net-work, eafily detached, and not capable of being renewed.

2. CANES. Canes bear fo near a refemblance, in their ftructure, to palms, that it is not eafy to form diftinctive characters between them. A longitudinal fection of the common cane will at once fhow the resemblance, and almost identity of conformation; the central fibres are fo loofely difpofed, that the naked eye may, with ease, diftinguith the intervals, and air or fmoke may be, without difficulty, paffed through a stem of feveral feet. The fibres approach each other very fenfibly, as they recede from the centre, and neither concentric cylinders, nor medullary proceffes, can be difcovered.

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3. GRASSES. The fame appearances occur in the ftructure of all fuch graminaceous plants as have perennial stems, fuch as arundo bambos (bamboo) arundo donax, panicum arboreum, panicum latifolium, faccharum officin. (fugarcane) and many other fpecies, of this numerous tribe. The veffels are ranged parallel to each other, without forming concentric cylinders; the pith, or medullary fubftance, is diftributed in the fmall intervals between the fibres, which, as they approach the circumference, become more flender and compact, without any traces of medullary proceffes. But if the graffes are connected with the palms and canes, by the great diftinctive characters of monocotyledonous plants, they yet differ in feveral particulars which ought to be mentioned. The ftem is hollow, and divided by knots placed at regular diftances, which form tranfverfe valves in the interior of the ftem, contribute to its ftrength, and produce leaves and roots. The leaves are always fimple, embracing he ftalk; and, inftead of being folded in two, like the leaves of the palm before expanfion, they are rolled inward

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from the edges, and placed one within the other, according to the order of their expanfion, thofe which are to be produced laft occupying the centre,

into two grand natural claffes, whose characters are the following:

1. Vegetables, which have no diftinct concentric cylinders, whofe folidity de4. After having proved the identity creafes from the circumference towards the of ftructure in the three preceding or- centre, having pith interpofed between ders of plants, I was curious to know, the fibres, but giving out no medullary whether the genera of SMILAX, RUSCUS, proceffes-MONOCOTYLEDONOUS. and ASPARAGUS, whofe ftems ramify 2. Vegetables, with diftinct concenand apparently refemble thofe of the tric cylinders, whofe folidity increases dicotyledonous fhrubs, had any affinity from the circumference towards the in their internal arrangement; for this centre, having pith in a long tudinal purpofe, I procured fome old ftems of canal, with diverging medullary profmilax excelfa, fmilax afpera, rufcus ra- ceffes-DICOTYLEDONOUS. cemofus, rufcus androgynus, afparagus retrofractus, afparagus acutifolius; and, after examining them with a high magnifier, I can confidently affirm, that they have neither concentric cylinders nor medullary proceffes, and their fibres are clofer as they approach the circumfe

rence.

5. In the fame divifion may be ranged the DRACONTIUM, YUCCA, AGAVE, ALOE, and ALETRIS; all which plants greatly refemble the palm, in the pofition of their fibres. They have no concentric cylinders, and the pith between the fibres does not fend out any lateral proceffes or diverging rays. The outer covering of the item is not a proper bark, but merely an aggregation of the dead fibres of former leaf-ftalks, with deep circular rings, denoting the number of years of growth.

5. Allthe ligneous LILIACEOUS plants, as well as the ANANAS and PANDANUS ODORATISSIMUS, are fimilar in ftructure to the rest of the monocotyledonous plants.

6. The arborefcent FILICES, like the palms, have their trunks crowned with a tuft of leaves, the trunk ittelf being compofed of coarfe fibres, becoming compact in proportion as they recede from the centre; and covered with a folid bark, formed of the fibres of former leaf-ftalks.

7. The items of the perennial LycoPORIUM, and other MUSCI, bear a very near affinity to the other plants with one feminal leaf, in the ftructure of their ftems, though they differ confiderably in the foliage and organs of fructification.

To thefe general obfervations, not a fingle exception has been found, though a very great number of the living and dried plants, in the rich collection of the National Mufeum of Natural Hifter, has been examined, with this particular object in view.

We may, therefore, divide vegetables

PROCEEDINGS OF THE JURY OF ARTS AT PARIS.

This Jury was established by a Decree of the

Convention, and conifts of celebrated Artists and fcentific Profeffors. They were appointed to diftribute Prizes and Recompences to men who diftinguish themfelves in the Arts, &c. Prizes decreed to Works of ARCHITEC

TURE, SCULPTURE, and PAINTING. THE artift MOITE, of Paris, was defired

to prefent the model in relievo of his plan of a Triumphal Arch, in memory of the Iranfactions of October 6th. Three other artifis obtained pecuniary prizes for fimilar models.

Some of the candidates received pecuniary prizes for the beft plan of a Column to be erected in the Pantheon, inferibing the names of thofe Warriors that have died for their country. Of thefe prizes PERCIER and MEUNIER, of Paris, and FONTAINE, of Pontoife, obtained the molt confiderable.

The Jury, however, dapproved of the form of a Column, as of all others the worft adapted to Infcription.

LAHURE, of Paris, received the medium of pecuniary prizes for his plan of an Amphitheatre, on the tite of the ancient Opera. Here alfo the Jury cenfured the Programma (the paper which invited competition) as injudicious; faying, it was impoffible to conftruct an edi fice capable of containing the immenfe population of Paris, and worthy to celebrate the National Feftival, &c. within fuch narrow precincts as thofe of the ancient Opera,

Some pecuniary prizes were adjudged to fome of the models exhibited of a Monument in the Place des Victoires, in honour of the citizens who died for their country on the 10th of August.

The Jury adjudged the first prize, that is, pronounced the defign worthy of being executed at the national expence, ro

the

1796.] Proceedings of the Confervatory of Mufic, at Paris.

the artifts DURAND and THIBAUD, of Paris, for their plan of a Temple to be erected to Equality, on the area of the Garden of Beaujon. The Jury pronounced this plan to be novel, replete with character, and perfectly correfponding to the ideas of the Programma. They judged the Garden Beaujon, however, to be not extenfive enough for the ground-work of fo auguft a ftructure.

Some inferior prizes were then adjudged to feveral artists, for the belt plans of Rural Edifices, Primary Affemblies, Decadary Temples, Prifons and Houfes of Arreft, and Baths and Fountains, &c.

The models of National Theatres did not gain the approbation of the Jury, and no prizes were beftowed.

PERCIER, of Paris, and FONTAINE, of Pontoife, obtained the first pecuniary prizes, for their plans of embellishment

for Paris.

The project of the Temple of Equality is the only one which will be recommended by the Jury to Government, as worthy of being erected at the public charge. It does not follow, however, that the other plans difcovered a mediocrity of genius or invention in the artifts; many of them certainly evinced confiderable genius, but as the construction of National Edifices muft neceffarily require much time and immenfe expence, the Jury was obliged to exercise a rigid feverity in its decifions, and to exclude all defigns which did not approximate to their own ideas of perfection.

THE CONSERVATORY OF MUSIC.

ON the first of Brumaire (Oct. 22) the fchool of mufical inftruction was opened at Paris, in the Confervatory of Mufic, in prefence of a deputation of the National Institute, and the Director-general of public inftruction, in the name of the Minister of the Interior. The fitting was public; the members of the Confervatory were prefent, and about four hundred pupils of both fexes, with their relatives, &c. The deportment of the profeffors, and the fedate yet eager attention of the scholars, muft neceffarily have made an impreffion even on fuch as from the want of organs, inftruction, or reflection, attach the leaft value to the art of mufic.

After reading the law which authorized the establishment of the Confervatory, JARRETTE, commiffary of organization, pronounced a difcourfe, wherein

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he laid open the faults in the ancient modes of mufical inftruction, the immenfe lofs fuftained by the art a number of years paft, in the want of all instruction, even the most imperfect, and the advantages likely to redound to harmony from the prefent eftablishment, and the modes of culture introduced into it. The regulations propofed by the commiffary, adopted by the Infpectors of Inftruétion, and approved by the Executive Directory, were then recited.

The fitting terminated with a concife, but interciting oration, delivered by GosSEC, dean of the infpećtors of inftruc

tion.

The general effect of this fitting could not fail to excite the most ardent hopes in the breaft of every lover of the art; nɔpes which feem to be on the point of being realized. On the following day, the five inspectors proceeded to examine the pupils, with a view to diftribute them into claffes. This important duty, discharged with a truly paternal zeal, took up the whole of the eight following days; and on the 6th Brumaire, the learners, who had been previously examined, were arranged into claffes. The zeal of the adminiftrators, and of the different profeffors, keeps pace with that of the infpectors of inftruction, and the inftitution would be already in a state of entire establishment, if temporary embarraffments did not intervene. It is expected, however, that the prompt and vigorous ailiftance of government will remove thefe confiderable obftacles, &c.

[In our next we shall have the pleasure of prefenting to our Readers, the useful Proceedings of all the Sittings of the LYCEUM OF ARTS.]

MATHEMATICAL CORRESPONDENCE.

To the Editor of the Monthly Magazine.

SIR,

N your Magazine for Auguft, a cor

refpondent, under the fignature of Exotericus, has made fome remarks on a little work of mine on Algebra, lately published; and I might, perhaps, have rather left the noticing of them to others, had not an opportunity been thus offered to me, of correcting an error in my obfervations on Cardan's Rule. Exotericus has properly brought the inftance of the equation 3+27-280, in which I deny the propriety of following the ufual mode, by making a+b=1; for as the

former

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Upon equations of this form, I have (Algebra, p. 213) inadvertently faid: When is of fuch a magnitude that 3ab is not equal to q, it is evident that the rule fails.' This is true generally, and is the reason why, in feverai cafes, Cardan's rule fails; but it does not apply to the cafe in question, += 3. in which 3ab may be always equal to q I go on " Thus let 3+x=68, in which cafe a-64 with q=1, and, confequently, 3ab must be greater than one." Now this is not true; for a-b may be equal to 4, and at the fame time zab=1; for a may be a whole number, with a de cimal, and b a decimal; fo that 3ab may be not only equal to unity, but to any affignable number lefs than unity. As a familiar inftance, let a-b=1, and a=4,01, and b=,01 : 3ab=3 X 4,01 X ,01,1203 = number lefs than unity.

Exotericus properly afks, what advantages will be gained, by giving up the mode of working by negative numbers? I anfwer: the Icholar is not taught a falfe principle; he is not taught to take a number away from another lefs than itfelf, that is to perform an impoflibility. Confequently, when he comes to any thing leading to fuch an operation, he paules; renews his work; and admits nothing which is not confiftent with plain fenfe. If it is fad, that fir Ifaac Newton followed this mode; I anfwer, Alexander alfo cut the Gordian knot, and grcat names are no excuse for unjusti

fable actions.

QUESTION XVIII (No. VI).—Anfwered by Mr. J. F-1.

This problem may be folved by feveral eafy methods: one, which is perhaps count of the extenfive ufe of the theothe most proper for our purpofe, on acrem from which it is derived, is the following:

Ferguson, in his "Select Lectures," page 362, fhows, that if we put A= fine of fun's altitude, L and/ fine and cofine and co-fine fine latitude, D and d fun's declination, and H = fine of the fun's hour-angle from VI, then the relation of H to A will have three varieties, viz.

the elevated pole, and the hour nearer noon than VI is, A=LD+Hld and HA-LD

1. When the declination is towards

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When A comes out negative in any of the above formula, it indicates that the

fun is below the horizon, and is then the fine of its depreffion.

From the data, we eafily get the hour of the fun's rifing above the visible borizon from the mountain; from which, by is, in this cafe, the fine of his then dethe foregoing method, we get A, which preflion below the rational horizon of the place.

This angle of depreffion may also be obtained (as indeed all the foregoing expreffions are) by the folution of one oblique-angled fpherical triangle, two fides fun and co-latitude of the place, the whereof are the polar diftance of the contained angle the hour-angle from the fun's zenith distance. But the fornoon; and the third fide to be found is

You will permit me, fir, to add my thanks to feveral namclefs correfpondents, and my hopes that they will continue to favour me with their communica-mula themselves are fo extremely convetions. As my Algebra may not fall into the way of feveral of your readers, I have enclofed the refolution of an equation of the third order, true to fix places of decimals, which, with a little more trouble, might be carried on to twice that number. Your's, &c.

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nient in a great variety of other cafes, and fo cafily applicable even by perfons who are not converfant in fpherics, that they feemed worth infertion.

marked log-rifing," in Tab. XVI of A proper application of the column the "Requifite Tables," published by the Board of Longitude, will also give the depreffion required with as much cafe as either of the foregoing methods.

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Having found the depreffion of the vifible horizon, we have the height of the mountain from one analogy, viz. Co-fine angle depreffion radius: earth's femidiameter earth's femidiameter + the height of the mountain required.

We may alfo, to avoid the neceffity of ufing fuch large numbers as will occur in the preceding analogy, take the following for a near approximation: Reduce an arc of the earth's circumference, whofe quantity is equal to that of the angle of depreffion before found (and which will confequently be the femidiameter of the vifible horizon from 'the mountain) into yards or feet, and we fhall have radius: tangent angle depreffion :: the diftance fo found: twice the height required, very nearly.

In the cafe before us, the difference of the times of fun rifing given, is fuppofed to be the difference of the times of the true rifing of his centre above the rational horizon of the place, and the vifible horizon from the fummit of the mountain, both properly corrected for refraction and parallax.

The fame anfvered by J. H. Having the latitude and declination given, per fpherical trigonometry, as radius is to the co-tangent of the complement of latitude, fo is the tangent of declination to a third number, which is the time of fun rifing before fix o'clock (if latitude and declination are both north). To this add the given difference of fun rifing on the top of the hill; and that will be the included angle of a fpherical triangle, the two fides of which are given, viz. the fun's polar diftance and the co-latitude, whence the third fide, or zenith distance, will be found, and confequently the fun's depreffion from the true horizon, or the diftance from the bottom of the hill on the arc of a great circle, where a tangent drawn from the top of the hill to the fun, will touch the furface of the earth. If that point of contact, the top of the hill, and the centre of the earth, be joined by three lines, a right-angled triangle will be formed, in which are all the angles, and the earth's femidiameter given; whence, as the cofine of the angle of the fun's depreffion (abave found) is to the carth's femidia

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meter, fo is radius to the hypothenuse; from which fubtract the femidiameter, and that gives the height of the hill required.

This Queftion was alfo anfivered by Mr. Joon Dawes, and Mr. John Haycock.

QUESTION XIX (No. VI).-Answered by Philalethes.

=

Of feven numbers in continued geometrical progreifions, having given the fum of the two leaft 90, and the fum of the two greatest 281250; make the first number, and the common ratio; then will x, xz, xz2, x23, x24, xzs, xz, reprefent the feven numbers. Therefore, by the queftion x+x=90, and +6281250; dividing the lat ter of thefe by the former, gives x5= 281250903125; therefore %= 5/3125=5. Confequently, x=90÷1+ = 15; and, therefore, the numbers fought are, 15, 75, 375, 1875, 9375, 46875, 234375.

J. Fr, after his folution of this queftion, adds this remark, viz. If there be n number in geometrical progreffion, a being the first term, and r the common ratio, the fum of the two firft being = a, and that of the two laft = b; then, か generally, it will be r=n-2/-, and x=

r

a

a

Anfwers to this Queftion were also given by Meffrs. W. Adam, W. Clavey, John Col lins, H. Cox, L.W.D. J. H. John Haycock. Laycey, B. W., X. and Hermes of Bath.

NEW MATHEMATICAL QUESTIONS. QUESTION XXIII.—By Mr. B. IV. Which is the greateft, an arithmetical or a geometrical mean, between any two quantities, a and b?

QUESTION XXIV.—By the fame. If a pendulum, 39 inches long, fwing feconds, in what time will it fwing, when carried into a latitude where its weight is diminished by the 300th part of an inch, and its length increased by the heat the 10th part of an inch?

Erratum, p. 721. In the folution to Question XVI, 1. 5, for 44, read 41.

TO CORRESPONDENTS.

The Notice to fome of our Poetical Friends, in our last Number, will particularly apply to the pieces figned E. S. J.

Our obliging correspondent will obferve, that notice has been taken of the Mufical Work from Cambridge. His future correfpondence will be acceptable.

Biographical Notices of remarkable end diftinguished Characters are folicited.

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