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1796.] Monocotyledonous and Dicotyledonous Vegetables. layers are to be discovered, nor centralmit, it preserves its original form and pith, nor medullary processes; the lig. proportions, whether the new cylinder neous fibres, placed by the side of each of wood be greater or less. It has been other, are envelopped in pith filling up the mentioned, in the former part of this interftices; as they approach the cire paper, that the inner bark of bicotyledocumference, they are brought nearer to nous trees is renewed every syring, and, gether, grow more compact, and, there- therefore, that the number of concentric fore, are more slender : so that the trunk cylinders is greatest at the foot of the is stronger, and more dense, at its cir- tree, the branches of a year's growth cumference than its centre, directly con. poffeffing only a single layer of wood. trary, in this respect, to the dicotyledo. Nothing fimilar takes place, with renous plants.

spect to the bark of the palın, that being · When a palm nut begins to vegetate, merely an expansion of the fibres at the it throws out successively, for the four bale of the leaf-falks, covering the or five first years, a nuinber of leaves, trunk with a coarse imbricated kind of which, by the union of their footstalks, net-work, cafily detached, and not caform a bulb just above the root fibres; pable of being renewed. this bulb increases, by degrees, in fize 2. CANES. Canes bear so near a reand solidity, and at length rises through semblance, iri their structure, to palms, the ground, forming the trunk, being, at that it is not easy to form distinctive chaits first appearance, as dense and thick as racters between them. A longitudinal it ever will be. The figure, therefore, fection of the common cane will at once is that of an exact cylinder, whose dia- fhow the resemblance, and almost idenmeter is always the same, though its' tity of conformation ; the central fibres axis is continually increasing.

are so loosely disposed, that thc naked It happens, however, sometimes, that eye may, with eale, diftinguith the inthe trunk does not preserve a regular tervals, and air or smoke may be, withcylinder throughout : this irregularity out difficulty, passed through a stem of takes place on account of the greater or several feet. The fibres approach each less abforption of nutrition by the roots ; other very fenfibly, as they recede from thus, if a young plant be moved from a the centre, and neither concentric cylinvery dry to a moist situation, the nutri- ders, nor medullary processes, can be distive juices being more abundant, the up covered. per part of the trunk will be thicker

3. GRASSES. The same appearances than the lower, and vice versa. Of this occur in the structure of all such gramivariation, a cycas, in the National Gar naceous plants as have perennial steins, den, furnishes a remarkable example. such as arundo bambos (bamboo) arunThis plant was transplanted from the do donax, panicum arboreum, panicum Ile of France, in a tub, in the year latifolium, faccharum officin. (sugar1789; when aşrived at Paris, it lan-' cane) and many other species, of this guished for a long time, during which its numerous tribe.

The vessels are Item, however, increased in length a few ranged parallel to each other, without inches ; but the whole of this elongation forming concentric cylinders ; the pith, was much less in diameter than the rest or medullary substance, is distributed in of the trunk. By Now degree, the tree the small intervals between the fibres, recovered; the shoots became more vi- which, as they approach the circumfegorous and larger, but the strangulated rence, become more fender and com. part continued, and still continues, of its pact, without any traces of medullary foriner dimensions. That portion of processes. But if the grasses are trunk which was produced in its na nected with the palins and canes, by the tive country, is 23 inches in circumfe- great distinctive characters of monocotyrence, the strangulated part 14 inches ; ledonous plants, they yet differ in fevethe upper part is 19 inches, and the in- ral particulars which ought to be menferiority in size of this, to the lower tioned. The stem is ho'low, and divided part of the stem, may be fairly attribut- by knots placed at regular distances, ed to the deteriorating influence of a fo- which forin transverse valves in the inreign climate. The same cause could terior of the stem, contribute to its never produce the same effect in a tree strength, and produce leaves and roors. with two seminal leaves, because, its in- The leaves are always simple, embracing crease in bulk being owing to the fuc- the Italk ; and, instead of being folded cessive application of concentric cylin- in two, like the leaves of the palm beders, extending from its base to its sum- fore expansion, they are rolled inward

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from the edges, and placed one within into two grand natural classes, whose the other, according to the order of their characters are the following: expansion, thole which are to be pro 1. Vegetables, which have no distinct duced lait occupying the centre: concentric cylinders, whose solidity de

4. After having proved the identity crcates from the circumference towards the of structure in the three preceding or- centre, having pith interposed between ders of plants, I was curious to know, the fibres, but giving out no medullary whether the genera of SMILAX, RUSCUS, procesus—MONOCOTYLEDONOUS. and ASPARAGUS, whose steins ramify 2. Vegetablus, with diftinét concenand apparently resemble those of the tric cylinders, whose folidity increases dicotyledonous shrubs, had any affinity from the circumference towards the in their internal arrangement; for this centre, having pith in a long tudinal purpose, I procured some vid ftems of canal, with diverging medullary prosmilax excelia, smilax aspera, ruscus ra celles-DICOTYLE. ONOUS. cemolus, ruscus andros; uus, asparagus retrofractus, asparagus acutifolius ; aid, PROCEEDINGS OF THE JURY OF ARTS after examining them with a high mag

Ar Paris. nitier, I can confidently affirm, that they This Jury was established by a Decree of the have neither concentric cylinders nor

Convention, and connits of celebrated Artists medullary processes, and their fibres are

and scentific Professors. They were appointed closer as they approach the circumfe to distribute Prizes and Recompences to men

who distinguish themselves in the Arts, &c. 5. In the same division may be ranged the DRACONTUM, YUCCA, AGAVE,

Prizes droveed to Works of ARCHITECALOE, and ALETRIS; all which plants

TURE, SCULPTURE, and PAINTING. g eatly resemble the palm, in the pofi- THE artist Morte, of Paris, was defired tion of their fibres. They have no con to present the model in relievo of his centric cylinders, and the pith between plan of a Triumphai Arch, in memory thi fibris does not send out any lateral of the Transactions of October 6th. proctifes er diverging rays. The outer Three other artists obtained pecuniary covering of the tem is

net a proper prizes for fimilar modeis. bark, but inerely an aggregation of the

Some of the ca didates received pecudead fibres of former leaf-stalks, with niary prizes for the best plan of a Column deep circular rings, denoting the num to be erected in the Pantheon, infcribing ber of years of growth.

the names of those Warriors that have 5. All the ligneous LILIACEOUS plants, died for their country. Of these prizes as well as the ANANAS and PANDANUS PERCIER and M UNIER, of Paris, and ODORATISSIMUS, are similar in struc- FONTAINE, of Pontoise, obtained the ture to the rest of the monocotyle donous most considerable. plants.

The Jury, however, di approved of the 6. The arborescent FILICES, like the form of a 'Column, as of all others the palms, have their trunks crowned with wortt adapted to Infcription. a tuft of leaves, the truck ittelf being LAHURé, of Paris, received the me. composed of coarse fibres, becoming con- dium of pecuniary prizes for his plan of paci in proportion as they recede from an Amphitheatre, on the lite of the anthe centre; and covered with a felid cient Opera. Here also the Jury cenbark, fermed of the fivrés of former sured the Programma (the paper which leaf-stalks.

insired competition) as injudicious ; say7. The items of the perennial 1700- ing, it was impcfible to construct an ediPOLIUM, and other MOSCI, Luar a very fice capable of containing the immense near affinity to the other plants with population of Paris, and worthy to celeone feminal leaf, in ihe fructure of their brute the National Festival, &c. within ftems, though they differ considerably in such narrow precincts as those of the anthe foliage and organs of fructification. cient Opera,

To these general observations, not a Some pecuniary prizes were adjudged single exception has been found, though to fome of the models exhibited of a a very great number of the living and Monun.ent in the Place des Vicroires, in dried plants, in the rich collection of the honour of the citizens who died for their National Museum of Natural Hiftory, country on the roth of August. has been examined, with this particurar The Jury adjudged the first prize, cbject in view.

that is, pronounced the design worthy of We may, therefore, divide vegetables being executed at the national expence, ro



1796.] Proceedings of the Conservatory of Music, at Paris. the artists Durand and THIBAUD, of he laid open the faults in the ancient Paris, for their plan of a Temple to be modes of musical instruction, the immense erected to Equality, on the area of the lofs sustained by the art a number of years Garden of Beaujon. The Jury pro- past, in the want of all instruction, even nounced this plan to be novel, replete the most imperfect, and the advantages with character, and perfectly correspond- likely to redound to harmony from the ing to the ideas of the Programma. present establishment, and the modes of They judged the Garden Beaujon, how- culture introduced into it. The regulaever, to be not extensive enough for the tions proposed by the commissary, adoptground-work of fo august a structure. ed by the Inspectors of Instruction, and

Some inferior prizes were then ad- approved by the Executive Directory, judged to several artists, for the belt were then recited. plans of Rural Edifices, Primary Affem The sitting terminated with a concise, blies, Decadary Temples, Prisons and but interciting oration, delivered by GosHouses of Arrest, and Baths and Foun- SEC, dean of the infpectors of instructains, &c.

tion. The models of National Theatres did The general effect of this sitting could not gain the approbation of the Jury, not fail to excite the most ardent hopes in and no prizes were bestowed.

the breast of every lover of the art; nypes Percier, of Paris, and FONTAINE, which seem to be on the point of being of Pontoise, obtained the first pecuniary realized. On the following day, the five prizes, for their plans of embellishment inspectors proceeded to examine the

pum, for Paris.

pils, with a view to distribute them into The project of the Temple of Equa- classes. This important duty, discharged lity is the only one which will be recom with a truly paternal zeal, took up the mended by the Jury to Government, as

whole of the eight following days; and worthy of being erected at the public on the 6th Brumaire, the learners, who charge. It does not follow, however, had been previoudly examined, were arthat the other plans discovered a medio- ranged into claffes. The zeal of the crity of genius or invention in the artists; administrators, and of the different promany of them certainly evinced consides fessors, keeps pace with that of the inrable genius, but as the conítruction of fpectors of instruction, and the instituNational Edifices must necesarily require tion would be already in a state of entire much time and immense expence, the establishment, if temporary embarrafiJury was obliged to exercise a rigid feve ments did not intervene. It is expected, rity' in its decisions, and to exciude all however, that the prompt and vigorous defigns which did not approxima:e to

ailistance of government will remove their own ideas of perfection.

these considerable obstacles, &c.

[In our next we Thall have the plcasure of

presenting to our Readers, the useful ProceedOn the first of Brumaire (Oct. 22) the ings of all the Sittings of the LYCEUM OF school of musical instruction was open- Arts.] ed at Paris, in the Conservatory of Music, in presence of a deputation of the National

MATHEMATICAL CORRESPONDENCE. Inititute, and the Director-general of public instruction, in the name of the Minister of the Interior. The fitting

To the Editor of the Monthly Magazine. was public; the members of the Con SIR, fervatory were present, and about four IN your Magazine for August, a corhundred pupils of both sexes, with their respondent, under the signature of relatives, &c. The deportment of the Exctericus, has made some iemarks on a professors, and the sedate yet eager at little work of mine on Algebra, lately tention of the scholars, muft necessarily published ; and I might, perhaps, have have made an imprelion even on such as rather left the noticing of them to others, from the want of organs, instruction, or had not an opportunity been thus ullired Teflection, attach the least value to the art to me, of correcting an error in iny obof music.

fervations on Cardan's Rule. Exotericus After reading the law which authoriz- has properly brought the inftance of the ed the establiíħment of the Conservac equation +274–28=0, in which I tory, JARRETTE, commissary of orga- deny the propriety of following the ulual nization, pronounced a discourse, wherein mode, by making a+b=1; for as the





equal to ?.



former equation has only one root, which QUESTION XVIII (No. VI).—Answered is unity, zab must be less than q, or 27.

by Mr. 7. --r. To solve equations in this form, xshould This problem may be solved by fevebe made equal to ab, from which will ral eafy methods : one, which is perhaps result an equation aó—ra3=5, an equa

the most proper for our purpofe, on ac

count of the extensive use of the theo. tion which admits of only one root; and rem from which it is derived, is the folfrom the resolution of this equation, a lowing: may be found, and thence b, which is Ferguson, in his “ Select Lectures,”

page 362, thows, that if we put A= fine

of fun’s altitude, L and i= fine and coза

fine and co-fine Upon equations of this form, I have fine latitude, D and d (Algebra, p. 213) inadvertently faid: fun's declination, and H = fine of the .: When x is of such a magnitude that jum's hour-angle from VI, then the rezab is not equal to 9, it is evident that lation of H to A will have three va. the rule faiis.” This is true generally,

ricties, viz. and is the reason why, in several cales,

1. When the declination is towards Cardan's rule fails; but it does not ap- the elevated pole, and the hour nearer ply to the case in question, #3+=;

noon than VI is, A=LD+Hld and H= in which zab may be always equal

A--LD I go on : “ Thus let x3+=, in Id which case arb=4, with q=1, and, con 2. When the declination is towards sequently, zab must be greater than one.” the elevated pole, and the hour nearer Now this is not true ; for amb may be midnight than VI is; then A=LDequal to 4, and at the same time zub=1;

LD-A for a may be a whole number, with a de- Hd, and H=

Il cimal, and b a decimal; fo that 3ab may 3. When the declination is towards the be not only equal to unity, but to any depressed pole, A=Hd-LD, and H= affignable numbeč less than unity. As AULD a familiar instance, let (b=1, and

Id a=4,01, and b=,01 : 3ub=3 X 4,01 X

When A comes out negative in any of 2015,1203 = number less than unity.

the above formulæ, it indicates that the Exotericus properly asks, what advan

fun is below the horizon, and is then the tages will be gained, by giving up the

hine of its depression. mode of working by negative numbers ? I answer : the icholar is not taught a

From the data, we easily get the hour false principle; he is not taught to take a

of the sun's rising above the visible bori. number away from another less than it

zon from the mountain ; from which, by felf, that is to perform an impoflibility. is, in this case, the fine of his then de

the foregoing method, we get A, which Consequently, when he comes to any thing leading to such an operation, he preilion below the rational horizon of the paules; renews his work, and admits place. nothing which is not confifte:t with

This angle of depreffion may also be plain lense. If it is faid, that fir Ifaac obtained (as indeed all the foregoing exNewton followed this mode ; I answer, pressions are) by the solution of one obAlexander also cut the Gordiản knot, and lique-angled Tpherical triangle, tivo fides grcat names are no excuse for unjufti- fun and co-latitude of the place, the

whereof are the polar diitance of the fable actions. You will permit me, sir, to add my

contained angle the hour-angle from thanks to several nanieless correspond the fun's zenith distance. But the for

noon ; and the third fide to be found is ents, and my hopes that thcy will conti.

mulæ themselves are so extremely convenue to favour me with their communications. As my Algebra may not fall into and so easily applicable even by persons

nient in a great variety of other cafes, the way of several of your readers, I have enclosed the resolution of an equa. they seemed worth insertion.

who are not conversant in spherics, that tion of the third order, true to six places of decimals, wh with a little

A proper application of the column

marked 5 more trouble, might be carried on

log-rising,”. in Tab. XVI of twice that number. Your's, &c.

the “ Requisite Tables," published by

the Board of Longitude, will also give Inner Tempir,

W. FREND. the depression required with as much Dec. 15, 1796.

case as cither of the foregning methods.


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1795.] Mathematical Questions.

881 Having found the depression of the vi

meter, fo is radius to the hypothenuse ; fible horizon, we have the height of the from which subtract the femidiameter, mountain from one analogy, viz. Co-fine and that gives the height of the hill reangle depression : radius :: earth’s femi- quired. diameter : earth's femidiameter of the This Question was also answered by Mr. beigbı of ike mountain required.

Joon Dawes, and Mr. Jobn Haycock. We may also, to avoid the necessity of using such large numbers as will occur in the preceding analogy, take the follow- QUESTION XIX (No. VI).- Answered ing for a near approximation : Reduce

by Philalethes. an arc of the earth's circumference, Of seven numbers in continued geowhose quantity is equal to that of the metrical progreisions, having given the angle of depression before found (and sum of the two least = 90, and the sum which will consequently be the semidia- of the two greatest = 281250 ; make meter of the visible horizon from the

* = the first number, and x=the commountain) into yards or feet, and we mon ratio; then will x, xz, xz2, 423, x24, shall have radius : tangent angle depref- *25, xz6, represent the feven numbers. fion :: the distance fo found : twice the Therefore, by the question x+xx=90, height required, very nearly.

and x25+x26=281250; dividing the latIn the case before us, the difference of ter of these by the former, gives zs= the times of sun rising given, is supposed 281250 = 90 = 3125; therefore % to be the difference of the times of the 5V 3125=5. Consequently, x=90+1+ true rising of his centre above the rational

%=15; and, therefore, the numbers horizon of the place, and the visible ho- sought are, i5, 75, 375, 1875, 93750 rizon from the summit of the mountain, 46875, 234375. both properly corrected for refraction J. F-my, after his solution of this and parallax.

question, adds this remark, viz. If there

be n number in geometrical progression, The same answered by 7. H.

x being the first term, and r the common Having the latitude and declination ratio, the sum of the two first being = a, given, per spherical trigonometry, as ra and that of the two last = b; then, dius is to the co-tangent of the comple

bi ment of latitude, so is the tangent of de- generally, it will be r=1-2W -, and x= clination to a third number, which is the time of fun rising before fix o'clock (if iti latitude and declination are both north). Answers to this question were also given To this add the given difference of fun by Meffrs. W. Adam, W. Clavey, John Cole rising on the top of the hill; and that lins, Ã. Cox, L.W.D. J. H. John Haycock, will be the included angle of a spherical Lajcey, B. W., X. and Hermes of Bath. triangle, the two sides of which are given, viz. the sun's polar distance and the New MATHEMATICAL QUESTIONS. co-latitude, whence the third fide, or zenith distance, will be found, and confe

QUESTION XXIII.—By Mr. B. I. quently the sun's depression from the Which is the greatest, an arithmetical true horizon, or the distance from the or a geometrical mean, between any two bottom of the hill on the arc of a great quantities, a and 0 ? circle, where a tangent drawn from the top of the hill to the sun, will touch the QUESTION XXIV.-By the same. surface of the earth. If that point of If a pendulum, 39 inches long, swing contact, the top of the hill, and the centre seconds, in what time will it swing, when of the earth, be joined by three lines, a carried into a latitude where its weight right-angled triangle will be formed, in is diminished by the 300th part of an which are all the angles, and the earth's inch, and its length increased by the heat femidiameter given ; whence, as the co the 10th part of an inch : line of the angle of the sun's depression Erratum, p. 721. In the solution to (abave found) is to the carth's femidia- Question XVI, 1. 5, for 4*, read 47.

TO CORRESPONDENTS. The Notice to some of our Poctical Friends, in our last Number, will particularly apply to tbe pieces signed E. S. 7.

Our obliging correspondent will observe, that notice bas been taken of the Musical Work from Cambridge. His future correspondence will be acceptable. Biograpbical Notices of remarkable exdi distinguished Characters are solicited.



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