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have waxed old; she may be in a state of aware of my liability to incur this cene

renovation and of return, to be a fit ha- sure, when I profess to consider all con* bitation for animals of a constitution jectures vain as to the immediate utility

similar to those upon our globe; and to of these arrangements, of which the inthe former, and the future, more useful habitants of the satellites can alone stales of the satellite, her motions and judge, and which “ while this muddy external relations, though not so neces- vesture of decay doth hem us in," we sary in her present situation, may be more cannot comprehend, though we may peculiarly adapted.

hope the tiine will arrive when we shall Morch 8th, 1811.

see all doubtful things made clear.

If I have not transgressed my proper To the Editor of the Monthly Magazine. limits, I beg to add a few remarks on SIR,

some astronomical terms, which I think ALBEIT unused to abstract specu. ought to keep pace with the improve

A lations, my musings on “Coper. ments of the science itself; those of the micus's" query, (which met my eye in rising and setting of the sun, the sun's your last Number) hare led me to some path in the heavens, and several others observations, which may perhaps find a equally figurative, are still in use, while place in your next Number, if unoccu- the errors which gave rise to them have pied by a worthier claimant. The be- been long exploded: the young mind is fanefits which accrue to the satellites, from miliarized to the ideas they excite,and cantheir always presenting the same hemis- not easily divest itseltofthem, Anobstacle phere to their primaries, can, I imagine, is thus laid to the reception of truth; and be duly appreciated by their inhabitants I have known young persons go through alone, as they only perceive the utility the common routine of astronomical lecof the appointed length of their days, tures, without obtaining any clear concepwhich, in reasoning from analogy, we tions of the relative situations of the hea. must conclude are adapted to their pe. venly bodies, from early but strong im. culiar circumstances. The cause of the pressions of an erroneous theory. Why same hemisphere being thus presented, then not abandon these figurative expresarises it seems from these Satellites sions to poets, and fauniliarize the young turning once only on their axis during the mind to the truth, by clothing it in its period of revolution round their prima- own native simplicity? ries, and, as the length of the natural day

PENSATRICE. in any planet depends on the length of time it requires to turn on its own axis, To the Editor of the Monthly Magazine, this day must vary in these secondary SIR, planets according to the different por. THE writer who, in your last Numtions of time in which they revolve round 1 ber, page 156, bas given us an actheir primaries. If an inserior planet, count of the latter part of the life of the to enable buth its hemispheres to enjoy Maid of Baldock, has not favoured us the light of its primary, were not to turn with any account of her youth, nor the on its axis at the same time that it re. event which gave rise to the celebrated volved round the primary, the length of song; therefore, the following informa. the day would be regulated by the period tion may not be unacceptable to the of the primary's revolution round the sun, lovers of rural manners. which might put the inhabitants to great . The maid of Baldock's mill, had at one inconvenience. Now, as throughout na. timc four lovers; “ the grave and the ture, we find a constant adaptation of the gay, the clown and the beau." The first creatures to the circumstances in which of these was a young clergyman; the they are placed, or vice versa, we must second a gentleman, young and gay; and suppose that the creatures of the moon the other cwo were well described by the find their advantage in the length of their “clown and the beau." day, (viz. twenty-seven of our days and Love inspired the Muse of this young five hours,) and, to all the rest of the divine, and it was he who wrote the song, satellites, the privation of the light of which was at that time, and for many their primary to our heroisphere is in all years afterwards, universally admired. probability more than compensated by. This maid of the mill was extremely the convenient length of their days. beautiful, and it was said, that this Ignorance is indeed prone to think furyoung divine was deeply in love with her; ther investigations useless in a subject and indeed it appears so from the four that it cannot comprehend, and I am last lines of the song. This maid was as

modest SIR,

modest as she was beautiful; for, after both in Bourne's poems, and in the the song was published, it was very dif- Lusus Poetici of Dr. Jortin. The faine ficult for a stranger to get a sight of her. indeed, of both these scholars, is too

The writer of this article had the above firmly established to be in the least inaccount from a gentleman who knew this jured by the tearing out from their works celebrated beauty, about the time that the leat which contains this ode. The the song was published.

W. chaplets which encircle their brows are St. Austin-street.

composed of every sweet, of every P.S. Mr. William Mason, the poet, in. choicest flower; their fragrance is too vented the piano-forte. Sup. Ency. Britane strong to be destroyed by the plucking nica, vol. 2, p. 866

out of this, a flower of most exquisile

perfume; it is nevertheless right in To the Editor of the Monthly Magazine. literary, as in every other species of proSIR,

perty, to render unto every one bis own, R. Knox, in his Essay on the or, to speak in the words of Dr. Ji him

Life and Writings of Dr. Jortin, self, makes the following remarks: “ Among “Palmam qui meruit, ferat." modern Latin poets, there are few who Coventry, 1811.

D. do not yield to Dr. Jortin; the little ode in which the calmi life of a philosopher is To the Editor of the Monthly Maguzine. compared to a gentle stream gliding through a silent grove, is highly pleasing to the mind, and perfectly elegant in

A S you have thought the letters which

A share hitberto sent you, deserving composition." I should suppose, that there are few of your readers who have

ů a place in your Magazine, I am induced not read the ode to which the doctor to believe that the following will obtain alludes; but for the benefit of those few

similar favour. it is bere subjoined:

In the 28th volume of the Gentleman's

Magaziwe, for the year 1758, page 307, Qualis per nemorum nigra silentia

Mr. Emerson called the attention of the Vallesque irriguas, et virides dunios,

public to the theorx of the equilibration Serpit fons placidus murmure languido

of arches, which he had before published Secretum peragens iter :

in his works. It is manifest from this Flexas per patrios circumagens aquas

paper, important as to the elucidation of Paulum ludit agros, et sinuat fugam,

Mr. Einerson's idea of an arch, as well as Donec præcipiti jam pede defluens

from the accompanying diagram, and the Miscetur gremio maris :

diagrains in his publications, that Mr. Talis per tacitam devia semitam

Emerson conceived that arches were Ætas diffugeat, non opibus gravis,

built by inverted offsets, and he was un. Non experta fori jurgia turbedi, aut acquainted with the circumstance, that Palme sanguineum decus.

voussoirs invariably in Europe, whatever Cumque instant tenebræ, et lux brevis occidit, may be the custom in China, are the Et ludo satura et fessa laboribus,

constituents of an arch. There can be Somni frater iners membra jacentia

no mistake respecting this fact, as in Componat gelida manu.

those diagrams the joints of the stones or In referring to Dr. Jortin's Lusus bricks of which his arch was to be comPoetici, I find the ode, verbatim, as posed, are shewo. above; the same is also to be found, with D r. Ilutton, in his work on this theory, the variation of about half-a-dozen defines an arch “ an opening of a bridge words, a nong the poems of Vincent through or under which the water Bourne, under the title, “ Votum.” I passes.” Others, who sopport this theory, think Dr. Knox must bave seen it there when compelled to the admission of vousalso; what reason he could have in at- soirs, say that, by the theory, they must tributing it 10 Dr. Joriin, in preference be infinitely short. Dr. Hutton, so far to Buurne, I am at a loss to conjecture, from considering that voussoirs bave atiy It must, however, be evident to every relation to the theory, speaks of thein as one, that it cannot be the production of quite separate things, in the same manner both of them: the writer of this will as le does of the balustrade, or cornice : therefore be obliged to any one who will and gives the following practical rule, by jsform him, through the medium of your which he evidently considers the arch ont Magazine, to which of them it really be of the reach of the theory, or otherwise longs, and how it came to be inserted so eminent a mathematician could not MONTHLY MAG, No. 211.

2F .

have

have given so unscientific a description of the wall theory must be framed anew to it. “ The key.stone should be about 15 a novel series of curves; if the arch be or to of the span, and the rest should in- spiritual, then the infinite ascension of crease in size all the way down to ibe the two points of the forked extradoses impost; the more they increase the bet- of the semicircular, elliptical, and cyter.” In the propositions, he considers cloidal, arches, have properly intercourse the whole thickness at the vertex as so with the aërial regions; or these, and the inuch wall standing upon a mathematical unicorn of the cissoid, inight serve at curve, in the same manner as Mr. Emer. Balmiberbi, to prevent the descent of the son does. Even in speaking of the arch flying island of Laputa. of Blackfriars-bridge, he considers the It is not difficult to conceive, that the whole thickness at the vertex as wall, and mathematician who, in a mathematical the archi, as he above defines it.

work, could seriously give an account of The leading proposition of Emerson's an automaton which could play at chess, . theory, is thus: “ The nature of a curve might have his risible faculties so orgaforming an arch being given, to find the nised as to be unsusceptible of the ahnature of the curve, bounding the top of surdities merely exemplified in the diathe wall supported by that arch, by the grams of this theory. But it is difficult pressure or weight of which wall, all the to conceive that an enlightened philosoparts of the arch are kept in equilibrio pher should thus slander“ most innocent without falling." Here the arch is con. Nature." "She, good cateress, means sidered as sumething given, not some- her provisions” for the uses of mankind : thing to be discovered; it is true, if the in the contemplation of a bridge, she arch is to be considered as of infinite could not have prescribed a form which thiness, it would be absurd for any would render it impassable; the bounty useful purposes to attempt to determine of Nature, in respect of bridges, has exits shape; but it would be mathemnatically ceeded any other instance of her provi. proper to discover the infinitesimal in. dence. What in other cases are impediCreinents from the vertex. If it is of ments to perfection, in this instance are some thickness, as practice requires, auxiliaries; what in other cases oppose it is anomalous to set about deterinining the artist, and increase his errors, in this what it shall bear, until it is itself deter- instance assist him, and are antidotes to mined; for its extrados is the curve upon his mistakes: could a semicircular or which the Emerson theory proceeds to elliptical arch be built after the wall the determine the wall to be placed upon it. ory, cohesion and friction might prevent

As by this, or, rather as it may be siy, for a minute the ruin which, without nificantly termed, the reall theory, the their aid, must instantly ensue. arch can have but an imaginary exis. The first proposition on which the tence, it follows that in proportion as the whole of this theory depends, most cer. arch is practically secure and stable by tainly does not apply to the question of the increase, in consequence of the depth the equilibration of arches, and is not of the voussoirs, in that proportion it is true in itself, as stated in the tracis in insecure and unstable liy ihe theory. the support of this theory; it is still furWhat the wall is, as applied to bridges, ther froin the truth than the proposition which is to stand upon the arch, an ar- of the funicular polygon, acted upon in a chitect would be at a loss to guess; but vertical plane by weights in different it is consistent that an imaginary wall points of the cord, when the weight of should stand upon an imaginary arch. The cord itself is not taken into the ac

Were the wall theory the true theory, count. In the question of an arch, it is the propositions could have no applicae all cord--all voussoirs. When the voustion in respect of bridges among scien- soirs balance each other, there is no wall vific inen. The practice of arch-building but the parapet er fence-wall, which, it froin Michael Angelo at the Rialto, is hardly possible to belicve, has bech through the most enlightened architects thought to be in the thickness the depth on the Continent, to Mr. Labelye and of the vault. The filling-in of the span. Mr. Mylne, bave been to increase each drels, is but another mode of balancing voussoir in depih, from the vertex to the the voussoirs, or giving them the same springing; mor has there been wanting perpendicular action, when from ecoeminent mathematicians to confirm this nomy, or other causes, it has been judged principle, and the relative increase has expedient to give the arch-stones on the not been a matter of guess; hence, if the face the same depth. In this primary arch bave substance, the propositions of proposition, the tangential forees are

peither

neither opposite, nor are they equal; and force exerted perpendicularly, may be those forces are assumed which are to be every where the same; or that the same discovered, and that is to be found out adjustment should he obtained by art in which is given. In the question of the an arch which, in a chain suspended at equilibration of arches, justly considered, its extremities, naturally appertains to it. some one force is given (generally that at The distinction between the weight and the vertex, as there the perpendicular the chain is not real. A catenary may action is equal to its whole absolute gra- be formed of links of uneq al weights, vity,) to find the two adjoining forces, or as well as of equal weights; though the any others in the systein, which is pre- curve would he different, the operation cisely the question of the simple catenary, to discover that curve would be the sanie. where there are no weights but those ille Whatever the weight is, or wherever it corporated in the chain. The wall theory is, it must be incorporated in the chain; is a plagiary, garbled and misunderstood, and the perpendicular action of cach from the familiar mechanical method of force, in a system of forces in equilibra. suspending from a chain bits of chain, tion solicited by gravity, whether an arch their lower extremities forming a given or chain, must be constant, or everyline of roadway to determine the curve. where the saine; and it is the constant This method is untrue, and could only force which must determine the other be made to approximate to truth, as Dr. forces. Robison has observed, by making the Architects well acquainted with the Foussoirs bear the same proportion to the facility to be derived on some occasions weight as the chain does to that of the by the methods of investigation by albits of chain. The result from this ope- gebra and fluxions, affect generally to ration is untrue, inasmuch as it differs disregard them as marks in their profrom that of the simple catenaria.

fession rather of speculative than real In the investigation of the catenaria, knowledge ; but there would be no afthe powers considered were the absolute fectation in asserting, that they would as gravity of the particle, or link, “abso- soon apply a theodolite to measure a lutam gravitatem particula Dd;" and cornice, as their knowledge of fuxions to that part of the gravity which acis per. the simple and plane theory of equilipendicularly, “gravitatis partem eain bration, and ihe easy proposition of deque normaliter in Dd agii :" now it is scribing the extrados of an arch of equiadmitted by all, that the actions of the libration. There are mathematical bervoussoirs of an arch are similar to the mits, as well as religious hermits; the links in a chain, and that the conclusion common practices of mankind are myselicited from the one, that the action of teries to the one as well as to the other. gravity, perpendicularly exerted on the There is also a superior order of learned correspondent parts of the chain Du, men, who condescend to try their thewill be every where the same, “graoretical knowledge by the practice of vitatis actio in partes correspondentes the workmen, or their own experiments; catenæ Dd normaliter exerta etiam in the praise of such men, ihe skilful constans erit, sive ubique eadam," apo builder will become an enthusiast; and plies equally to the other. To produce froin such men, he will be proud to acan arch of equilibration, cach voussoir, koowledge bimself indebied for the best or the weight incorporated in each vous acquirements in bis art. soir, requires to be increased, so that the Mr. Thomas Simpson, in his answer to

the three questions proposed by the Com

mittee for building a bridge at Black. Dr. Milner, in his answer to the Select friars, seems to reason on the subject not Committee of the House of Commons, to like a theorist, but an architect, not. questions submitted to him on this subject, withstanding that Emerson's notions most justly observes: “It is not from any had been oublished some time. indeed. Error of computation, that erroneous practical throughout the papers published previa inferences are apt to be made by the theorists; ausiue to the erection of Blackfriars. the errors almost always arise from the assumptions made at the setting out of the

bridge, although Emerson volunteered

ho solution of the problem. Dr. Milner thinks

his opinions to the public, they seem he is within bounds in believing, that for one to have been wholly neglected; and error in the fluxionary and algebraical part of they would have remained so to the calculations, a hundred have been made by present time, among other proposi. discordant and unnatural hypotheses, respect. tions, as the curious wanderings of a ing powers, forces, and modes of action." mathematician, had it not been for the

doubly doubly-unfortunate dilapidations of the let in light." If there were wanting any bridges on the river Tyne.

instances of the absurdities which great Professor Robison certainly inserted and eminent men have been led into by The Emerson theory in the Encyclopædia the modern analysis, when they have Britannica, and at first held it in some not been sufficiently attentive to deter. esteem, out of respect to common opi- mine the truth of the first proposition, nion; for he really believed, from the depending merely on the principles of mode in which it was introduced to the mechanics, Emerson's Extradoses of public, that it was the " codinon theory" Arches, and especially of domes, would of architects and builders. But froin the stand like the full and perfect warning article “ Roof," to the article “ Arch," which a wreck offers to the heedless in the Supplement, until we come to the mariner; his charts and books lying nee conclusions of the latter, we perceive, in glected in his chest. Not even those on the gradual unravelling, how ditticult it whom the authority of the Woolwich is long to deceive men who look beyond Academy has imposed Emerson's theory their own speculations and libraries for of arches, cant contemplate with a seknowledge. Speaking of the fallacious- rious countenance, the monstrosities of ness of the theory, from the test of nue his conclusions in respect of domes. It merous experiments wiich be had been is difficult for a mason to resist exclaimat the trouble and expense of making, ing, in this instance, “Multos se deliros he says, “ But the clearest proof is, that senes sæpe vidisse, sed qui magis, quam arches very rarely fail, where their load Phormio, deliraret, vidisse neminem !" differs most remarkably from that which. The methods by analysis and geometry, this theory allows." sind, again spenkresemble the progress of a young and ing of those arches which have stood the an old hound. The former, if he get test of ages, he says, “ Here is a most a right scent, and keep it, will soon remarkable deviation from the theory, overtake the pursued; but, on a wrong for, as is already observed, the load is scent, his feetness but removes him frequently not the fuurth part of what further from the object: the old hound the theors requires." The supporters is oftener in at the death, and is always of the wall theory say, and it is all which' near the victim. Notwithstanding the can be obtained in explanation of the importance which has been attached by theory, that they have “ exploded" the inathematicians to the question of the wedyc-cheory, and that their theory is, equilibration of arches, it is a question “ the true theory;" and that those who of little worth to the builder, in compacannot “perceive the force of it, are rison with that of the piers. On this part ignorant and prejudiced."

of arch-building little has been written, Permit ine to recommend to your and still less understood, except by those readers to peruse attentively the first who have been uursed in the practice. proposition of Dr. David Gregory's Should you think the above worth ina paper on the catenaria; and to dwell on serting in your Magazine, and hold of the second, and its corollaries; to turn in any value the theory which bas in fact their mind Dr. Hooke's deduction, (de- been, from the first arch which ever cyphered)" ut pendet continuoun flexile, stood, the theory which has guided the sic stabit contiguum rigidum inversum ;" builder, though unconscious of the extent Dr. Johnson's three Letters; Mr. Simp- of his knowledge, and which I hare at. son's Answer to the Committee for teinpted to detail from Dr. Gregory's building Blackfriars Bridge; the An- paper, and Dr. Hooke's conclusion; I swer of the Monthly Review, (written, as shall, at my leisure, send you a paper on Dr. Hutton states, by Mr. Woodhouse, the subject of piers; shewing their pronow sufliciently eminent,) June, 1802; perties involved, and dependent on the the Letters in Answer to your Review, accurate reasoning of Gregory and and the Monthly Review, in the Monthly Hooke, in which an extraordinary vaMagazine, August and October, 1802; riation between false theory and true they will then exclaim, in the words of practice, extracted from the second Rethe commencement of one of Dr. John. port of the Committee of the House of sun's Letters, “It is the cominon fate of Commons on the Holy-liead Roads and erroneous positions, that they are be- Harbour, printed June, 1810, may further trayed by defence, and obscured by ex- illustrate this subject. LAPICIDA. planation; their authors devinte from the P.S. See letters on this subject, Monthly main question into incidental disquisi- Magazine, Sept. 1809, Nov. 1809, Aug. cious, and raise a mist where they should 1810, and Nov. 1810. .

To

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