« PredošláPokračovať »
SCHOLIUM II. If a circle be described, the diameter of which bears the same proportion to the perimeter of the given trapezium that radius bears to the fum of the four cotangenis to the four half angles of it, and if a tangent be drawn to this circle, equal to the file of a square which has the lame proportion to the area of the walk tot radius has to the lum of the said four cotangents; the difference between the radius of this cucle and the fecant to that tangent will be the breadth of the walk.
Another ANSWER to the same, by Mr. GEO. SANDERSON,
ANAL Y SI S. Suppose thething done, and ABCDthe pond, EFGH the outward boundary of the walk, AIEK, BLFM, &c. trapezia, inade by perpendiculars froin the angles
N of the pond on the sides of the walk. Then because
L the perpendiculars are equal, the trapezia, as well as the ongles E, F, G, and A, are bitected by the lines AE, BF, &c. but the angles are given, therefore the ratios of the perpendiculars to the corresponding sides of the trapezia are given. Morcover it is manifest that a rectangle on one of the equal perpendiculars, K A. D and the sum of the lides IE, LF, &c. of the trapezia,
Р together with a rectangle under the same perpendicuJar, and the sum of the sides of the pond is equal to
E I the area of the walk; whence the following
CONSTRUCTION, Make ak equal to the sum of the sides of a the pond, and let R be the fide of a square that is equal to the area of the walk. To ak draw the indefinite perpendicular kr, on which take kg to ak in the given ratio of IE to Al,
R and gb : ak :: LF :LB (IA); bf': ak:: NG:
Zpg CN and fr: ak::PH:DP, join ar, and on ak take ae a third proportional to ak and R; then by Problem 3. Book I, of Mr. Wales's Deter. Section, cut ea in o, so that the square on ao imay be to the rect. contained by eo and ak in the ratio of ak to hr; and having erected the perpendiculars AI,BL,CN, and DP (fig. 1)each
k equal to ao, through the points 1, L,N,P, diaw
Join ag, ab, af, and diaw og parallel to kr, cutting them in the points I, n, p, q, Try fimilar triangles, and the conftr. ao: 0 :: ak: kg :: AI:JE, but AI = ao by construction; therefore IE col. And by the same itafuning, LF=In, NG= np, and PH=19. And becausc o and AIE are right angles, a rect, on ao and olis. equal to a rectangle under Aland IP-trapezium AIEK, and a rect. under ao and in (iwice triangle lan) = trapezium BLFM, : a rect. under ao and op is equal to the sum of the trapezia AIEK, BLFM, &c. Again ak: kr :: 202 : 0€ x ak (by const.) = ai-ao x ak -- ac x ak-ak x 60; but ae x ak=R? by conft. therefore ak : kr:: oa?: RP-ekxac::00:09::202 : 09 Xay, wherefore Reak X00 +oq xao, but ak is equal to the sum of the lives of the pond by conft. and ao=AI=BL, &c. Theree føre, the rectangles Al, BN, &c. together with the sum of the four trapezia are cqual 10 R2 the given area of the walk, as required,
22. QUESTION I. by MATHEMATICUS, of Greenwich. It is required to determine that parallel of latitude, in which if two places be situated tl at differ 180° in longitude, the distance between them, reckoned on the parall I, may exceed their distance on the meridian by the greatest quantity pofiible.
23. Question II. by ASTRONOMICUS. To find the declination of that star whose change in azimuth is the greateit or least possible in palling from one given almicanter to another given one, in a given latitude,
24. Question III. by NUMERICUS. A father on his death-bed divided his cash, consisting of a number of guineas, among his children in the following manner: He ordered the first to take i guinea and th part of what remained; the second to take 2 guineas and th of what remained; the third to take 3 guineas and 4th of what remained; and fo on, successively, for the others. Now, this diftribution being made, it was found that each child had an equal portion. What number of guineas did the old man distribute, and how many children had he?
25. Question IV. by Mr. Reuben Robbins. In a plane triangle, there is given the rectangle of the fides about the vertical angle, the perpendicular on the base, and the difference of the segments of the bale, made by it, to conftruct the triangle.
26. QUESTION V. by Mr. GEORGE SANDERSON. Suppose AEB a given semi-circle, the center of which is C; and let D be a given point in the diameter: now, if the point E be supposed to move, in the circumference, with an equable celerity; it is required to find its place when the angular velocities of the two lines ÉD, EC are equal.
The answers to these questions must be sent, post-paid, to Mr. Baldwin, in Paternofter-row, London, before the ift of January, 1784.
FOR THE LONDON MAGAZINE. ON THE CHARACTER OF CORDELIA, IN SHAKSPEARE'S KING LEAR.
. different kinds. Of confequence, conduct proceeds from mere feeling. the actions that flow from them are It entitles you to the praise of sensibimore or less beneficial, and more or lity, but not of reflection. You are less entitled to praise. We are moved again in the same situation. But the by inconfiderate impulse to the per- fymptoms of distress do not produce formance of beneficent actions, as we on you the same ardent effects. You are moved by inconfiderate impulse to are moved with no violent agitation: the perpetration of guilt. - You fee an and you feel little sympathy. But you unhappy perfon: you discern the visita- perceive diftrefs, you are convinced that tions of grief in his features: you hear ilie sufferer suffers unjustly. Youknow them in the plaintive tones of his voice: that you are bound to relieve him; and you are warmed with sudden and re- in consequence of these convictions you liitless emotion: you never enquire afford him relief. Your conduct proconcerning the propriety of your de- ceeds from sense of duty, and though portment, or the merits of the sufferer; it entitles you to the credit of rational
humanity, it does not entitle you in It is no vicious blot, murder, or foulness, this initance to the praise of fine sensi
No unchalte action or dithonour'd step bility.
That hath depriv'd me of your grace and fatour, Those who perforın beneficent actions
She displays the same gentleness, from immediate feeling or impetuous accompanied with much delicacy of impulse have a great deal of pleasure. reproof, in her reply to a mercenary Their conduct, too, by the influence of lover. fympathetic affection, imparts pleasure
Peace be with Burgundy! to the beholder. The joy felt both by Since that respects of fortune are his love
I thall not be his wife. the agent and the beholder is ardent, and approaches to rapture. There is
Even to her sisters, though she has also an energy in the principle, which perfect discernment of their characters, produces great and uncommon exer- and though her misfortune was owing to tions. Yet both the principle of their dissimulation, the expresses nothing action, and the pleasure it produces are
virulent nor unbecoming. She expresses, tranfitory. Beauteous
however, in a suitable manner, and with ing cloud or the early dew,"like them, no improper irony, a sense of their detoo, they pass away. The pleasure ceit, and apprehenfions of their difafarising from sense of duty is less im- feciion to Lear. petuous; it has no arproaches to rap Ye jewels of our father with warh'd eyes iure, it seldom makes the heart throb, Cordelia leaves you: I know what you are, or the tear descend; and as it produces Your faults as they are nam d.
And like a filter am moit lorh to call no transporting enjoyment, it feldom leads to uncommon exertion. But the
Towards the close of the tragedy, joy it affords is uniform, steady, and when he receives complete informalasting
tion concerning the violent outrages · As the conduct is most perfect, so
committed against her father, the fuf. our happiness is most complete when ferings he has undergone, the ruin of both principles are united: when our
his understanding, and has the fullest sense of duty is animated with sensibi
evidence of the guilt and atrocity of lity, and sensibility guided is by sense
her sisters, the preserves the same conand duty. No happiness can be more
fiftency of character: notwith/tanding desirable than that which is both ardent her wrongs, she feels and is affected and lasting. It is indeed to be re
with the deepest sorrow for the misgretted that feeling and a sense of fortunes of Lear: she has the most enduty are not always united. It is
tire abhorrence of the temper displayed dreply to be regretted, that unless fen- by Goneril and Regan: yet her forfibility he regulated by that fenfe of rows, her resentment, and indignation duty which arises from rcllection on
are guided by that sense of propriety, our own condition, and krowledge of which does not in the smallest degree, human nature, it may produce unliap- impair her tenderneis and fenfibility, piness both to ourselves and others; bui directs to that conduct and debut chiefly to ourselves.
meanour, which are suitable, amiable, Shakspeare, in his character of Cor- and interesting. Tenderness, affection, delia, has given us a fine example of and sentibility, meling into grief, and exquifite sensibility, governed by rea- mingled with sentiments of reluctant fon, and guided by the golden rule of disapprobation, were never delineated propriety.
with :nore delicacy than in the deThis amiable character indeed, is con- fcription of Cordelia, when fre receives ceived and executed with no less kill intelligence of her father's misfortunes. and invention than that of her father. Kint. Did your letters pierce the Queen to Treated with rigour and injustice by any demonttration of grief? Lear, the utters no violent resentment;
Gent. I say the took 'em, read 'em in iny hut expreiles becoming anxiety for re
And now and then an ample tear trillid down putation.
Her delicate cheek: it seein'd she was a queen 1 yet beseech your Maje.ty
Over her patrion, which most rebel-like That you make known
Sought to be King over her.
Rent. O then it mov'd her.
We regard it with respectful attention, Which thould express her goodlieft; you have seen
our whole behaviour, left by any imSunshine and rain at once. Those happiettimiles propriety we should disturb that conThat play'd on her ripe lip feem'd not to know certed tranquillity, which it requires lo What gucits were in her eyes, which parted thence,
great an effort to support.”-Cordelin, As pearls from diamonds dropt-in brief Sorrow would be a rarity most belov'd,
full of affection, feels for the distress 11 ail could to become it.
of her father: her fense of propriety Kent, Made the no verbal question? impoles restraint on her exprellions of Gint. Once or twice
sorrow: the conflict is painful: full of She heav'd the name of father, Pantingly forth, as if it prett her heart. fensibility, and of a delicate structure ; Ery'd, Sisters! Sisters ! what? i'th' itorm of the conflict is more than she can endure; night?
she muít indulge her emotions; her Let pity De er believe it! then the shook
sense of propriety again interposes; the The holy water from her heav'nly eyes, And then retir’d to deal with griet alone.
must rent them in secret, and not with Minds highly enlightened, contem
loud lamentation. plating the same object, both reason
She thakes and are affected in a similar manner.
The holy water from her heavenly eyes,
And then retires to deal with griet alone. The tone of thought in the following passage in “ the theory of moral fenti
There are few instances in any poet ments," accords perfectly with Siak- where the influences of contending emo1pear's account of Cordelia. “ What tions are so nicely balanced and distinnoble propriety and grace do we feel guilhed: for while in this amiable picture, in the conduct of those who, in their we difcern the corrected severity of own cafe, exert that recollection and that behaviour which a sense of profelf-command which constitute the dig- priety dietates, mitigated and brought nity of every paffion, and which bring down by fine sensibility, and the softit down to what others can enter into? ness of female character, we also sce We are disgusted with that clamorous this softness upheld, and this fenfibigrief, which, without any delicacy, lity rendered itill mere engaging, by calls upon our compallion with fighs the influences of a sense of
propriety, and tears, and importunate lamenta We may, therefore, deduce from the tions.. But we reverence that reserved, whole, that the conduct is most perthat filent, and majentic forrow, which fect, and the demeanour most cngaging discovers itself only in the swelling of where “ fenfibility is guided by a fenfe the eyes, in the quireriag of the lips of duty and propriety; and the sense and cheeks, and in the diftant, but af- of propriety animated or softened by fecting, coldness of the whole behaviour. fine fenfibility.” It imposes the like fience upon us.
ACCOUNT OF THE EARTHQUAKES IN CALABRIA, AND VARIOUS
PARTS OF SICILY. COMMUNICATED TO THE ROYAL SOCIETY BY SIR WILLIAM HAMILTON
(Continued from page 228.) FROM Terra Nuova I went to Op- their course, and formed great lakes,
pido. This city is situated on a as we are told; it was (as at 'Terra mountain of a ferrugineous fort of Nuova) huge pieces of the plain on the gritty stone, unlike the clay foil of its edge of the ravine, that had been deneighbourhood, and is surrounded by tached into it, rearly filled it up, and two rivers in a ravine decper and ftupped the course of the rivers, the broader than that of Terra Nuova. waters of which are now forming two Instead of the mountain on which Op- great lakes. It is true, that part of the pido was situated having split in two, rock on which Oppido stood was deand by its fall on the rivers Atopped tached with several houses into the
ravine; but that is a trifling circum- finitely greater. The enormous inasses ftance, in comparison of the very great of the plain, detached from each fide tracts of land, with large plantations of of the ravine, lie sometimes in confused vines and olive-trees, which have been heaps, forming real mountains, and detached from one side of the ravine having stopped the course of two rivers clear over to the other, though the (one of which is very considerable) distance is more than half a mile. It great lakes are already formed, and, if is well attested, that a countryman, not affisted by nature or art, so as to who was ploughing his field in this give the rivers their due course, must neighbourhood with a pair of oxen, infallibly be the cause of a general inwas transported, with his field and fection in the neighbourhood. Someteam, clear from one fide of a ravine to times I met with a detached piece of the other, and that neither he nor his the surface of the plain (of many acres oxen were hurt. After what I have in extent) with the large oaks and seen, I verily believe this may have olive-trees, with lupines or corn under happened. A large volume might be them, growing as well, and in as good composed of the curious facts and ac order at the bottom of the ravine, as cidents of this kind, produced by the their companions, from whom they earthquakes in the valley; and I suppose were separated, do on their native soil many will be recorded in the account of in the plain, at least 500 feet higher, the late formidable earthquakes, which and at the distance of about three quarthe academy of Naples intend to publith, ters of a mile. I met with whole vinethe president having already sent into Ca- yards in the fame order in the bottom, labriafitteen members, with draftsmen in that had likewise taken the same jours proportion, to collect the facts, and make ney. As the banks of the ravine, from drawings, for the fole purpose of giving whence these pieces came, are now a satisfactory and ample account of the bare and perpendicular, I perceived late calamity to the publick; but unless that the upper foil was a reddish earth, they attend, as I did, to the nature of and the under one a sandy white clay, the soil of the local where those accidents very compact, and like a fost stone; happened, their reports will generally the impulse these huge masses received, meet with little credit, except froin either from the violent motion of the those who are profeffed dilettanti of earth alone, or that asiated with the miracles, and many such do certainly additional one of the volcanick exhalaexist in this country. I met with a tions fer at liberty, seems to have acted remarkable initance here of the degree with greater force on the lower and of immediate distress to which the un more compact stratum, than on the fortunate inhabitants of the destroyed upper cultivated crust: for 1 constantly towns were reduced. Don Marcillo obierved, where these cultivated illands Grillo, a gentleman of fortune, and of lay (for fo they appeared to be on the great
landed property, having escaped barren bottom of the ravine) the under from his houie at Oppido, which was 1ł ratum of compact clay had been driven destroyed by the earthquake, and his fome hundred yards' farther, and laty money (no less than twelve thousand in confused blocks, and, as I observed, pieces of gold) having been buried un many of these blocks were of a cubical der the ruins of it, remained several form. The under foil having had a days without food or fhelter during greater impulse, and leaving the upper heavy rains, and was obliged to a in its flight, naturally accounts for the hermit in the neighbourhood for the order in which the trees, vineyards, loan of a clean thirt
. Having walked and vegetation, fell and remain at preover the ruins of Oppido, I defcended sent in the bottom of the ravine. This into the ravine, and examined carefully curious fact, I thought, deserved to be the whole of it. Here I faw, indeed, recorded, but it is not ealily described the wonderful force of the earthquake, by words. When the drawings and which has produced exactly the fame plans of the academy are published, this eftctts as I have described in the ravine account (imperfect as it is) inay, perof Terra Nuova; but on a scale in- baps, hare iis utility; had my time