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line given, whose angles, at the base, ther seen, that every figure may, either shall be quintuple to that at the vertex; directly or circuitously, be commuted which may easily be done by the in- into a triangle, of corresponding area : tersection of a quadratrix, or any other but it may be necessary, at the same curve of the second kind.
time, to observe, that the squaring of SURVEYING. This important art, the circle has not hitherto been perhowever difficult its attainment may ap- fected; though we have arrived so nearpear, is nevertheless to be comprised ly to the completion of that object, as to within a very few general rules. The ac- leave no room for regret at the want of curacy of the work must depend entirely absolute precision. on the correctness of the instruments em- These points being completely under. ployed, the steadiness of the hand and stood, the learner may proceed to the rueye of the operator, and the faithfully diments of surveying ; supposing him to tracing the given lines and angles on the be grounded in the few preliminary propaper designed to exhibit the estate, or blems which enable bim to describe the premises under examination. The fol- ordinary figures : should he not have oblowing leading principles will give an in- tained any previous information on that sight into the mode of displaying the re- subject, we recommend that he turn back sults, whatever may be the means em. to the heads of GEOMETRY and MATHEployed for their computation. First. We MATICAL instruments : under which he are to reject the actual curvature of our will find various items indispensable toglobe, in all land surveys; that is, where wards his progress. no current of water, or the level of any We shall submit a few propositions, fluid is under consideration : sucb curva- which the student may work with his ture amounts to about eight inches in compasses, plain scale, and protractor : every mile, either of latitude or of longi. when able to do all that may be needful tude. In brief, we consider the earth to on paper, he may then try his hand with be flat, instead of spherical. Secondly. one or other of the various instruments in We must ever carry in mind, that every use among surveyors. triangle is equal to half a parallelogram Proposition 1. “To ascertain the conof equal base and altitude; as shewn un- tents of the square field ABCD, fig. 1. der the head of GEOMETRY. Thirdly. Plate XV. Miscel.” Here little is to be That wherever there is a deviation from done; one of these sides being measured, the borizontal, there will be a greater ex. say 70 yards, and multiplied by itself, tent of surface displayed on a site than will give 4,900 square yards for the area; if the same were horizontal. To illustrate or one acre (i. e. 4,800 square yards) and this, let an orange be cut through in the 100 square yards. middle, and the flat part, i. e. the section, Proposition II. “To survey the field be placed on a level table : it is evident ABCD, fig. 2.” This figare having the that the round surface of the half orange sides AB and CD parallel, and at right will offer more surface than the flat section angles to AD, add the lengths of those which lays upon the table: but, if it were parallels, say 70 and 90 yards, together ; required to build on the semi-spherical divide half their sum (i. e. 80) and multisurface, it would be found that no more ply that half by the depth of AD, say 70; houses, &c. could be raised thereon, than which being multiplied by the medium would stand on the extent of the flat sec- length, GF, gives an area of 5,800 square tion. The reason of which is, that no yards. The parallelogram, ABED, might more perpendiculars can be raised on have been computed by simply multiplyone than on the other. This shows how ing its length by its breadth ; and the fallacious is the mode of purchasing what triangle, BCE, might be taken separateis called side-long, or hanging, land by ly, thus: the depth, (or altitude) BE, 70 the acre. The greater the deviation from yards, to be multiplied by half CE, (i.e. the horizontal, the more is the base di. 10 yards) this would give 700 ; and the minished. Fourthly. The surveyor must produce of AB, which is 70, by BE, which recollect, that all planes, of whatever ex. is also 70, would be 4,900: making in all tent or form, may be divided into, and be 5,600, as above shown. represented by, triangles of various forms Proposition III. “ To survey the inand dimensions, whose aggregate will clined parallelogram ABCD, fig. 3.” It amount to the measurement of the area is to be observed that, in all inclined fi. thus partitioned off: for, as Euclid justly gures, the altitude is ascertained by a per. observes, “ All the parts, taken together, pendicular from the base, as at C, to the are equal to the whole." It will be fur: parallel of that base, as at E, on the line VOL. XI.
AB. Now the triangle BEC being equal amount to the whole area of the pentato the triangle DFA, and likewise simi. gon. lar thereto, it is evident that, by transpos.
Proposition VII. “ To ascertain the ing the former from the right to the left area of the irregular six-sided figure, or of the figure, it would make it rectangu. hexagon, (fig. 7) ABCDEF.” In this lar, as shown by the dotted line: there.
some of the angles point inward. First fore multiply the base DC, say 100 yards, draw the line CE, which will divide the by the altitude CE, say 80 yards, and the figure into two trapezia, viz. CEBA and area will be found to contain 8,000 square CEFD, next divide each of these trape. yards.
zia by the diagonals, BE and CD, into Proposition IV. “To survey the irre. two triangles respectively: the areas of gulars, fig. 4.” Here AC and BD are the four triangles, BAE, BCE, FCD, and parallel, but neither CD nor AB are per. CED, will, when added together, exhibit pendicular thereto, nor parallel between the contents of the whole figure. themselves. We must, therefore, cut off Proposition VIII. “ To measure the the triangles AEB and CFD ; whose area irregular field ABCDE, fig. 8.” The will be found by multiplying half their figure here given has two curved sides, respective breadths by their whole
one of which projects, the other of whicla depths : or their whole breadths by half inflects: the ordinary parts which can be their depths: the centre part, ECBF, is divided into triangles are worked in the treated as a parallelogram, already de. manner already shown; but the curved scribed. The whole of the calculations parts must be measured in the following being added together give the area of the mode: Draw the line ED, and from it entire figure ACBD.
make three or more off-sets to the curvProposition V. “ To ascertain the area ed part; take from E to 1, as a base, of the trapezium, ABCD.” This figure and half the depth of the off-set 1, as an is no where parallel, and has all its sides altitude; multiply them together: then of unequal lengths. The easiest mode of take from 1 to 2, as a base, and the mean surveying it is, by drawing a diagonal be- of the depths of the off-sets 2 and 3, for tween the two most distant points, C and the altitude; multiply these also together: B; and making off-sets, rectangular to do the same for the space between 2 and that diagonal, from E to A, and from F to 3, and calculate the end, between 3 and D. These off-sets give the altitudes; EA D, as was done from E to 1 ; the sum of being the altitude of the triangle CAB, their several products, added together, say 40 yards; and FD being the altitude will show the area of the curve. As of the triangle BDC, which we will take the other curve bends inward, draw the at 80 yards Now the diagonal, CB, be. line AE, and treat it the same as was comes a base common to both triangles; done regarding ED: then considering therefore add the two altitudes together; the entire triangle, AED, as a part of the namely, 40 to 80, which makes 120 ; take field, compute its contents, and deduct their half = 60, and multiply by the base from it the measures taken, by means of which we will call 140 : the area will con- the off-sets 4, 5, 6: the residue added tain 8,400 square yards. It will be seen to the contents of the curve from E to D, that this proportion is, in a great mea- and the triangles, ABC and ACD, will sure, the foundation of all horizontal com- show the area of the whole figure putation ; and the student should remark, ABCDE. It is obvious that, in this man. that all figures, having many sides, may ner, the extent of water may be deducted be divided into trapezia, and those again from the area of any field. into triangles : each figure will have two The next figure, No. 10, shows the sides more than the numbers of triangles method of surveying with a plain-table, it contains: thus, fig. 5 has four sides, which usually stands upon three legs, and and contains two triangles; fig. 6. has has a compass attached to
one side. five sides, and contains three triangles. There is a box-wood frame that fits on
Proposition VI. “To survey the pen. the board of the plain-table, and is gradu. tagon, or five-sided field, ABCDE, fig. ated with 360 degrees. This serves to 6.” Divide it into the three triangles, show the direction of any line from the ABC, DAC, EAD, and having found centre of the board, where there is a their respective altitudes, as already brass stud, or plate, let in; and it also shown, by perpendiculars drawn to their compresses the paper so as to prevent its summits from their respective bases, shifting. To this instrument there is a multiply half those altitudes by those brass rule of two feet long, with ends bases, and the three products will turned up at right angles, in which are slits, or sights, to direct the surveyor's the points A and B being established at a eye. He places the rule so as to touch the certain distance, and the two angles they brass centre, and directing it to any par. mutually form with C being ascertained ticular point, observes the angle it makes, by the graduated edge of the instrument, according to the index on the box-wood it follows that the intersection of the two frame; while an assistant measures the sights, from B to C, and from A to C, distance, from the centre under the will determine the exact locality of C: plain-table to the point observed. The let the line BC be measured on the same surveyor draws a line on the paper, in scale from which AB was taken, and it the direction of the brass rule, from the will show the distance of C from B. In exact centre of the plain-table, and notes this manner the whole horizon may be down, at the side of that line, what its surveyed from the base line AB; except length may be in chains, links, &c. ac. such parts as may lay in, that is, occupy cording to Gunter's scale ; or else in the same direction therewith. And it is yards and feet, as in familiar measure. to be observed, that in laying a base line, ment. Thus, in fig. 10. A represents the the nearer the angle of intersection, as plain-table, placed in the centre of the at C, is to a right angle, the more exactly field BCDE: f g is the rule with sights: will the distance be denoted. Hence a the figures written on the sides of the great extent of base line is to be prefer. lines proceeding to the four corners ex- red, when at command; and if practicapress their several distances from the cen. ble, no angle under twenty degrees tre of the plain-table. This mode of sur- should be made : it is always better to veying is peculiarly suited to small sur. take a new station than to make acute veys, especially to the interiors of en- angles with the object to be surveyed; closed places ; and has the advantage of which may, for the most part, be easily forming the plan on the paper, as the avoided in horizontal sights; but in vertisurvey proceeds; for the number of yards, cal observations, very acute angles will &c. being set off, from the scale on the ordinarily occur. brass rule, on the several directing lines, Thus, in Proposition X. " which relates as from the centre A to B, C, D, and E, to ascertaining the heights of P and 0, respectively : and their lengths being de. (fig. 12.) from the level of C, and the termined by their several due measures, distance of C from B, cannot be effected the lines BC, CD, DE, EB, will give a but by acute angles." Here, in lieu of true fac simile of the shape of the field. laying the base line, AB, as nearly as The contents must be ascertained by die possible square with the point c, we viding the field, as before explained, into place it in the exact direction therewith. triangles, whose conjoint ineasurements Then, after taking the angles of elevation will amount to its contents.
from the horizon at the station B, to the Although the plain-table is not a suffi. two points O and P, and measuring the cient instrument for general purposes, it exact length of the base line AB, the is in the foregoing instance extremely instrument is removed from B to A; convenient: its use may be extended, where two more sights are taken to O under due precaution, to ascertaining the and P. We have thus the two angles, PBA distances of remote, or of inaccessible ob. and PAB, determining the locality of P; jects, situated on the same level with it and the two angles, OBA and OAB, deself. But for such purposes a theodolite, termining the locality of 0. Now the standard-triangle, circumferentor, or some line BA being prolonged, and the perinstrument capable of taking heights as pendicular, PO, being likewise continu. well as levels, is ordinarily employed.ed, will intersect in č. The lines, PB, The following proposition will illustrate OB, and CB, being measured on the the above point.
same scale whence the base line AB was Proposition XI. s To ascertain the dis- taken, the altitudes of P and of 0, with tance of an object at C, from the point B, their intermediate distance, will be given; fig. 11.”
Draw the base line, BA, in while the distance of C from B will be any convenient direction, and from each exhibited. station (commonly marked by surveyors
We shall conclude this article with a O) observe what angle is made ; viz. at few words on the manner of carrying a B, ascertain the value (or extent) of the line of sight over a hill, as is often done angle CBA, and at A, the value of the for the formation of a road, or for the angle CAB: take care to be very correct conducting a canal over a rising ground: as to the measurement of your base line ; in which case the level must be preserv. which we will take at 120 yards. Now, ed.
Proposition XT “To carry a line of jaw curving inwards, and capable, from sight or a level, in the direction of AB, their size, strength, and sharpness, of in. over the rising ground C.” Ascertain Aicting the most dreadful wounds. Before where the line of sight strikes the hill at these animals attain their third year they e; carry the instrument to that point, are gregarious, and, when danger is at and, in the extract direction of the former hand, particularly, they muster in nume. sight, take a second sight from e a, or
rous parties, and with great promptitude, to any convenient spot, where a pole and at the signal of alarm. Uniting thus, they target should be fixed. See LEVELS. As present so formidable an array, as speedithis survey for a canal is to be taken by ly to disperse the enemy, few creatures, means of a spirit level, the exact altitude or none, daring to commence an attack of each sight must be taken, by noting against such a combination of strength the height of the target from the plain, and valour as they exhibit. When the AB, at every sight, or by following up wild boar is complete in growth, he de. a regular succession of levels, each of pends upon his solitary exertions for his which will be the height of the instru. protection, is seldom seen in society, ment above the last. Thus the hill will
ranging the forests alone; rarely combe ascended: the descent on the other mencing an attack, as his food consists alside is effected by the inversion of the most solely of roots and vegetables, but foregoing mode ; always taking the de- repelling one with all the fierceness of scending levels of the target for canals ; courage, and all the resentment of retabut for roads, or for laying down a meri- liation. dional line, when once the summit is gain. These animals are often hunted by dogs, ed, a long sight may be taken to a distant particularly of the mastiff breed. After object: this subject is pleasingly exempli- many pauses in their progress, in which fied in a new work published by Longman they turn round, and defy their enemies and Co.entitled “Mathematics simplified, to the attack, which, however, is gene. and practically illustrated,” in which a rally declined, they at length refuse to great variety of instructive and useful mat. proceed, and halt for the grand and final ter will be found, together with a descrip- conflict; in which, though eventually tion of a new instrument on a very simple overpowered by the number of dogs, construction, said to be equal to every and the spears of the hunters, they debranch of surveying.
fend themselves with the most astonishSUS, the hog, in natural history, a ge- ing intrepidity, perseverance, and energy; nus of Mammalia, of the order of Belluæ. and, regarding their case as absolutely Generic character: four front teeth in desperate, determine, at least, not to die the upper jaw, converging; six in the unrevenged. See Mammalia, Plate XXI. lower, projecting: two tusks in the up.
fig. 1. per jaw, short; two in the lower, stand. The common hog has smaller tusks and ing out; snout truncate, prominent, and larger ears than the wild boar, and is gemoveable : feet cloven. These animals nerally of a dull, or dirty, yellowish are allied by their teeth to the carnivo. white. It is clumsy in its shape, filthy in rous quadrupeds, and by their cloven feet its manners, and gross and ravenous in to the ruminating ones. They feed almost its food, devouring almost every variety indifferently upon animal and vegetable of rejected animal or vegetable substance, substances, devouring with avidity what and distinguished by the quantity nearly is most nauseous and disgusting. They as much as by the rankness of its food. use their snout for digging up the ground The offal of the kitchen, garden, and in quest of roots, are fond of rolling and barn, furnishes it with an excellent ban. wallowing in mud, and are distinguished quet. It was rejected as unclean both by extreme fecundity. There are six spe. by the founders of the Jewish and Macies, of which the following are the most hometan religion, as unfit for human sus. important:
tenance, for which it is, nevertheless, S. scrofa, the common hog. All the most admirably adapted, and of incalculavarieties of this animal originate in the ble value. The sailors of the British navy wild boar, which is found in most of the are in a great degree supported by the temperate regions of Europe and Asia. It flesh of that animal, which Moses and is smaller than the domesticated animal, Mahomet decided to be unfit for the food and uniformly of a dark grey colour, ap- of man; and in most countries of Europe, proaching to black. It is armed with for. it is an important and indispensable artimidable tusks, sometimes ten inches, or cle of the food of the inhabitants. The even more, in length ; throse in the under hog is possessed of an acute smell, and is
highly agitated during the violent blow. in mechanics, are those points in the axis ing of certain winds, uttering the most or beam of a balance, wherein the weights dreadful screams, and exhibiting the are applied, or from which they are sushighest restlessness, apprehension, and pended. turbulence. It is fattened to an extraor. SUSPENSION of arms, in war, a short dinary size, and has been known to attain truce agreed on by both armies, in order the almost incredible weight of 1215 to bury the dead, wait for fresh instrucpounds. It produces two litters in the tions, or the like. year, and in each from ten to twenty SUSPENSION, in rhetoric, is the carrying young ones. The male must be kept at on a period or discourse, in such a mana distance from these, as it will other- ner as to keep the reader in expectation wise destroy and devour them, and the of something considerable in the conclufemale herself has often acted this unna- sion. But great care must be taken that tural part, and is particularly apt to do it, the reader's expectation be not disapif observed attentively, during the crisis pointed; for nothing is more contemptiof parturition. The bog was unknown ble than to promise much and perform in America when that quarter of the little; or to usher in an errant trifle with world was discovered by the Spaniards, the formality of preface and solemn but now abounds in every part of it. The preparation. Chinese breed is most valued in England. SWABBER, an inferior officer on There is an accidental variety of the do- board ships of war, whose employment it mestic hog with undivided hoofs.
is to see that the decks are kept neat S. Ethiopicus, or the Ethiopian hog, is and clean. very similar to the last. It is fierce and SWARTZIA, in botany, so named in formidable in the highest degree, and honour of Olof Swartz, M. D. a genus of burrows in the ground, in deep
recesses, the Polyadelphia Polyandria class and orwhich it prepares with both its hoofs and der. Essential character: calyx four-leav.
It is particularly distinguished ed; petals single, lateral, flat; legume by a large lobe, or wattle, beneath each one-celled, bivalve; seeds arillated. There eye.
are six species. S. baby-roussa is remarkable for the SWEDENBORGIANS, a religious soform and situation of the upper tusks, ciety, who have been so called from which are placed externally, and turn Emanuel Swedenborg, in whose theologiupwards in a curve towards the forehead. cal works are taught the doctrines which It abounds in the Indian islands, lives they receive. He was born at Stockholm solely on vegetables, and rests itself, in in Sweden, Jan. 29, A. D. 1689; and died sleep, by hooking its upper tusks round in London, the 29th March, A. D. 1772. the branch of a tree. It can swim with His father was Jesper Swedberg, bishop rapidity, and is valued for food.
of West Gothia, and president of the S. sajassu, or the Mexican hog, or pe- Swedish church in Pennsylvania and cari, is the only animal of the genus na- London. In the year 1716, at the age of tive of America, where it is gregarious, 28, he was associated by Charles XII. fierce, and dangerous, and is occasionally with the celebrated Polhamman,called the seen in herds of several hundreds. It Swedish Archimedes, to assist him in the feeds on fruits and roots, and also on direction of buildings and mechanical serpents, lizards, and toads; and will at- works, and without solicitation appointed tack and devour the rattlesnake, we are extraordinary assessor to the Royal Coltold, without the slightest injury: It is lege of the Mines, the King having given less than the common hog, has bristles him the choice either of this office, or nearly resembling the prickles of an that of professor in the Royal Academy hedge-bog, and is also distinguished by of Upsal. “ An universal knowledge in an orifice on its back, from which per- the belles-lettres, (says Monsieur Sandel, petually issues a most fetid watery hu- in his eulogium delivered in the name of
The pecari will skin snakes by the ACADEMY OF SCIENCES at STOCKHOLM) means of its teeth and feet, before it and a remarkable degree of learning, had devours them, with great dexterity. The at that time made his name known both common hog is reported, on ood within and without the kingdom.” “You thority, to attack and eat the rattlesnake may find in him at once (says the same with the same impunity as the pecari. gentleman) a happy assemblage of an For the baby-roussa, see Mammalia, Plate excellent memory, a prompt conception, XX. fig. 2.
and a most clear judgment, united to a SUSPENSION, or Points of Suspension, desire that was never cloyed, and the