PARTICULAR DISLocations. Lower jaw. This bone can only be luxated forwards, when the condyloid processes advance beyond the eminentiae articulares. In this case the mouth remains open, and cannot be shut; there is pain; impaired and almost destroyed articulation and deglutition, &c. One or both condyles may be displaced. To reduce it, the thumbs, well covered, should be introduced as far backward as possible along the grinding teeth. The surgeon then elevates the front of the bone with his fingers and the palms of his hands, while he depresses the condyles with his thumbs; and the latter prominences are thus forced back into the glenoid cavities of the temporal bones. Dislocations of the head and vertebrae are probably imaginary occurrences, as we know hitherto of no well attested example of their occurrence. The os humeri is probably luxated more frequently than any other bone. It may be displaced downwards, forwards, and backwards. In all these cases a vacancy is distinguishable under the acromion, in Consequence of the absence of the head of the humerous from the glenoid cavity of the scapula. The head of the bone forms a preternatural tumour in some situations. The elbow cannot be carried close to the chest, nor can the limb be elevated, without extreme pain, to a line with the acromion. Great pain is caused by the pressure of the head of the bone in its unnatural position, particularly when it lies in the axilla. Our object is, to dislodge the head of the os brachii from its unnatural situation, in order to bring it on a level with the glenoid cavity of the scapula. To accomplish this purpose, extension must be made; that is, the limb must be drawn forcibly outwards; and the bone itself should be made to operate as a lever, which can be best ef. fected by the surgeon’s knee placed under it towards the head, while he depresses the elbow at the propertime, so as to raise the head towards the glenoid cavity. The patient’s body should be fixed, by placing a broad towel round the chest, and tying it to some immoveable point. The extension should be gradual, and kept up unremittingly, which can be best effected by means of pullies. The elbow should be bent, and the extending power applied just above the condyles of the humerus. When the surgeon finds that the head of the bone is drawn out of its unnatural position, he may allow the extention to be remitted, and depress the elbow. The arm should afterwards be kept quietly in a sling, a piece of soap plaster, and a spica bandage, being applied to the shoulder. Elbow, Dislocations at this joint are very difficult to discover, from the swelling which comes on so ‘. The radius may be displaced forwards; and here the flexion of the elbow is almost entirely destroyed. The ulna may at the same time be driven backwards: it may also be pushed inwards, so as to occupy the place of the radius. All these are easily reduced, when they are ascertained. Leeches and cold washes should be employed afterwards. Wrist. The distortion consequent on a displacement of the carpus is so considerable, that the nature of the case is rendered immediately obvious. The reduction is easy ; and after it has been accomplished, the hand and fore-arm should be bound on a splint, and supported by a sling. Thigh. The os femoris may be displaced downwards and inwards, so that the head rests on the obturator foramen ; upwards and outwards, when the head is towards the sacro-ischiatic foramen, and the trochanter forwards, and upwards and forwards, so that the head rests upon the os pubis. In the first case, the toes are turned out, and the limb elongated. In the second, the limb is shortened, the foot turned inwards, and the buttock more prominent. Great pain is excited by attempting to move the limb in all cases of luxation, and a vacuity is discernible in the natural situation of the head of the bone. The patient should be placed on the side opposite to the accident, and his pelvis should be fixed by means of a sheet passed under the perineum. Extension may be made by fixing a broad towel, or the pullies, just above the condyles. When the head of the bone is on the dorsum ilii, the extension is to be continued until it has been brought to the acetabulum, into which the surgeon must guide it. In the dislocation of the obturator foramen, we should make a lever of the bone, by passing a towel under the thigh, near the trochanter, and elevating it, after a slight extension has been made, the condyles being at the same time depressed. The patella may be dislocated either inwards or outwards. Its reduction is very easy, when the muscles inserted into it have been relaxed. The knee hardly admits of complete luxation, without such injury of the parts as would render the loss of the limb necessary. The nature of the accident must be obvious from the altered figure of the parts, and replacement is perfectly easy. Inflammation must be guarded against afterwards. The ankle may be dislocated outwards, the fibulae being at the same time broken. This is generally a compound luxation ; the extremity of the tibia, when displaced from the astragulus, very often penetrating the integuments. Formerly this accident was considered as a cause of amputation; and many practitioners have been in the habit of sawing off the projecting portion. Yet, by replacing the bone, closing the wound, keeping the parts quiet, &c. the injury has been often recovered. Luxation may also occur in the opposite direction, and forwards. The latter is very difficult to retain in place, as the muscles of the calf are so apt to move the foot. SURIANA, in botany, so named in honour of Joseph Donat Surian, a genus of the Decandria Pentagynia class and order. Natural order of Succulentae. Rosaceae, Jussieu. Essential character: calyx fiveleaved; petals five ; styles inserted into the inner side of the germs: seeds five, naked. There is but one species, viz. S. maritima, a native of the sea coast of South America, and the islands of the West Indies. SURRENDER, in law, a deed or instrument, testifying that the particular tenant of lands or tenements for life, or years, doth sufficiently consent and agree, that he which has the next or immediate remainder, or reversion thereof, shall also have the present estate of the same in possession; and that he yields and gives up the same unto him; for every surrenderer ought forthwith to give possession of the things surrendered. Where a surrender is made in consequence of a fresh lease, and that lease turns out invalid, the surrender is considered as not valid, and the former lease is established. Surrender into the hands of the lord is the mode of passing copyholds, and a surrender to the use of a will is o, in order to pass them by a will. SURROGATE, one who is substituted or appointed in the room of another; as the bishop or chancellor's surrogate. SURSOLID, in arithmetic and algebra, the fifth power, or fourth multiplication of any number or quantity, considered as a root. See Root. SURsolin problem, in mathematics, is that which cannot be resolved but by curves of a higher nature than a conic section, v. gr. in order to describe a regular endecagon, or figure of eleven sides in a circle, it is required to describe an isosceles triangle on a right line given, whose angles, at the base, shall be quintuple to that at the vertex; which may easily be done by the intersection of a quadratrix, or any other curve of the second kind. SURVEYING. This important art, however difficult its attainment may appear, is nevertheless to be comprised within a very few general rules. The accuracy of the work must depend entirely on the correctness of the instruments employed, the steadiness of the hand and eye of the operator, and the faithfully tracing the given lines and angles on the paper designed to exhibit the estate, or premises under examination. The following leading principles will give an insight into the mode of displaying the results, whatever may be the means employed for their computation. First. We are to reject the actual curvature of our globe, in all land surveys; that is, where no current of water, or the level of any fluid is under consideration: such curvature amounts to about eight inches in every mile, either of latitude or of longitude. In brief, we consider the earth to be flat, instead of spherical. Secondly. We must ever carry in mind, that every triangle is equal to half a parallelogram of equal base and altitude; as shewn under the head of GeoMETRY. Thirdly. That wherever there is a deviation from the horizontal, there will be a greater extent of surface displayed on a site than if the same were horizontal. To illustrate this, let an orange be cut through in the middle, and the flat part, i. e. the section, be placed on a level table: it is evident that the round surface of the half orange will offer more surface than the flat section which lays upon the table: but, if it were required to build on the semi-spherical surface, it would be found that no more houses, &c. could be raised thereon, than would stand on the extent of the flat section. The reason of which is, that no more perpendiculars can be raised on one than on the other. This shows how fallacious is the mode of purchasing what is called side-long, or hanging, land by the acre. The greater the deviation from the horizontal, the more is the base diminished. . Fourthly. The surveyor must recollect, that all planes, of whatever extent or form, may be divided into, and be represented by, triangles of various forms and dimensions, whose aggregate will amount to the measurement of the area thus partitioned off: for, as Euclid justly observes, “All the parts, taken together, are equal to the whole.” It will be furVOL, XII. ther seen, that every figure may, either directly or circuitously, be commuted into a triangle, of corresponding area: but it may be necessary, at the same time, to observe, that the squaring of the circle has not hitherto been perfected; though we have arrived so nearly to the completion of that object, as to leave no room for regret at the want of absolute precision. These points being completely understood, the learner may proceed to the rudiments of surveying; supposing him to be grounded in the few preliminary problems which enable him to describe the ordinary figures: should he not have obtained any previous information on that subject, we recommend that he turn back to the heads of GeoMETRY and MATHEMATICAL instruments : under which he will find various items indispensable towards his progress. We shall submit a few propositions, which the student may work with his compasses, plain scale, and protractor: when able to do all that may be needful on paper, he may then try his hand with one or other of the various instruments in use among surveyors. Proposition I. “To ascertain the contents of the square field ABCD, fig. 1. Plate XV. Miscel.” Here little is to be done; one of these sides being measured, say 70 yards, and multiplied by itself, will give 4,900 square yards for the area; or one acre (i.e. 4,800 square yards) and 100 square yards. Proposition II. “To survey the field ABCD, fig. 2.” This figure having the sides AB and CD parallel, and at right angles to AD, add the lengths of those parallels, say 70 and 90 yards, together; divide half their sum (i.e. 80) and multiply that half by the depth of AD, say 70; which being multiplied by the medium length, GF, gives an area of 5,600 square ards. The parallelogram, ABED, might }. been computed by simply multiplying its length by its breadth ; and the triangle, BCE, might be taken separately, thus: the depth, (or altitude) BE, 70 yards, to be multiplied by half CE, (i.e. 10 yards) this would give 700; and the produce of AB, which is 70, by BE, which is also 70, would be 4,900: making in all 5,600, as above shown. Proposition III. “To survey the inclined parallelogram ABCD, fig. 3.” It is to be observed that, in all inclined figures, the altitude is ascertained by a perpendicular from the base, as at C. to the parallel of that base, as at E, on the line B AB. Now the triangle BEC being equal to the triangle DFA, and likewise similar thereto, it is evident that, by transposing the former from the right to the left of the figure, it would make it rectangular, as shown by the dotted line: therefore multiply the base DC, say 100 yards, by the altitude CE, say 80 yards, and the area will be found to contain 8,000 square yards. Proposition IV. “To survey the irregulars, fig. 4.” Here AC and BD are parallel, but neither CD nor AB are perpendicular thereto, nor parallel between themselves. We must, therefore, cut off the triangles AEB and CFD; whose area will be found by multiplying half their respective breadths by their whole depths: or their whole breadths by half their depths: the centre part, ECBF, is treated as a parallelogram, already described. The whole of the calculations being added together give the area of the entire figure ACBD. Proposition W. “To ascertain the area of the trapezium, ABCD.” This figure is no where parallel, and has all its sides of unequal lengths. The easiest mode of surveying it is, by drawing a diagonal between the two most distant points, C and B; and making off-sets, rectangular to that diagonal, from E to A, and from F to D. These off-sets give the altitudes; EA being the altitude of the triangle CAB, say 40 yards; and FD being the altitude of the triangle BDC, which we will take at 80 yards Now the diagonal, CB, becomes a base common to both triangles; therefore add the two altitudes together; namely, 40 to 80, which makes 120; take their half = 60, and multiply by the base which we will call 140 : the area will contain 8,400 square yards. It will be seen that this proportion is, in a great measure, the foundation of all horizontal computation; and the student should remark, that all figures, having many sides, may be divided into trapezia, and those again into triangles: each figure will have two sides more than the numbers of triangles it contains: thus, fig. 5 has four sides, and contains two triangles; fig. 6. has five sides, and contains three triangles. Proposition VI. “To survey the pentagon, or five-sided field, ABCDE, fig. 6.” Divide it into the three triangles, ABC, DAC, EAD, and having found their respective altitudes, as already shown, by perpendiculars drawn to their summits from their respective bases, multiply half those altitudes by those bases, and the three products will amount to the whole area of the pentaon. § Proposition VII. “To ascertain the area of the irregular six-sided figure, or hexagon, (fig. 7) ABCDEF.” In this some of the angles point inward. First draw the line CE, which will divide the figure into two trapezia, viz., CEBA and CEFD, next divide each of these trapezia by the diagonals, BE and CD, into two triangles respectively: the areas of the four triangles, BAE, BCE, FCD, and CED, will, when added together, exhibit the contents of the whole figure. Proposition VIII. “To measure the irregular field ABCDE, fig. 8.” The figure here given has two curved sides, one of which projects, the other of which inflects: the ordinary parts which, can be divided into triangles are worked in the manner already shown; but the curved parts must be measured in the following mode: Draw the line ED, and from it make three or more offsets to the curved part; take from E to 1, as a base, and half the depth of the off-set 1, as an altitude; multiply them together: then take from 1 to 2, as a base, and the mean of the depths of the off-sets 2 and 3, for the altitude; multiply these also together: do the same for the space between 2 and 3, and calculate the end, between 3 and D, as was done from E to 1 ; the sum of their several products, added together, will show the area of the curve. As the other curve bends inward, draw the line AE, and treat it the same as was done regarding ED : then considering the entire triangle, AED, as a part of the field, compute its contents, and deduct from it the measures taken, by means of the off-sets 4, 5, 6: the residue added to the contents of the curve from E to D, and the triangles, ABC and ACD, will show the area of the whole figure ABCDE. It is obvious that, in this manner, the extent of water may be deducted from the area of any field. The next figure, No. 10, shows the method of surveying with a plain-table, which usually stands upon three legs, and has a compass attached to one side. There is a box-wood frame that fits on the board of the plain-table, and is graduated with 360 degrees. This serves to show the direction of any line from the centre of the board, where there is a brass stud, or plate, let in; and it also compresses the paper so as to prevent its shifting. To this instrument there is a brass rule of two feet long, with ends turned up at right angles, in which are |