ch. lin. ch. lin. ch. lin. ch. lin. ch. lin. ch. lin. ch. lin.ch. lin. ch. lin. acres. acres. acres. whole quantities of easting, will give the terminations of these lines, which, being pricked off, have only afterwards to be joined, and the plot will be completed. To compute the Area of the Plot.-Rule six additional columns. In the first of these, or ninth column of the traverse table, set the sums of the total northings, and in the tenth, the sums of the total eastings at the beginning and end of each line in the survey, which sums will be found by adding together each pair of succeeding numbers in the two preceding columns. In the eleventh column set the products of the eastings made on the respective lines of the survey, found in the fifth column, multiplied by the corresponding sums of the total northings in the ninth column; and in the twelfth column set the products of the westings found in the sixth column, and the corresponding sums of the total northings in the ninth column. Sum up the eleventh and twelfth columns, and the difference of the totals thus found will be twice the area of the plot. Again in the thirteenth and fourteenth columns set the products of the northings and southings in the third and fourth columns, multiplied by the corresponding sums of the total eastings in the tenth column, and the difference of the sums of the thirteenth and fourteenth columns will again be twice the area of the plot, and, if agreeing nearly with the double area before found, shows the calculations to have been correctly performed. (We give an example in the opposite page.) The near agreement of the sums of the third and fourth, and of the fifth and sixth columns is a test of the accuracy of the survey; in columns 7 and 8 we have the distances to be set off by the plotting scale; in column 9 we have the multipliers by which the east and west products in columns 11 and 12 are found; and in column 10 we have the multipliers for finding the north and south products in columns 13 and 14. The difference of the sums of the eleventh and twelfth columns gives double the area, the difference of the sums of the thirteenth and fourteenth gives again double the area, and, taking the mean of these results, by adding them together and dividing by 4, we obtain the area most probably to within a quarter of a perch, since the two double areas differ by less than a perch. THE STATION POINTER. When the principal features of a country have been laid down by the methods already pointed out, the details may be put in with great rapidity by means of the instrument which we are now about to describe. A A, B B, C C, are three arms moveable about a cominon center, o, and carrying three fine wires stretched quite tight, the prolongation of which would pass exactly through the center, o. The arms, B B, and cc, carry each a graduated arc, bb, and c c; and the arm A A carries two verniers, a, a', adapted to the graduated arcs, b b, and c c, respectively The angles L O M, and L O N, subtended, at one of the points which we wish to put in, by L, M, and N, three of the principal points of the survey already laid down, having been observed by means of the prismatic compass, or pocket sex tant, the arms of the station pointer are opened out till the verniers point out these angles upon the graduated limbs, bb, and c c, respectively. The station pointer being then placed upon the paper, and moved about till the fine wires pass exactly over the stations L, M, N, as marked already upon the plot, the center will be exactly over the point to be filled in, and its place is to be marked by passing a pricking point through a small opening, which is made at the center to serve this purpose. PART IV. ON ASTRONOMICAL INSTRUMENTS. THE space which we have occupied with the former parts of this work will compel us to be more brief than we had contemplated in the description of the Astronomical Instruments. We shall, therefore, confine our attention more particularly to Hadley's Sextant; Troughton's Reflecting Circle; The Transit Instrument; The Collimator; Altitude and Azimuth Instruments; with some brief remarks upon other instruments, used for astronomical purposes. HADLEY'S SEXTANT. This instrument differs from the pocket sextant, already described, in its appearance, from the absence of the box in which the pocket sextant is fixed, in its size, varying usually from 4 inches to 6 inches radius, and in its requiring and admitting of more perfect and minute adjustment. LL is the graduated limb of the instrument, graduated from 0° to 140° at every 10' or 20', according to the size of the instrument, and subdivided by the vernier, v, to 10′′ or 20", thus enabling us to read off angles by estimation, to 5". The limb is also graduated through a small space, called the arc of excess, on the other side of the zero point. T is the tangent screw for giving a slow motion to the index bar, after it has been clamped by screw at the back of the instrument, a not shown in the figure. M is a D microscope, attached to the index bar by an arm moveable round the center, N, so as to command a view of the vernier throughout its entire length. I is the index glass, or first reflector, attached to and moving with the index bar; and H is the horizon glass, having its lower half silvered to form the second reflector, and its upper half transparent. Four dark glasses are placed at c, any one or more of which can be turned down between the index glass and horizon glass to moderate the intensity of the light from any very bright object viewed by reflection; and at G are three dark glasses, any one or more of which can be turned up to moderate the intensity of the light from any bright object, viewed directly through the transparent part of the horizon glass. D is a ring for carrying the telescope, attached to a stem s, called the up and down piece, which can be raised or lowered by means of a milled-headed screw. The use of this up and down piece is to raise or lower the telescope, till the objects seen directly and by reflection appear of the same brightness. K is the handle by which the instrument is held. In selecting an instrument care must be taken that all the joints of the frame are close, without the least opening or looseness, and that all the screws act well, and remain steady, while the instrument is shaken by being carried from place to place. All the divisions on the limb and vernier, when viewed through the microscope, must appear exceedingly fine and distinct, and the inlaid plates, upon which the divisions are marked, must be perfectly level with the surface of the instrument. The index, or zero, of the vernier, should also be brought into exact coincidence successively with each division of the limb, till the last division upon the vernier reaches the last division upon the limb; and, if the last division of the vernier do not in each case also exactly coincide with a division upon the limb, the instrument is badly graduated, and must be rejected. All the glass used in the instrument should be of the best quality, and the glasses of the reflectors should each have their faces ground and polished perfectly parallel to each other, to avoid refraction. Look, therefore, into each reflector, separately, in a very oblique direction, and observe the image of some distant object; and if the image appears clear and distinct in every part of the reflector, the glass is of good quality; but if the image appears notched, or drawn with small lines, the glass is veiny, and must be rejected. Again, if the image appears singly, and well defined about the edges, the two surfaces of the glass are truly parallel; but if the edge of the image appears misty, or separated like two images, the two surfaces are inclined to one another. The examination will be more perfect, if the image be examined with a small telescope. A plain tube and two telescopes, one showing objects inverted, and the other erect, are usually supplied with the sextant. The manner of testing the telescopes has already been explained in the part of the work devoted to optical in |