The products against the second, fourth, and fifth stations, would be set in the column of south areas, and that against the third station, on account of its being on the west side of the meridian, would be placed in the column of north areas, and would be subtracted from the footing of the south areas. When a survey is calculated from a meridian running through the map, it is always best to set the first departure in the lower place, as it saves one multiplication. On Distributing Estates. A farm is to be distributed among a number of heirs. A survey is made, and the difference between the columns of latitude, and between those of departure, are two rods for each. The survey is balanced, and calculated arithmetically, and is found to contain two hundred acres. The surveyor next draws his map, by which the divisions are to be made, according to the courses and distances. The plan does not close by nearly two rods and three-quarters. He next corrects the lines, and makes the map close as well as he can; and when the divisions are made, they may not agree with the first calculation by two or three acres, or more. Should the map be drawn as before directed, by the meridian distances and the latitudes as balanced, it would close, and would be in exact conformity to the calculation made arithmetically. If the divisions are made arithmetically, without the use of the scale and dividers, the calculations must be made according to the balancing, or the divisions will not agree with the first calculation. It will be acknowledged by every experienced surveyor, that it is a difficult matter to make the amount of a considerable number of divisions agree with the whole, when calculated by itself. It is the common practice in distributions, to make the divisions with scale and dividers; this method will answer very well provided the map is drawn on a large scale. The following is a useful rule in dividing lands, when any quantity is to be added to, or taken from, a division in the form of a triangle. Having the area, the contained angle, and one side of a tri RULE. To the sine of the given angle, or its supplement if obtuse, add the logarithm of the given side; subtract radius from this sum, and subtract the remainder from the logarithm of the double area, the last remainder will be the logarithm of the side required. In taking a survey, go around with the sun, not that you can work more correctly, or that it will have any effect in calculating, but when you put your courses and distances on your map they will follow around with the lines, from the left to the right. Wherever you begin, set your compass on the angle and cause a stake or a flag-staff to be erected at the next. When your line runs over a hill, cause a stake to be erected at each end of it, and take your station on the top of the hill, directly between them. If bushes obstruct the sight, make an offset, or set your compass a little distance from the line, from whence you may see the back flag, and cause the forward flag or stake to be set against the bound in a direction with the compass and the back flag. When the line is measured, measure the distance from the flag to the bound, and calculate your true course by Trigonometry. If your next line is of such a distance that you cannot see through the whole length of it, run as near the true line as you can, and if you do not exactly strike the bound, measure the distance from the termination of your random line, and calculate your course as before directed, or if you can discover a tree standing near the termination of your line, take the course and distance to that, thence to the bound, and calculate your true course and distance. By practice and experience, a method for taking courses will soon become familiar, in all cases. In measuring hills and inclined surfaces, the horizontal distances must be taken. A plummet should be suspended from the end of the chain, when it is levelled. Where hills are very steep, the surveyor should assist the chainmen, and when the best is done in levelling and plumbing the chain, judgment must frequently be called into exercise. Even when rises and descents are easy, there is danger of making too much measure. In such cases, chainmea often make allowances, but the surveyor would do better to keep them to close measure, and from the shape of the ground judge himself what allowances ought to be made. If he is ex APPENDIX. 101 than inexperienced chainmen. Particular care must be taken that the chain is carried on a straight line, and that it is well straightened. When a tally is ended, and the hinder chainman brings up the sticks, they must be counted. When on counting the sticks it is discovered that one is lost, the chainmen should not leave the chain and go back to find it, but, from the last mark, should measure back to the point where the tally began, to see whether one chain is lost from their measure. Many blunders in this way have been left undetected by not taking this care. A careful accurate chainman never lost a stick or miscounted a tally. Young surveyors should practice much for their own. instruction, and should make correct practice familiar, before they offer their services. It is as necessary that they should spend some time in acquiring a practical knowledge, as it is that they should spend any time in acquiring a knowledge of theory. A young surveyor should bear in mind that if he is detected in one error in the beginning of his practice, it will be more to his disadvantage than to be detected in two when he shall be well established. If an error is committed in a survey, it is not against the surveyor provided he detects and corrects it, but if he cannot detect and correct his own errors, that is sufficient evidence of his deficiency in point of knowledge and skill. 00 W. 40 00 to a white-oak tree, to a pine tree, 6. S. 85 When a survey is calculated by chains and links, the numbers are less than when it is calculated by rods and decimal parts. Every method by which the numbers are diminished is an improvement. In a hilly country, the two-pole chain is preferable and is more commonly used, because it can be levelled better. Hills are often found so steep that even the two-pole chain MISCELLANEOUS. When a survey is calculated by chains and links, and the contents stand in acres and decimal parts of an acre, it may be multiplied by the price of an acre, and the product will be the amount. EXAMPLE. A piece of land, 12 chains and 25 links in length, and 10 chains and 25 links in breadth, is sold for $20 25, per acre;-what is the price of it? Length 12.25 The writer of these pages knows not who invented the following rules for finding contained angles. For plainness, none of the kind exceeds them. N. 620 E. S. 720 E. S. 25 E. N. 640 E. N. 570 W. S. 25 E. When the first letters are alike, and the two last are unlike, add the degrees of both courses together, which gives the contained angle. and When the two first and the two last letters are alike, subtract one course from the other, the remainder will be the contained angle. When the two first letters are unlike, and the two last alike, add both courses together, and subtract their sum from 180, the remainder will be the contained angle. When the two first and the two last letters are unlike, subtract one course from the other, the remainder from 180, and the remainder will be the contained angle. Application of the above Rules. the angle. Suppose yourself standing at the point where these Reverse the letters of the first course, and they courses meet. will stand thus, S. 670 E. } N. 28 E. The third rule applies in this case. When the quantity of any angle in a survey is wanted, the preceding course must be reversed; then both courses will run from the same point. Converging of Meridians. The breadth of a degree of longitude in any parallel of latitude is to the breadth of a degree upon the equator, as the Co-sine of that Lat. is to Radius. R.: 60 Miles :: Co-sine of the Lat. : the breadth of a degree on that Lat. 1. At a certain point I took the elevation of a tower 30 15/ -then measured toward the tower on an angle of depression 70 333 feet to a level with the base of the tower, when I took the elevation again 80.-Required the height of the tower and the distance from the second place of observation to the base; also how much higher the land was at the place of the first observation than at the second. Ans.-Height, Distance required, 99.6 feet. 708.6 feet. Difference in the height of land, 40.58 feet. 2. Two persons made observations on the altitude of a meteor, both being on the same side of it, and in a vertical plane passing through it. The distance of their stations were 200 rods apart, and at one the angle of elevation was 360 25', at |