half degrees of 30' each; then a vernier of the extent of 29 of these half degrees, divided into 30 equal parts, will also read to minutes. Further, if 1o be divided into 6 equal parts of 10' each, and if 59 of these parts be divided into 60 on the vernier, then it will follow that ==10". From this it appears that an instrument thus divided shews 10" directly, on which the reading may be carried on to 5" by estimation. RECONNOISSANCE. In seeking the best route for a turnpike road, railway, or canal, so far as level is concerned, the engineer's labour is much abridged by duly considering the operations of nature, in the formation of mountains and valleys, which, at first sight, would seem to present an endless variety of forms and combinations. Upon a closer and more careful inspection, however, we shall find that the two grand features of almost every country, present lines whose sinuosities are not very abruptly or violently distorted. The water courses form the lowest lines of the valleys, while the summits of the ridges inclosing these valleys, form the highest. These two classes of lines, visibly delineated on the surface of every country, are remarkable for being lines of greatest declivity of the surfaces to which they belong. These two facts being known, the engineer, after a careful examination of the country, will feel no difficulty in finding the best level for his intended line of road or canal. From the general configuration of any segment of the earth's surface, we at once see that lines of communication necessarily divide themselves into two classes. First, it may be necessary to form a line of communication between two points situate in the same valley. Secondly, it may be required to open a line of communication between two places separated by a dividing ridge. In seeking the best direction in the former case, the engineer is not to go out of the valley; in the latter case, he must pass the dividing ridge at its lowest point, it being a loss of time and labour to look for any other point at which to pass higher up the ridge. When an engineer is called upon to ascertain the best line of road or canal, a good map of the country through which the road or canal is to run, will assist him in his reconnoissance, as it contains with sufficient accuracy, the water courses, which usually give direction to the valleys and dividing ridges, and which last are generally shewn on such maps. If upon examining the map of any portion of a country, you see the water courses diverging from any particular locality, you may, without farther trial, conclude that that locality occupies the highest position; being led to this conclusion from the well known fact, that water runs from a higher point to a lower. Again, if you see on the map several water courses converging towards a particular point, the inference to be drawn from this geographical delineation is, that that point occupies the lowest position in that portion of the country. This we know also from the well known property of fluids, by which they invariably seek the lowest level. These are properties and established facts, to which the engineer should particularly attend; indeed every common observer is aware of them, though men of experience sometimes neglect taking advantage of the instruction they afford. After a general examination of the features of the country, for the purpose of ascertaining the best probable directions, you next level in these directions, and compare the results, which will determine the particular direction to be taken. RAILWAY SURVEYING. After the engineer has determined the direction of the proposed road, a surveyor is generally employed to make a survey of all the inclosures through which it passes. Sometimes, such surveys are executed with the chain only, which in many cases answers very well; but we would recommend invariably to use the theodolite and chain. Let EF be the line of road to be measured. First, measure with great care the base line AB, according to the directions given before; then returning to the point A, where a flag staff is erected, ascertain the angle the base line makes with the magnetic meridian, which you will register in the field-book. Next measure the angles 21a, 31a; then chain from station 1 to station 2, taking offsets to the left as you proceed; in the same manner, chain from station 1 to station 3, taking only one offset to the boundary line, being perfectly straight and parallel to the station line 1, 3. These measurements being registered in the field-book, the next thing to be done is to measure the angle 1, 2, 5, and chain from station 2 to station 5, taking offsets to the left and right, as you go along. In like manner, take the angle 1, 3, 4, and chain from 3 to 4, and measure two offsets to the right. In measuring the base line, false stations should be left at the crossing of the fence a, also at b, c, d, e, &c., and at every point at which a fence crosses it. The angles which have been taken, and the measurement of the lines 3, 4, and 2, 5, mark the position of the fence crossing the line at a. Next, take the angles 6, 4, 20, and 4, 6, 7; then chain the lines 4, 6; 4, 20; 6, 7. Chain the fence passing through a, as also that connecting 7, 20, which will serve to check the work, when plotted. The chainage of these check lines should never be neglected. The next thing to be done is to measure the angle 6, 5, 9; and chaining from 5 to 9, take the angles 5, 9, 8, and then chain the line 9, 8, taking care to measure the offsets as you proceed. Any one acquainted with the common principles of geometry can never be at a loss to know the sides and angles necessary to be measured, in order to mark the position and extent of the different inclosures along the line. A fewer number of observations and chain measurements might often mark the position of the several lines; but the extra work answers as a check to prove the correctness of the several operations, which is a duty never to be neglected. When, in the progress of the work, you are obstructed by a wood, lake, house, or other obstacle, then you measure across the obstruction by the method taught in the part of the work devoted to parish surveying. If your base line be not ranged out with poles, the compass would be a tolerably correct guide. Take the bearing of the line approaching the obstacle, and after having passed it, take the bearing of the line receding from it: if these coincide, it establishes the correctness of the work; but if there be a considerable difference between the two bearings, an error must have been committed in the work, which must be corrected by going over the same ground again. It would be desirable to compare the bearing of the base line at the subsequent stations, with its bearing as ascertained at the commencement of the survey, as their equality would form a presumptive evidence of the correctness of the work. CROSS SECTIONS. When the ground slopes at right angles to the line of road, cross sections must be taken at right angles to it; and this cross section as well as the longitudinal section, must be drawn to a large scale, to guide the working engineer in his operations. The cross sections may be taken at the same time you are taking the levels of the main line. After having brought up the levels to any point of the line where you think it necessary to take a cross section, place a picket firmly in the ground, at which point place the staff, and without removing the instrument, take the level at that point, and also at two points at right angles to the line there; and the distance between these two last points being measured, you will have sufficient data for laying down the cross sections along the line. If you do not think it sufficient, from the nature of the ground, take the levels of several points on each side the main line, at right angles thereto, which, when plotted, will give the exact contour of the |