of this line at D, in continuation of that of the station-line at B. As soon as the obstacle is passed, set off the perpendicular EG equal to AC and to B D. Then G will be a point in the station-line beyond the obstacle, and the inaccessible distance BG will be equal to D E. By repeating the process, an additional point H in the station-line may be found.

The problem may also be solved by means of similar triangles. At A (Fig. 6) two diverging lines A F and A E are ranged past the two sides of the obstacle. In these lines, measure the distances AD and AC of two points D and C, which lie in one straight line with B. Continue the chaining of AF and A E, and make those distances respectively proportional to AD and A C. Measure D C, noting the position of B, and measure EF, in which line take the point G, dividing E F in the ratio in which B divides CD. Then G will be a point in the stationline beyond the obstacle. Other points may be found in a similar AB CE The inaccessible distance is equal to A C. When the obstacle can be seen over, but neither chained across, nor chained round, as in the case of a station-line interrupted by a river or ravine, a pole must be ranged and fixed at D (Fig. 7) in the station-line beyond the obstacle. BD being the inaccessible distance, at B set out BC perpendicular to the station-line. At C range CA perpendicular to CD, cutting the station-line at A. Measure AB, BC; then BD is equal to BCA B.

manner.

Surveying with the Chain only. In this method of surveying, the surface is to be divided into a series of imaginary triangles;

the triangle being the only plane figure of which the form cannot be altered, if the sides remain constant. The triangles should be as large as the nature of the ground will allow, and as nearly equilateral as possible. The sides of these triangles are first measured, and a straight line is measured from one of the angles to a point in the middle of the opposite side. This fourth line is called a tie-line or proof-line, and is an efficient means of detecting errors. Within the larger triangles, as many smaller triangles and tie-lines are measured as may be required for determining the position of all the objects included in the survey. The directions of the lines forming the sides of these secondary triangles are so placed that the offsets to be measured from them may be as short and as few in number as practicable. Pickets are placed in the ground at each angle of the triangles, the general form and position of which are noted for reference in a hand-sketch, distinctive letters being written at each point of intersection. The points of intersection of all straight lines, as well as the angles of the triangles, are always points measured to or from. They are called stations, and the lines connecting them station-lines. Secondary stations are best marked by whites, which are cleft sticks holding small pieces of white paper, on which a number may be pencilled.

In carrying out a survey with the chain only, it is necessary to attend to the following rules:-Walk two or three times over the ground in order to get a good idea of it, helping your memory with a rough sketch. The first line should be made as long as the place to be surveyed will allow, so that it may form a convenient base with which the other lines may be connected. Select a suitable station on each side of the base-line near the boundary of the work. To these stations, lines should be measured from each end of the base-line, thus forming two large triangles, one on each side of the base-line. On the sides of these

triangles, smaller triangles must be marked out, so as to cover all the ground to be surveyed.

The rough sketch is usually made in the field-book-a book in which every step of the operations gone through in the survey is to be carefully entered at the time. The field-book is ruled with a column down the centre of the page. In this are set down the distances on the station-line at which any offset is made, and on the right and left of the column are entered the offsets and observations made on those sides respectively of the station-line. The middle column represents the chain. It is, therefore, advisable to begin the entries at the bottom of the page; the chain and field-book being thus placed in the same position at the station-line with respect to the surveyor, who

keeps his face directed towards the distant station. The crossing of fences, roads, or streams is to be shown by joining lines in a way similar to the form which they present on the ground.

The following example shows the manner in which the fieldnotes may be entered in the survey of a triangular piece of ground:

In booking, certain conventional signs are adopted for the remarks that occur frequently. The commencement of a stationline, for example, is represented by a small circle or a triangle, and its termination by a line drawn across the page. A station left in a line, to or from which another line is to be measured, is usually represented by its number enclosed in a circle. A turn to the right or left is indicated thus f,7.

Proper attention in keeping the field-book saves much time in plotting, and guards against errors likely to arise from reference to confused notes. In fact, notes ought to be kept so clearly that a draughtsman should be able to plot the survey without further instruction from the surveyor

In spite of its apparent want of accuracy, the method of surveying with the chain alone gives, in the hands of an accomplished surveyor, very satisfactory results. At the same time, though sometimes used for the surface-surveys of small collieries, it is not considered sufficiently accurate for surveys of metalliferous mine royalties.

Chain used in Trigonometrical Surveys.-Before compensating bars were invented, steel chains were employed for basemeasurement in the Great Trigonometrical Survey of the

United Kingdom. In using the steel chain, a drawing-post and a weight-post were used; a 56-lb. weight being always applied to one end of the chain, whilst the other was fixed to the drawing-post. The chain was made to rest in deal coffers supported by trestles, in order to obtain a perfectly level surface, and thermometers were placed at different distances in order to ascertain the temperature of the chain, so that the base might be reduced to its value at a given temperature. The chain was 100 feet long, and consisted of 40 links, each inch square.

(b.) Rods. When very accurate measurements were required, deal rods were at one time largely used instead of the chain for measuring long lines. They were, however, soon discarded in exact operations, as experience showed that they were liable to sudden and irregular changes in length from dryness or humidity. Saturated with boiling oil, and afterwards covered with a thick coat of varnish, well-seasoned wooden rods will be found sufficiently exact for ordinary purposes. Such rods are usually made of lance wood, and are 5 feet in length. They must be placed in line very carefully end to end. They are rarely placed directly on the ground, which, as a rule, is too uneven. A horizontal line may be constructed along the base to be measured, by means of a stretched cord.

On the Trigonometrical Survey of the United Kingdom, glass rods were substituted for wood in the measurement of the Hounslow base in 1784. Their ends were protected with metal caps. The results obtained were perfectly satisfactory, measurements with the glass rods and a check measurement with a steel chain of perfect workmanship, giving results that differed by little more than half an inch in the base-line of 27,404 feet. Steel rods also have been found useful for geodetic measure

ments.

For the measurement of the Loch Foyle base, an apparatus was devised by Colonel Colby. In this he obtained an unalterable linear measure by using compensating expansions. Two bars, one of iron, the other of brass, 10 feet long, were placed parallel to each other, and rivetted at the centre, it having been found by numerous experiments that they expanded or contracted in the proportion of 3 to 5. The brass bar was coated with some non-conducting substance, in order to equalise the susceptibility of the two metals to change of temperature. Across each end of these combined bars was fixed a tongue of iron, with a minute dot of platinum so situated on this tongue that, with every change of contraction or expansion, the dots at each end always remained at the constant distance of 10 feet.

On the Continent, rods 3 to 4 yards in length are employed,

terminated by two points, and provided in the middle with a builder's level and a handle. This apparatus is known as the field-compasses, and is often used for filling in the details of a survey.

(c.) Steel Bands.-The most suitable instrument for measuring lengths in mine-surveys is the steel band. It is more convenient and less liable to inaccuracy than the chain. It is usually 100 feet, or 100 links, in length, with feet etched on one side and links on the other. It is provided with a handle at each end, and is wound on a steel or wooden cross. It is employed in precisely the same way as the chain. Like that instrument, it presents the advantage of rapidity; but it has the additional advantage of representing a length of which the variations are dependent only on the temperature, since it does not kink, stretch, nor wear so as to change its length.

In surveying the anthracite mines of Pennsylvania, Mr. E. B. Coxe * uses a measuring-tape made of a ribbon of tempered steel, 0.08 inch broad and 0·015 inch thick. It is 500 feet long, and weighs 2 lbs. 7 oz. At each tenth foot a small piece of brass wire is soldered across the tape, the white solder extending about an inch on each side of the wire. In the latter is filed a small notch which marks the exact spot where the tenth foot ends. The distances from the zero point of the tape are marked upon the solder by counter-sunk figures. The white solder enables the 10-feet notches to be found very easily, and the counter-sunk figures, being filled with dirt, stand out upon the white ground of solder. The tape is wound upon a simple wooden reel, 10 inches in diameter, which can be held in one hand and turned by the other. Two brass handles, which can be detached, accompany the tape, and are carried upon the reel.

The advantages of the tape are (1) the greater facility in measuring up and down slopes, or along the face of the coal; (2) greater accuracy in measuring from one station to another, as the tape forms a straight line from one station to the other, and there is no error from the use of arrows; (3) the tape does not stretch appreciably. Its disadvantages are—(1) it is liable to break, unless carefully handled; (2) it is necessary to roll it up and unroll it again when the distances vary very much. The tape, however, can be easily mended when it breaks. For this purpose, a small sleeve of brass is made tinned inside, in which the broken ends of the tape are slipped and then soldered by heating the sleeve with a red-hot poker.

There are three sources of error in the use of the steel tape,

* Trans. Amer. Inst. M.E., vol. ii., 1874, p. 219.