"You will tell Branchu to get a wooden shed built to keep his tools in, and to keep the lime under cover till it is slacked. If we had a contractor, or some one with whom a bargain had been made, we should not have to trouble ourselves about the quantity or content of the materials brought to the ground; but as it is, we must employ ele mentary means, for Branchu has not capital with which to provide materials. We shall therefore give him the ma terials we buy, or which the estate supplies, on account. You perceive the necessity of preventing these materials from being abstracted or wasted. We pay him only for the labour. This plan obliges us to be more attentive and vigilant, but we are at least secured from being deceived as to the quality of the materials by a contractor, who might think it his interest, if he.bought them, to supply us with some of a quality inferior to that contemplated in the estimate.
"We shall make the same terms with the carpenter. Your father tells me he has some oak timbers that have been cut more than two years, and put in the wood-yard near the Noiret farm. Let us go and have a look at them, and mark those that can be employed. Our figured plan gives us the lengths of the flooring joists." Passing by the side of the rivulet that flows along the little valley, Eugene was looking attentively at its steep banks, and was striking the rock faces with the iron shod end of his stick."What do you observe there?"said Paul.
"I think we shall find here good materials for our cellar vaulting...-. Look at this yellowish stone, porous like a sponge. It is a present to us from this little water-course. It brings down in its waters carbonate of lime, which is incessantly being deposited on the grasses and vegetable detritus on its banks and in its bed. This rivulet thus forms a light and very porous tufa, which is soft and friable as long as it is thoroughly moist, but which acquires a certain degree of hardness in drying. Formerly this rivulet was larger than it is now, and it appears to me to have deposited a considerable thickness of this tufa as presented on its banks in their actual condition. Take this bit, and look at it attentively. You see that it is filled with cavities, - little cylindrical passages; they represent the twigs around which carbonate of lime was deposited. The twigs themselves decayed and disappeared long ago; the coating has remained and been hardened in the air. Observe how light this kind of stone is, being composed of cells scarcely thicker than egg-shells. Yet, try to crush it under your heel. It resists, and the pressure scarcely blunts its asperities. Well, dry it, and in a week it will be even harder. A smart blow with a hammer will be required to break it.
"This material is perhaps the best for vaults, on account of its lightness, its toughness, its cavities, and that roughness of surface which makes the mortar adhere so closely to the joints that it cannot be separated, and the whole, when sufficiently dry, seems to form only a single piece.
"We shall send two excavators to get out a few cubic yards of it. It is no difficult operation; and when this tufa is in a damp state in its natural bed, it can be very readily cut up into brick-shaped pieces." They soon reached the Noiret farm; and there in fact, under a shed along the wall of the barn, were piled up pieces of timber roughly squared and blackened by damp. Eugene marked a certain number of them with his knife, leaving those that were crooked, knotty, or cross-grained.
"What is a cross-grained piece of timber?"asked Paul.
"Cross-grained timbers are those whose fibres form a spiral round the heart. You can understand how the fibres of the wood not being vertical, and forming spirals more or less complete, lose their resisting property; these fibres, on account of the circuit they make, - and which is not a regular one, - become disjoined, and leave deep cracks between them. These timbers, therefore, are rejected as defective, as are also those whose heart is unsound, or which have what they call soft rings; that is, diseased parts between their layers - a sort of interior ulcers which not only deprive the wood of its homo geneity of resistance but develop decay around them. It often happens that these soft rings are not observed, and that timbers which appear very sound fall rapidly to dust. And as these diseases are frequent or rare according- to the soils in which the wood grew, it is essential to know whence the timbers employed in- buildings came. One forest will produce oak admirable in appearance, but which rapidly decays; another furnishes timber that is always sound. Generally, timber grown on light and
dry soils is good; the produce of damp, clayey ground is bad.
"You will have these cross-grained and crooked timbers put on one side; they will do to make the centres for the cellars; they are fit for nothing else, unless it be for firewood. As to these fir poles, they will serve for scaffolding." It was late, so the cousins asked for breakfast at the farm. While they were laying the table, Paul said,"I want to know how you use the theodolite." "In the case of an operation such as we have just been performing, it is the simplest thing in the world. I asked Branchu to send my instrument to the chateau, that I might not be troubled with it all the morning; but there is no need to have it here to show how to use it. You know that the theodolite consists of a graduated circle, divided into 36o degrees. This circle, movable on its centre, is furnished with an air-bubble level, and a tele scope above, both of which turn horizontally on a pivot in the centre of the circle. The level and the centre of the telescope are perfectly parallel to the plane of the circle. This is placed upon a stand with three legs, and the circle is first fixed horizontally by means of three regulating screws, and by turning the level. The air-bubble must be always at the centre, to whatever degree of the circle the tube is directed. This being done, and the feet being placed at the point marked on the ground - verifying the position by means of a plumb-lime passing through the centre of the plate - the glass is directed towards a fixed point where a `sight' is placed. The glass of the tele scope is crossed by two hairs at right angles, which mark its centre. The intersection of the two hairs must fall on the point on which the telescope is directed. But pre viously the indicator or vernier below the telescope is set to the zero of the circle. It is therefore the entire instrument that has been turned. If, then, for example, we wish to construct a right angle on the line joining the point where you are standing with the first sight, you turn the glass till its indicator stands at 90 degrees (the quarter of the circle). You send a man with another sight in the direction of the glass, and have this sight carried to right or left until its centre is exactly on the line of the vertical hair of the glass. You have this sight fixed. It is then certain that the line drawn from the point where you stand in the direction of the second sight forms a right angle with the first base line, since two diameters cutting a circle divided into 36o degrees at right angles give 90 degrees for each quarter of the circle. By the help of this instru ment, having previously indicated on the plan of a building whose foundations you are laying out, the angles which certain lines, starting from any point, form with each other, you can transfer these angles to the ground. Suppose you have to lay the foundations of a semi-circular portico. Having fixed the centre, and traced the semi-circle on the ground, placing the theodolite on this centre, you will be able to direct lines that will cut this circumfer ence at regular intervals, and which would mark, for instance, the centres of the columns or pillars. Since from point A to point B you have 18o degrees (Fig. 2o), you will divide these 180 degrees into as many parts as you choose on the circle of the theodolite, and the centre of the glass will give you, at a great distance, the same divisions on the semi-circular portico. In the same way as the theodolite serves the purpose of laying the foundations of a building, it enables us to take the bearings of a tract of country. For suppose the base, E F, to be a known length which you have measured : placing your instrument at E, you direct the glass on a point C, - a tree, a steeple, or a pole; you have then the number of degrees on the circle comprised by the angle C E F. You transfer this angle to your paper, then moving the instrument to the point F, you direct it thence on this same point C; you obtain similarly the angle C F E, which, transferred to the paper, gives you exactly the position of the point C, and the unknown distance from E to C and from F to C; then either of these lengths will serve you for a base in its turn, and operating from the point C and the point F, and sighting a fourth point D, you know the lengths C D and F D. Thus you can operate over a whole country; this is what is called triangulation, the first operation re quired for getting a map of the country. But we are getting into another region of knowledge. Let us go to breakfast !"