o. For signals in the triangulation, to show the places of the station marks, I made a number of short wooden cylinders, 1 1/4 diam., painted white, and standing on three legs of wire (see Fig. 10, Pl. xv). In order to enable these to be centred over the station marks by a plumb-bob, the cylinder was cut in two across the middle; a diaphragm of thin card was then put in it, with a hole truly centred by adjusting a circle on the card to the outline of the cylinder; and the two halves of the cylinder were pegged together again. Then, having a plumb-bob hanging by a silk thread through the hole, at whatever angle the cylinder could stand the bob would be always beneath its centre. The bob was fixed to hang at the right height, according to the irregularities of the rock, by drawing the thread through the hole, and pressing it down on a dab of wax on the top of the cylinder.
The plumb-bobs are all of a new pattern (see Fig. 11, Pl. xv). The point of suspension is generally too near to the centre of gravity, so that a slight shift in it would move the position of the lower end a good deal more. Hence the suspension and the end of the bob are here made equidistant from the middle. To avoid the complication of screw plugs to each bob, there was a large horizontal hole through the neck, to hold the knot; and a smaller vertical hole in the axis of the bob for the thread to pass.
The finest white silk fishing line was found to be the best thread for plumb-lines, or for stretching for offset measures; it does not tend to untwist, or to spin the bob; it is only 1/50 inch diam., well defined and clean, and very visible. Wax is invaluable for hanging plumb-lines in any position; and a piece of wood an inch square, well waxed, if pressed against a stone warmed by a candle, will hold up several pounds weight.
For station marks on rocks or stones, I entirely discarded the bronze and lead forms. They may be very good in a law-abiding country, but I found that half of those put down by Mr. Gill, in 1874, were stolen or damaged in 1880. The neat triangular stones in which they were sunk also attracted attention. I therefore uniformly used holes drilled in the rock, and filled up with blue-tinted plaster; they are easily seen when looked for, but are not attractive. To further protect them, I made the real station mark a small hole ·15 diam.; and, to find it easier, and yet draw attention from it if seen, I put two 1/2-inch holes, one on each side of it; usually 5 inches from it, N.E. and S.W. Thus, if an Arab picked out the plaster (which would not be easy, as the holes are 1 to 1 1/2 inches deep) he would be sure to attack a large hole, which is unimportant. Where special definition was wanted, as in the main points round the Great Pyramid, a pencil lead was set in the middle of the plaster. This cannot be pulled out, like a bit of wire, but crumbles away if broken; and yet it is imperishable by weathering. To clean the surface of the marks, if they become indistinct, a thin shaving can be taken off the rock, plaster, and central graphite altogether. Where I had to place a stone for a station mark, I sunk it in the ground; and for the base terminals I took large pieces of basalt, and sunk them beneath the surface; thus a couple of inches of sand usually covers them, and they cannot be found without directions.
On reading this description of the instruments, it might be asked what need there could be for doing so much in adjustment, alteration, and manufacture, with my own hands. But no one who has experienced the delays, mistakes, expense, and general trouble of getting any new work done for them, will wonder at such a course. Beside this, it often happens that a fitting has to be practically experimented on, and trials made of it, before its form can be settled. And, further, for the instinctive knowledge of instruments that grows from handling, cleaning, and altering them, and for the sense of their capabilities and defects, the more an observer has to do with his own instruments the better for him and for them.
* This is preferable to the type of the standard chain of the Standards Department, as that has such a flat curve at the end of the eye that it is not certain to pull to the maximum length; and in a light thin chain such a form would be liable to bend.
* Instrument makers seem to ignore the fact that there is a definite law for the power of reading microscopes; the angular width to the eye of a minute as seen in the telescope should equal the width of a minute as seen in the microscopes, else there must be a waste of accuracy somewhere. The formula is—focal length of object-glass: radius of circle::focal distance of eye-piece: focal distance of microscope. Of course, in compound eyepieces and microscopes the equivalent focal distance must be employed, inversely to that deceptive term “magnifying power.”
* Spider line from webs is useless, as it is covered with sticky globules to catch small flies; the path-threads of the spider are clean, but thick; so that the best way of all is to catch a very small spider, and make it spin to reach the ground, winding up the thread as fast as it spins it out, dangling in mid-air.
CHAPTER III.
METHODS OF MEASUREMENT.
11. FOR the general questions of the principles of the arrangement of a triangulation, and of the reduction of the observations, we must refer to the two appendices on these subjects. They are so purely technical, and uninteresting to any but a specialist, that they are therefore omitted from the general course of this account. We begin here with lineal measure, and then proceed to angular measure, including theodolite work in general.
For lineal dimensions, I always used the system of a pair of rods butting end to end, and laid down alternately, instead of making marks at each rod length. In testing measures, the value of the sum of two rods can also be obtained more accurately than the exact butt length of either of them alone. But for the more important points, the direct measurement of a space by a rod has been often abandoned for the more accurate method of referring all parts to horizontal and vertical planes of known position. This is a necessary refinement when precision is needed, and it specifies a form in every element of size, angle, and place. In the passages, where the use of horizontal planes was impracticable, a plane at a given angle was adopted, and the roof and floor were referred to that.
In the Great Pyramid, the King’s Chamber was measured by hanging a plumb-line from the roof in each corner of the room; and measuring the offsets from the lines to the top and bottom of each course on each side of the corner. Then the distances of the plumb-lines apart were measured by the steel tape on the floor. The heights of the courses were read on a rod placed in each corner. For the levels, the 5-inch theodolite was placed just about the level of the first course; then at 24 points round the side a rod was rested on the floor, and the level and the first course read on the rod.
The coffer was measured by means of a frame of wood, slightly larger than the top, resting upon it; with threads stretched just beyond the edges of the wood, around the four sides. The threads gave true straight lines, whose distances and diagonals were measured. Then offsets were taken to the coffer sides from a plumb-line hung at intervals over the edge of the wood; its distance from the straight stretched thread, being added to the offsets, thus gave the distances of the coffer sides from true vertical planes of known relation to each other, at various points all over the sides. Similarly, the inside was measured by a frame, slightly smaller inside it than the coffer. The bottom was measured by raising the coffer 8 or 9 inches; the theodolite was placed to sight under it, and offsets were thus read off to the outside bottom from a level plane, also reading the height of the plane of sight on a vertical rod; then the theodolite was raised so as to sight over the top of the coffer, the height of its plane on the same fixed rod was read off to give its change of level, and then long offsets were taken to points on the inside bottom of the coffer. Thus the thickness of the bottom is determined by the differences of level of the theodolite, minus the two offsets. Besides this, a check on the sides was taken by a direct measurement