D. The pine poles were only used for common purposes, being correct to about ·02.
E. F. G. H. All these rods were divided from the standard scale. I made a right-angled triangle of sheet steel and stout brass tube, to slide along the edge of the standard. It was 13· in its bearing length, with a straight edge 4·3 long at right angles, for ruling by. It carried a fine line on inlaid German silver, by which it was adjusted (with a magnifier) to successive inches of the standard, for the successive cuts to be made. Altogether I divided 80 feet of rods into 1-inch spaces by this, with an average error of ·0015 inch.
The jointing rods were connected by a slip joint (see Fig. 4, Pl. xv.); a screw on each rod slipping through a hole in the other, and then sliding in a slot until the rod butted against the stop, S. Both the butt and rod ends were made by a screw in the end, sunk up to its head, the screw being screwed in until only slightly in excess, and then ground down to a true length, with a radius equal to the length of the rod. The levelling rods I made with similar jointing and fittings. A base-rod of 60 inches stood on the ground, having a flange against which the upper rods could be slid up or down by hand. It had also a block on the side, carrying a circular level, by which its verticality could be observed. The mode of work was for the staff-holder to hold the base-rod vertical, and slide the upper rods up or down, till a finely-divided scale at the top was in the field of the telescope; then setting the rods, so that one of the inch cuts on them should agree with the zero line on the base-rod, the fractions of an inch were read by the level telescope, and the whole inches reported by the staff-holder. This method enables a larger scale to be used for reading on than if there were similar divisions all down the rods; and yet it takes but little time for adjustment, as that is only done to the nearest whole inch or two, and it does not sacrifice any accuracy.
The other scales do not need any remark.
Q. The calipers (see Fig. 5, Pl. xv.) were made for gauging the thickness of the coffer sides; the arms were of equal length, so that variations were read on the scale of their actual value at the other end. The scale was the gun-metal scale, 0, screwed temporarily on to the projection at the top, and read by a line on a brass plate, underlapping it, on the opposite limb. The zero of the scale was repeatedly read, during the series of measurements, by putting an iron bar of known length (±·0002 inch) and parallel ends, between the steel points at the bottom, in place of the side of the coffer. The limbs I made of pine, 71 × 4 × 1, lightened by holes cut through them. The hinge was of steel plates, with copper foil washers between them to prevent friction, and closely fitting on a stout iron pin. The readings of the scale value corresponding to the gauge-piece were four times 5·77, and once 5·76, showing that there was no appreciable shake or flexure in the instrument as used.
R. As the steel tape and chain were often used, suspended in catenary curves, two terminal supports were made to hold the ends six inches from the ground. One support was simply a wedge-shaped stand with a hook on it; the other support carried a lever arm, weighted so that it balanced with 10 lbs. horizontal pull from the point where the tape was attached; hence the stand was drawn back until the arm swung freely, and then there was 10 lbs. tension on the tape. But transferring apparatus was needed, to transfer down from the marks on the tape to the station mark; and to be able to read as instantaneously as if the tape lay on the station mark, for simultaneous readings at each end. After several experiments I adopted a horizontal mirror, levelled in the direction of the tape length, and supported at half the height of the tape. The edge of this mirror being placed just beneath the tape, the reflection of the tape marks could be seen side by side with the station mark; both marks being at the same virtual distance from the eye, and therefore both in focus together. Motion of the eye does not affect the coincidence, except when the mirror is not level, or not at half the height of the tape; and even then only if large variations occur together. The mirror, its stand, and level, I arranged to pack inside the wedge-shaped terminal support.
S. The thermometers were common mercurial and spirit tubes. I graduated them by freezing point, and a hot bath with a fine chemical thermometer in it. Divisions are most easily and visibly marked on the tubes by coating one side with whiting and a trace of gum, then scratching the lines through that with a point; and then fixing, by dipping the tube in thick varnish. The tubes were mounted with the divisions placed behind, and thus much spread out from side to side, as seen through the tube. The wooden frames were thick enough to protect the whole bulb and tube sunk in them; and the numbering could be safely trusted to the frame, though the accuracy of the divisions was secured on the tube. This plan of seeing the scale through the tube, might be improved on by instrument makers flashing a thin coat of opaque white glass down the back of the tube, and then etching out the divisions through it.
10. a. The principal angular instrument was a splendid theodolite by Gambay, said to have been used by the French in their share of the Anglo-French triangulation. It was of a very unusual form, the support of the upper parts and altitude circle being a pillar formed of the cone axis of the lower or azimuth circle; and the 10-inch or altitude circle being set on a horizontal axis parallel to the plane of it, so that it could be turned over horizontal, as an azimuth circle, with its centre over the axis of the fixed or 7-inch horizontal circle. This was a bold device for making available the full accuracy of the finest of the circles for either altitudes or azimuths, and it was quite successful, as I could never detect the least shake in the converting axis, even though this was taken apart every time the instrument was packed The total weight was so small—being only 37 lbs.—that I could freely carry it, as set up for work, from station to station; but to avoid straining it in travelling, and to carry it easier over rough ground, it was usually packed in three boxes: one for the 7-inch circle and feet, one for the 10-inch circle, and one for the telescope, levels, and counterpoise. Its original case was ludicrously clumsy, heavy, and dangerous—a sort of thing to need two stout sappers to haul it about, and to take care that it never was turned over.
The 10-inch circle was very finely graduated on silver to 5′, the lines being so close as to show diffraction spectra. It was read by four very long verniers of 100 divisions each, one division equal to 3″. The magnifying power originally provided was quite inefficient,* being but single lenses of 1 1/2 inch focus. One of these I retained for index reading, and then fitted four microscopes of 1/4-inch equivalent focus (or magnifying 20 diams. on 5-inch standard, or 40 diams., as opticians are pleased to magnify it): with these the reading was excellent, the average error of a single reading and graduation being only ·4″; or, combined with errors of parallax, by the planes of the circles being about 1/400 inch different, it was ·7″. The circle errors were determined by repeating the quadrants of the verniers around it many times, and then going round the circle by stepping the length of each vernier; thus each quadrant was divided up by the mean stepping of four vernier lengths of 8 1/4° each. These four values were mapped in curves, and a mean curve was drawn through them; this mean curve was ever after used (along with corrections for level, &c.) in correcting all the observations of each vernier independently, so as to detect any extraordinary error or reading. The instrumental errors were all small: the eccentricity of the circles was in the 10-inch=4·8″, in the 7-inch=15·5”; the difference of axes of inner and outer cones of repeating motion=5·2″; the difference between the two ends of the transit level-bearing and the steel pivots sunk in them=6·6″; the difference of the diameters of the pivots, and their errors of circularity, inappreciable. The runs of the four verniers were ·42″, ·92″, ·25, and ·12″ on 5′ or 300″. Of course, in field work, the errors of pointing, of vibration of the instrument, and personal errors due to wind, sand, heat, glare, and constrained positions, increased the mean error of reading; and, on the average, it is 1·1″ for a single observation.
The 7-inch circle was scarcely ever used; the long cone of it was so finely ground that, on being