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The Pyramids and Temples of Gizeh by Sir Flinders Petrie - Instruments


The Pyramids and Temples of Gizeh by W. M. Flinders Petrie


Chap. 2. Instruments Pages 10 - 21

8. p 10 The list of instruments employed was as follows:

A*

b*

C

D

E*

F*


G*


H*

J

K

L

M*

N*

O*

P*

Q

R

S

a


b


c


d

e

f

g

h

j

k

l

m

n

o

Standard scale, steel ..... ..... ..... ..... ..... ..... ..... ..... ..... .....

Steel tape ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....

Steel chain ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....

Pine poles, a pair 1 inch diam ..... ..... ..... ..... ..... ..... ..... .....

Pine rods, a pair 1 x 2 inches ..... ..... ..... ..... ..... ..... ..... .....

Pine rods, 10 of 1/2 x 1 inches ..... ..... ..... ..... ..... ..... .....

(joining together into two lengths of) ..... ..... ..... ..... ..... .....

Pine rods for levelling 3 of 1/2 x 2 inches ..... ..... ..... ..... .....

Pine rods for levelling 2 of 1/2 x 1 inches ..... ..... ..... ..... .....

Pine rods, 2 of 1/2 x 1 inches ..... ..... ..... ..... ..... ..... ..... .....

Box of mahogany rods, 2 of 1 x 1 ..... ..... ..... ..... ..... ..... .....

Boxwood scale 1.25 x .13 ..... ..... ..... ..... ..... ..... ..... .....

Steel scale, 1.07 x .04 ..... ..... ..... ..... ..... ..... ..... ..... .....

Ivory scales, 2 of 1.18 x .08 ..... ..... ..... ..... ..... ..... ..... .....

Boxwood scale, 1.18 x .08 ..... ..... ..... ..... ..... ..... ..... .....

Gun metal scale, 1.06 x .09 ..... ..... ..... ..... ..... ..... ..... .....

Ivory scale, 1.0 x .08 ..... ..... ..... ..... ..... ..... ..... .....

The divisions of those marked *

are all known to within 1/1000 inch

Double calipers 72 inches long ..... ..... ..... ..... ..... ..... ..... .....

Supports for catenary measurement by tape and chain ..... .....

10 thermometers for scale temperatures ..... ..... ..... ..... .....

Theodolite by Gambay 10 inch circle, divisions 5', vernier 3" .....

Theodolite by Gambay 7 inch circle, divisions 10', vernier 10" .....

Theodolite by King 5 inch circle, divisions 30', vernier 1' ..... .....

Theodolite by King 5 inch semicircle, divisions 30', vernier 1' .....

Theodolite by Troughton 4 inch circle, 30', vernier 1' ..... ..... .....

Theodolite by Troughton 4 inch semicircle, 30', vernier 1' .... .....

Box sextant by Troughton 1.64 inch radius, division 30', vernier 1'.

Hand level in brass case.

Gun metal protractor, by Troughton, 5.9 diam, divisions 30'

Mahogany goniometer 11 and 9 inch limbs.

Queen's chamber air channel goniometer,

Sheet steel square, 35 and 45 inches in the sides.

Folding wooden tripod stand, old pattern.

Rigid tripod stand, 30 inches high, octahedral. p 11

Rigid tripod stand, 16 inches high, octahedral.

Rigid iron tripod 12 inches high, octahedral.

12 signals, with plumb bobs.

100 inches long, divided to 1 inch.

1,200 inches long, divided to 50 inch.

1,000 inches long, divided to 20 inch.

140 inches long, divided to 10 inch.

100 inches long, divided to 1 inch.

60 inches long, divided to 1 inch.

250 inches each.

60 inches long, divided to 1 inch.

60 inches long, divided to 1 inch.

20/40 inches long, divided to 1 inch.

25 inches long, divided to 1/10 inch.

12 inches long, divided to 1/50 inch.

12 inches long, divided to 1/10 inch.

10 inches long, divided to 1/50 inch.

10 inches long, divided to 1/50 inch.

6 inches long, divided to 1/50 inch.

1 inches long, divided to 1/100 inch.


telescope x 35


telescope x 6


telescope x 8

The above were all used, most of them continually; a few other instruments were also taken out, but were not needed.


9Several of these instruments were of new or unusual patterns, whichas well as various fittings adapted to themrequire some explanation. The dimensions are all in inches. (A.) The steel standard and straight-edge was on a new principle, employing the stiffness of a tube to maintain the straightness of a strip. It was skilfully executed by Mr. Munroe, of King's Cross. A steel tube, 102 inches long, 2.0 diam., and .06 thick (see fig. 1, pl. xv.) was supported at the two neutral points, 20.8 per cent. from the ends, resting on two feet at one point and one at the other. This tube carried a series of 15 flat beds, all dressed exactly to a straight line when the tube rested on its supports. These beds supported the actual standard, which was formed of three independent strips of steel, each 34 inches long, 2.0 wide, and .1 thick, butting end to end. These strips bore on the upper face, along the front edge, very fine graduations, the lines being about 1/1000 wide. To ascertain the mean temperature throughout the whole length of the standard, a rod of zinc was screwed tightly to one end of the standard, and bore a scale divided to 1/200 ths at the other end; the scale rising through a slot in the standard. The value of the divisions for various temperatures was carefully ascertained. As this standard was also a straight-edge, the edges of the three strips were all true straight lines, with a mean error of 1/1200 th inch; and the edges were brought into one continuous straight line by adjusting screws set in the supporting beds, at the ends of the Back edge of each strip. The object of having three separate strips was that they could be dismounted for independent use in measuring or drawing. and for testing each other's straightness; that unequal heating of one edge should not cause as much distortion, in length or straightness, as if it were in one continuous piece; and that the weight should not be too great for the rigidity, in handling it when detached from the supports. The principle of separating the stiff part from the actual scale was adopted in order to use the regular drawn weldless steel tube, which is the stiffest thing for its weight that can be had, and also to prevent any unequal heating warping the straightness, as the tube was boxed in by a thin wooden sheath, and so was sheltered far more than the scale could be. The minor details were that strips were held down by screws with countersunk heads, bearing on steel spring washers; and they were pressed Home against each other's ends, and also against the Back adjusting screws, by diagonally acting springs. Along the front of the tube were projecting screws, nutted on and adjusted to form a right angle with the face of the strip; so that the sLandard could be applied to any surface exactly at ight angles.

p 12 The value of the divisions was ascertained by comparison with a brass standard scale. This scale was tested by Capt. Kater in 1820, 1824, 1830, and 1831; and by the Standards Department in 1875 (see a report on it in the Report of the Warden of the Standards, 1875, Appendix x., pp. 36-41) : as the steel standard was sufficient for comparisons, this scale was not taken to Egypt for fear of injury. The form of this brass standard is a bar, 42.14 long, 1.58 wide, .17 thick; bearing a scale of 41 inches in length, divided to .1 inch, with a vernier of 1/1000 ths, and also bearing a metre divided to millimetres. The steel standard was ascertained, by means of this brass standard, to be exact at 19.6 cent.; and the mean error of graduation and reading combined was .0002, the greatest error being .0005. By the intermediary of a steel tape, the steel standard was further compared with the public Trafalgar Square standard; and according to that it was I in 60,000 longer, or true length at 17.8 cent., or a difference of .021 on the length of the public standard, after allowing for the published error of .019 inch. This is a guarantee that the lcngth of the tape, which was used to transfer from the steel standard to the public standard, has no greater error than this; and, on the whole, I should place as much, or rather more, confidence in the series of comparisons between the Imperial, the brass, the steel standard, and the steel tape, made under the best circumstances in doors, rather than in comparisons between the steel tape, the Trafalgar Square standard, and certain steel rod measures, made in the open air, with wind and varying temperature. The difference in any case is immaterial, in regard to any of the points measured, in the present inquiry.

(B.) The steel tape was over 100 feet long, .37 inch wide, and .008 thick, and weighed just over a pound. It was coiled on an unusually large drum (4.2 diam.), to avoid any chance of permanent distortion. Etched divisions, in the ordinary style, being too ill-defined, I had an unmarked length of tape, and divided it by fine cut lines at every 50 inches ; the position of each line was shown by heating the steel to brown oxidation, and marking the number out of the brown by acid. It was found on trial that such lines did not weaken a piece of tape, even when it was violently twisted and wrenched ; and that the steel, being hard drawn and not tempered, nothing under red heat softened it. The cuts were not put on with any special care, as their exact value was to be ascertained; but the worst error throughout was .0098, the mean error .0039 inch, and the total length true at 19.8 cent. This companson was made when the tape was lying unstretched, on a flat surface, as ascertained by measuring successive 100-inch lengths on the steel standard. It stretched .0127 per lb. on the whole length of 1,200 inches.

(C.) The steel chain of 1,000 inches I made on an entirely new pattern; and it proved, both in Egypt, and, some years before, at Stonehenge, to be very handy in use. Tile links are each 20 inches long, made of wire .092 diam., this being p 13 as thin as can be used with fair care. The eyes (see fig. 3, pl. xv.) are wide enough to fold up one in the other, without any intermediate rings. They are rhomboidal, so that they cannot hitch one on the other, but will always slip down when pulled; and the internal curvature of the end of the eye is only just greater than that of the section of the wire, so that the linkage is sure when in use to come to its maximum length.*

* 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 certan to pull to the maximum length; and in a light thin chain such a form would be liable to bend.

The junction of the eye is made with a long lapping piece, cut one-third away, and tinned to the stern. The whole was tested with 100 lbs. pull, to bring it to its bearings, before marking the divisions. The exact length of the links is unimportant, as, after the chain was made and stretched, a iiarrow collar of sheet copper was soldered about the middle of each link, the collars being adjusted to exactly 20 inches apart. Besides this, each link bore its own number, marked by a broad collar of copper for each 100, and a narrow collar for each 20 inches or link; thus, at 340 inches there were three broad and two narrow collars by the side of the central dividing mark on the link. These collars were put towards one end of the link, apart from the dividing inark, and counted from each end up to the middle, as usual. The central eye of the chain was not tinned up, but was held by a slip clutch; thus the chain could be separated into two 500-inch lengths if needed, each complete in itself, as for base lines for offsets. The handles were kept separately, hooking into any link at which accurate readings under tension might be needed. They were of the same wire as the chain, with wooden cross-bars. One of them included an inverted spring (see fig. 2, pl. xv.), so that the pull compressed the spring. When the pull reached 10 lbs., a small catch (not shown in the Figure) sprang out from the stem, and caught the coils. This left only a very small amount of play; and hence, when using it, the regulation of the tension did not require to be looked at, but was felt by the finger when at 10 lbs. pull. The advantages of this pattern are: (1) Great lightness and compactness of the chain, as it only weighs 2 lbs., and forms a sheaf 1 inch diam.; (2) consequent small error by catenary curves, and ease of carrying it clear of the ground by its two ends; (3) accuracy of the divisions; (4) freedom from errors in the linkage; (5) that no counting of the links is required, each being numbered; and (6) that standard tension can be maintained by touch, while the eyes are used on reading the chain length. The worst error of division was .03, the average error .01, and the total length, with 10 lbs. tension, true at 15.8 cent.; the stretching .0l per lb. on the 1,000-inch total length.

(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 p 14 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 X 4 X 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 p 15 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 there- fore 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 smallbeing only 37 lbs.that I could freely carry it, as set up for work, from station to station ; but to avoid straining it in p 16 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 dangerousa 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 inch focus.

* 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."

One of these I retained for index reading, and then fitted four microscopes of -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 each. These four values were mapped in curves, and a mean cune 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 I0-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 set on an ordinary table (soon after I had thoroughly cleaned it), the whole of the upper part of the instrument (about 18 lbs. weight) was seen to be slowly revolving in azimuth, without any apparent cause. On p 17 examining it, it was found that, not being quite level, and the counterpoise of 5 lbs. not being put on it, its centre of gravity was not at the lowest point attainable ; hence the rotation. The telescope was equal in character to the rest of the instrument, the object-glass being 1.66 diam., and 16 inches focal length, and the eye-piece of high power and large field; thus it magnified 35 diameters. The form of the slow motions was far superior to that of English instruments ; all the tangent screws had a steel ball on the shank, which worked between two circular holes, in plates which were clamped together by a fixed screw; the nuts were also spherical, cut into two separate halves, and also clamped between circular holes. Thus there was practically perfect absence of shake, and great working smoothness, even when stiffly clamped. Another excellent device was the use of spring steel washers to all screws whose tension was in question; the screws were all made to run dead Home on a seat, and to produce pressure through a curved washer, which they flattened, either for fixed tension, or for rotation of an axis. Thus a slight loosening of a screw made no difference or shake and no delicate tightening up was needed; if the pressure had to be altered, the washer was taken out and bent accordingly.

The three levels of the theodolite were suitably delicate, the value of one division being 2.47" (altitude), 4.92" (transit), and I2.8" (cross level). For these and every other level used, I adopted a distinctive system of numbering. Every level had a different number for the mean position of the bubble end, and the divisions were numbered uniformly in one direction, and not simply on each side of the mean. Thus the ranges were respectively from 5 to 15, 16 to 24, 28 to 32, 40 to 60, &c., on the levels called No.10, No.20, No.30, No.50, &c.; and when once a number was recorded (the mean of the two ends was always taken mentally), it showed which level was read, and in which direction, with any doubt, or further note.

Other adjuncts that I provided for this, and also for the other theodolites, were slit caps (see figs. 6, 7, 8, pl. xv.). It is manifest that objects seen through a fine hole are always in equally good focus, no matter what maybe the distance; hence, if an object-glass is limited to a small hole, it does not need focussing. But definition is commonly required in only one direction at once, either vertically or horizontally; hence a slit which admits more light will be as effective as a hole. When a line is quite invisible, by being out of focus, placing a slit cap over the object-glass, parallel with the line, will make it clear ; and it will be well defined in proportion to the fineness of the slit. Each of the theodolites were therefore fitted with two movable slit caps, fine and wide, to cover the object-glasses. As focussing is always liable to introduce small errors, by shake of the tubes in each other, these slit caps were adopted to avoid the need of changing focus continually from near to distant objects; they also serve to bring near points in view, at only a foot or two from the glass. To be able to p 18 place the slit-cap on the end of the telescope, without shaking it, was essential. This I did by making the slit of thin steel spring; soldered to brass clutches, so as to grip the telescope by three points; provided also with a projecting tongue above, and another below it, whereby to bend it open for clipping it on (see figs. 6, 7, 8, pl. xv.). The smaller theodolites were also fitted with diagonal mirrors clipping on to the object-glass ; these enabled the instruments to be very accurately centred without a plumb-line.

(b.) The 5-inch theodolite, by King, was an old one, and was obtained for rough work; but it had never been adjusted, so I had to take it in hand; and on finding its errors, after correction, to be even less than those of the 4-inch Troughton, I generally used it for all small work. I corrected it in the rectangularity of cones to the circles, of transit axis to the cones, and of cradle axis to transit axis; also in adjustment of verniers for run. The telescope was of long focussing-range when I got it, and I increased the range from infinite down to 5 feet focus, which made it very useful in near levelling, as in buildings; also I did away with the mere fit of sliding tubes for focussing; and made the inner tube run on four points, slightly punched up in the outer tube, and pressed in contact with them by a spring on the opposite side of it. The old level I replaced by a good one of Baker's, running 41.5" to .1 inch. Microscopes of inch equivalent focus were fitted to two arms, which were slipped together when required for use, and rode round on the compass-box; with these the average error of reading on the 1' verniers was 7".

The spider lines in this, and the next theodolite, were somewhat different to the usual pattern. When either a single vertical line, or a diagonal cross, is used, it blocks out any very small signal; and I have even heard of an engineer hunting in vain for his signal, because the line exactly hid it. To ensure greater accuracy, I therefore put in two parallel lines, crossed by one horizontal (needed for levelling) ; the lines being about 1/400 inch apart; if closer they may cling together if vibrated, and it is awkward to separate them while in the field. Thus the interval of the vertical lines was about 1', and signals could be very accurately centred between them.*

* 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.

(c.) The 4-inch theodolite by Troughton was not often used, except where lightness was important; I fitted it with two microscopes, similarly to the 5-inch; and its mean error of reading was about 8" on the I' vernier.

Though neither of these were transit theodolites, yet in practice I used them as such for all accurate work. By reversing the telescope, end for end, and upside down, and turning the circle I80, all the errors are compensated as p 19 in a transiting instrument; the only extra source of error is irregularity in the form of the rings, which can be tested by revolving the telescope in its cradle.

(h.) For ascertaining the angles of the Queen's Chamber air channels I needed to measure as long a length of slope as possible, at about 8 feet inside a passage which was only .8 inches square. For this I pivoted an arm on the end of a long rod (see fig. 9, pl. xv.), and passed it into the passage in the dotted position at A; on reaching the slope it turned itself up to the angle by pressure, the main rod touching the passage roof. The arm carried an index, which touched a scale attached to the main rod. This scale was divided by actual trial, by applying a protractor to the limbs and marking the scale. To read it, a candle was carried on an arm, which shaded the direct light from the eye; and the scale was inspected by a short-focus telescope. Thus the readings were made without needing to withdraw the goniometer from the narrow channel, and hence the arm of it could be much longer than would be otherwise possible.

(j.) A large square, 35 and 45 inches in the sides, of sheet steel strips, 2 inches wide, and tinned together, I made for testing angles; it was not exactly adjusted to squareness, but its angles were very carefully fixed, by triangulating a system of fine punched dots on the face of it; and the edges were adjusted straight within about .003 throughout their length. It could be used for the absolute value of slopes of about 51 50' and 26 20', by means of a rider level placed pn one edge of it, and reading by means of a divided head screw at one end. To render the square stiff enough sideways, it was screwed down (with round projecting screw heads, not countersunk) to a frame of wooden bars, 2 x 1 inch in section. I generally found, however, that it was best to measure a slope by theodolite and offsets.

(k, l, m, n, ) These stands were used for the theodolites. Generally the 10-inch theodolite could be placed directly on the rock, or on a stone; but when a stand was needed I used one about 30 inches high, that I made of 1 X 1 pine rod; the top was stouter and about 12 inches triangle, and the feet about 30 inches apart, connected by cross bars. Thus it was of the octahedral pattern, a triangular face at the top, another at the base, and six faces around; this being the only form absolutely free from racking. The screw feet of the theodolite rested on leaden trays on the top of the stand, which allowed free sliding for adjusting its centring. A similar octahedral stand about 16 high, was made of X 1 inch pine, for the 5-inch theodolite; in order to stand it in chambers or on stones. The instrument was clamped on to the stand by a screw from beneath, passing through a plate under the triangular top of the stand, and screwing into the base plate of the theodolite, which rested upon the top of the stand. Thus it could be slid about on the stand, to adjust its centring, and then clamped tight after wards. The iron stand was of just the same pattern, but made of inch iron rod; the rods p 20 were bent parallel where joined, and passed into sections of iron tube, the whole filled up with tinning. These small stands would stand on the top of the large one when required.

(o.) For signals in the triangulation, to show the places of the station marks, I made a number of short wooden cylinders, 1 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 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 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 p 21 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.

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