CHAPTER X.

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LARGE THEODOLITES USED ONLY FOR GEODETIC SURVEYS—STANLEY'S 10- AND 12-INCH—14-INCH ALTAZIMUTH—COLONEL STRANGE'S 36-INCH THEODOLITE.

474.—Large theodolites employed upon geodetic surveys. Where the complete survey of a country has to be made, a system of large triangles is formed over the country from convenient positions which are naturally or artificially elevated so as to obtain distant views with the telescope. These triangles are correctly measured by angles subtended from a very carefully measured base or bases set out upon approximately level planes, which are generally of a mile or more in length. Where measurements are derived from such bases by constant intersection of angular positions extended therefrom to large triangles or other polygons, it becomes important that the theodolite employed should measure such angles with great accuracy. In this case the vernier reading does not possess sufficient refinement, and the divisions representing the degrees have to be magnified to appear wider apart, so that they can be more finely subdivided for the reading to be taken by means of a micrometer microscope capable of subdividing the divisions made upon the instrument even to single seconds of arc. The theodolites used for the superior triangulation of Great Britain were Ramsden's 36-inch and 18-inch, which, although constructed in the last century, remain excellent instruments.

475.—The construction of large theodolites is varied very considerably according to the conditions present in the country to be surveyed. This subject if carried into detail would extend much beyond the intended limits of this work. This chapter will therefore be limited to the description of a 10- or 12-inch instrument, and to two historical instruments which have been used successfully for geodetic work.

Fig. 196.—Stanley's 10-inch transit theodolite.

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476.—10- or 12-inch Theodolite.—These instruments approach the limit in size of portability for movable stations in triangulation. The illustration, Fig. 196, is of the author's latest 10-inch model, the patterns of which were made for a theodolite with vernier readings to be used for the construction of a spiral tunnel through the Andes, now completed. The object in its construction was to obtain great rigidity with moderate weight. To this end the gun-metal of which it is made is shaped out from castings as comprehensive in unity of parts as possible. It has a framed mahogany stand (not shown) which is braced in every way and provided with a very rigid head. In general construction of the instrument illustrated it has a mechanical sliding stage and an extra powerful clamp and tangent arrangement for the lower limb, the adjusting screws being all covered to exclude dust. The circles are divided to 5 minutes, and are read by micrometers to single seconds of arc. Two vertical arcs are used, the second one carrying the clamp and tangent arrangements, which also serves to balance the trunnion. The 10-inch instrument carries a 16-inch telescope with 2-inch object-glass, and the 12-inch instrument an 18-inch telescope with 2-1/8-inch object-glass. The tangent screws all act against springs to avoid loss of time.

Fig. 197.—14-inch altazimuth theodolite.

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477.—14-inch Theodolite.—For this description a modern instrument is taken which Colonel A. R. Clark selected for illustration in his excellent article on Geodesy in the ninth edition of the EncyclopÆdia Britannica, to the publishers of which the author is indebted for the illustration, Fig. 197. The instrument is a combination of a transit theodolite with special arrangements as an altazimuth instrument with fixed base, one side of the vertical circle being divided to place the zero in a direction coincident with the polar axis. The construction as a simple fixed transit theodolite for support upon a pedestal in stone wherein the axis remains permanent for a principal geodetic station, and therefore requires only a single setting to bring it to true north and south for zero, renders change of position of horizontal limb unnecessary for a permanent station. For this the instrument is well adapted, and will be discussed here. The telescope is of 18 inches focus, with 2 inches clear object-glass. The axis pivots are of hard steel: one is perforated for illumination by a lamp. The vertical circle is placed almost directly upon the side of the telescope, and the tangent arm on the opposite side is of nearly equal weight, so that there is no counterbalance necessary. There are three Ramsden eye-pieces giving powers of 17, 35, and 54, and one diagonal eye-piece. A level is attached inside the standard, divided to read 10 of arc: this has cemented ends, art. 177, and is enclosed in an outer tube for protection. Two other exactly similar levels are attached to the exterior axis of the instrument. The circle is divided to 5' of arc and reads by two micrometer microscopes to single seconds. The vertical axis of the instrument is of steel. It is placed with the apex of the cone upwards, and terminates on a triangular spring with three adjusting screws by which any portion of the weight of the upper part of the instrument can be relieved from the axis, so that the whole instrument moves quite freely. The horizontal circle reads with three micrometer microscopes on the upper circle to single seconds. Originally the light was thrown down on the divisions by three ivory cones placed over the fronts of the microscopes, as shown in the illustration; but these have been changed in the present instrument for concave swivelled reflectors, which may be set to any angle convenient to throw sufficient light upon the circle. The microscopes are supported from the body of the instrument upon hollow conical arms upon the same excellent plan originally used by Ramsden. The microscopes have adjustments in three directions, so as to bring them exactly into place for trisection of the horizontal circle. The clamp and tangent motion is placed directly upon the divided circle, and has adjustments to secure freedom from strain; but this is not perfect—it is perhaps the worst feature in the instrument, some modification of the plan shown, Fig. 196, being much better for large instruments.

The whole instrument is mounted on a tribrach frame, which is adapted to stand upon a portable table or upon masonry. The screws have lateral adjustment to prevent loss of time by wear.

478.—It is a common custom with this class of instrument to make the axes of hard steel. This plan is no doubt very satisfactory as it leaves the optician's hands, but the author very much prefers good hard bell-metal. When he saw the above described instrument at Southampton, there was quite sufficient evidence of rust on the pivots to destroy all perfection of centring, and this could scarcely have occurred with bell-metal. Of course the brittleness of bell-metal would be objectionable where the instrument might be subjected to severe jar in carriage from place to place; but the author has obviated this by a plan he would strongly recommend for general adoption—of having the axis of good gun-metal, and to silver-solder a ring of bell-metal thereon where the fitting surfaces occur. If the gun-metal is pure it will bear the average reliable strain of hardened steel, which in hardening and tempering is not with certainty always free from flaws; and the average wear of pure bell-metal is perhaps quite as good as steel.

479.—36-inch Theodolite, Fig. 198, was designed by the late Colonel A. Strange and constructed by Messrs. Troughton & Simms for the Great Trigonometrical Survey of India. It is probably the most complete and perfect theodolite ever constructed. The leading characteristics of this important instrument only will be given. It has a horizontal circle 36 inches diameter, and a vertical circle 24 inches diameter. The telescope has a focal length of 36 inches: the aperture of the object-glass is 3·25 inches.

Fig. 198.—36-inch theodolite—Great Indian Survey. From a photograph.

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480.—The Stand has three massive mahogany legs AA braced together with horizontal and oblique wrought-iron bars B. Each leg is divided vertically, and contains a long, gun-metal, square-threaded screw C which is made to rotate by means of a worm-wheel and endless screw worked by a winch handle D, and capable of being firmly clamped after adjustment at points about 15 inches apart E. The upper ends of these screws are conical, and fit into three inverted radial grooves formed in the lower side of a cast-iron circle or table, which is thus supported by the three screws without being attached to them, and is therefore free to accommodate itself to expansional changes without restraint. The upper surface of the cast-iron circle is turned flat and true to receive the tribrach of the instrument. The three screws F which pass through the side of this circle are intended to adjust the centre of the instrument over the station mark. A lever G also passes through the side of the circle and actuates three rollers, which, when in action, support the greater part of the weight of the instrument, and so enables the horizontal zero to be set without difficulty. As the instrument weighs over 400 lbs., it will be seen that some such arrangement is absolutely necessary to enable it to be moved on the cast-iron circle. When the correct position has been obtained, the lever is thrown out of action, and the instrument remains immovably seated upon its circular frame.

481.—The Foot Screws are tapped through the ends of the tribrach arms in the usual way, but have a range of motion not exceeding 1/10 inch. This range may appear small, but is really much more than is required, as the upper surface of the cast-iron circle can be levelled by the long screws in the mahogany legs before the instrument is placed on it, so that not more than about 1/100 inch of motion is required. The foot screws do not rest directly on the cast-iron circle, but on the extremities of an intermediate three-armed plate, securely bolted to the centre of the instrument, the distance between the tribrach and the plate being about 1/10 inch. The object of this arrangement is to obviate the disturbance of level and azimuth which arises from clamping foot screws of the ordinary construction after adjustment, as well as that due to looseness of the foot screws in the tribrach arms. The arms of the spring plate, being of considerable width, have great horizontal rigidity, but being comparatively thin are easily bent vertically. The outer ends of the arms rest on the cast-iron circle or stand; the foot screws pass through the tribrach arms, but not through the spring arms. It is evident therefore that when the foot screw is turned inwards with the screwing motion, the solid end of the tribrach will be raised and the slit between the two arms widened; but since the end of the screw does not rest on the stand, but on an intermediate arm, which is actually a portion of the tribrach itself, it is clear that if a lateral pressure be applied to the tribrach no motion will be caused thereby, however loose the screw may be, so long as the pressure is less than the lateral rigidity of the intermediate arm. The lateral pressure caused by turning the instrument in azimuth when taking observations is greatly within this limit. This plan is perfectly successful, but it is only available where a moderate range of vertical movement is needed. In the present instance, as the cast-iron ring or stand on which the instrument is supported is always first made practically level, the vertical range of the foot screws need not be more than a small fraction of an inch. Another point with regard to the foot screws is their delicacy and certainty of action. This is attained by applying to them a clamp and tangent screw arrangement H very similar in principle to that sometimes applied to circles. Although the foot screws themselves are rather coarse, having only about eight threads to the inch, the arrangement is such that one entire revolution of the slow motion tangent screw alters the level only about one second of arc. Hence the foot screws in this instrument, though coarse and strong enough to bear great weight are probably for the first time made in keeping, in point of refinement, with its most delicate parts.

482.—The Horizontal Circles.—The inner or working circle is 36 inches in diameter. It is very finely divided on silver to 5 minutes, and is read by five equidistant micrometer microscopes to tenths of a second of arc. It is fixed at the centre to the tribrach, but everywhere else is perfectly free. The outer or guard circle consists of a second horizontal circle exterior to and concentric with the inner circle. There is a space of about 1/10 inch all round between the two circles, and the upper plane of the outer circle stands about the same quantity above that of the inner or principal circle. The guard circle is supported by radii of its own, quite independent of those of the inner circle. This circle has several functions. It protects the working circle from accidental injury; it helps to distribute changes of temperature uniformly over the circumference of the working circle; it receives the clamp and tangent screw, leaving the working circle absolutely free from contact at all times; and it bears a strongly-cut set of divisions, more visible to the naked eye than those of the working circle, which are exceedingly fine, and therefore would be inconvenient for setting the instrument approximately in azimuth.

483.—The Horizontal Tangent Screws.—It will be seen at II' that there are two clamps and two tangent screws to the horizontal circle. It is necessary to have both, on account of the large size of the circle. In use, of course, they are not both used at the same time. In the present position of the instrument the clamp and tangent screw on the left-hand side of the illustration would be employed; but on reversing the telescope this clamp would be released and the one on the opposite side made use of. It is necessary with this, as with smaller instruments, to avoid loss of motion in the tangent screws. Many methods have been employed to obviate this loss of motion, but while they are suitable to small instruments they are not so effective with large ones, such as that under consideration. The plan adopted in this case is that known as the divided nut principle. The block into which the tangent screw is tapped is divided transversely and the two halves are forced asunder, and therefore act against the contrary sides of the screw threads by four internal spiral springs. The tension of these springs is necessarily constant, and therefore not subject to the disturbance and slow recovery of elastic force unavoidable in an external spring. Means are supplied for regulating the tension of the four springs, which must be a little in excess of the force necessary to move the revolving mass, without taking the parts to pieces.

484.—The Vertical Axis is a truncated cone of steel with its base downwards. It is about 6·5 inches high and 3·3 inches and 2 inches in diameter at the base and summit respectively, the flange being about 4·5 inches in diameter and constructed on the isolated principle. The vertical axis socket and the five horizontal microscopic arms are cast in one piece of aluminium bronze, the elliptical table carrying the telescope supports being bolted to the central boss in which the socket of the vertical axis is formed. The vertical axis and the elliptical table are both perforated in the centre so as to allow of a look-down telescope being employed in adjusting the instrument accurately over the station mark.

485.—The Telescope is furnished with two separate eye-ends, carrying respectively a vertical and a horizontal parallel wire micrometer J. It is also supplied with both bright and dark field illumination, the latter being employed when faint stars are observed. The vertical circle K is divided on silver similar to the horizontal circle, and is read by two opposite micrometer microscopes when the instrument is used for terrestrial work: but when required for astronomical purposes four micrometers can be used, and they can be shifted to any part of the circle on which they are clamped. In the illustration the four micrometers are shown in position. The two rods or handles seen parallel with the telescope at LL' are attached to the middle of the transit axis where the telescope passes through it, and are intended to raise or depress the telescope without touching it by hand. These rods are also used for carrying adjustable counterpoises, the instrument being so balanced in every part that the equipoise is as nearly perfect as practicable through any diametrical section of the vertical axis.

486.—The Spirit Levels, both horizontal M and vertical N, are very delicate. They are constructed so that the divisions on their scales represent as nearly as possible one second of arc. The scales are divided to twenty per inch. The glass bubble tubes are mounted on V bearings, and are kept in position by light springs in such a manner that they are free to adapt themselves to changes of temperature with perfect freedom. They are also enclosed in external cylindrical glass covers to protect them from sudden changes of temperature. The arrangements for adjusting the levels are such as to obviate strains without risk of shake, and to ensure delicacy of action.

487.—The Five Micrometer Microscopes O for reading the horizontal circle are carried by the same number of equidistant radial arms branching from the central boss which carries the whole of the instrument above the horizontal circles. These micrometers are made on Robinson's principle, Fig. 199, that is, with a short bow spring S having a central nut tapped through it to keep the tension between the bearing of the micrometer screw on the end of the outer box and the slide which carries the webs constant with whatever part of the screw may be in use. The radial arms each carry a vertical socket which is bored out cylindrically to receive the microscope. These sockets are slotted vertically, and have three clamping screws at the side to hold the microscopes firmly in position when they are once adjusted. The two webs in these micrometers are placed parallel to one another, and at such a distance apart that when in proper adjustment they are a trifle wider apart than the width of one line on the circle, as shown in Fig. 200. The micrometer heads are divided into sixty parts, and the whole is arranged so that in practice ten revolutions of the micrometer screw traverse the webs over ten minutes of arc or two divisions on the circle. Each division therefore on the micrometer head represents one second of arc; and as the divisions are clearly cut on silver and about one-tenth of an inch apart, there is no difficulty in reading to the tenth of a second, which, on a circle of 36 inches in diameter, is equal to the ·00000872 of an inch, or the three-thousandth part of one division of the circle; this, as before stated, is equal to five minutes of arc, or the ·02616 of an inch. The illumination of the microscopes, or rather of the divisions of the circle, is a most important matter. When such exact measures are to be taken it is effected by means of perforated silver reflectors attached to the micrometer arms and mounted quite independently of the micrometers themselves. The axis of each reflector coincides with the axis of its microscope. All the reflectors have both vertical and horizontal movements, and are therefore readily adjustable to the best position for securing effective illumination under the varying conditions in which the instrument may be employed.

Fig. 199.—Robinson's micrometer.

Fig. 200.—Webs of micrometer.

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488.—Relieving Apparatus.—It will be readily understood that the moving parts of so large an instrument must necessarily be very heavy. In this case the telescope, vertical circle, pillars, elliptical table, horizontal micrometer arms, and vertical axis socket weigh nearly 300 lbs. It would of course be impossible to take horizontal angles with so much friction on the flange of the vertical axis as this weight would produce, hence the necessity for some form of relieving apparatus. That employed in this case is a system of forty spiral springs, each of a definite length, which when adjusted support about 6·25 lbs. The spiral springs are mounted on a flat ring in two circles with projecting pins to keep them in position. The upper ends of the springs support a steel ring with a circular groove on its upper surface, between which and a corresponding groove in the outer part of the vertical axis socket three equidistant, nearly frictionless steel rollers run; so that by this means about 250 lbs. weight is taken off the flange of the vertical axis, the remaining weight being sufficient to allow of the instrument moving with the necessary freedom, and at the same time giving all the stability requisite for accurate levelling.

                                                                                                                                                                                                                                                                                                           

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