See also: Geoid The geoid is essentially the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of sea water , the mean sea level surface in the absence of currents and air pressure variations, and continued under the continental masses. The geoid, unlike the reference ellipsoid , is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between the geoid and the reference ellipsoid is called the geoidal undulation. A reference ellipsoid , customarily chosen to be the same size volume as the geoid, is described by its semi-major axis equatorial radius a and flattening f.
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Hill station and tent. Ground -level plaun Fig. Bilby steel tower. The two vanes are at right angles in plan, and each is either all shaded or all in sunHght.
The instrument 1. Convenient but generally bad, as it is difficult to plumb down to ground level. Used in India in the nineteenth century, but now expensive. An inner tower of about inch diameter at the top, with a central 6-inch hole for plumbing, supports the theodolite, while an independent outer tower supports the observer and tent.
Wooden trestles resembling d below, but not portable. Much c used in North America, but now being superseded by d. The Bilby tower, Fig. Weight of foot tower, 3 tons: maximum weight of any one piece, 60 lb.
Section 3. Theodolite Observations 1. Two main types of theodoHte are now in use for primary triangulation : a The long-established micrometer theodolites, similar in prin- ciple to the old and inch instruments made years ago. The old instruments were clumsy, but much of their work can still be accepted as of primary accuracy.
In the twentieth century they have been replaced by smaller instruments such as the Troughton and Simms inch or the Parkhurst 9-inch. The advantages of the glass arc are very great, namely: i Lightness and small size: 34 lb. This at least halves observing time, and also saves disturbance of the instrument, iii The easy reading of the circles makes an eye-piece micro un- necessary, iv No adjustment for micrometer run.
Early models of the first glass arcs had a tendency for the vertical axis to warp and tighten, , , and , but this has now been remedied, and both the 5j-inch Wild and 5-inch Tavistock can be recommended as very convenient and capable of the best work. Suitable theodolites for secondary work are the old type 8-inch micro obsolete , the 3f-inch Wild and the 3J-inch Tavistock. The 12 -inch T. Apart from its size this is very similar to the 5-inch micro which every surveyor knows.
The necessary adjustments are: b LevelHng, and adjustment of the levels. Apart from details due to minor differences of construction these adjustments are made in exactly the same way as those of a 5-inch micro, but the following points may be noted: Centring.
The precision required is given by the rule that 1 foot subtends 1 second at 40 miles. Care isrequired when plumbing down from a high tower, when an optical plummet on the theodoKte stand or a vertical colHmator on the ground must be used, after adjustment if necessary. To test it, level the theodolite or colKmator to get the axis vertical, rotate the instrument, and if the adjustment is not perfect the intersection of the cross-wires will describe a small circle, with the true plumb point at its centre.
If this circle is too large, adjustment is required. A levelhng error of d" will produce an error of up to 6" tana in the horizontal direction of an object of elevation a. A few seconds off level thus seldom matter except in astronomical work, but more should not be allowed. Change of face does not cancel the error. The fixed wires and micro wire cannot be in the same plane.
If the micro eye-piece is being used for horizontal angles, bring the image into its plane. The resulting small parallax will not affect vertical angles seriously. Object-glass focus should seldom need change. Stijf hearings and loose joints. An important test. Clamp the hori- zontal circle, intersect some sharp object with the vertical wire, and while looking through the telescope press the eye-end gently sideways. The wire will move off the object, but should return when the pressure isremoved.
Only experience can say what pressure is reasonable. Loose foot-screws, or the joints between wood and metal in the stand, Fig. The Precision Wild theodolite.
The Geodetic Tavistock theodolite. Foot-screws should be tight in their bearings, and not unscrewed too far. Any unusual stiffness of the vertical or horizontal axis is serious. Micrometers also should move freely and without jerks, in both directions. Micro run. With a strange theodolite the observer will have no idea how much to move the object glass so he should try one full turn and : make subsequent necessary changes in proportion.
Several approxi- mations may be required. Run should be made correct to within 1 or 2 seconds per 10 minutes in the mean of all micros on four zeros. Transit axis. A dislevelment of 6" when the axis is vertical produces an error of 6" tan oc in the direction of an object at an elevation ol, but it is cancelled by change of face. A dislevelment of 10" is harmless. The constant error of an observed elevation on one face is the so-called colHmation error in altitude.
It is cancelled by change of face, and adjustment is only required if differences between FR and FL are annoying, or if the Hne of sight is seriously off the mechanical axis of the telescope. This calibrates the bubble against a micro screw of known pitch. Note that the value of one division of the eye-piece micro, as obtained by comparison with the horizontal circle, needs to be multipUed by the cosine of the elevation of the object on which the calibration is carried out.
The micro value should be correct to within about 1 per cent. Full details of these adjustments are given in , , and . The Precision Wild. The 5 -inch horizontal circle is divided to 4 minutes, and the micro to seconds.
Pointings t The line of collimation is the perpendicular from the optical centre of the object glass to the horizontal axis, the optical centre being the point through which light passes undeviated.
The collimation error is the angle 6.
Geodesy by Bomford
9780198519461 - Geodesy by Bomford, Guy