582.—Field-book.—The field-book as shown above, Fig. 254, was recommended by the inventor.

583.—Mode of Operating with the Omnimeter.—Carefully set the instrument up at its station in perfect adjustment as a theodolite, noting the departure point upon the scale reading through the microscope. Place the stadium in a vertical position at the point to which measurements are required. Direct the telescope so that the horizontal web cuts the upper line of the stadium, and lightly clamp it. Now read the microscope and record the reading as observed in the field-book. Unclamp the telescope and take the reading of the lower point of the staff and record this. Record the bearing of the instrument on the horizontal circle as with a theodolite.

584.—To Determine the Horizontal Distance in Feet.—Divide the constant radius of 1,500,000 given before by the difference of the two readings of the stadium mark, which are 10 feet apart. For example:—

then

The process is somewhat simplified by logarithms, as we have only the log. of the difference to subtract from the constant, the 1,500,000 mantissa of which is 1,760,913. Thus—

585.—To Determine Horizontal Distance in Chains the stadium should be marked as just described for feet, but at 20 links distance from line to line. Then the radius 150,000 × 20 gives 3,000,000. Taking for example, readings as before with difference of 3285 we have—

To Determine Horizontal Distance in Metres, the stadium is divided to 4 metres. Then radius 150,000 × 4 = 600,000. Taking, for example, difference of reading as before 3285 then

586.—Levelling—Taking Altitudes.—To take the elevation of the staff above the level of the instrument, subtract the reading of the scale, when the axis of the telescope is level, from the lower reading of the staff on the scale, and divide by the distance difference, as found by the method discussed before, then multiply this by 10 feet. Thus taking the lower reading as before 64,450 and the constant for the level position of the instrument, say 50,010, we then have—

then

The heights, in relation to the position of the instrument, are positive or negative according as the scale readings are greater or less than the constant level reading or departure point.

587.—Work of the Omnimeter.—The perfection of the principles of the omnimeter would lead anyone to infer that work might be done with it of the highest degree of accuracy. The testimony of the greatest authorities show by comparison that it is unable to compete in this respect with the best made tacheometers. A large number of these instruments are employed in India. Colonel Laughton reports upon it—"It has been found to give very accurate heights of buildings, etc., also to be wonderfully accurate when used as a levelling instrument; but it is not so accurate for measuring distances over 600 feet, and even at this distance the error sometimes amounts to as much as 1 foot. It is recommended as admirably adapted for city surveys and traversing, also in hilly and jungly countries, and for railway and similar purposes."[33]

588.—Wherein the instrument fails to give exact results is no doubt in the difficulty of its manipulation. For taking two readings, which are necessary for every operation in distance, the instrument has necessarily to be set twice, the hand being placed upon the micrometer for the second observation while the attention is upon the sighting of the telescope; and even when the readings are taken by the telescope, the microscope has to be separately adjusted to read the micrometer scale. In the repetition of these processes it is almost impossible to avoid some slight disturbance of centre by pressure. In distant readings atmospheric changes giving difference of refraction occur quickly, so that there is more risk of error from two separate observations than if the observations of the subtense webs are taken simultaneously, as with the tacheometer. Further, any defect in workmanship or wear tells seriously against the readings of the instrument. Its advantages are theoretically that a wide angle is subtended by the stadium with the omnimeter in short distances which must be in every way an advantage. Further, since the early general use of the omnimeter, the tacheometer has been greatly improved, particularly in providing it with a larger and better object-glass so as to obtain greater field of view, that fairly near stations may be taken with it that were formerly only possible of reading with the omnimeter. The manufacture of omnimeters is now very limited; the subject is only retained in this edition because there are still some hundreds of these instruments in use.

589.—Improvement in the Omnimeter.—One improvement in this instrument by Mr. W. N. Bakewell, M.Inst.C.E., consists in turning the body of the microscope to a right angle at the position of the transverse axis of the omnimeter, and placing a reflecting prism at the angle. By this means the eye-pieces of the telescope and the microscope are brought side by side, greatly facilitating the joint readings. A second improvement is in making the scale 1,000,000 instead of 150,000, which much facilitates calculation, but it is doubtful if these improvements will stay the declining popularity of the omnimeter.

590.—Bakewell's Tangential Arrangement to a Theodolite for Measuring Distances.—This arrangement, which gives the distances by direct reading without calculation, was devised by Mr. W. N. Bakewell to extend the power of an ordinary 6-inch transit theodolite fitted with subtense webs. The observations are made on marks at 3 feet and 13 feet on an ordinary Sopwith staff—a 10-feet base, as is usual with the omnimeter. Any other base may be used if the distances registered are proportionally altered, or the scale may be divided to suit. It was first applied by the author to a theodolite that had been in good service, without the necessity of making any structural alterations in the instrument.[34] The measuring apparatus consists of a tangent screw impinging upon a radial plane, with micrometer and vernier. The details will be readily comprehended from the engraving, Fig. 255, and the following full description.

591.—The transverse axis of a theodolite, upon the opposite side of the telescope to that upon which the vertical arc is fixed, is turned down to a cylindrical surface true with the pivots. A collar A, which fits the cylindrical surface, is slit up on one side to enable it to be clamped firmly to any position of the axis by a clamping screw B. The collar is connected in the same gun-metal casting with the radial arm C that terminates at T in a plane, which is made truly radial with the transverse axis of the telescope. This radial arm C has a long German-silver spring S at the opposite side to the radial plane, which keeps it up firmly in contact with the point of the micrometer screw. A screw is cut on the drum of the micrometer D; on the spiral the scale of distances is engraved; and readings are taken from a line on the index I which slides on the bar E. The scale being one of reciprocals the divisions are at unequal distances, so a vernier cannot be used; consequently at long ranges where the divisions are close, the subdivisions must be estimated. Where this is too rough a method, resort must be had to calculation. The outer end of the drum D is divided into 200, and reads by vernier V carried by the arm E in 5 or thousandths of a revolution. The micrometer screw has twenty-five threads to an inch, and the radius of the arm C is 4 inches. One complete revolution of the screw is one-hundredth of the radius, and using a base of 10 the radius factor is 1000 × 100 × 10 or 1,000,000; consequently Barlow's or any other table of reciprocals can be used, and the distances obtained, by inspection with comparatively little labour. This additional part has not range sufficient for altitudes, being available for about 2 degrees only. The distance may be taken as a subtense or small tangential angle at a radius which, with the azimuthal angle taken by the vertical arc of the theodolite, will give altitude by its sine and horizontal distance by its cosine in the usual manner. The principle is that of the omnimeter, and it possesses the same objection for perfect performance, that the theodolite has to be handled twice for the two observations necessary.

592.—The Gradienter Screw.—This is no doubt a simplified copy of Bakewell's tangential arrangement and is shown at Fig. 256.

It is a micrometer screw fitted to a tangent arm, which can be clamped to the trunnion of telescope when the latter is in any position.

The screw is cut of a value that causes the web of the telescope to move 50/100 of a foot at 100 feet distance for each revolution, and the head of the screw is divided into 50 parts, consequently each division upon the head represents a movement of the cross web of the telescope of 1/100 of a foot upon a scale placed at 100 feet distance. The scale on the arm over the gradienter screw indicates the number of complete revolutions of the head, therefore, if the screw be revolved two whole revolutions the two divisions covered on this scale indicate 50/100 × 2 = 1 foot to the 100 feet.

To establish any grade with this screw.—Set the gradienter head to zero, then level the telescope and clamp the gradienter arm. Suppose grade required be 1·75. Turn the gradienter head through three whole revolutions, which will equal 150, then go on turning through 25 of the divisions on the head and the total movement will be 1·75, the required grade.

For Measuring Distance.—First with a staff for moderate distances. Any space on the staff covered by two complete revolutions of head is 1/100th part of distance, thus, if the difference between the two readings be 3·475 feet the staff is distant 347·5 feet.

Second Method.—For long distances with any rod of known length, such as a 20-foot stadia rod. Send out a man with the rod which he holds vertical at place to be measured. Then measure its length with the gradienter screw; say it takes 2 revolutions and 45 divisions over, thus 2 revolutions = 100 and 45 extra divisions = 145. Then—

Another instance.—Suppose the man at a distance has no stadia rod. He simply holds up any stick, say a walking stick. Measure this in telescope. Say it subtends 1 revolution and 28 divisions. This = 78. When your man comes in with the stick, measure its length. Say it was 3·25 feet. Then—

The above illustrations are for readings taken approximately level. If there be much elevation or depression the angle must be read and the difference of hypo and base calculated and the stadia rod or staff must be inclined so that its face is at right angles to the line of sight from telescope. This can be done by the rod man inclining the staff or rod until the shortest reading is given if a staff be used, or the longest measurement is recorded by the gradienter screw head if a stadia rod be used. It is better in this case to have the staff fitted with a director (see art. 561), so that the person holding the staff may sight into the telescope of the instrument, thus ensuring the staff being exactly at right angles to the line of sight.

No constant should be added with either this, Bakewell's, or omnimeter measurements, as the angles are taken from the centre of the instrument. This gradienter screw has the same fault as mentioned for the two foregoing, viz., that all readings are taken by two movements of the instrument.