to the level. This should be repeated until the bubble keeps its central position, whichever way the rule may be placed upon the table. This presupposes the plane of the board to be true. If two levels are on the rule they are examined and adjusted in a like manner.

Great care should be exercised in manipulation, lest the table be disturbed.

3. Parallax.-Move the eye-glass until the cross-hairs are perfectly distinct, and then direct the telescope to some distant well-defined object. If the contact remain perfect when the position of the eye is changed in any way, there is no parallax; but if it does not, then the focus of the object-glass must be changed until there is no displacement of the contact. When this is the case the cross-hairs are in the common focus of the object and eye glasses.

4. To make the line of collimation perpendicular to the axis of revolution of the telescope, and the axis of revolu tion parallel to the plane of the rule.-The instrument is set up and carefully leveled, and the cross-hairs directed to a plumb or other vertical line. If the cross-hairs cover the line when the telescope is elevated and depressed, the adjustments are perfect; should they deviate, however, from the vertical line, this error may be attributable to two causes: 1st, the line of collimation is not perpendicular to the horizontal axis; or, 2d, the axis is not horizontal, and consequently not parallel to the piane of the rule. In the first case the motion of the cross-hairs will be in a curve, and, upon being made to cover the vertical line when the telescope is horizontal, will deviate from it to the same side both upon elevation and depression. In the second case the movement of the cross hairs will be in a straight line oblique to the horizon, and, when made to cover the vertical line when the telescope is horizontal, they will, upon being elevated and depressed, appear upon different sides of the vertical line. These two cases will be considered separately.

When the construction of the telescope admits of it, the perpendicularity of the line of collimation to the axis may be examined as follows: Direct the cross hairs to a well-defined, distant object, as nearly upon a level with the telescope as may be; draw a line along the fiducial edge; then reverse the rule 180°, again placing the edge along this line; revolve the telescope upon its axis and again observe the object; if the cross-hairs cover it, the adjustment is perfect; if not, one-half the error must be corrected by moving the cross-hairs by means of the adjusting screws of the diaphragm, and the other half with the tangent screw of the table, and the operation should be repeated until the adjustment is complete.

In using the method just given it may be taken for granted that the line of collimation revolves in the vertical plane of the fiducial edge, as any error arising from this not being the case would be inappreciable.

After this adjustment the horizontality of its axis should be examined. Direct the cross-hairs to a distant, well-defined, elevated or depressed object, having the table carefully leveled; draw a line along the fiducial edge, reverse the rule, and again direct toward the object; if the cross-hairs cover it the axis is horizontal; if they do not, one half of the deviation should be corrected by means of the screws attaching the upper plate to the top of the standard, or by means of the screws attaching the standard to the rule. The level attached to the axis should then be made central.

5. To make the line of collimation parallel to the vertical plane of the fiducial edge.-The exact parallelism of these is not absolutely necessary, but it is essential that the deviation should remain constant. This adjustment may be examined by means of two needles stuck in the table. The table is so turned that the needles sight exactly to some distant object; the fiducial edge is then placed against them and the telescope directed to the object. If the cross-hairs bisect it the adjustment is correct, but if they do not it can be corrected by means of the screws attaching the standard to the rule.

6. Zero of the vertical arc.—When the line of sight is horizontal the vernier of the vertical arc should read o`, or the index error should be known. This may be examined by means of the distant sea-horizon, or by setting up the alidade so that the centre of the telescope is in the line of sight of an accurately-adjusted leveling instrument, and then directing both instruments, while level, to a distant object; if any error be discovered, it may be corrected by setting the vernier at o°, and adjusting the horizontal wire to the sea horizon or object.

When the above means are not available the following method may be used: Set up the instrument at a point, measure the angle of elevation or depression of a distant object, remove the instrument to that object, and measure the angle of depression or elevation of the first point. These angles should be equal if the adjustment be correct; and, if not equal, the index error will be one half the difference of the two readings.

The following method of making this adjustment, where you have neither a separate level, a sea horizon, nor an elevation, may be employed: Set up the table and level it carefully on any level piece of ground between two equidistant points, A and B, say 600 or 800 metres apart. Determine, with the table, the difference of level of these two points, and remove the table to A. Measure carefully the distance from the ground to the centre of the axis of the telescope, and add or subtract this from the difference of level of the point B, according as it is lower or higher than A. Set up a target or distinct point at this height at B, direct the cross-hairs upon it, and correct the verrier accordingly.

A longitudinal striding level placed upon the telescope, or a level permanently fastened upon the top of the telescope, parallel to the optical axis, and adjusted to the horizontal wire, will give the error at once.

The alidade consists of a brass rule about twenty-two inches long, having a circular level on its upper face. Near the middle of the rule is a perpendicular cylindrical column of brass, called the "standard," surmounted by two square brass plates joined by screws, and supporting horizontally a conical journal, through which extends a closely-fitting cone of brass, coming from and attached to the side of the telescope. This cone forms the axis of the vertical movement of the telescope, and is secured at the extremity by a screw which holds it in its place. The telescope itself has the usual cross-hairs and means of focal adjustment.

A transverse level is fastened to the edge of the upper of the two plates at the top of the standard by means of adjusting screws.

The telescope is so placed that its line of collimation is above and in the same vertical plane with the fiducial edge of the rule.

A vertical arc with a tangent screw and clamp is attached to the telescopic side of the lower brass plate, and, with a vernier which moves in arc as the telescope is raised or depressed, is used in the measurement of vertical angles for heights.

TELEMETER.

Art. 412. In consequence of some of the disadvantages resulting from the employment of the chain, among which are the necessity of frequent dependence for correct distances upon the chainmen, the number of persons required, the time consumed in its management, and the impediments to its use found in the features of some sections of country, another instrument, styled the telemeter, has been advantageously introduced in the topographical work of the Coast Survey,

It appears that instruments of this class were at first generally regarded by scientific men as merely ingenious inventions, and not as valuable in most respects as the ordinary method of chaining, the filling in of details forming a principal exception. From the experience of its use by the officers of the Coast Survey, however, it has been satisfactorily ascertained that the rapidity with which the details of a survey can be determined and sketched, the smaller number of men necessary to be employed, so that whatever errors may occur rest with the observer only, and the facility in using it in places where the use of the chain is impracticable, or at best difficult, render the telemeter a very important acquisition. It is not considered that it will ever entirely supersede the chain as a measuring instrument, but it is undoubtedly a facile and useful substitute under certain conditions.

The telemeter, as used in the Coast Survey, is simply a scale of equal parts, painted upon a wooden rod about 10 feet long, 5 inches wide, and 1/4 inch thick, so graduated that the number of divisions upon it, as seen between the upper and lower horizontal wires of the telescope, is equal to the number of units in the distance between the observer's eye and the rod held at right angles to the line of sight.

In all cases the telemeter should be graduated experimentally for the particular instrument and eye of the observer who has it in use.

The horizontal wires in the diaphragm of the telescope should be accurately adjusted, and the divisions of the telemeter made to correspond in length with the distance included between the upper and lower wires of the telescope at a carefully measured distance, and then divided into as many equal parts as there are units in the distance measured.

For convenience of transportation it can be hinged in the middle, and secured on the side when in use by a sliding bolt; and as it is necessary, when observed upon, that it should be held accurately at right angles to the line of sight, a small brass movable bar, with sights or a groove upon its upper edge, should be fixed upon the side of the rod at a convenient height for the eye of the rodman, and which, when in position, will be perpendicular to the plane of the telemeter and directly in the line of sight of the telescope.

The correctness of the telemeter depends upon the closeness of the reading and the accuracy with which the rod is held perpendicularly to the line of sight.

With ordinary care an error of reading should not occur even at the greatest distance denoted on the rod. With the observations carefully made, and the reading of the rod reduced to a horizontal plane, the greatest distance given by it, as usually divided, can be relied on as practically correct. There is no sensible error at any distance greater than 20 metres and less than 260, and, generally speaking, the telescopes of the Coast Survey alidades have not sufficient reading power beyond 400 metres, but it wil generally be safe to rely upon it for any distance from 15 to 500 metres, beyond which it cannot be read with accuracy for use in constructing a map on a scale of TOOOO.

The telemeter has been recommended for use in a great variety of cases where it becomes necessary to determine distances, in such close filling in as the corners of streets, wharves, &c., deter mination of all classes of detail, in traverse, shore line, and even the establishment of positions, but in the latter it is safe only to depend upon good intersections. It has been employed, however, in all manner of detail, and is preferred by some to the chain, in all cases save on long lines, where the distances are so great that the telescope will not admit of the accurate reading of the rod, and it is maintained by some that where only a single point is to be seen positions can be readily and accurately determined.

PORTABLE MICROMETER-TELESCOPE.*

120

80

60

Art. 413. This instrument is constructed on the divided-object-glass principle, originated by Dolland, and applied in the heliometer of the Königsberg Observatory, described by Bessel in Astronomische Nachrichten, vol. viii, pp. 411-426. Its novelty consists in a new arrangement of the slides and micrometer screw, by means of which it is made sufficiently compact for a portable instrument. Each one is provided with an ordinary terrestrial eye-piece, magnifying about fourteen (14) diameters, for use on shore or on board ship, and an inverting eye-piece, magnifying about ten (10) diameters, especially designed for use in boats or on horseback, &c. The cap, which fits both eye-pieces, has a revolving diaphragm, with three colored glasses for observing bright objects.

Rest the tube nearest the object-glass between the thumb and palm of either hand, the back of the hand toward the eye, the thumb

clasping the telescope, and the micrometer head between the first two fingers; with the other hand hold the eye-piece up to the eye. The micrometer head is revolved by the first two fingers.

eter head standing as in Fig.

FIG. I.

1, the reading will be 32 from the scale and 65 from the micrometer head, or 3265. Standing as in Fig. 2, the reading is 1121. The micrometer head makes one complete revolution for each division of the scale on the face of the object-glass.

* Roger's Portable Micrometer-Telescope.-Gorringe.

To find the Zero Reading.

The zero reading is that shown by the scale and micrometer head when the two images of any object on which the telescope is directed exactly coincide, one only being seen. This is intended to be when the reading is 2000;

that is, when the scale marks 20 and the micrometer head stands at zero. To find the zero reading: direct the telescope to the sun; revolve the micrometer head in either direction until the upper and lower edges of the two images are in contact; read the scale and micrometer head and note the reading. Revolve the micrometer head in the opposite direction until the two images cross each other and their opposite edges are

in contact; read the scale and micrometer head and note the reading. The mean of these two readings (that is, half their sum) is the zero reading.

EXAMPLES. The reading greater than 2000 being 2528, and less than 2000 being 1482; then the zero reading is 2528 +1482

2005.

In another instrument the reading greater than 2000 may be 2527, and that less than 2000, 1473; then the 2527+1473 zero reading would be

= 2000.

2

2523+1471

2

In another instrument the readings may be 2523 and 1471; then the zero reading would be = 1997. In measuring angles, it is convenient to apply the difference between the zero reading and 2000 to all readings, calling it the index correction. If the zero reading is greater than 2000, the index correction is subtractive; if less than 2000, it is additive.

To find the Number of Micrometer Divisions.

The difference between the zero reading and scale reading, when the contact is made of the opposite edges or ends of any object, is the number of micrometer divisions. The index correction must always be applied to the scale reading if the zero reading is assumed to be 2000.

EXAMPLE. The scale reading is 2163, the index correction -5; then the required number of micrometer divisions is 2163-5 2000= 158. The scale reading is 1281, the index correction+3; then the required number of micrometer divisions is 2000 — 1281+3=716.

To find the Value in Seconds of Arc of each Micrometer Division.

Find in the Nautical Almanac the sun's semi-diameter for the day, and reduce it to the hour of observation. With the telescope bring the upper and lower limbs of the sun's images in contact on each side of the zero reading as many times as convenient, noting the readings. Take the mean of all the readings greater than the zero reading and the mean of all the readings less than the zero reading; half the difference between these means is the number of micrometer divisions in the sun's apparent diameter. The value in seconds of arc of each division is determined by dividing the sun's apparent diameter by the number of micrometer divisions. To find the sun's apparent diameter, subtract from the true diameter the difference of refraction for the difference of altitude between its upper and lower limbs.

EXAMPLE. September 1, 1876, sun's semi-diameter at Greenwich, apparent noon, 15' 53".86. Increase in twenty-four hours, o".23. Longitude, 5.13. Time of observation, noon. Altitude of sun's centre, 59°. Difference of refraction to 10 of altitude, when altitude is 59°, 0.23.

This value is approximately determined for each instrument, and engraved on it. the time and by the observer when very accurate results are desired.

It should be determined at

To Measure the Angle Subtended by a Vertical Object.

The instrument having been brought to focus and directed to the object, revolve the micrometer head in either direction until the upper and lower edges or ends of the two images are in contact. The relative distinctness of the two images may be varied by moving the eye from side to side across the eye-piece at right angles to the direction of the micrometer screw, and it will assist in making a good contact to rock the instrument gently in the hand, to the right and left, so as alternately to separate the images laterally and bring them together again. The observation being complete, read the scale, apply the index correction, and note the number of microme:er divisions, which, multiplied by the value of each division, gives the angle subtended by the object.

EXAMPLE. Scale reading, 2083; index correction, 5; value of each division, 3".65; 2083-5-2000=78, the required number of micrometer divisions; 78 x 3.65 284.7, the angle required.

It would be conducive to accuracy to take the mean of two observations, one greater, the other less, than the zero reading. The required number of divisions would then be half the difference between the two readings, and it would be unnecessary to apply the index correction.

To find the Distance of the Object Observed.

Find, as above, the angle subtended by the object; then, if h = its height, d = the distance required, and x= the angle observed:

I tan x'

A small table may be formed for each instrument containing values of with the micrometer readings as the argument. Multiply the tabular number by the height of the object observed; the result will be the distance required. The distances measured are to be counted from the object-glass.

BEAM COMPASSES.

Art. 414. Beam Compasses consist of an angular bar of wood or metal, upon which two instruments termed beam-heads are fitted in such a manner that the bar may slide easily through them. A clamping-screw attached to

For

one side of the beam-head will fix it in any part
of its course along the beam. Upon each head
a socket is constructed to carry a plain poir t,
exchangeable for an ink or a pencil point
exact purposes the beam-head placed at the end
of the beam has a fine adjustment, which moves
the point a short distance to correct any error in
the first rough setting of the instrument. This
adjustment generally consists of a milled-head
screw, which passes through a nut fixed upon the
end of the beam head, which it carries with its
motion.

PROPORTIONAL DIVIDERS.

Art. 415. Proportional Dividers are principally employed for reducing or enlarging drawings in any given proportion.

This instrument consists of two narrow, flat pieces of metal, each having a dovetail groove up the centre for the greater part of its length, and a steel point at each end. These two pieces are united by a pair of slides, fitted together upon one pin, and also fitted in the grooves so that they will slide along them; a milled-head screw clamps them together upon the pin, which forms the axis of the dividers. There is a stud on one of the sides, and a corresponding notch in the other, which bring the points over each other when the instrument is closed, and prevent any shift in the sides when moving the slides to set the instrument. The milled-head screw is sometimes fitted to move in a rack on the sides, affording a finer adjustment. On one side is the scale of lines and on the other the scale of circles. The scales are read off when the instrument is closed, by bringing the line upon the slide opposite the required division.

THREE-ARMED PROTRACTOR.*

Art. 416. The Station Pointer or Three-Armed Protractor is less known than the protractor or scale, though it is an instrument that no Navigator should be without. Its principal use in surveying is to plot the angles for soundings, but it is also used for fixing the ship's position, &c. It is a graduated circle with three arms; the centre arm is fixed, while with the other two the angles observed are laid off; and, when the edges of the arms pass through the three stations between which angles were measured, the centre marks the position of the observer at the time the angles were taken. Adjustable arms are provided which can be fitted to the end of the arms when signals are distant.

A piece of tracing paper may be made to answer the purpose. To use the tracing paper, draw a line, making a dot on it to represent the centre station, and with the centre of the protractor on the dot,

lay off the two observed angles right and left of the line; then, laying this on the plan, move it about till the three lines pass exactly through the three stations observed. The dot from which they were laid off will be on the position of the observer, and must be pricked lightly through or marked underneath in pencil.

* Marine Surveying.-MAYNE.

Art. 417. Definitions.-Surveying is the art of representing upon paper the surface of the earth, giving its characteristic features; of land, the position of prominent objects, heights and depressions, &c.; and of water,

the depth, character of bottom, position of shoals, &c.

Topographical Surveying deline ates the characteristic features of the

land, and Hydrographic Surveying of the water.

Geodesy is a higher kind of surveying, which takes into account the curvature of the earth. To points determined by such a survey other surveys are referred.

In this chapter the methods applicable to the use of such instruments as are generally supplied the Navigator will be given; also a general sketch of the methods of the U. S. Coast and Geodetic Survey.

Art. 418. The Geodetic Survey has for its object the determination, with the nearest approach to accuracy possible, of points on the surface of the earth by a process of triangulation, in which all the positions are determined trigonometrically and astronomically, and the differences caused by the curvature of the earth mathematically reconciled.

The measured base from which the triangulation commences is upon ground selected as affording the desired length, and as nearly level and free from obstructions as possible. The distance between the extremities is measured by a "Base-measuring Apparatus," consisting of compensated metallic rods. All precautions are taken to insure the nearest possible approach to the actual distance.

A reconnaissance sketch is made with a surveyor's compass, showing the relative positions of prominent points, from which are determined the points that are to be occupied as stations. At the points so selected signals are erected. Occupying each station in turn, the angles between all the other stations visible are observed. Observations with the transit instrument and zenith telescope are also taken for calculating the astronomical positions. Dip, variation, &c., are also determined.

The extremities of the base form two of these stations. The astronomical bearing of the base line, as also of some of the sides of the triangles, are determined.

At suitable points in the triangu lation check base lines are measured, which serve to detect errors in the calculated length of the various s des of the triangle; and then where the errors are small they are divided among the different triangles.

The elements of the various triangles are calculated, the trigonometric positions thus obtained corrected for the curvature of the earth, and reconciled with the positions as determined by the astronomical observations. The positions (or triangulation points) are then plotted upon the projection, according to their latitudes, longitudes, relative directions, and distances. From the Primary Triangulation a scheme of secondary and tertiary triangulation is made to determine suffi cient points for the Topographer and Hydrographer. In the determination of these intermediate points much less time is expended.

The Topographer starts with a plane table sheet on which are plotted all the triangulation points included in the area covered by the projection, which is on a scale suitable to the importance of the portion to be surveyed; and proceeds to delineate all the features of the land which the scale of his sheet will permit, using the plane-table

and telemeter.

The Hydrographer is furnished with a sheet which includes the water area to be surveyed, the coast line and adjacent features as determined by the topographer, and all triangulation points visible from the water. The