596.--_To take Cross Sections when the L_Surveying and Levelling Instruments, Theoretically and Practically Described. For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

operation is similar to that explained above for taking cross sections

when the line is straight, except that being on a curve a variation

of the tangential angle must be made at each peg or section. As this

is performed mechanically by a single movement of the angle repeater

and no reading of the angle is required, the work is just as readily

performed. To more clearly elucidate the method, we will take a case in

point and assume that the number of sections to be taken is 15 and that

the radius of the curve is 50 chains, which the accompanying diagram

illustrates.

Diagram (Fig. 261) showing the adjustment of the instrument for taking

sections on curves and the variation of the tangential angles for each

section.

[Illustration: Fig. 261.

If the centre pegs be taken as slope pegs, the diagram applies to

illustrate the setting out of half widths.]

Having set up the instrument at A, Fig. 261, over the centre peg of the

series in the manner before described, ascertain the tangential angle

for the first chain of the curve by dividing the constant, 1719, by

the radius of the curve in chains, which gives the angle in minutes or

1719 ÷ 50 = 34′ 24″, and set the angle repeater to give a movement of

double this angle or 1° 8′ 48″, ready for application at each change

of section.

Set the horizontal arc to the tangential angle for the seventh peg

from the instrument at which the first section has to be taken, or

34′ 24″ × 7 = 4° 0′ 48″, and direct the telescope to the peg. Zero

is now on the chord line AD, which is parallel to the tangent at the

seventh peg, and at an angle of 8° 1′ 36″, from the tangent line AB,

which divided by 7 gives the variation of the tangential angle at

each section, or 1° 8′ 48″, to which the angle repeater has been

set. Release the horizontal arc and bring it round to an angle of 90°

from zero, and the vertical arc will be at a right angle to the line

A D and parallel with the section line at the seventh peg. Release

the telescope from the arc and turn it at right angles thereto in the

direction of the zero line AD. Now, by working the back adjusting

screw of the tribrach, tilt the instrument until the cross web comes

somewhat above the seventh centre peg, then tilt the vertical arc until

the cross web is parallel with the lateral inclination of the ground

surface. Clamp the arc and note the angle thereon to determine the

inclination of the base to plot the sections from, and the instrument

is then in adjustment for taking the first section at the seventh peg

in the manner already described, being careful that the lateral bubble

on the instrument is in a perfectly level condition. To take the second

section at the sixth peg, one movement of the angle repeater must be

made and the lateral bubble adjusted, which operation must be repeated

for every succeeding section.

The movement of the angle repeater brings the vertical arc parallel

to the section line at each peg, and the adjustment of the bubble

maintains the angle of the inclined base uniform throughout.

When the sections are all taken on this side of the instrument, the

telescope is turned to the other side and the operation continued until

the whole fifteen are completed.

From the above detailed description it may be thought that the

adjustment of the instrument for the operation is somewhat complicated,

but in practice it is not so. After the first experience and the method

is understood, it is only a matter of two or three minutes, and once in

position the sections may be taken as rapidly as on level ground, and

the saving of labour is practically the same as in taking sections when

the line is straight.

597.--_To set out Half Widths or Slope Pegs when the Line is

straight._--In commencing this operation it is necessary in the first

instance to set out two or more half widths, according to the length

of the cutting or embankment. These may be a quarter of a mile apart,

or so far as a ranging rod may be clearly seen from one point to the

other. The pegs put in at these points act as normals from which to

"bone" or range in all intermediate pegs by sight simply, without

further recourse to levelling measurement or calculation. If the ground

surface be comparatively flat, these normals may be put in in the usual

way by using the instrument as a level, but if the surface is much

inclined and the slope deep, a simpler method may be adopted, which

will be hereafter explained.

[Illustration: Fig. 262.]

Assuming that the normals have been put in, set up the instrument at

any intermediate peg in such a position that the telescope when set

to the angle of the slope shall line with the top of the peg, as per

sketch, Fig. 262. Then release the telescope from the vertical arc and

direct it to one or other of the nearest normals, adjusting the cross

web to cut the top of the peg by turning the instrument on its axis.

Clamp in this position and the telescope will revolve in the plane of

the slope, and any point on the intermediate surface intersected by

the cross web is the outcrop of the slope and the position of the peg.

When all the pegs on the one side of the instrument are put in, turn

the telescope to the other side to cut the next normal and proceed in

the same manner. When all the pegs have been put in for this half mile

distance, the instrument may be moved to the next half mile normal

and the operation repeated, until the whole cutting or embankment is

completed, the last normal point being in all cases the formation width

at the ends.

In speaking of half-mile distances we are assuming the most favourable

conditions of surface and application of the method, but in practice

where the surface is undulating the positions of the normals should be

at the most elevated points from which a considerable range of sight

may be obtained.

In fixing the points for the slope pegs, a rod should be held in an

inclined position and be brought to line exactly with the cross web of

the telescope, the pegs should then be driven level with the ground

surface where the foot of the rod has rested.

598.--_To set out Slope Pegs when the Line is on a Curve._--The

operation is similar to that described above, except as explained for

taking cross sections on a curve. A variation of the tangential angle

must be made for each peg, and if the centre peg shown on the diagram

accompanying that explanation be taken as one of the slope pegs, it

will also serve the purpose of illustrating the present one, and a

brief recapitulation of the manipulation of the instrument to bring it

into adjustment for the operation is all that will be required.

The normal slope pegs having been set out and the instrument set up

at an intermediate one, as before explained, instead of directing the

telescope in the first instance to intersect one of the next normals,

set the angle repeater to double the tangential angle for the first

chain in the curve, and the horizontal arc to the tangential angle for

the distance in chains that the normal is from the instrument. Then

turn the telescope to cut the normal peg and clamp the lower limb. Now

bring the horizontal arc round to an angle of 90° from zero and clamp.

Release the telescope from the vertical arc and turn it at a right

angle thereto in the direction of the zero line AD, and by working

the back adjusting screw tilt the instrument until the cross web cuts

the normal peg again. Adjust the lateral bubble on the instrument to a

level condition and it is in adjustment for the operation.

To put in the first peg from the normal, make one movement of the angle

repeater and adjust the bubble. To put in the second one, make another

movement of the repeater and adjust the bubble, and so on until the

whole is completed. It will thus be seen that by a simple mechanical

operation a vast amount of work can be done in an incredibly short

space of time as compared with the levelling method, and that with

little or no effort on the part of the operator.

599.--_Alternative method of setting out the Normal Pegs._--Let the

diagram, Fig. 263, represent the section of a cutting at the point

opposite which the normal has to be set out, when the section depth may

be assumed to be 16 feet, the formation width 30 feet, and the slope

1½ to 1, or at an inclination of 56° 18′. The distance _bc_ for a

1½ to 1 slope is one-third the formation width, or 10 feet. The data

required for the operation is the distance _ad_ from the centre peg

to the plane of the slope, which is found by multiplying _ac_ by the

natural sine of the slope angle 56° 18′, thus: 26 × ·831 = 21·60 feet.

The operation when the line is straight is to set up the instrument

at a centre peg some distance away from the normal in the manner

previously described, _viz._, with the front legs set across the centre

line, the back leg on the centre line, and the bubble on the tribrach

set level before adjusting the instrument, which manipulation produces

a perfectly vertical tilt.

After adjustment, set the horizontal arc to zero and direct the

telescope to the centre line, clamp the lower limb, set the vertical

arc to the angle of the slope, and bring the horizontal arc round to

an angle of 90°, or a right angle to the centre line. Liberate the

telescope and direct it again to the centre line, and by working the

back adjusting screw tilt the instrument until the cross web intersects

the top of the centre peg at the normal. The telescope will now revolve

in the line _ag_ parallel with the plane of the slope and at a distance

of 21·60 feet from it. Therefore any point on the surface in the line

of the slope where 21·60 can be read on the staff is the outcrop of the

slope and the position of the peg.

In this example, when the required reading is higher than the ordinary

staff, lower the tilt and take an intermediate reading, as at _f_ in

the diagram, Fig. 263, which may read, say, 12·00, when the required

reading on the peg will be reduced to 9·60.

[Illustration: Fig. 263.]

In setting out normals on a curve by this method the only difference

in the operation to that above described is that instead of in the

first instance clamping the instrument with zero on the centre line,

it must be clamped with zero on the chord line, _i.e._, at double the

tangential angle for the distance the instrument is from the peg, as

before explained in detail for operations on curves.

By this method two normals may be set out at least 20 chains apart from

one setting of the instrument, or several slope pegs may be set out in

like manner, which under certain contingent difficulties of ground

surface is an advantage of considerable importance.

In this connection there is also an alternative method of putting

in the slope pegs after the normals have been set out, which, under

certain conditions, may be employed with advantage.

Instead of setting up the instrument at the back of the normal with

the telescope set to line with the plane of the slope, and to range

the pegs in by means of a rod or staff held at the inclination of the

slope, as before described, it may be set up in any position in the

line of slope where a reading can be taken on the peg, as at _a_ on the

sketch (Fig. 264), and at the point read, as at _b_, a disc should be

clamped to the staff, as this can be much more clearly seen than the

staff graduations when sighting long distances. The staff should then

be transferred to the next normal and held on the peg. If the telescope

be now turned in this direction and the cross web adjusted to cut the

disc, any point on the intermediate surface where the disc can be

intersected is the outcrop of the slope and position of the slope peg.

[Illustration: Fig. 264.]

It is necessary to observe in the setting out of slope pegs that when

there is a change of gradient the operation must cease, but if the

point where this occurs be made the position of a normal the operation

may be proceeded with, if the instrument be set up at this point.

600.--_To set out Slope Pegs on both sides of the Line simultaneously

without moving the Instrument from the Centre Line._--CONDITIONS.

Single Line. (_ab_) Formation 15 feet. (_cd_) Depth of cutting 14 feet.

Slope 1 to 1.

The point _e_, Fig. 265, is the extension of the slope lines to cut the

centre line, and its depths below formation for 1 to 1 slope is half

the formation width, or 7′ 6″.

[Illustration: Fig. 265.]

OPERATION.--The instrument being set over a centre peg with the

telescope at the slope angle, turn the telescope to any other peg

and adjust the cross web to line therewith (on line _c f_). Take the

section depth _cd_ (14 feet), to which add _de_ (7′ 6″) = 21′ 6″.

This multiplied by ·707, the natural sine of the slope angle (45°) will

give the distance from the axis of the instrument to the slope line,

thus: 21·50 × ·707 = 15·20 feet, and the point on the surface at _g_

where 15·20 can be read on the staff is the position of the slope peg.

This is similar to that described in the last paragraph, _but_ if the

telescope be now changed to the angle of the slope on the other side

of the line _ch_, the peg _i_ is instantly found by the same reading

(15·20).

601.--_The Use of the Inclinometer in Mining._--A lode having been

discovered, it is required to mark out on the ground the general line

of the outcrop. Hitherto the method employed has been to find the

strike and drift of the lode and to level and survey the surrounding

country and plot on a contour plan. Lines parallel to the strike and

spaced according to the trigonometrically calculated bases are ruled

in. The points of intersection of the contour line with that of the

parallel line to the strike of the same height above datum will be a

point of outcrop. The bearings of these points are read, and their

distances scaled from the plan, the theodolite is then taken to the

field, and the points found are marked out on the ground. This entails

a considerable amount of labour and careful work both in the field

and office, and then only points at intervals are obtained and not a

continuous line.

The inclinometer, having an adjustable axis at right angles to the

horizontal, enables the line of sight to be made to revolve in any

plane. If at the spot where the lode has been discovered the instrument

be set up in line with the strike, and the movable axis adjusted to

the angle of dip, it is evident the line of sight lies wholly in that

plane, and a continuous line of outcrop may be pegged out on a flat

or undulating country, which can be produced to any length required

by taking the instrument to a fresh station. This feature of the

instrument is equally, if not more, important than its use for rapidly

pegging out railway slopes.

602.--=The Gradiometer.=--This instrument, while performing all the

duties of a first-class level, is designed also for taking vertical

inclines at small fixed angles for railways, drainage works, steep

incline levelling, etc., etc., and also telemetrical readings up to

great distances.

In general construction, as regards telescope, stand, etc., it

resembles a level, and when set at zero is equal in every way to one of

the best, with the additional advantage that it may be used for rapid

work without the trouble of setting up by the levelling screws, as the

telescope may be levelled at any sight by means of the gradienter drum

milled head. The gradiometric arrangement is effected by the telescope

being mounted in trunnions, one pair being adjusted vertically; the

amount of elevation or depression is indicated by a drum carrying an

open extended scale graduated to read rise or fall, from 1 in 12 to 1

in 1,200, which may be conveniently and distinctly read without the use

of a vernier.

The additional parts do not increase the bulk of the case and add very

little to the weight.

[Illustration: Fig. 266.--_Stanley's gradiometer._]

By its use a great saving of work is effected. For instance, for a town

drainage in which it is desired to work out an inclination, say the

levels indicate a fall of 10 feet between the extreme points: if the

line the drainage is intended to take be measured, however angular or

zigzag it may be, and the length of that line be divided by the amount

of fall, this will give the gradient; say the line of streets measures

5,000 feet, this, divided by 10 feet, gives a gradient of 1 foot in

500. Therefore if the drum be set to that proportion, all the pipes may

be laid directly without further setting. The gradients for any railway

may be instantly found by merely turning the drum until the telescope

sights, up or down the incline to be measured, a reading on the staff

equal to the height of the instrument, and taking the reading of the

drum at the position of the indicator.

For levelling steep inclines it also saves a great number of settings

up, as, instead of levelling for, say every 14 feet rise or fall, the

gradient of the total distance can be taken and also the distance

measured by stadia reading, when the incline is not too great for

taking one reading with telescope level, or by gradient reading when

this cannot be done, and by adding the staff reading to the distance

divided by the gradient, and deducting the height of the instrument the

difference of level can at once be ascertained.

Example: Sighting a staff at a gradient which falls conveniently

upon it, say 1 in 35 and this reads 8·7 feet. Distance measured, as

explained later, say 735 feet, then 735/35 = 21 feet + 8·7 feet = 29·7

feet; deduct the height of instrument, say 4·9 feet, difference of

level 24·8 feet.

For measuring long distances beyond the range of the stadia lines or

points in the diaphragm, or for measuring distance on inclines, the

gradiometer will also be found very useful, as by taking the difference

of any two suitable gradients, the base distance is given without

calculation for difference of hypo and base.

If the gradient be not very steep or below the height of the staff,

the simplest method is to sight the staff with the telescope level and

take the staff reading; say this is 12·45 feet, then set the gradient

drum to 1 in 100 and again take the staff reading and, say this is 4·30

feet, the difference between these readings = 8·15 feet. Strike out the

decimal point which multiplies it by 100 and we have the base distance

815 feet.

For shorter distances a larger base upon the staff may be taken, thus

giving greater accuracy; for instance, if the gradient drum after

taking the level reading be set to 1 in 50 and the resulting difference

divided by 2, any error in taking exact readings is reduced by one

half, or 1 in 33-1/3 and divide difference by 3; or 1 in 25 and divide

difference by 4: or 1 in 20 and divide difference by 5, etc. Any error

of reading would be reduced by one third, one fourth, one fifth, etc.

The difference of readings obtained by either of the following two

gradients will also give base measurement without any calculation

whatever: 100 and 50 | 63-2/3 and 40 | 60 and 37½ | 50 and 33-1/3 |

33-1/3 and 25 | 25 and 20 | 20 and 16-2/3 | 12½ and 11-1/9 | 11-1/9

and 10.

Example: Suppose the top of staff is below level altogether,

turn the drum until the top of staff is sighted in the telescope;

say the gradient of this is 27½ go on turning until gradient 25

is indicated and take the staff reading; say this is 12·75, then

move the drum until gradient 20 is indicated and take the

staff reading: suppose this to be 3·40, then 12·75

- 3·40

------

= 9·35

Omit the decimal point and the measurement reads 935 feet, which is the

horizontal distance. The two most suitable gradients would of course be

used according to the position.

Distances may be set out with equal facility with the gradiometer

by the subtense method, by working out a subtense suitable for the

distance. This is easily done by dividing the distance required by any

two numbers having a difference of the required subtense, the result

being two gradients, which, when worked with, will give that subtense

at the required distance.

Example: If the distance required to be set out be 650 feet,

a suitable size for an object to be plainly visible at this distance

would be 10 feet. Then take as divisors two numbers

having a difference of 10, say 10 and 20.

650 ÷ 10 = 65

650 ÷ 20 = 32½

These two gradients will give a subtense of 10 feet at a distance

of 650 feet, and all that is necessary is to send a man out in the

required direction with a 10-feet rod (preferably having ⊤ ends, thus

⊢ ⊣, for long distances, to facilitate distinct reading), and signal

him to move farther off, or nearer until the length of the rod, held

vertically, is exactly covered by the movement of the telescope caused

by revolving the drum between gradients 65 and 32½.

[Illustration: Fig. 267.--_Stanley's gradioplane._]

It is always preferable to make the subtense as large as possible, as

the larger it is the more accurate the result will be. All distances

set out by this method are base distances, no matter what the

difference of level may be, and such figures for divisors should be

used as give the gradients below 100. Gradients between 12 and 65 are

the best and quickest to work with, and with care more accurate results

are obtained than with chaining.

Thus, at one time, a distance may be set out or measured, the

difference of level taken, and also the gradient ascertained, and the

drum can instantly be set to zero and all ordinary levelling operations

continued.

If preferred the gradient drum can be divided to percentage gradients

·001 to 8 instead of ordinary gradients 1 in 12 to 1 in 1,200.

603.--=Gradioplane.=--This is a new instrument, specially designed

by the reviser for very accurate underground surveying, such as is

required for large sewage work or water works, long tunnels, or any

work requiring a very rigid and accurate instrument, with a very

powerful telescope for measuring all horizontal and small vertical

angles.

The horizontal circle is 6 inches diameter, and reads by two verniers

to 20 seconds of arc, or it is fitted with micrometer microscopes

reading to five seconds of arc if desired.

In the former case it carries a floating bevelled aluminium ring

compass divided to ¼ degrees, reading by microscope, and in the

latter a long trough compass.

Vertical angles are measured by a very accurate form of gradiometer

screw carrying a drum with open extended scale in exactly the same

manner as the foregoing instrument, and the remarks regarding that and

its working apply equally to this instrument. The telescope, which is

14 inches long and carries a 1¾ inch object glass is so mounted that

it will revolve in the plane of any inclination set by the gradiometer

drum, and is provided with a locking arrangement for fixing it

absolutely true for fore or back sight, and it carries a long sensitive

spirit bubble to enable it to be used as a most accurate level and

for rapid levelling; this may instantly be set level by the drum at

any sight without troubling to level the instrument. The diaphragm is

fitted for subtense measurements.

A further refinement is fitted to the telescope when desired, by

which any grade may be instantly divided into any desired number of

parts; this is effected by means of a horizontal circle fitted to the

stage under the telescope, which is read by a vernier attached to the

telescope. This circle is divided from 0 when the telescope is fixed at

zero round each way to 90 degrees into 100 parts, the vernier divided

to read 100ths or 10ths of each division. It will be seen that when the

telescope is in line with the gradient drum, that is at zero, it will

be raised or depressed to whatever grade is indicated upon the drum,

and is then capable of being revolved 180 degrees for taking a back

sight, when it sights the opposite grade to that which it does when at

zero. When it has revolved 90 degrees only the telescope becomes level

at any grade, and therefore at any position it is set between zero and

90 degrees it sights a part of that grade; supposing the telescope

at zero is set by the gradienter drum at 1 = 1,000 then by revolving

the telescope from that to level, it passes over 100 parts of that

grade, each of which may be subdivided by the vernier to 100 parts

again, consequently 100 × 100 × 1,000 which equals 1 in 10,000,000

or any desired number of 10,000,000ths may be readily set by means

of the clamp and tangent fitted to the telescope, or if the grade be

set by the gradient drum to 1 = 100 then 100 × 100 × 100 equals 1 in

1,000,000, or any other grade which is set by the gradient drum may,

with equal ease, be divided by 10,000 or any other proportion that the

horizontal circle vernier may be divided to give.

A sliding lower plate is provided for accurately centring the

instrument, the levelling screws are adjustable for wear, and the

tribrach is fitted with quick-setting spherical joint.

This instrument will also be found of great utility in mining work,

to mark out the general line of the outcrop when a lode has been

discovered. This, by the ordinary method, entails a considerable amount

of labour and careful work both in the field and office, and then only

points at intervals are obtained, not a continuous line. With this

instrument the line of sight may be made to revolve in any plane, so

that if it be set up in line with the strike at the spot where the

lode has been discovered and the gradient drum adjusted to the angle

of dip, it is evident that the line of sight will be wholly in that

plane, and a continuous line of outcrop may be pegged out on a flat or

undulating country and can be produced to any length required by taking

the instrument to a fresh station.

[Illustration: Fig. 268.--_Stanley's gradioplane._]

The above illustration, Fig. 268, shows the gradioplane fitted with a

horizontal circle to the telescope for subdividing the grades of the

gradienter drum, and when thus fitted forms the most exact instrument

for setting out or ascertaining gradients that has been devised.

604.--=Abney's Clinometer.=--This very popular little instrument, the

invention of Captain Abney, Fig. 269, embraces the same form of sighted

level with reflector as that shown in section, Fig. 87, p. 142, but

the level instead of being fixed in line with the tube is placed above

it upon an axis which forms the centre of a divided arc. The axis with

the bubble is turned to any angle by means of a light milled-edged

wheel placed in front of the arc. It carries an index which reads

on the arc the angular position of the level to the centre of the

instrument by a vernier to 10′. There is also a scale placed upon the

arc giving gradients from 1 in 1 to 1 in 10. As the bubble of the level

in its course passes the centre over the axis its reflection is made

to become coincident with the sight line through the tube only when it

is quite level. Therefore whatever the inclination of the tube, the

bubble may be brought level by turning the milled head until it appears

centrally in the sight axis of the tube, and the angle at which this

occurs can be clearly read afterwards upon the arc. The size of the

instrument in its case is 5 by 2½ by 1½ inches; weight, 8 oz.

[Illustration: Fig. 269.--_Abney's clinometer._]

[Illustration: Fig. 270.--_Troughton's clinometer._]

605.--=Troughton's Abney's Clinometer.=--In the Troughton form, Fig.

270, the arc is toothed, and it is moved by a pinion similar to the

movement of the box sextant, so that the bubble moves slowly in

relation to the motion of the fingers when adjusting. The arc is read

by a single index line instead of by a vernier.

606.--=Telescopic Hand Clinometer.=--The author has recently added a

telescope to the Abney form of clinometer, as shown Fig. 271. The arc

is moved by rack and pinion and reads by a vernier to single minutes,

therefore good reading within one minute of arc may be made with it.

Captain East, R.E., suggested a mode of steadying the instrument for

observation which appears to answer admirably for hand observation. He

puts the hook-end of his walking-stick into his waistcoat pocket and

clutches a part of the stick by his right hand at the height of his

eye. Then holding the instrument in his right hand supported by the

stick it is kept quite steady for observation.

[Illustration: Fig. 271.--_Telescopic Abney clinometer._]

607.--=De Lisle's Reflecting Clinometer.=--There have been several

arrangements made for converting the Burel level, Fig. 89, into

a clinometer; that devised by General A. De Lisle, R.E., with

modifications by Colonel Bell and Mr. Alfred Cooke, as represented in

Fig. 272, is the most popular. In this a heavy arc is constructed upon

the lower part of the instrument. This is jointed upon a vertical axis

at _C_ so that it may be revolved to bring the mass of the arc either

forward or backward, to take inclines upwards or downwards, or to rest

at an intermediate position to make the instrument flat and portable

in its case, it takes the position shown in the figure. The arc has a

stiff centre axis with a radial bar, the edge of which forms the index.

A sliding weight is placed on the radial bar, which is sufficiently

heavy when at its greatest extension to exactly counterbalance the

weight of the arc in a horizontal position and to make the mirror quite

vertical. In this position it forms a simple Burel level. A set of

graduations are made upon the arc, which are numbered 1 to 50 to 1 to

1. The radial bar index set to one of these numbers gives the amount of

inclination that will result from the coincidence of the reflection of

the centre of the pupil of the eye cutting the object to be observed.

The length of this instrument is about 6 inches; its weight about 10 oz.

[Illustration: Fig. 272.--_De Lisle's reflecting clinometer._]

608.--=Prismatic Clinometer.=--This instrument was originally devised

by the author about 1860. The form of the instrument, Fig. 273, is that

of a prismatic compass, art. 155. A similar metal or card and talc dial

to that of the prismatic is used, but this is centred upon a transverse

axis which is pointed at the ends to fit into hollow centres. This

card is weighted on one side, so that when the sights are in a truly

horizontal position the prism will show the zero of the card cutting

the sight line. If the instrument be inclined upwards or downwards,

the degrees of elevation or depression will be indicated by the card

retaining its pendulous position. This is a very convenient instrument

for use with the box sextant, and as it is only of about half an inch

in thickness, and of the same diameter, it will pack conveniently in

the case with that instrument--weight, 8 oz.

[Illustration: Fig. 273.--_Stanley's prismatic clinometer._]

[Illustration: Fig. 274.--_Barker's clinometer._]

_In Using this Form of Clinometer_ the prism is raised or lowered

in its sliding fitting until the divisions of the card are sharply

defined. Then in looking over the edge of the prism through the slot

above it, the hair in the window of the back sight will appear to cut

the divisions of the card; and the object seen in the distance, in

front of the hair to which the instrument is directed, will appear

coincident with the number of degrees of inclination indicated by the

card.

This clinometer is sometimes fitted upon a prismatic compass, so that

inclines may be read by the same prism and sight arrangement. This is,

however, done more neatly by the arrangement next described, if the

instrument is intended to be used with the prismatic compass only, and

is not wanted separately for use with the chain.

609.--=Barker's Combined Prismatic Compass and Clinometer=,[36] Fig.

274.--The prismatic compass of this arrangement is that of Hutchison's

form, art. 155. The clinometer is of the same kind as that just

described, but this, instead of being a separate part of the instrument

capable of detachment, remains permanent. To effect this arrangement

the clinometer card is mounted over the compass card on a pin axis

instead of centres. A part of the clinometer card is cut away so as

to permit the compass card to be read beneath. This cut-away part

is held by a stop to a position out of the field of the prism when

the instrument is to be used as a prismatic compass. When the stop

is released and the instrument is held with its face vertical, the

pendulous clinometer card comes into view, and cuts by its reading

through the prism the sight line, as before described for the prismatic

clinometer. The prism is focussed to the upper or lower dial by a long,

sliding fitting. It is used as the instrument last described.

[Illustration: Fig. 275.--_Continental form of clinometer (Burnier)._]

[Illustration: Fig. 276.--_Section of the same._]

610.--=Continental Form of Clinometer.=--Hand clinometers on the

Continent are generally made on Captain Burnier's plan, Fig. 275,

which was explained for the prismatic compass, art. 156. Indeed this

instrument is more generally combined with the prismatic compass. The

graduation is set up on a plated ring vertical to the plane of the

swing of a pendulum, shown in section Fig. 276. The reading index is a

hair which is read on the graduation by means of a cylindrical lens,

_B_, when this is brought coincident with the sights _D′W′_ as described

for Burnier's compass. When the clinometer and compass are combined

the vertical rims stand opposite to each other, _AC_. A lifter, Fig.

275, _L_, is provided to take the working parts out of bearing, and a

stop _S′_ to prevent oscillation. The illustrations show the combined

instrument: _B_ cylindrical lens reading the drums; _A_ clinometer; _C_

compass; _DD′_ fore sight; _WW′_ windows, both of which fold down on

the top of the instrument.

[Illustration: Fig. 277.--_Major Watkins clinometer._]

611.--Major Watkins' Clinometer.[37]--The vertical plane of division

is adopted, as in that of Captain Burnier, but the reading, instead of

being taken on the exterior of the ring by a magnifier, which entails

a projection, is placed on its interior. This reading is magnified

by a concave reflector, shown Fig. 277 at _R_, which reads to a line

on a slip of ivory placed just beside the eye-hole _E_ shown in the

engraving. The pendulum is stopped by a pin, upon which it springs when

the box is rotated vertically to prevent wear when out of use. There

is much less work in making this instrument than Burnier's, and the

round form is more portable. The only point on which it does not bear

comparison is in that the concave mirror represents a uniform distance

sight which makes the reading indistinct to persons of weak sight,

whereas Burnier's admits of adjustment by placing the instrument nearer

to or further from the eye, the cylindrical lens being made large to

admit of this form of adjustment. This instrument could be improved by

the mirror being made adjustable. Weight, 6 oz.

[Illustration: Fig. 278.--_Compass with clinometer sight._]

612.--=Clinometer Sights.=--A clinometer sight is often attached to

a light pocket compass, as shown Fig. 278 at the upper part of the

engraving, consisting of a pin hole and hair cross. This, used in the

manner shown by the position of the eye in the engraving, can only be

made to take sight inclines by another person reading the pendulum

index, which marks the inclination in the degrees to which the compass

is divided. This portable pocket instrument is, however, useful in

other ways. Standing face to the instrument it will measure inclines

directly very fairly by looking over the top edge and bringing this to

the visual rate of inclination at which the pendulum index can be read

in front view. Geologists commonly use it in this way to take the dip

of strata. It can also be used by putting it on or against any inclined

surface. The case is generally gilt or nickel plated, and is about 2

inches diameter, and the instrument weighs about 3 oz.

[Illustration: Fig. 279.--_Rule form clinometer._]

613.--=Rule Form Clinometer.=--This is made in the form of a stout

12-inch, one-fold boxwood rule, Fig. 279. It is much used by civil

engineers as a working tool, and intended to be applied directly to

an inclined surface, either placed on a straight-edge or otherwise,

generally to take the inclination of earth work. It may be placed upon

a picket laid upon the ground to take natural slope. When used in this

manner the lower surface is placed on the straight-edge or picket, and

the rule is slowly opened until the bubble in the level in the upper

limb becomes central. The arc of the head joint will then indicate

the inclination. It may be used in another way: the lower limb may be

set level on the dumpy level compass or on any flat plane, and the

inclination may be sighted through the pin-hole and cross-hair sights

shown at the ends of the upper part of the instrument. Its size is

6¾ by 1¾ by ½ inches; weight 9 oz. There are several varieties

of this instrument.

[Illustration: Fig. 280.--_Road tracer._]

614.--=The Road Tracer= is a balanced clinometer much used by natives

in India and China for road making, Fig. 280. It consists of a

pendulum, supported upon a stand that carries a sighted tube which

indicates the level of the ground when the weight is carried in the

axis of suspension. The weight is adjustable to a scale by a screw. The

scales read inclines, by displacement of the weight, up and down in

percentages or gradients, to which it may be divided.

[Illustration: Fig. 281.--_Bellamy's road tracer._]

This instrument has been improved by Mr. C. V. Bellamy, M.I.C.E.,

M.I.M.E., F.G.S., &c., Director of Public Works, Lagos, West Africa,

a civil engineer who has had great experience in the colonies, and it

will be found much more accurate, less liable to get out of order and

far more convenient to use than the old forms. It is shown at Fig. 281.

The chief feature of this pattern lies in the adoption of the arc of a

circle instead of a straight scale, and a pendulum weight actuated by

a rack and pinion in place of the screw and sliding weight. This admits

of greater nicety in the divisions and allows a stronger and lighter

construction.

The sighting tube is provided with reversible sliding shutters, so

that back readings may be taken without unclamping the instrument or

altering the vernier or index. A powerful clamp is provided for locking

at any desired grade.

A recent further improvement by Mr. Bellamy has been made by making

this instrument in a form to give readings in degrees of arc as well as

in gradients. Fig. 282.

[Illustration: Fig. 282.--_Bellamy's improved road tracer._]

FOOTNOTES:

[35] Lister's Patent, No. 2375, 1864.

[36] Francis Barker's patent, No. 1926, 1881.

[37] British patent, No. 217, 1884.

CHAPTER XIV.

INSTRUMENTS OF REFLECTION--OCTANT OR QUADRANT--REFLECTING

CIRCLE--SEXTANT--PRINCIPLE--PARALLAX--CONSTRUCTION--EXAMINATION--

ADJUSTMENT--ARTIFICIAL HORIZON--SOUNDING SEXTANT--BOX SEXTANT--

SUPPLEMENTARY ARC--IMPROVEMENTS UPON THIS--OPTICAL SQUARE--OPTICAL

CROSS--APOMECOMETER.

615.--=The Octant or Quadrant= measures angles within 90° by an arc of

45°. This instrument is generally termed an _octant_ on the Continent

from the space of the divisions; a quadrant by English-speaking races,

from the extent of angles it takes. The idea of bringing the reflection

of an object from a mirror in line with the direct sight line from

another object, to measure the angle at the position of the observer

subtended by the two objects, was originally proposed and worked out

in a manner by Hooke,[38] and also by Newton.[39] Newton's invention

was the more simple and important. This was communicated to Dr. Halley,

then Astronomer Royal, but it was left unpublished until after his

death, when it was found in Newton's own handwriting among Dr. Halley's

papers.

Newton employed two mirrors to obtain the reflection of an object

placed at any angle of less than 90° to the axis of the telescope or

sight tube, to throw an image directly through the tube. One of these

mirrors was placed at an angle of 45° to the axis of the telescope and

covered half its field aperture, so that a direct image of an object

could be received by the eye from the open uncovered part of the

telescope at the same time as the reflected image of another object

from the mirror. The second mirror was placed so as to throw its

reflection into the mirror on the end of the telescope without giving

any obstruction to the open aperture. This side mirror was fixed with

the centre of its plane over the axis of a movable arm which read upon

an arc the amount of its angular displacement to 90°. The mirrors were

so arranged that their faces should be parallel to each other when the

movable arm was placed at the zero of the arc. The graduation of the

arc was of double the closeness of the ordinary arc reading, so that

the angular positions of the two mirrors in relation to each other was

indicated according to the following law:--

_That the angle between two reflections in the same plane is equal to

twice the inclination of the reflecting surfaces to each other._

616.--=Hadley's Quadrant.=--In Newton's quadrant the arc was brought

most inconveniently in front of the face. By Hadley's arrangement the

telescope or sight line is brought in a direction about parallel with

the chord of the arc, producing the very convenient form of instrument

now in use. This instrument was exhibited at the Royal Society,

13th May, 1731.[40] It was tried experimentally by the Astronomer

Royal, August, 1732, in a yacht excursion, when readings were taken

satisfactorily within a minute of arc.[41] It afterwards came into

general use.

The quadrant was at first held to be sufficient for measuring the sun's

altitude for obtaining latitude, but Hadley, as early as 1731, saw the

advantage of extending the arc so as to be able to observe the

opposite horizon if the direct one was obscured. It was also found

that measuring the moon's angular distance from a star beyond 90°

was serviceable in determining longitude. He therefore proposed by a

duplicate system of reflections to extend the arc by what is termed

a _back sight_ to 220°. The means he suggested, which were commonly

carried out in instruments of the period, were found to be too

complicated for practice.[42] In the meantime the construction of these

instruments, originally framed of a combination of wood, ivory, and

metal, was much improved by making the frame entirely of metal. There

were also great improvements made in the optical parts, by which the

arc of 90° was extended. In 1757 Captain Campbell had an instrument

constructed of metal of 60° of arc which therefore read to 120°. This

instrument, with details of improvement, principally by Ramsden,[43]

became the modern sextant.

617.--=Reflecting Circle.=--As soon as the success of the sextant was

assured there appeared to be a general desire to complete the circle

by reflections, many inventors thinking this would possess great

advantages over the arc of 120°, and we find therefore no lack of

inventions to this end, even by eminent men. _Reflecting circles_, as

they are termed, that were of sufficient merit to come into limited

use, were designed by Mayer, 1770; Borda, 1787; Mendoza, 1801; Hassler,

1824; Fayrer, 1830. Troughton's circle of about this period was no

doubt the best instrument of the class.[44] We have also meritorious

reflecting circles by Pistor and Martins, and by Amici.[45] Although

these instruments were used at sea to a limited extent, particularly on

foreign ships, they were also used on land, where indeed they were more

manageable. As no further reference to these reflecting circles will

be given, anyone interested in the matter may refer to the books

mentioned in the notes, where very full particulars of their structure

are given. It was felt necessary to mention the subject here, as the

same ideas are constantly cropping up as assumed advantages where

previous experience is forgotten. Reflecting instruments at sea are

tedious to use when the angle to be taken exceeds that taken in by

the eye without movement of the whole body. On land, when the angle

exceeds 120°, a theodolite is better; but supplementary angles may be

taken with the sextant conveniently on land, where the portability of

the instrument is of great consideration. This will be again brought

forward in discussing box sextants with supplementary arc.

618.--=The Sextant=, of the invention of which some particulars have

just been given, is only used as a surveying instrument for the

exploration of new countries, for which employment--it may be used with

or without a tripod or stand--it is found to be a most convenient,

light, and portable instrument for the traveller for ascertaining

longitude, latitude, and time with the aid only of an artificial

horizon. Triangulation may also be taken with it of terrestrial

objects, even for the complete circle, by repetitions from station to

station in angles within 120°. The same principles which are followed

in the construction of the nautical sextant are followed also in the

manufacture of two modified forms of this sextant which are used for

surveying only, the _sounding sextant_ and the _box sextant_. As the

nautical sextant is most open to observation of its parts it will be

more convenient to discuss the construction and general arrangements of

this instrument first.

619.--_Optical Arrangements of the Sextant._--Newton in the description

of his instrument placed the mirrors parallel to each other, that

is, to zero of the arc, in his illustration for the demonstration of

the principle. In this position he showed that the direction of the

reflected ray is coincident with the direct ray entering the eye from

the same object or star. This scheme the author has generally found the

clearest for illustrating the principle to persons not well acquainted

with optics, there being some difficulty in explaining the law just

given, art. 615, from a more complicated scheme.

[Illustration: Fig. 283.--_Reflection in direct line from two plain

mirrors._]

620.--_If two mirrors be placed with their faces parallel to each other

in such a manner that a ray of light may continue after two reflections

from them, the ray will continue its path parallel in its direction to

its incidence upon the first mirror._

Let _MM′_, Fig. 283, be two mirrors placed with their faces opposite

and parallel to each other. Let the incident ray _IM_ fall on the

mirror _M_ whose normal is _a_. Then, as the angles of incidence and

reflection are equal, art. 54, it will be reflected at equal and

opposite angle to the normal to _M′_. Let the normal of _M′_ be _a′_.

Then again, the incident line _MM′_ will be reflected at equal angles

to the normal to _D′_, that is, as shown by the diagram, it will

continue parallel with the incident ray and in such a position that an

object at _P_ would appear to the eye, placed at _D′_, as though it

were at _P′_ in the direct line of sight.

621.--_Parallax._--It will be seen by the figure that the point _P_

does not appear to the eye at _D′_ in its true position but at _P′_

therefore with the mirrors _MM′_ quite parallel, the points _P_ and

_P′_ appear coincident, and would read as one point with the index of

the sextant set at zero, that is, at the position when the mirrors

are parallel to each other; whereas the points _P_ and _P′_ really

subtend a small angle if direct lines be drawn from them to _D′_. It is

therefore clear that the angle read by coincident reflection and direct

or, as it is sometimes called, visual image is less than the true angle

at about the position shown. This difference is called the _error

of parallax_. When the object is distant this error is immeasurably

small. The parallax error varies proportionately to the distance of

the mirrors apart and with their angular position. If the mirrors are

in such an angular position that the rays proceeding from an object

impinging upon the centre of the first mirror would, if continued,

reach the eye, there would be no error of parallax. This occurs in the

nautical sextant at about 60°, and the parallax error increases on

either side of this point.

622.--In the practice of surveying this small error is neglected.

When the box sextant is used the mirrors are placed at a very small

distance apart, and the parallax error therefore is extremely small

even for near objects. Where two objects are to be triangulated, the

one near and the other distant, the parallax error is much decreased or

eliminated by taking the near object by direct vision, and the distant

object by reflection. In this case, if the near object be towards

the right hand, the sextant must be used in an inverted position. If

the two objects be both near, a distant object may be sighted in the

direction of one of them for the reflected image.

623.--It is readily seen that if the parallelism of the glasses shown

in the figure be disturbed, say by a change in the relative angular

position of _M′_ so that the planes _M_ and _M′_ continued to subtend

an angle to each other, then the normal of _M′_ must also be changed in

direction equal to this; but the ray _MM′_ remaining constant, as there

is no movement of _M_, this ray will therefore be displaced in its

reflection from _M′_ an amount equal to the angle of incidence on _M′_

from its normal, plus the angle of reflection from the opposite side

of the normal, that is, to double the amount of angular change of the

position of the mirror or of its normal, which is the same thing. The

sextant therefore reads, by change of position of one of its mirrors,

half the angle of reflection upon its arc; and to make it read to the

angular value of its reflection the divisions on the arc are made twice

as close, that is, half degrees are made to read as degrees. This will

be better explained by the following scheme.--

[Illustration: Fig. 284.--_Principles of reflection of the sextant._]

624.--The above scheme, Fig. 284, is taken from Captain Magnaghi's

admirable work before mentioned, which gives a very clear geometrical

demonstration of the value of angular positions in compound reflection.

A ray of light _SR_ directed to a plane mirror _R_ is reflected

therefrom to a plane mirror _R′_, following a plane of reflection

perpendicular to the intersection of the two mirrors. The direction

_R′T_ of the ray reflected by the second mirror falls into the same

plane of reflection, and makes with the direction _SA_ of the incident

ray an angle double that which is comprised between the two mirrors.

The two planes of reflection _SAB_ and _ABT_ unite in one because they

both contain the line _AB_ and the normal _BP_ to the mirror _R′_.

In prolonging the normals of the mirrors to their point of intersection

_P_ we find that--

_BTS_ = _BAS_ - _ABT_;

but as ½ _BAS_ - ½ _ABT_ = _BPA_ = _BDA_,

therefore _BTS_ = 2 _BDA_.

625.--The mirrors being placed in the position shown in the figure, if

we look through a telescope whose visual axis is placed in the line

_ET_, with its objective to the mirror _R′_, we see in the centre of

the field of view the image of the object _S_ reflected consecutively

by the mirrors _R_ and _R′_. We also see in the telescope whether the

mirror _R′_ is only a certain height above the plane of reflection, so

as to permit half of the object-glass to receive the rays coming from

the point _E_ situated in the prolongation of the line _TB_, also the

image of _E_ which is necessarily coincident with that of _S_, because

the rays by which each image is formed enter the telescope in the same

direction _BT_. Therefore when the images of the two objects _E_ and

_S_ appear superimposed or coincident in the middle of the field of

view, we have an index given that the mirrors form an angle with each

other which is half that which is made at the point _T_ from the same

objects, and when one is known the other is easily deduced.

626.--=Nautical Sextant.=--The ordinary construction of this

instrument, Fig. 285, consists of a cast gun-metal frame, forming

approximately in outline a segment of a circular disc _AA″_ including

within its extreme radii about 155°.

[Illustration: Fig. 285.--_Nautical or astronomical sextant._]

627.--_The Limb G_, which is made only about 1/12 inch in thickness,

has generally a face of about ¾ inch in width, which is inlaid with

silver or platinum, as Fig. 127, p. 186, to take the graduation to

about 140°. The limb is stiffened by a deep, thin rib about ½ inch

wide, supported by a corner hollow. The exterior radial arms and

interspace framing, Fig. 285 _MM_, which vary very much in design

according to the taste of the maker, is made generally of about 1/14 of

an inch in width upon the face of the bars, with a depth of 3/8 inch.

This arrangement of the bars placed edgewise gives great stiffness

to the surface of the arc with little weight. A handle _L_, made

generally of ebony, is supported on two standards or _brace-pieces_

_N_, which are carried off to about 2 inches from the back of the frame

to hold the handle parallel with the face. The handle has sometimes

a hole bushed through it with metal, to support the sextant upon a

corresponding pin forming part of a stand or tripod when the instrument

is used for taking observations on land. Three feet are placed at the

corners of the frame of the sextant, one shown at _Q_, to support it

conveniently on a table to take the reading of an observation just made.

628.--At the centre of the arc a female axis of about 1½ inches in

depth _E_ is attached by three screws to the frame perpendicular to

the plane of graduation. This carries the male axis, which centres the

vernier on the vernier arm _M_. The axis is covered by a protecting

tube which forms one of the three feet upon which the instrument rests

when laid down. The vernier arm is made of gun-metal of about 1/16 inch

in thickness and from 1 inch diminishing to ¾ inch in width. This is

stiffened by a light rib on its upper side.

629.--_The Vernier V_ reads upon an 8-inch sextant, that is, one of

eight inches radius, to 10″, the graduations being to 20′ and the

vernier taking 120 divisions. A description of the vernier reading was

given, art. 318. The vernier falls upon the arc on the plan shown Fig.

127, p. 186. It is clamped near to position by the milled-headed screw

_H_, and is adjusted by the tangent _I_. A magnifier _J_ is placed on a

jointed sling-piece _K_ which traverses the vernier. This is sometimes

provided with a ground glass shade to dull the silver for reading. The

sling-piece moves the magnifier opposite to any division of the vernier.

630.--Over the axis of the vernier arm a large, oblong mirror, termed

the _index glass_, _A_, is fixed with its face in a plane cutting the

centre of the axis. _The index glass_ is placed with its longest sides

approximately in line with the vernier arm. This mirror is placed in a

metal tray and is sometimes made adjustable by three screws; but it is

better fixed by the maker by screwing the flange-piece, which forms one

end of the tray, hard down. The index glass moves with the index arm

and gives the first reflection of sun, moon, or star which falls thence

upon the _horizon glass B_.

631.--_The Horizon Glass B_ is placed upon a spur-piece formed in

the same casting as the frame. This glass, which is worked perfectly

parallel, has the lower half of its surface next the frame silvered.

The silver is cut to a sharp line against the plain part. The horizon

glass placed in its metal tray has adjustments given to it by means of

capstan-headed screws in a manner that will be presently described.

632.--_The Telescope_ screws into a ring fitted at _R_, which stands

upon a bar erect from near the edge of the frame. The female screw

by which the telescope is held is formed of two rings which adjust

for the amount and direction of separation, so that the telescope may

be directed coincident with the horizon glass. The bar or standard

supports the ring fitting and is made of either square or triangular

section, fitted accurately in a deep socket fitting, in which it slides

to raise or lower the ring by means of a milled-headed screw placed on

the end of the bar. This permits adjustment only sufficient to bring

the axis of the telescope opposite the line of division between the

plain and silvered parts of the horizon glass.

633.--_Four Circular Shades_, carried in square frames fitted with

dark bluish-grey glasses, are jointed to the frame at _C_. These have

nib-pieces at the upper corners, so that one or more of the shades may

be turned up at a time by the finger-nail to intercept any surplus

amount of light from a luminous body reflected from the index-glass;

or the whole of the shades may be turned up when observation is made

of the mid-day sun. Three other similar shades, but placed in circular

frames are fixed at _D_, which hinge over and back, to be thrown in or

out of interception, and are used to subdue the light from the horizon

if required.

634.--_The Telescopes_ used as a part of the sextant are generally

two in number. One for _direct vision_ is a short tube of about 3

inches in length, focussing at about 4 inches. The optical arrangement

is the same as that of an opera glass, consisting of an achromatic

object-glass of about 4 inches focus and a concave eye-glass of about 2

inches negative focus, Fig. 14. The second telescope is about 7 inches

to 8 inches in length. This has two Huygenian eye-pieces, which have

each a wired diaphragm at the mutual focus of the eye-piece and the

object-glass. One of these has two fine wires placed parallel for use

in adjusting the telescope, and the other has two pairs of crossed

wires to indicate the centre of the field of view. There is also a

plain pin-hole sight provided for open vision.

635.--_The Case_ in which the instrument is packed is generally made

of well-seasoned mahogany, dovetailed together at its corners. The

fittings are made to put the instrument back in its case as it was

last used within a wide range. A tommy-pin for adjustments and a hand

magnifier are supplied with the instrument. The case is generally

French polished inside as well as out to prevent absorption of moisture

from sea air.

636.--_Manufacture and Examination of the Nautical Sextant._--Besides

the general good work that this instrument demands, the important

points to be observed are, that the glasses should be of hard crown

glass worked perfectly parallel from face to face; they should also be

well polished. These observations apply to both the reflecting glasses

and the shades. The silvering of the mirror should be protected with

a good coating of copal varnish. The mirrors should be held by three

points only, and be quite free from strain. The upper of the three

points should detach, so as to be able to remove the glass at any time

for resilvering. The axis should be fitted with all the care necessary

for a theodolite, and be placed truly central to the arc. The extremity

of the vernier arm when free of its clamp should traverse the arc at

equal distance from its face and move with very light friction. The

extreme lines of the vernier should cut equal divisions all along the

arc 0° to 140°, observations being taken particularly at both ends and

in the centre of the arc. The vernier should lie flat on the limb from

end to end of the arc. The standard or stem-piece for elevating the

telescope should move upwards and downwards stiffly but equally by the

motion of its milled-headed screw. The division lines of the limb and

vernier should be cut fine but very deep: they should be cut on the

dividing engine from the axis of the sextant to ensure true centring of

the arc, and not as in the usual plan of having the axis adjusted to

the divisions.

[Illustration: Fig. 286.--_Section of axis and index glass of sextant._]

[Illustration: Fig. 287.--_Section of limb and clamp and tangent._]

637.--_Axis._--This is the most important part of the instrument,

and requires the greatest care in construction. Fig. 286 represents

this to a scale half size. _a_ the axis, made of hard gun-metal, has a

collar by which it is attached to the index arm. The axis is ground and

burnished carefully into _S_ the socket-piece, which is fitted into the

frame and held down by three screws. At the end of the socket there is

a collar-piece _B_ attached upon an angular or tight conical fitting by

the screw _D_, which prevents the axis rising out of its socket. The

axis is covered by a cap _L_ which protects it from injury, and this

at the same time forms a leg to the instrument as before mentioned.

The index glass _I_ is mounted in a tray _T_ shown in section. There

are two points of contact at the lower part of the back of this glass,

formed by pins, and one point of adjustment pressing against the clip

_G_ by a spring _C_ in front, acting _contra_ to a screw at the back

_E_, which adjusts only a small distance to bring the index glass to

perpendicularity. The flange-piece _F_ is adjusted in the manufacture

so as to leave very small separate adjusting to the index glass

necessary.

638.--_Section of the Limb and Clamp and Tangent._--The general

arrangement is shown in Fig. 287. _M_ arms of the frame; _J_ section of

the limb; _C_ clamp attached to the tangent _N_ for clamp and tangent

motion, described art. 346; _O_ milled head to clamp; _N_ milled head

to tangent. The vernier is shown at _V_, reading through an opening on

the face of the index arm _P_. The rib to stiffen this arm is shown at

_R_.

[Illustration: Fig. 288.--_Vertical section of horizon glass._]

[Illustration: Fig. 289.--_Plan of section A to B._]

639.--_The Adjustment Arrangement of the Horizon Glass._--This most

important adjustment is constructed in various ways. The plan now

generally thought to be the best is for the maker to fix the horizon

glass frame firmly in its true position perfectly perpendicular to

the surface of the frame, and to allow a small amount of adjustment

to the glass only. A convenient plan of doing this is shown in the

vertical section full size in Fig. 288. The frame _FF_ is made in one

casting, which has its base collar firmly fixed to the frame of the

sextant. Fig. 289 is a cross section _A_ to _B_. _H_ the horizon glass

is held upon its face by three points, one of which is shown at _L_,

which is placed in the centre of the top. The lower front points are

the exterior corners of a plate which is cut away between. This plate

is held by the screw _G_. The screw _G_ forms a kind of hinge which,

together with the elasticity of the plate, gives a slight pressure

directing the glass hard upon the points of the screws _J_ and _Q_.

The screw _J_ resists this pressure lightly and permits adjustment of

the horizon glass _H_ to angular position in relation to the plane of

the index glass to a small extent, by means of a pin placed in the

capstan head _J_. The perpendicular position of the horizon glass, _H_,

is secured by slight adjustment of the capstan head _K_, which moves

against a spring _L_ in the vertical centre of the top of _H_. This

piece, with screw and spring, is attached to the horizon glass frame

_FF′_ by the screw M, so that it may be easily removed to replace or

resilver the glass. The silver on the glass is cut to a sharp line at

about the point _H_ with a razor.

640.--_Testing the Parallelism of the Surfaces of the Glasses._--The

best method is to firmly fix a telescope provided with webbed or

pointed index diaphragm so that the webs or points cut a distant,

sharply defined object, or its edge only, quite clearly. If the glass

to be tested be now placed in four directions agreeing with its four

sides in front of the object-glass of the telescope, and it is worked

perfectly parallel, and is free from striæ, the distant object will

not appear to be displaced by its presence in the slightest degree at

any position. If the glass be not mounted and is quite square, should

there be any very small error, the thickest or thinnest edge should be

placed towards the frame; but in this case only a very small error is

permissible. The coloured glasses require the same test as the white

ones. Where the parallel glass to be tested is small, the object-glass

of the telescope may be covered by a paper cap, with a small hole only

left through its centre, sufficient to take the glass.

641.--The glasses, when fixed in the sextant, may be examined for

parallelism approximately by setting them end up singly to the sun,

with the sextant set at an angle that the direct and reflected

images of the sun's limb appear just to touch, the eye-piece of the

telescope being constantly covered by the sun-glass. If there be a

want of parallelism, the image will be disturbed. One reason that

the telescopic plan first proposed is better to be followed in the

construction of the instrument, is that the telescope is fixed and that

there is no indistinctness from unavoidable motion of the body, such as

occurs when the sextant is held in the hand.

642.--_The Quality of the Surfaces of the Glasses_ may be examined,

both for flatness and brightness and for equality of density, by

holding them so that the reflected image of a straight body, as for

instance a stretched thin string placed at a distance, may be observed

by reflection in glancing over the surfaces with the eye nearly

parallel with its plane. If the glass be imperfect the image that

reaches the eye will appear to be wavy. If the reflection appear misty,

this is generally due to want of parallelism of the glass; but this

mode of observation is altogether somewhat technical and difficult to

attain without skill.

643.--_To Silver the Index or Horizon Glass with Mercury._--Clean the

glass thoroughly by boiling it in water containing an alkali (potash

or soda), and then polish it off with whiting and water, using a clean

piece of old linen or perfectly clean wash-leather. Do not touch the

surface with the fingers. Take a piece of clean tin-foil freshly opened

from the roll and cut out a piece slightly larger than the glass to

be silvered. Lay this upon a smooth pad--an old leather book-cover

answers. Place a single drop of clean mercury about the size of an

ordinary shot upon the tin-foil and rub this gently over the surface

until it is entirely silvered. Now pour very gently sufficient mercury

upon the foil till the surface appears to be flooded. Take a sharply

cut straight-edge formed of stiff writing-paper, and draw this over

the surface of the mercury to clear it. Take a slip of clean smooth

writing-paper very little wider than the foil and of about one and a

half times its length: spring the paper to a slight curve and place

one part of it over the silvered foil so that when it springs open it

will cover it and exclude the air from the surface. Now give the glass

a final polish and lay it upon the paper over the foil. Hold the glass

down with slight pressure with the left hand, and slowly and steadily

draw out the slip of paper in the linear direction of the surface of

the glass with the right hand. This will take out the air between the

foil and the glass, so as to bring the mercury in contact and leave a

perfect mirror. It must now be set aside with the glass turned face

downwards in an inclined position, so that the surplus mercury may

drain off from the foil. Small slips of foil should be put at its lower

edge, which, by their attraction for the mercury, will accelerate the

draining. The mirror should not be touched after setting it up to drain

for twelve hours at least, after which the surplus foil may be trimmed

off. After another thirty hours or more it may have any varnish or

other protection applied to the back of the silver.

644.--Where instruments are taken abroad mercury silvering may become

spotted, so that a small store of mercury and tin-foil should be taken

out with the sextant for resilvering. But it should be particularly

observed that the mercury should never be placed in the same case with

the instrument, as the smallest particle, if it touch the frame, will

eat into the brass and destroy its strength. Sealing-wax dissolved in

spirit answers for a varnish at the back of the foil fairly well after

resilvering if proper varnish be not at hand. It is advisable before

attempting to silver a sextant mirror to practise on a few slips of

ordinary glass in order to get into the way of doing it. In modern

practice base silver is deposited, and no mercury is used, but the

process requires special skill.

645.--_Adjustment of the Index Glass._--Hold the sextant clamped to

about 60° in a horizontal position with the index glass near the eye.

Look nearly along the plane of the glass in such a manner as to be able

to see one part of the plane of the arc by direct vision, and another

part by reflection of it at the same time. If the direct view and the

reflected join in one line, and the arc appears as the continuity of

a single plane, the index glass is perpendicular to the plane of the

sextant. If this be not the case it can be adjusted by turning the set

screw placed at the back of its upper centre, Fig. 286 _E_, very gently.

646.--_Adjustment of the Horizon Glass to Perpendicularity._--Place the

vernier at zero. Hold the plane of the sextant parallel to the horizon

and observe if the image of the horizon seen by reflection at the edge

of the silver line coincides exactly with the image received directly

through the plain part of the glass. If it does so the horizon glass

is perpendicular to the plane of the instrument, that is, assuming the

index glass is also perpendicular. In this adjustment it is well to

rock the plane of the instrument say 20°, to see that the horizon is

cut as a clear line about its horizontal position for this amount of

angle. If the mirror be not perpendicular adjust gently by the single

screw at the top of the horizon glass frame. If the horizon be not

water, the sharp outline of any distinct distant object will answer, or

a piece of fine string placed at a distance and stretched straight.

647.--_Adjustment for Index._--This is the adjustment for parallelism

of the two mirrors at the zero of the arc. The sextant is clamped at

zero as before: the arc of the instrument is turned in a vertical

position and the horizon again observed. If this appears to cut a clear

line through the plain glass and the mirror there is no index error,

and the planes of the glasses are truly parallel to each other in this

position. If the line is not continuous adjust gently by the lower

screw, Fig. 288, at _G_.

648.--_Adjustment of the Horizon Glass by the Sun._--This is a better

adjustment than that given above, except that it introduces any error

that may be due to the imperfection of the shades; and it is more

difficult particularly for the first approximate adjustment. Arrange

the telescope and shades so that a clear outline of the sun's limb

may be observed without distressing the eye. Place the vernier at

zero. Observe the sun, which will be most conveniently sighted at

about 40° elevation, first with the plane of the frame vertical, and

then horizontally perpendicular to this. If the sun presents a round

disc in both these positions the sextant is in adjustment. If in the

vertical position there appears to be a small notch at top and bottom

of the sun's limb, the glass is not perpendicular to the plane of the

instrument, and this requires adjustment by the screw at Fig. 288 _K_.

If notches appear at the sides of the limb when it is held horizontally

there is an index error, which may be adjusted at _G_ if it be small.

649.--_Index Error after Adjustment Allowance._--The limb of the

sextant is graduated 5° beyond the zero position when the glasses are

parallel to each other. This is called the _arc of excess_. The vernier

is also divided three lines beyond its zero position, which is marked

by an arrow. These extra divisions are placed on the instrument for

correcting the index error by measurement of the angle subtended by the

diameter of the sun's disc alternately on one side and the other of

the zero line, in which observations, if the two readings agree, the

sextant must be in perfect adjustment; when they do not agree half the

error may be adjusted by the horizon glass. The same observations may

also be made with a bright star by setting the index alternately on

one and the other side of zero. When the sun is used the reflected and

direct images are brought together, so that the two suns that appear

in the instrument just touch limb to limb, first upon direct reading

and then upon the arc of excess. When the division is adjusted very

nearly, any small error, plus or minus, may be allowed as a constant

for all readings. In observations of the sun care should be taken that

the eye is protected, both by the sun-glass cover to the telescope and

by sufficient use of the shades.

650.--_Adjustment of the Telescope to Set its Axis Parallel to the

Plane of the Sextant._--In fixing up the instrument after manufacture,

the ring standard which carries the telescope is set at a measured

distance from the plane of the frame, so that the centre of the ring

coincides with the height of the silver line cut on the horizon

glass. This is necessarily a primary adjustment. For final adjustment

the long, inverting telescope is screwed home in the ring, and the

eye-piece which has two parallel wires across its diaphragm placed

in it. The telescope is brought to focus on any distant object, the

eye-piece being turned at the same time to bring the wires parallel

with the face of the instrument. Two objects are taken subtending an

angle of 90° or over,--as the sun and moon, or the moon and a bright

star,--and the index is moved so as to bring the objects, say the limbs

of sun and moon, in contact with the wire nearest to the sextant, and

fixed there. Then by changing the position of the instrument a little,

the images are made to appear upon the wire furthest from the sextant.

If the limbs of the sun and moon still remain in exact contact as they

appeared before, the axis of the telescope is truly adjusted. If the

limbs of the two objects appear to separate at the wire furthest from

the sextant, the ring-adjusting screw furthest must be loosened a very

little and the screw nearest the sextant tightened the same amount. If

the reverse, and the images appear to overlap, adjust in the reverse

direction. By repeating this operation a few times the contact will

appear to be the same at both wires, and the axis of the telescope will

be in collimation, that is parallel with the plane of the instrument.

After the telescope is truly adjusted it may be raised or lowered a

little to make the reflected and direct images appear equally clear.

651.--_Final Examination of the Sextant._--It will be readily seen that

an instrument, although correct in theory but depending upon perfection

of workmanship in centring, division, surface and parallelism of

glasses, and also in its adjustments, can scarcely be brought to

perfection. The errors generally increase from the zero point, where

adjustments are possible, and are greatest at 140°. In the ordinary

commercial sextant of the dealers the errors of centring alone are

commonly 3 minutes to 5 minutes, with like errors in other parts. It is

therefore better, where the sextant has to be absolutely relied upon,

to subject it to actual trial. The zero point can be readily fixed by

rules already given; besides this the meridian altitude of several

bright stars subtending angles of about 30°, 60°, 90°, and 120° should

be measured either from a clear horizon or from a mercury artificial

horizon, to be described presently, for angles under 60°, and the

errors plus or minus tabulated. The data for the meridian altitudes of

certain stars upon any night may be taken from the _Nautical Almanac_,

which will require correction for the latitude and longitude of the

observer. This subject is too complicated to be entered upon in detail

here. At the present time the National Physical Laboratory undertakes

the examination of sextants for a moderate fee. This is effected by

means of fixed collimators, art. 229. For angles distributed over the

arc the parallax error is eliminated by placing the collimators in

pairs. The N.P.L. certificate may now be had with good instruments when

purchased. It may be noted that an originally well-made instrument

retains its qualities for all time, the wear of such instruments being

inappreciable.

652.--_To Use the Sextant_ the right foot should be placed nearly 2

feet in advance of the left and directed at right angles to it. In

this position the body is firm. The instrument is supported by the

right hand, the elbow being brought down firmly upon the body. The

clamp screw first and then the tangent screw are moved by the thumb

and finger of the left hand. Some practice is required to make a

steady observation. To bring two objects into apparent juxtaposition,

methods of observation for terrestrial objects will be reconsidered

in discussing the box sextant further on. As regards celestial

observations reference should be made to works on practical astronomy,

as the subject would take too much space to be entered upon here. The

whole subject, with many refinements of correction of parallax, etc.,

which fall beyond the limits of practical surveying with the sextant,

is ably discussed in Chauvenet's _Spherical and Practical Astronomy_.

653.--=Artificial Horizon.=--For ascertaining the latitude of a place

from the observation of a celestial body by means of a sextant, it is

necessary to have some means of estimating the position of the horizon.

A method of doing this, originally proposed by the elder George Adams,

optician, 1748,[46] was to float a parallel disc of glass upon a basin

of mercury, and to receive the reflected image of a star from the

mercury by the sextant simultaneously with its direct image. The angle

then given by the reading of the arc is double the angle at which

the true horizon is placed relatively at the same time. This idea,

carried out in a practical form in an instrument henceforth called the

_artificial horizon_[47] is due to Wm. Jones, a well-known optician at

the end of the 18th and beginning of the last centuries, who arranged

convenient means of making the instrument portable, and to keep the

mercury from disturbance of the air by covering it with a glass roof.

The form of artificial horizon that he invented has been in common use

ever since. He also invented another simpler form, which was that of

taking the reflection from a piece of silvered, or of black, glass.

The performance of the artificial horizon depends in any case entirely

upon means of obtaining a reflection from a perfectly horizontal

surface.

[Illustration: Fig. 290.--_Diagram of artificial horizon._]

654.--_Theory of the Artificial Horizon._--A ray _M′_ Fig. 290, from a

luminous body, at infinite distance will have its image reflected from

a level reflecting surface _SS′_ at an angle equal and opposite to the

incident ray, the angles _M′AS_ and _EAS′_ being equal. Let _E_ be

the place of the eye or the sextant: this will receive a ray from the

same distant body in direction _ME_, which is sensibly parallel with

_M′A_. The angle _MEA_ being double the angle of incidence _M′AS_, the

half of this angle will therefore produce the horizontal line

_EH_ at the height of the observer's eye if the plane of reflection

_SS′_ be level. Therefore if we take half this angle _MEA_ as it

appears in the sextant, it will give an angular position of the object

in relation to the horizon at the height of the eye, or be tangential

to the surface of the earth. If _M′AS_ be 30°, the angle _AEM_ will

be 60°, showing the elevation of object half this or 30°. The sextant

takes 120° with certainty; therefore 60° will be the limit of meridian

altitude the artificial horizon will measure.

[Illustration: Fig. 291.--_Artificial horizon of black glass._]

655.--=Artificial Horizon in Black Glass.=--This instrument is the most

portable, packing in a close pocket case. It is made of both circular

and square form in plan. Fig. 291 is the Admiralty pattern. The black

glass should have a truly plane surface. It is fixed over a brass

tray by being floated on plaster of Paris to avoid strain. A light rim

of brass is screwed down over the glass to keep it in position. There

are three adjusting screws _AA′A″_. It is adjusted to level by a

loose level tube ground on its under face _P_. The level tube shown in

detail Fig. 51, p. 94, is placed on the surface lineally with the two

screws, Fig. 291 _AA′_, and afterwards at a right angle to its first

position with one end of the tube towards _A″_. It is finally tested

by traversing at the position shown in the Fig. 291, and at right

angles to this direction. There is a great risk of getting a strain on

the glass in fixing it in its frame. The author therefore prefers the

circular form that leaves the glass quite free except at its fixings

at three equidistant points only. In this kind of artificial horizon

there is only one surface of glass to be worked true; therefore, there

is perhaps less risk of error on this account than in other forms. On

the other hand the mercury presents a more perfectly level plane. The

circular artificial horizons are commonly made 3¼ inches diameter;

weight, ¾ lb.; the oblong, Fig. 291, 4 inches by 3 inches; weight 2

lbs.

[Illustration: Fig. 292.--_Artificial horizon, mercury._]

[Illustration: Fig. 293.--_Mercury bottle to the same._]

656.--=Artificial Horizon of Mercury=, Fig. 292. This instrument

consists of an oblong tray of about 6 inches by 3 inches by ¾ inch in

depth made of wrought iron. It is covered by a roof with two sloping

sides at about 45° to the plane. The sides of the roof are glazed with

worked parallel glass fixed by screws at three points. The mercury when

out of use is contained in an iron screw-stoppered bottle, Fig. 293.

It is poured into the open tray for use, and the tray is afterwards

covered by the roof to prevent currents of air disturbing the level of

the surface. After use the mercury is poured back into the bottle from

the corner of the tray. It should be particularly observed that it is

perfectly drained, as any free particles in the case in which all parts

of the instrument are packed would be certain to attack the roof, which

is made of brass and simply varnished. The instrument is packed in a

mahogany case, size 7½ inches by 6 inches by 5 inches; weight, with

1 lb. of mercury, about 4¾ lbs.

657.--_The Bottle_, Fig. 293, is made of cast iron. It has a screwed

plug stopper with a leather collar and a covering cap with a small

hole through its apex. To pour out the mercury the cap and stopper are

unscrewed, the plug is taken away, and the cover is screwed on again.

The mercury then issues from the small hole in the cap. To return the

mercury the cap is reversed and screwed upon the bottle. It then forms

a funnel. The tray has a covered corner at which there is a small

hole. This permits the mercury to be poured into the funnel without

splashing. Both plug and cap are then screwed down firmly, and the

bottle is placed in a secure fitting in the case.

[Illustration: Fig. 294.--_Captain George's artificial horizon._]

658.--=Captain George's Artificial Horizon=,[48] Fig. 294. This is a

great improvement on that last described. The instrument being made

entirely of iron there is no risk of getting it injured by escape of

the mercury. It is also much more portable and convenient. Two chambers

_E_ and _M_ are connected together by a tube through a stem-piece in

which there is a strong iron cock at _a_. The chamber E is cored out

and form a bottle into which about 1 lb. of mercury is introduced by

removing a screwed stopper at _B_. The chamber _M_ is an open tray with

a cover formed of a piece of parallel glass placed in an iron rim which

screws down upon it. A milled-headed screw at _C_ forms an air plug.

The cock moves very stiffly by the leverage given by a tommy-pin, shown

_a′_, which is inserted in the hole at _a_. The chamber _E_ is slightly

elevated to cause the mercury to flow from it to _M_, the cock being

turned on at the same time and the air screw _C_ released a little. By

the same arrangement, _M_ being raised, the mercury flows back into the

bottle for storage.

659.--_For Using this Artificial Horizon_, when the mercury is poured

out in the tray _M_, it is levelled by the three screws _AA′A″_ so

that it covers the bottom of the tray and presents a clear, level

surface. A separate disc of parallel glass, which fits the tray _M_

very loosely, is provided with the instrument. This floats on the

surface of the mercury and keeps it quite still, even when the covering

glass is removed. This arrangement is useful also in case of an

accident to either of the glass covers. The disc is kept when out of

use in a soft leather bag which fits in the tray _M_. This artificial

horizon is generally carried in a solid leather case with sling to go

over the shoulder. Its weight complete is about 4½ lbs.; size, 9½

inches by 4 inches by 1½ inches. The surface of mercury is a circle

of 3 inches diameter.

660.--=Improved Captain George's Artificial Horizon.=--Mr. S. A.

Ionides, C.E., has devised an improved form of the foregoing instrument

shown at Fig. 295.

[Illustration: Fig. 295.--_Ionides's artificial horizon._]

In this the container is formed beneath the horizon box with a plug tap

fitted in the thickness of metal between the two; this form makes the

whole much lighter and less than half the size of the usual Captain

George's pattern.

661.--_In Using the Artificial Horizon with the Sextant_ it is

generally placed on the ground at such a distance in front of the

observer that he can conveniently see the required reflection of

the star or sun, the observer moving about until the reflection is

obtained. This is a tedious process and requires some practice. It is

much more easily effected if the sextant be mounted on a tripod or

other stand. When a stand is used it has generally a universal joint,

so as to be able to take surface angles also from the fixed position.

When the altitude of objects on the earth is taken, the observation

requires reduction for refraction, which becomes an important factor,

although this is variable with atmospheric conditions; but upon the

whole it always tends to make the object appear higher than it really

is. Commonly one-seventh of curvature is used as an approximate

correction. For solar and stellar refraction, works on astronomy should

be consulted.

The index error of the sextant is corrected before refraction, when the

natural horizon is employed. When the artificial horizon is used the

index error is allowed before taking its half as a single measure. The

artificial horizon is used also with the theodolite. It forms the most

perfect means of adjusting the transverse axis by taking an observation

of the pole star with the telescope, first directly and then by its

reflection from the artificial horizon. If the images cut the centre of

the webs in the two positions by the movement of the transverse axis

only from the one to the other, this axis is proved perfectly level.

662.--Various schemes for obtaining the horizon by some system of

levelling apparatus attached to the sextant have been devised, none

of which are very practical, as they all depend upon a pendulum or a

gravitation surface of a liquid or a gyroscope, and are all unstable as

hand instruments. There have been numerous patents taken out with this

object from that of Winter (1760) downwards, which anyone interested

in the subject may consult.[49] The matter is mentioned here as the

recurrence of the idea appears to be frequent.

[Illustration: Fig. 296.--_Sounding sextant._]

663.--=The Sounding Sextant.=--This instrument is used for coast

surveys. Angles are taken with it of objects, buoys, etc., from the

land and also from a boat on the water for such objects or for others

upon land. It is constructed upon the same principle as the ordinary

nautical sextant; but as it is to be used as an all-day working

instrument, and not for a few diurnal observations only, it is made

much more solid, and its optical parts take a more extended field of

view. The graduation is also stronger, such precision of reading only

being required as may afterwards be plotted on a chart. This instrument

is shown in perspective, Fig. 296. The index glass is large--about

2¼ inches by 1¼ inches. This is secured on all sides by a

firm rim to the tray in which the glass is held at three points.

The adjustment of the index glass is left under control, as it may

occasionally be necessary to remove it from effects of spray upon and

about it. The horizon glass is made about 1½ inches in width and

¾ inch in depth. This is entirely enclosed in a tray, the whole

surface being a mirror without any plane part to the glass as with

the ordinary sextant, so that it is entirely protected by the metal.

By this arrangement the eye receives the direct ray from the object

immediately before it, and the reflected ray from an object whose

angular position is desired to be taken with it: but these images do

not come exactly into contact, as the narrow frame interposes. It is,

however, sufficiently near for terrestrial observations. The adjustment

of the horizon glass to the perpendicular of the plane of the arc

is the same as that shown in detail for the box sextant further on.

The adjustment of the horizon glass to the index is by a stiff arm

extended from the sole-plate projected into a loose opening, where

it is held firmly by two opposing capstan-headed screws, as before

described. The arc of the sextant is of 6 inches radius, graduated upon

silver to 20′, and reading by the vernier to single minutes only by the

microscope. The clamp and tangent are the same as those described for

the nautical sextant. The frame is straight braced. The telescope has

a wide field, with achromatic object-glass of 4½ inches focus, the

clear aperture being 1-1/8 inches. The supporting ring of the telescope

has no rising stem or collimating adjustment, but is solidly fixed in

its true position by the maker. The ring carries a plain disc pin-hole

sight, which takes the place of the telescope for near observations.

The instrument in use is held in the hand by a firm oblong handle.

The instrument rests, if required for reading, upon three legs as the

ordinary sextant. Its weight is about 2¾ lbs., or when packed in its

case, 5 lbs. Its examination and adjustment are of the same kind as

those just described for the nautical sextant.

664.--=Box Sextant.=--This very neat and portable instrument was

invented by the late William Jones.[50] It is used for taking angles

within 120° upon the surface of the land to within a single minute

of arc. It has become deservedly popular with British surveyors as a

land surveying instrument, and is equally so as a military one. It is

the same in principle as the nautical sextant already described, but

it possesses the great merit--as a surveying instrument constantly in

hand--that all its glasses and delicate parts are securely protected

from accidental injury by being covered; whereas the nautical sextant,

made for one or two diurnal observations only, has all these parts

exposed. And it is not only that all parts are protected when the

instrument is in use, but they are all doubly protected by the covering

box when carried about out of use; so that it is found that a well-made

box sextant set originally in perfect adjustment will retain this

adjustment in average use for very many years. The author has seen an

instrument twenty years in use still in perfect adjustment. The box

which covers the instrument out of use forms also a most convenient

handle or support for it when in use by attaching it in a reversed

position underneath, as it appears in Fig. 297. This attachment is made

either by a screw cut entirely round the body of the instrument, or,

what is much better, by a bayonet fitting, for the reason that large

screws of this description are liable to _cross thread_. The general

description of the outer parts is as follows:--

[Illustration: Fig. 297.--_Perspective view of the box sextant ready

for use._]

665.--_C_ a covering box which inverts from the position shown in the

figure and covers the instrument. This has a diameter of 3 inches and

a depth of 1½ inches. _B_ box containing the optical and moving

parts of the sextant. _A_ axis of index glass. This axis also carries

a toothed segment fixed close under the front of the box, by which

both the index glass and index are moved by means of a pinion to be

described. The index carries a vernier divided into 30, which reads

into the arc to single minutes; the arc is divided to half degrees

on silver. The magnifier is centred by a swivel hinge joint over the

axis, so as to permit it to be brought to focus upon the arc at any

position. This magnifier is held down on the front of the box when out

of use by a nib catch at a position of about 80° of the arc. _O_ a

milled head, the axis of which carries a pinion which works into the

segment above described under the index glass. The pinion is about 1 to

9 of the segment, so that the index traverses the arc of 60° (reading

120°) by one-and-a-half turns. This gives a conveniently slow motion to

the index glass, and enables this sextant, if it be well made, to be

set rapidly with great precision. _S_ two nibs, part of two levers for

putting the shades in or out of action.

666.--In the closed form of sextant the shades block the reflecting

position between the index and the horizon glass. For surface surveying

they have therefore to be opened out, through an opening closed by a

slide shutter which moves by a stud in a slot on the under side. The

shades consist of one green and one dense red glass which must be

worked parallel, as before described for the nautical sextant. These

are used for taking altitudes of the sun, for adjustments only.

667.--_The Key K_ is a milled head which screws out, and carries

a watch-key pipe at the end of its stem by which adjustments may

be made from three square-headed screws fitting its pipe, two of

which are close to _b_, the axis of the horizon glass. These adjust

perpendicularly to the plane of the arc. One screw at a adjusts the

parallelism of the index and horizon glasses when the index is at zero.

668.--_The Telescope_ is achromatic, with draw tube for focussing.

It magnifies about 2½ diameters. It has a concave eye-glass, and

therefore gives an erect image, Fig. 14. A sun-glass _E_ screws over

the eye-glass when it is required for sun observations. The telescope

is attached to the sextant by means of a crank-piece upon the telescope

which is fixed by the mill-headed screw _T′_ and two steady pins.

The crank-piece screws in reverse position upon the telescope for

portability before putting it by in its case.

669.--By some makers the telescope is made to slide into the body of

the sextant and thus become quite portable. This plan is a very neat

one, but it requires care to see that the shades do not interfere

before it is put by. The weight of the entire sextant with its solid

leather case is about 18 oz. only. For close work the telescope is not

generally used. A sliding shutter pierced with a small hole covers the

telescope opening into the sextant, which is used as a sight hole.

[Illustration: Fig. 298.--_Box sextant under the face._]

670.--_The Interior or Optical and Mechanical part of the Sextant_ is

shown Fig. 298. _I_ index glass, fixed over the toothed segment on

the same axis. The pinion is shown working into the segment moved by

the milled head _O_ of Fig. 297 on the face of the sextant. Fig. 298:

horizon glass, cut by _ED_, adjusts to the vertical by screws _CC′_,

which have square fittings on the face of the instrument, shown Figs.

299 and 300 full size. The differential adjustment between horizon and

index glasses is made by a screw with a square fitting at _P_. This

adjustment acts by screwing against a helical spring, shown at _Q_. The

reflected rays enter by a wide window in the side of the box, Fig. 298

_d_, the direct rays by a small window _f_. The path of a ray is shown

by fine lines from _R_ to _E_, for the positions in which the index

and horizon glasses are placed. The pin-hole opposite which the eye is

placed is shown white. _S_ shades with their axis are shown cut off,

to prevent confusion of other parts. They are simply round discs of

parallel glass on arms which rise from the back of the face by pressure

of the nibs at _S_.

[Illustration: Fig. 299.--_Plan of horizon glass._]

[Illustration: Fig. 300.--_Section of the same._]

671.--_The Construction of the Box Sextant_ may be fairly inferred

from inspection of the engravings. The face-plate is made of a casing

in brass 1/8 inch thick, which should be well hammered to harden and

stiffen it. The axis, which has a wide collar, is fitted into a hole

in the plate, first by turning it as exactly as possible, and then by

burnishing it in by friction, the hole being broached slightly conical

with a D-broach. The careful fitting of the axis is an important part.

The horizon glass frame, Fig. 300, is held down by a central screw

which fits tightly both in its fore hole and thread. The flange of the

tray _F_ is cut to an angle on its under side to permit adjusting to

verticality by rocking over this angle, by tightening and loosening

the adjusting screws _cc′_ which protrude in square heads to the face

of the instrument. The horizon glass, _H_, which is half silvered, is

fixed in a tray-piece which has two narrow fillets turned to the face

of the glass, and a spring-piece at the back brought up by a screw

_a_. This glass is entirely open at its unsilvered part. The toothed

segment should be cut upon its own axis, and although fitted to the

pinion without any looseness, it should not press the index axis. The

silver is inlaid in the arc on the plan shown Fig. 127. The vernier is

soldered closely on the index and should read down to a fine clean edge.

672.--_Examination of the Box Sextant._--The glasses should be cleanly

silvered, with a sharp, clear cut between the silver and the clear

glass of the horizon glass. The pinion should move softly and equally

in causing the index arm to traverse the arc. If the pinion be moved

in little jerks backwards and forwards there should be no shake, but

the index should follow every slight motion. The magnifier rising joint

should move rather stiffer than the traversing joint, so that the focus

is not changed by traversing across the arc. The magnifier should have

about 1 inch or less focus, and should stand square to the plane of the

sextant when in focus. The graduation should be deep and fine, and the

vernier should read 30 = 29 at the two ends and the centre of the arc.

If there be a small excess or defect of vernier to arc, this should be

noted and allowed for, either at the time of reading or as an index

error. The sliding fittings of the pin-hole sight, shades, and under

shutter should move firmly but not stiffly. The telescope should fit

without shake. The covering box should fit well in both positions of

cover or hand-hold.

673.--_Adjustment._--The box sextant is best adjusted by the sun upon

the plan described art. 648. The adjusting screws, as already stated,

are moved by the key, which unscrews from the face of the sextant, Fig.

297 _K_. The adjustment is made permanently by the maker, except only

that of the horizon glass, which is at the command of the user. The

adjustment to perpendicularity of face is made by the two screws upon

the face near _b_; adjustment to zero of arc by the screw at the side

_a_. In defect of appearance of the sun, the sextant may be adjusted

to any clear, sharp line, as that of a stretched piece of twine,

for perpendicularity of plane, and to any object of clear outline

sufficiently distant, say at half a mile, to avoid error of parallax

for index zero, art. 621.

674.--_Use of the Box Sextant._--The sextant has its under shutter

opened by pressing the stud attached over in its slot. The nibs of the

shade levers, Fig. 297 _S_, are then raised and the shades depressed.

The cover is then screwed, or slid on if it fixes with bayonet notches,

upon the under side of the sextant to form the hand-hold. The pin-hole

sight is pressed over for use if not already in its position, unless

it be intended to use the telescope. The box sextant is held in the

left hand, with the right-hand thumb and forefinger constantly holding

the milled head, and turning this so as to bring the two objects, of

which it is desired to obtain the angular position, from the observer,

exactly in apparent juxtaposition, the one over the other. In turning

the milled head it is better to let all the other fingers of the right

hand clutch and steady the instrument. To take angles objects should be

observed that cut sharp, erect outlines, as buildings, posts, trees,

etc., if possible. In open country it is necessary to use pickets, to

be described further on. With pickets the reflected image of the upper

half of one picket should form a continuous outline with the direct

image of the lower half of the other picket in the eye, so that the

pair of pickets appear as one. Where an angle greater than 120° is

required an intermediate picket is set up, and angles taken to the

right and left of this are added together.

675.--It must always be remembered that the sextant takes angular

positions _actually_, whereas plans are made in _azimuthal_ angles.

There are some not very satisfactory means of approximate correction

for this, for which books on surveying may be consulted; but altogether

the sextant is not very useful for taking angles for plans on other

than fairly level ground, wherein it has proved a most valuable and

sufficiently exact instrument. Where ground is undulatory fairly good

work may be done with it by taking stations for exterior triangles

at equal heights on the hillsides, as ascertained by a hand level or

clinometer to be described, or sometimes from hilltop to hilltop where

these are of fairly equal heights. For sketch plans of very hilly or

mountainous districts the prismatic compass, art. 148, is better, as

this gives, although with less precision than the sextant, its angles

in azimuth.

[Illustration: Fig. 301.--_Interior construction of box sextant with

supplementary arc._]

676.--=Box Sextant with Supplementary Arc.=--This sextant is preferred

by many because of its more extended use. It is complete as an ordinary

sextant for angles up to 120°; but if it be thought desirable to extend

the angles to 220°--by a single observation this may be done. The

ordinary arrangement of the box sextant just described is left intact

and forms the upper part of the instrument. This arrangement, as in the

box sextant, is attached entirely to the face or arc plate, the only

difference being that the index glass is made of less depth. For the

supplementary arc arrangement a mirror is fixed upon the lower or _sole

plate_ exactly under the position of the index glass. This mirror is

termed the _supplementary index glass_. The position of the face of the

index glass is at right angles to the face of the ordinary index glass

when the index is at zero. The arrangement of glasses is shown Fig.

301: _MM′_ index glasses. The supplementary angle is read through a

separate pin-hole sight which is placed at about 90° from the pin-hole

sight of the proper sextant and a little lower down on the rim. The

arc of this sextant reads in the ordinary manner, left to right, to an

inner circle of figures for angles from 0° to 130°. The supplementary

arc reads by the same vernier, and is figured in the same manner at

the tens; but it reads into an outer circle of figures which progress

in the _reverse direction_, that is, right to left. The readings of the

supplementary arc are from 90° to 220°, so that for a certain range,

that is, for angles from 90° to 130°, these may be taken either by

direct arc or by supplementary arc. The supplementary angle is taken by

means of the coincident images of _two reflections_, one from the index

glass and one from the supplementary index glass, and not by one direct

and one reflected image as in the sextant proper.

[Illustration: Figs. 302, 303.--_Diagram of supplementary arc sextant._]

677.--_Theory of Supplementary Angles to the Sextant._--For the

measurement of these angles we have to consider direct reflections

only of two reflecting planes placed one above the other nearly in

contact, so that the images projected from both planes may reach

the eye superimposed. Let Fig. 302 _II′_ be the surface of a mirror

(_index glass_) which is movable to any angle in relation to the face

of the mirror _SS′_ (_supplementary index_). For demonstration of the

principle these mirrors are shown in this diagram at 90° to each other;

therefore coincident reflections will be at 90° + 90° = 180°. Let the

lines _FC_ and _BC_ form a right line (180°); _F_ fore sight and

_B_ back sight. An object at _F_ would be reflected from the mirror

_II′_ to the eye at _E_, the angles _FCI_ and _ECI′_ being equal.

Another object at _B_ reflected from the face of the mirror _SS′_ would

also reach the eye at _E_, the angles _BCS′_ and _ECS′_ being

equal. And as the angles _FCI_ and _BCI′_ are equal in crossing a

right line, the line _FCB_ must be also a right line (180°) which is

indicated by the angle of coincidence of the two reflections to _E_.

The positions of the reflections are shown as angular measurements upon

the graduated arc.

678.--In Fig. 303 let _SS′_ remain as before, angle _BCE_ will remain

as shown in both figures. Move the index glass from the position _II′_

of Fig. 302 to the position _JJ′_ of Fig. 303, so that after this

movement the eye at _E_ would receive the image of an object at a new

position _F′_ as reflected from the mirror _JJ′_, _F′CJ_ and _ECJ′_

being equal. In this process, as the reflector _JJ′_ in the angle _ICJ_

would have moved half the angle _JCF_, the record of this movement

upon the index, which moves with _JJ′_, is at the same time double the

true angular difference, as with the sextant proper fully described,

the graduations being in both cases the same _pro ratâ_. The increase

of angle is taken supplementary to the angle given by the first

reflection, by addition to this angle in a direction right to left from

the right line of the former sight _EC_; consequently this increase is

read backward on the sextant, that is, right to left, and is indicated

by the outer line of numerals.

679.--_Manufacture._--The general structure of this instrument is

nearly the same as the ordinary box sextant, except the parts just

referred to. The supplementary index glass is an ordinary mirror

similar to the index glass but of only ¼ inch in depth: it is mounted

in the same way. Its adjustments are similar to the horizon glass in

kind, but there are no exterior screws, this glass being permanently

fixed by the maker. Opposite the supplementary index glass a wide

window is cut through the rim of the case near the sole plate to take

sight of the object at angles exceeding 120°, so that in this sextant

two large windows are cut out opposite to each other. The diameter of

this sextant is 3 inches; the exterior depth about 1-5/8 inches, that

is, 1/8 inch deeper than the ordinary box sextant. It weighs about 20

oz. It is carried in a solid leather case with strap to pass over the

shoulder.

680.--_Examination and Adjustment._--Examination will be nearly the

same as for the common box sextant. The most important point is

that the readings taken within both arcs should be alike, assuming,

which is necessary, that the part comprising the sextant proper is

perfectly adjusted. Thus there is a 90° on both direct and reverse

arcs. The 90° may be measured by any pair of objects on the direct

arc, and afterwards compared by shifting the index to the 90°, on the

supplementary arc. If no object be found at 90°, then 95° 30′ or any

other quantity may be compared. It is also well to compare readings

at or about 120° on both arcs. The 90° and 120° fall in the same

position in the reading, and this checks any error in either. If the

adjustment be not fairly perfect, the instrument should be returned to

the maker. Indeed, this sextant would be better without any external

means of adjustment, leaving these to be made by the optician in such

a permanent form that they will not be liable to change. It is, as the

plain box sextant, exceptionally protected from accident.

681.--_In using this instrument_ the arc up to 120° is taken exactly as

with the plain box sextant. Beyond 120° the sextant is shifted to take

sight through the supplementary pin-hole, being particular to observe

that the pinion is now turned the _reverse way to increase the angle_,

and that the vernier reads for the supplementary arc right to left.

It is in this reversing, if not carefully performed, that a little

difficulty is experienced in using this instrument.

682.--=Box Sextant, with Continuous Arc to 240°.=--This instrument is

an improvement by the author upon one originally designed by Mr. W.

Franklin. The reading is taken continuously from the same sight-hole

and by the same arc, and in a direct manner without any reversal for

part of the arc. This sextant reads with certainty to 240°.

683.--In the construction of this sextant there are two horizon glasses

superimposed one above the other and crossing each other, with faces

which are adjustable for perpendicularity at an angle of 120°. The

horizon glass is divided top from bottom by a clear band cut through

it, as in the old form of back-sight nautical sextants. One of the wide

glasses reflects into the upper, and the other into the lower mirror of

the horizon glass. The pin-hole sight or the telescope is placed in the

same position as in the plain box sextant described. The horizon glass

is fixed and both the index mirrors adjust to angular positions, or one

index glass only and the horizon glass is adjusted, this arrangement

being optional. The arc is graduated as the plain box sextant, but

it reads with two rows of figures from 0° to 120°, and from 120° to

240°, the 0° of the under line being under 120° of the upper. When the

arc is set to zero the index glasses are in such a position that the

direct vision and the reflection as seen in the upper mirror of the

horizon glass are coincident for direct images, as at the zero of the

plain sextant, but at this point the lower mirror of the horizon glass

reflects to the eye an object at 120°. When the index is moved forward

the angles continue onward, reflected from both glasses, so that the

upper reads on 10°, 20°, 30°, etc., whereas the lower read 130°, 140°,

150°, etc.; so that if the objects desired to be triangulated are

under 120° the coincidence is seen in the upper mirror, and if over

this in the lower, the great distance of 120° apart of the angles

preventing the risk of accidentally taking the one for the other. In

the compact form of a box sextant this instrument embraces the uses

of the ordinary reflecting circle of double the diameter, due to the

entire circle graduation; and the range is sufficient, as beyond 240°

the head materially interferes with observation. The size and weight

of the instrument are generally but little over that of the plain box

sextant. The adjustments are made permanently by the maker. The use

of this instrument is fully inferred from the description given. The

construction is shown in Fig. 304, _E_ place of the eye with direct ray

through the horizon glass _H_ to _O_. The index glass _I_ is that of

the ordinary sextant, shown by dotted lines, throwing the image of an

object at _P_ to the upper horizon glass and thence to the eye at _E_.

_B_ is the fixed supplementary glass with its surface at 60° to the

lower horizon glass at _A_. The sight lines from an object at _Q_ are

reflected from _B_ to _A_ and thence to _E_. A spring arrangement shown

_SS_ with a milled head underneath permits the lower glass _A_ to be

drawn down to convert the instrument into a simple box sextant.

[Illustration: Fig. 304.--_Stanley's continuous arc box sextant._]

[Illustration: Fig. 305.--_Section of supplementary horizon

arrangement._]

684.--_Details of Spring Arrangement_ to the supplementary horizon

glass are shown in Fig. 305 full size in section. The springs _SS_ in

Fig. 304 and _S_ Fig. 305 form two points of support to the horizon

glass, the silvered face of which is shown at _A_. A third point of

contact is near _D_, placed in the centre of the end of the supporting

plate for the horizon glass. When the screw _R_, which is placed in

a loose fitting, is released, the springs bring the supporting plate

tight up to _D_ and hold the horizon glass firmly in an elevated

position. When the screw _R_ is tightened it brings this glass down.

The horizon glass is adjusted over a rocking centre by the screws

_CC′_. A screw and collar b prevent the loss of the screw _R_. By

this arrangement the horizon glass is brought in or out of the field

of view, in order to use the supplementary arc or for leaving it as a

plain sextant.

[Illustration: Fig. 306.--_Stanley's portable surveying sextant._]

685.--=Open Surveying Sextants=, similar to nautical sextants but

generally smaller and of stronger construction, preceded the box

sextant, and are still used to a limited extent upon the Continent,

particularly with some form of supplementary arc, or arrangement to

produce a large part of the reflecting circle. These forms are also

occasionally revived by the opticians of our own country. The reason

of this is easily seen. To the optician who lives in a town, moves on

a level surface, and has comfortably warm hands, even in the winter,

to hold and move the separate parts of an instrument, the open sextant

appears the most perfect, as he can get at every part of it easily to

clean and adjust. The surveyor takes another view of the subject. He

is exposed in the open country to all weathers and all difficulties

of movement over the land; therefore that form of instrument which is

best protected and least liable to injury by a fall will be sure to be

popular with him. It is upon these conditions the box sextant of some

form is generally preferred.

A handy form of portable surveying sextant has been devised by the

author and is shown at Fig. 306.

The arc is of 4 inches radius and is divided on silver to read 20″, is

complete with shades and telescope and packs into a case 7 × 6 × 2½

inches.

[Illustration: Fig. 307.--_Optical square._]

[Illustration: Fig. 308.--_Double optical square._]

686.--=Optical Square.=--This extremely handy little instrument is

invaluable for taking offsets in chaining for any irregularity or

obliquity to the right line in the boundaries of fields, hedgerows,

fences, streams, etc., giving as it does instantly at sight a right

angle to any object that may be sighted on either hand. The instrument

is optically constructed exactly as a box sextant; but the glasses are

fixed with their faces permanently at the angle of 45° to each other,

by which means the reflection of 90° is truly given on principles

fully discussed at the commencement of this chapter. This instrument

being made very small, that is, 2 inches or less in diameter, it is

found most convenient for manipulation to place the adjustments to

the larger glass, that is, the index glass. The horizon glass, Fig.

307, _h_ is therefore fixed firmly, like the index glass of the box

sextant, by two screws to the sole plate. The index glass _i_ is held

and adjusted in exactly the same manner as the horizon glass of the box

sextant, as shown in detail, Figs. 299, 300, the only difference being

that the frame which holds the glass is made of the entire height. The

rim of the case of the optical square is formed of a short length,

3/8 inch to 5/8 inch, of a pair of telescope tubes which slide easily

together. One of these is attached to the sole plate and the other to

the cover, so that at first they close together as a box and lid. All

the openings required for sight, as Fig. 307 at _Q_ for horizon sight,

_o_ for index sight, and _e_ for pin-hole or eye sight, are cut through

the two tubes.

[Illustration: Fig. 309.--_Optical square._]

687.--The inner case is cut in the plane of some part of the

circumference of the instrument from a pin-hole into a bayonet notch,

made with a horizontal slot for the two cases to revolve upon each

other upon a pin, sufficiently to close and open the sight holes.

This plan secures the instrument from any intrusion of dust when it

is closed and out of use. An adjusting key is placed in the case,

held by a tube or stud at the position _k_. The weight of the entire

instrument is about 4 oz. if of ordinary make; but smaller ones are

made in German-silver or silver, 1¼ inches diameter, 3/8 inch thick,

weighing under 2 oz. These latter are very convenient for the waistcoat

pocket, and are equally as exact as the larger instruments. Fig. 309

shows the general outward appearance of the optical square.

688.--_Examination and Adjustment of the Optical Square._--Place two

pickets in an open space at a distance apart, the further the better.

Range an intermediate short picket in right line with these or the

top of a stake the height of the eye, or what is better still, if at

hand, the top of a tripod stand. Place the optical square over the

intermediate station or tripod. Place another picket, which we will

distinguish as the 90° _picket_, at a distance, and make this appear in

the optical square coincident by reflection with the direct sight of

one of the pickets in the right line from our station. Turn the optical

square right over on its place, and looking in the opposite direction

take a sight at the other right line picket and observe the 90° picket.

If this still appears coincident with the direct line in reflection

the optical square is in perfect adjustment. If it does not appear so,

half the difference must be adjusted by means of the key taken from the

interior of the case and placed on the square at _k_, Fig. 307, and

this observation repeated until the 90° is correct.

689.--_In Using the Optical Square_ it is customary to walk along the

chain line at about the desired position for taking an offset, looking

by direct vision through the plain part of the horizon glass _h_ at a

fore sight object until the required object is sighted by reflection at

right angles to this, where it appears by coincidence of image with the

fore sight. The heel of the forward foot in stepping indicates fairly

the vertical position of the optical square; but some surveyors prefer

the use of a drop arrow to fix the point. The offset is then chained in

the line.

690.--=Double Optical Square.=--This instrument is exactly what its

title indicates, that is two optical squares, the one placed exactly

over the other, the one reflecting to the right hand and the other to

the left. A simpler name, however, would be an _optical cross_. This

arrangement of reflectors greatly extends it use. First, as regards the

90°, this need not depend in any way upon the position of the observer,

as two objects may be observed, one to the right and one to the left,

to appear to cut the direct forward line of sight, and therefore to cut

the base line at the exact position of the instrument at right angles

to it. Secondly, an intermediate station can be found in direct line

between any two points, as the 90° + 90° forms this line.

691.--The arrangement of the optical part of the instrument is shown

Fig. 308. The two index glasses _CD_ are fixed at equal angles to

the direct line of sight _EO_. The two horizon glasses _AB_ are

superimposed with the interval of a small space, 1/16 inch, between

them. The horizon glasses are each separately adjusted so that their

reflecting planes are respectively 45° to the index glass from which

they receive the reflections. The diameter of the instrument as usually

made is about 2¼ inches; its depth 7/8 inch. The weight is about

9 oz. It is generally carried in a light, solid leather, sling case.

Total weight with instrument, 12 oz.

692.--_Examination and Adjustment of the Double Optical Square._--1.

Place the instrument, as already described for the optical square, at

a station intermediate between two pickets. Examine the right angles,

first looking towards one picket and then towards the other from the

same position, as with the optical square, turning it over for this

examination. 2. Turn the instrument half round and examine it this way

also by turning it over again in like manner. Adjust either horizon

glass if required. 3. Now take the position for the eye of the former

90° and see whether the extreme pickets appear in true position by the

exact coincidence of their images at 180°. 4. Do this again, facing

the opposite way and turning the instrument half round. If the extreme

pickets still range in line from the central station the adjustment

is perfect. If they do not do so half the error must be corrected by

returning to the first and second adjustments to find out between

which pair of mirrors it lies. For this adjustment the instrument is

much better to be placed upon the top of a tripod, as the position

of the axis should remain fixed after turning it over or changing the

direction of the instrument. It is only from severe accident that the

maker's adjustment will be disturbed.

693.--=Apomecometer.=--This little instrument, the invention of Mr.

R. C. Millar, is intended to measure the height of buildings, trees,

etc., by measuring the distance from the vertical upon the surface of

the ground. It performs one of the functions of the box sextant in the

same manner as the optical square, that is, to measure a single angle

by reflection. The angle measured is 45°, consequently by measuring a

space upon level ground up to a vertical, the vertical will be known,

this being equal to the horizontal. Of course this will always be

approximate, as the ground will seldom be truly level; but by taking

a position, even on an incline, as nearly as possible level with the

object, a very fair estimate may be made. Horizontal distances may be

measured in the same manner from a perpendicular to any line.

694.--The instrument is constructed in exactly the same manner as

the optical square just described as regards its mirrors and its

adjustments, but the faces of the mirrors are fixed at the angle of

22° 30′, so as to give a reflection of 45°, upon principles fully

discussed. In Fig. 310, _A_ is the index glass, _B_ the horizon glass,

_E_ the pin-hole sight. There is a window opposite the index glass,

and one behind the horizon glass, each sufficient to take in a wide

field of view at about 45° and in the direct line _E_ to _H_. These

windows close by rotation of the casing of the box, which is made as

the optical square. When closed the instrument is dust-tight and may be

carried in the waistcoat pocket loose, or in a light snap leather case.

Its size is 1¼ inches diameter, 3/8 inch in thickness, weight 2 oz.

in German silver.

695.--_The Use of the Apomecometer._--To measure the altitude of a

building the open side nearest level is selected, and a station for

observation is taken which is at a distance thought to be approximate

to the height. The instrument is held edgewise with the pin-hole sight

to the eye, and the reflection of a point of the building about level

with the eye is observed by direct vision through the instrument. At

the same time there will appear a reflection of the summit of the

building. If we now walk backwards or forwards, as the case demands,

keeping sight of a level object, as for instance in Fig. 311 the plinth

of a building, then at a certain point the summit of the building

will appear by coincident reflection. The height of the object will

be the same as the distance plus the height of the observer's eye.

This distance may be measured on the ground, or if a rough estimate is

sufficient it may be stepped, the principle of which is shown by Fig.

310 in the line _OH_, being equal to _FH_. If a part of an object is

required to be measured such part may be taken on the horizontal plane,

as for instance the height of the figure in Fig. 311, by _ab_ being =

_ed_, as the base _ab_ can easily be measured. An approximate may be

found by dropping a small pebble at _a_ and at _b_ and then measuring

the distance apart of these pebbles.

[Illustration: Fig. 310.--_Optical details of the apomecometer._]

[Illustration: Fig. 311.--_Scheme for measuring heights._]

696.--The distance of an inaccessible object may be measured, as for

instance a buoy at sea, by measuring in any straight line double

the distance and taking equal angles thereto by the apomecometer

on any direct line. An approximate idea may be formed by walking

over measuring points. As for instance, _b_ being a buoy at sea,

Fig. 312, walk from _e_, at which a walking-stick may be set up,

towards an object _o_. At _E_ the buoy and object _o_ will appear to

be coincident. Then drop a stone or make a mark directly under the

instrument. Walk on till beyond _E′_ and turn to face _e_. Now in

returning, the buoy and the object e will appear coincident at _E′_.

The distance _EE′_ is double that of the intermediate _a_ to _b_.

[Illustration: Fig. 312.--_Scheme for measuring distances._]

FOOTNOTES:

[38] _Posthumous Works_, p. 502; also _Animadversions to the_ Machina

Cælestis _of Helvetius_, p. 49.

[39] _Phil. Trans._, vol. xlii. p. 155.

[40] _Phil. Trans._, vol. xxxvii. p. 147.

[41] _Ibid._ p. 340.

[42] See Nicholson's _Navigator's Assistant_.

[43] Pearson's Practical Astronomy, p. 537.

[44] _Ibid._ p. 577.

[45] _Gli Strumenti a Reflessione per Mesurare Angoli_, by G. B.

Magnaghi, 1875.

[46] _Description of a New Quadrant_, by George Adams, 1748.

[47] Adams' _Geometrical Essays_, edited by William Jones, 1803.

[48] Prov. Patent No. 2624; Christopher George, 1868.

Surveying and Levelling Instruments, Theoretically and Practically Described. For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field. · 第 24 / 26 章

596.--_To take Cross Sections when the Line is on a Curve._--This