best form. Many mining engineers prefer a pair of equal slits, one of
which replaces a window. In this case, instead of the wire covering
the object sighted in the use of the instrument, the object is made to
appear in the centre of the forward sight slit. In this construction
the sight apertures are made much narrower so that they do not cover
too much of the field of view. Excellent work is done with this open
form of sight, and its construction is much more solid than that of
having loose hairs.
498.--_Universal Sight_, termed technically _hole and cross sight_,
consists of a small hole _C′_, Fig. 203, on the inner side of one sight
that is hollowed away on the outer side which comes next the eye, so
as to present a thin edge of the hole only. The fellow sight _C_ has a
hair cross placed centrally in a circular window. This is of occasional
use for sighting angles approximately in altitude and horizon
simultaneously; but the cross occupies so much of the sight space that
observation with it cannot be depended upon.
499.--_Ball and Socket Joint._--This is shown in elevation Fig. 201 at
_F_, and in section Fig. 204 _F, D_. It is one of the oldest forms
of adjustment, and is common to many dials. When the clamping screw
_G_ is released the ball is free in its socket _F_ to move about its
centre, to the extent of the opening at the top of the socket, in
any direction. A _plug_ _E_, which really forms the lower half of
the socket, is screwed into the part _F′_ at the lower part of what
is technically called the _socket-piece_. The plug is turned upwards
by its screws so as to tighten the ball by means of a tangent screw
_G_ which works in a rack thread cut in a part of the circumference
of the plug, thus forming a _screw and cross screw_, which, as the
construction indicates, clamps the ball with great rigidity. There are
several other ball and socket arrangements; these will be discussed in
describing the special instruments to which they are affixed. The only
objection to this form is that it elevates the dial very much more than
others.
500.--_The Tripod Stand of an Ordinary Miner's Dial._--The upper part
is shown in Fig. 205. This form of tripod is common to many dials. The
legs are made about 1¼ inches in diameter. The heads of the legs
are fitted directly without brasswork between the _book-plates_ _A_,
to which they are held by cross screws or bolts which form the joint
on which the legs move for extension. Unless the head be worked out of
the solid, the book-pieces are screwed to a plate that carries a male
plug centre to which the dial is fixed by a milled-headed screw shown
at Fig. 201 _L_. The plug is grooved at the position of the point of
the screw so as to permit rotation of the instrument when the screw
is slightly released. This tripod head remains permanently fixed to
the legs. Each leg is jointed to part in its centre by unscrewing,
to present when disjointed a metal point to hold the surface of the
ground, to form a short stand. The usual height of the full tripod
legs is 5 feet; the upper part only 2 feet 6 inches. The usual form of
joint is shown in detail in section Fig. 205. _C_ the male screw, which
is fitted to the woodwork by a socket and cross pinned to it. This
piece has a point at its lower end. _D_ the socket-piece is screwed
over the point to extend the leg when the tripod is required of full
length. The woodwork of this lower piece has a conical metal point to
bite the ground when it is set up in use. Occasionally for close work
shorter legs are provided, or the legs are jointed in three parts. In
the common dial shown, the legs are left exposed when out of use; with
superior instruments they are packed in a deal case that protects the
socket fitting to which the instrument is attached. Another much better
form of tripod will be discussed further on with the instrument to
which it is attached.
[Illustration: Fig. 205.--_Jointed tripod legs of a miner's dial._]
501.--_Examination and Adjustment of the Plain Miner's Dial._--The
tripod should be first set up to full length and each length separately
twisted to right and left to see that its socket fittings are good and
free from shakiness. The legs should each be separately pressed in and
out at its centre to see that the screws clamp the parts firmly and
are free from shakiness. The instrument should then be set up and its
socket fitting be felt to see that it is free from shake, and also be
turned round to see that it moves freely. The ball fitting should be
clamped and its rigidity be tested by fair pressure on the two ends
of the limb separately. The sights should be examined to see that
they are quite linear with hair and slit. The compass-box should be
levelled by the coincidence of the upper surface of the needle with the
plane of the division, and be reversed in every direction by turning
the compass-box, the reading being observed with the N. point of the
needle at N. E. W. S. to see that it bisects the graduation by angles
180° apart. The compass-box being level, the sights should be ranged
with an external object at a distance--a plumb-line is best--a piece
of string suspending a stone answers--to see that they are vertical,
and that they cut the same line with the position of the sights changed
fore to back. If the sights are coincident, but do not range with the
plumb-line, the needle is out of balance, and this may be corrected by
shifting the rider.
502.--=Henderson's Dial.=--This is an improvement upon an old form
of circumferentor,[19] in which four sights are centred in opposite
pairs so as to revolve about the vertical axis, so that one pair of
sights may take any angle to the other pair. In Mr. J. Henderson's
dial the improvement consists in making the compass larger, the needle
being made to read by a vernier placed upon one end to 3′ of arc. Mr.
Henderson prefers plain slit sights instead of slit and window sights,
as before stated, which avoids the accidental derangement of the
horse-hair.[20] The instrument combines some of the parts of Lean's
dial, to be next described. Illustration of this instrument is given in
Mr. B. H. Brough's _Mine Surveying_.
503.--=Lean's Dial.=--The inventor of this instrument was Mr. Joel
Lean, a Cornish mine manager, who was well known at the end of the 18th
century for his important improvements in mining apparatus. This dial
is still popular in Cornwall and other mineral districts. In general
construction the sights and limb on which they are mounted are the same
as in the plain dial just described, art. 491. The legs are also
the same--other parts are additional or modified. In the engraving,
Fig. 206, the sights and vertical arc with its telescope are shown
mounted together on the limb. This is done to show the relative
position of these parts: they could not in practice be used
simultaneously upon the instrument. They are separately attached to
the limb by the same pair of milled headed screws. As a general rule
the telescopic arrangement, which will be described further on, is
used above ground and the sight arrangement below. The details of
construction are as follows:--
[Illustration: Fig. 206.--_Mining circumferentor or Lean's dial._]
504.--_The Tripod_--of the mining circumferentor, in common with
many other forms of dial, has the legs fitted directly between
_book-pieces_, which are fixed to the lower parallel plate, as shown
Fig. 206, thus dispensing with the separate tripod head, common to
levels and theodolites. Otherwise the parallel plates are similar to
those described for levels and theodolites, art. 193, and are used in
the same manner. The upper parallel plate in this dial carries the male
axis, which fits into a socket attached below the centre of the limb in
the manner just described for plain dial. The tripod stand, with its
parallel plates attached, is generally packed in a pinewood case when
out of use. The reason for attaching the legs directly to the lower
parallel plate instead of having a tripod head is that it saves the
extra elevation of the instrument by the depth of one screw fitting.
At the same time it must be observed that it exposes the axis to the
air by separating the instrument at this part when it is put by, which
renders the axis difficult to be kept lubricated and in smooth working
order. On the Continent and in America it is general to detach the legs
only, on a plan shown, Fig. 85, p. 140. This keeps the axis attached,
and is probably the better plan, although it may be found a little more
troublesome to erect the instrument.
[Illustration: Fig. 207.--_Section of compass-box and axis of Lean's
dial._]
505.--_Revolving Compass_ forms a part of Lean's dial and many other
dials. It is shown in section Fig. 207. As the axis is constructed in
this instrument, the socket-piece _A_ is ground to fit the male axis
_S_, and at the same time it is shouldered to fit the surface of the
parallel plate _T_ to prevent excess of friction on the axis fitting,
so that it may move easily to set the needle to magnetic north of the
compass-box if desired. The socket-piece is attached to the compass-box
through a collar. The compass has a step _D_ which is divided to
degrees on its inner edge to read to the point of the needle, and
similarly to degrees on its outer edge to read with a vernier scale,
shown _D_ to 3′. The vernier is set off on each side of the zero line
in ten divisions, which are figured 30, 45, 0, 15, 30, art 322, p. 184.
The upper surface of the needle is made level with the upper surface
of the step. The bottom plate of the compass-box is divided to 10°:
in some difficult positions in the use of the instrument this last is
the only reading that can be sighted. The compass-box, which carries
the vernier _B_, is fixed centrally on the arm plate. The arm plate is
centred upon a step fitting between the compass and the socket-piece,
so that it carries the whole superstructure of the instrument around
the compass, its relative position being read by the vernier. The
edge of the compass plate is formed into a toothed wheel, as shown
in section in the figure on the right-hand side, into which a small
wheel or pinion _R_ is fixed in a box upon the arm plate that works by
means of a large milled-head screw _P_. By means of this milled head
the instrument may be rotated about the compass, so that the line of
division on the compass step reading into the vernier performs the
functions of the horizontal limb of a theodolite. In this manner angles
may be taken by means of the vernier, quite irrespective of the reading
of the needle. When the compass is set to the zero of the vernier at
north (360°) it may be fixed in this position by means of a pin fitting
in opposite holes to the arm plate and bottom plate of the compass,
_not shown_; and when thus fixed the needle only is used as in the
plain dial. Between the collar-piece _C_ and the socket-piece _A_ a
wedge-shaped lift raises the needle off its centre by pressing in a
slide shown at _L_.
506.--_The Vertical Arc_ is erected upon the limb as close as possible
to the compass-box, so as to leave room for a level to be placed
between the seatings of the arc and sights. The axis of this arc
is a simple hinge joint, brought down nearly to the surface of the
cover which protects the glass of the compass-box: this is done to
keep the instrument as low down as possible. The telescope, which is
of the same kind as that used for the theodolite, traverses the arc
tangentially, permitting it to be adjusted for reading the arc by its
vernier by means of a clamp and tangent motion at any position. The
arc is divided on one side into degrees, and reads by the vernier to
3′ in the same manner as the horizontal circle. On the opposite side
it is divided with a percentage scale of difference of hypotenuse and
base which reads to an index line. A spirit level is placed under the
telescope, in line with its axis, to which it is adjustable by means
of capstan-headed screws. The telescope when fixed is placed just
sufficiently above the arc to permit it to be brought to a vertical
position at 90°, or a degree or two over this, with the full aperture
of the object-glass beyond the extreme edge of the horizontal circle.
By this construction a bearing may be taken of any object upon the
surface from the top of a shaft, and a line may be sighted to the
bottom of the shaft in exact azimuth with this without changing the
horizontal adjustment of the instrument. In the same manner, if the
vertical axis be perfectly adjusted by the level on the vernier plate,
the telescope at 90° + _n_ will indicate a perfect vertical to the
station of the instrument above, the + _n_ being the allowance to be
made for the eccentricity of the telescope, provided the collimation
is perfect. If this is not perfect, the vertical may still be taken
accurately by means of three observations taken from equal division of
the entire horizontal circle, say at 360°, 120° and 240°.
507.--It will be noticed that the vernier to the compass circle
comes directly under the vertical arc, therefore it can only be read
obliquely when this arc is mounted: with open sights the vernier can be
read directly. This is a defect in this instrument, as the vernier is
mostly required for exact work when the telescope is used.
508.--Lean's dial possesses the qualities 1 and 4, pointed out in art.
490 as important to dials; in 4 the power of setting the telescope to
the vertical with great facility being the most important. This quality
has kept the dial a favourite with many mining engineers in mineral
districts for many years. Otherwise for general work the compass is
most inconveniently obstructed by the arc above it, and the instrument,
although, of course, of less height than the theodolite, some of the
functions of which it performs indifferently, is too high to be used
in shallow workings. The height of a 5-inch Lean's dial to the central
apex of the telescope is 9½ inches; to the top of the sights placed
in a level position, 8 inches; weight of instrument only, 6½ lbs.
The 6-inch instrument is about 1 inch higher, and weighs 1 lb. more.
509.--A number of variations have been made in Lean's dial; but none
that the author is aware of has proved successful. In an instrument
of this class, designed by Mr. J. Whitelaw,[21] the vertical arc is
brought down to the compass-box by placing pivots on each side of the
box after the manner of Hedley's dial, to be next described. This
lowers the instrument about an inch, and is an improvement; but this is
effected at the expense of placing a striding bar across the compass
box, which is a great impediment to the clear sighting of the compass.
Messrs. Newton & Son have made the telescope to detach from the arc of
Lean's dial to be placed directly upon the limb. In this way they claim
for it that it combines a miner's dial and dumpy level. The
arrangement appears to the author to make the instrument top heavy as a
dial, and to give too little power for a good level, added to which it
costs about the same as the two separate instruments of equal quality.
Of course any telescopic dial may be used as a level by clamping it at
zero. Practical surveyors generally object to compound instruments that
entail many loose pieces. These were a fashion in the middle of the
nineteenth century.
510.--_Examination of Lean's Dial._--As regards the stand, sights
and parallel plates, particulars have been given upon the plain dial
just described. The revolving compass should be turned round by the
milled head _P_, Fig. 207, of the pinion wheel _R_ to see that the
compass-box revolves steadily at all points without disturbance of the
needle. It may also be particularly observed that the needle does not
oscillate at any part of the circle, to be sure that the compass-box is
quite free from iron. The vernier should be examined at four opposite
positions of the needle to see that the needle is truly centred and is
in accord with the vernier. The lifter should be tried to see that it
lowers the needle gently on the centre, and that it holds the needle
firm off the centre. The telescope should be set up and directed to
an object, and all parts of the instrument clamped and the needle
observed. The telescope should then be detached and the sights set up,
to see that they range fairly with the telescope. If they do not do so
the difference should be noted and treated as a constant in any case
of change from telescope to sights on the same survey. The difference
ought to be very small, otherwise the instrument should be returned to
the maker.
511.--_The Adjustment of Lean's Dial_ is the same as that of the plain
theodolite, so far as this can be carried out; but generally the
adjustment is depended upon as it leaves the manufacturer. For the
general use of this and other dials some notes will be made further
on, but as regards vertical position and the taking of azimuth angles,
for which this dial is specially adapted, notes may be made here.
512.--_To set a line in Azimuth with one taken above Ground._--This is
necessary where there is local attraction to the needle below, or there
is a suspicion of this, so that the needle cannot be depended upon
with certainty. The instrument is placed on staging over the pit and a
vertical is taken to its centre either by the means briefly discussed
art. 506 by the instrument, or by suspending a plummet, a ball, or a
bullet from the centre of the instrument by a thread and burning the
thread when the ball is free from vibration. The ball is allowed to
fall upon a smooth horizontal surface formed of earth or otherwise,
in which it makes a dent which will be vertical to the axis of the
instrument if the ball has not been deflected by ventilation currents.
Two lights, as distant as possible to be seen to range in line with
the dent, are placed at the bottom of the pit. The lights, if thought
desirable, may range north and south with the needle; but in whatever
direction this may be set the correct azimuth of this may be taken by
cutting them by the webs of the nearly vertical telescope of the dial;
and this azimuth may be correctly set out on the surface by a pole or
other station mark, or its true direction by a pair of these, one on
each side of the pit's mouth, the second station mark being set out
after a shift of the horizontal vernier exactly 180° on the circle. A
straight-edged flooring board painted white may be made to cut the line
from light to light, which is more definite for bearing than the lights
themselves.
513.--=Hedley's Dial=, the invention of John Hedley, H.M. Inspector of
Mines, in 1850, has now become the most popular form of miner's dial,
modified, however, from its original form in various ways. The peculiar
feature of this form of dial is that the sights move upon a framework
centred upon a horizontal axis, so that they may by a rocking motion
take horizontal angles within a wide azimuth without obstruction to the
sight of the compass.
[Illustration: Fig. 208.--_Hedley's dial._]
514.--For consideration of the general features of Hedley's dial, the
tripod and the ball and socket are the same as that described for
the plain dial; but the socket is not cut down on one side to change
the position of the axis, as the compass-box in this instrument is
required to be kept uniformly level. The general appearance is shown
Fig. 208. For districts in which the working strata are fairly level,
parallel plates are put to this instrument in place of the ball and
socket joint. The compass-box revolves, as that described for Lean's
dial; but it is more general in this instrument to have a clamp and
tangent motion, as in a theodolite, than the rack and pinion motion.
Two levels for setting the compass horizontal are sunk into the plate
of the compass-dial low enough to miss the edge-bar needle. The step of
the compass is divided into degrees and the plate of the dial to 10°.
The vernier, which is placed on the opposite side of the box to the
vertical arc, reads to 3′, as described for Lean's dial.
515.--_The Rocking Centre_ forms the peculiar feature of Hedley's dial.
From opposite points of the under side of the compass two pivots are
projected. These are set perpendicular to the vertical axis, which is
placed above the ball and socket. The pivots are placed central with
the vernier and in line with E. to W. of the compass when this is set
to _zero_ (360°). The pivots form the axes of a stout ring--_rocking
ring_--which surrounds the compass-box, with space sufficient to clear
it when the ring is rocked about its axis. The ring has two extended
arms which carry sights as shown. These turn down upon the compass-box
when out of use. One of the pivots is prolonged for about ¾ inch
beyond the outer circumference of the ring. The prolongation is made
generally of triangular section. This forms a fitting to the vertical
arc, which is attached by a milled-headed screw when required, the arc
being an encumbrance when this dial is used for making horizontal plans
only.
516.--_The Vertical Arc_, with its index arm, forms a separate piece.
The arm is centred upon the arc with a ground fitting, which is
retained in its position by a collar fixed with three screws. The
arm-piece forms the axis, through the centre of which a triangular
hole is made to fit the triangular prolongation of the pivot, so that
the index arm remains fixed, and the arc moves with the rocking ring,
to which it is held by a pair of dowels. The arc is divided into
degrees on the outer edge of its surface, and a scale of difference
of hypotenuse and base upon its inner edge. The graduations read to a
single index line upon a fiducial edge carried down from an opening in
the index arm.
Hedley's dial can be locked by a pin, which is attached to the under
side of the compass-box, so as to work by the compass only. The ring
can also be locked level with the compass by a sling _latch-piece_ so
as to convert it into a plain dial.
517.--The great merit of Hedley's dial is that the rocking centre
permits a greater range of open sighting than any other; and the
instrument is very low, permitting its use in shallow workings.
Further, that it is a very strong instrument to resist accidents, and
is very portable. The height of a 6-inch Hedley's dial above the tripod
head, in a level position, is 9 inches to the top of the sights. Weight
of instrument, 7 to 10 lbs.
[Illustration: Fig. 209.--_Hedley's dial with ball clamp._]
518.--In the author's simple dial, Fig. 209, which is of a modern
form, the ball is clamped by a capping-piece over it moved to clamp by
two stout pins. This form gives a little less height and still holds
the dial firmly. The horizontal axis moves rather stiffly, so that no
clamp to the arc is required. It is a very cheap form of dial, but
substantially made. It answers for a small mine survey.
519.--There have been many variations made and proposed for Hedley's
dial. Mr. Casartelli, of Manchester, places the arc over the centre of
the compass-box.[22] This plan is intended to make the rocking centre
firm; but the arc interferes a little both with the sights and the
view of the compass box. Messrs. Davis and Son connect wheel-work with
the arc, so as to magnify the scale of motion. Other less important
variations in Hedley's dial are common.
520.--_Examination and Adjustment of Hedley's Dial._--The general
examination of the stand and of such parts of the instrument as
correspond with Lean's dial is the same as just given. The rocking ring
should be lifted and pressed down at each end alternately to see that
there is _no loss of time_ on the axis. The arc should be examined in
like manner. The dial should be set up in front of a plumbed line to
see that its sights range properly when the instrument is set level
by its bubbles. A point should be observed, say through the hole and
cross webs at the top of the sight; and with this point kept in view
the rocking ring should be moved upwards or downwards so that the
point traverses the plumb-line to the extent of the rocking motion. If
it does not do so, possibly the transverse level in the plate of the
compass-box may be adjusted to make it do so; but in this adjustment it
must be particularly observed that the balance of the needle remains
so that it still reads the graduation with its upper edge, and that
the sights traverse the same plumb-line when turned about, as it is
possible to set the level right with one pair of sights and throw other
parts out. There are no simple means of adjustment provided, so that if
the instrument is not accurate it should be returned to the maker for
correction.
521.--=Improvement in Hedley's Dial=, _by Addition of
Telescope_.--Surface work being generally performed with the
theodolite, surveying with open sights following this cannot be
effected with sufficient accuracy; therefore there becomes a necessity
for the use of the telescope, which was first placed on this instrument
by the author at the suggestion of Mr. W. Preece, C.E. In mines, also,
although sights present often the only possible means of directing
angular positions in cramped and tortuous workings, on the other hand,
better work can very often be done and the telescope be conveniently
used. Under these conditions, this addition forms an important
improvement in the instrument, to be at hand to apply when desired.
The telescope of this instrument detaches exactly as with Lean's dial,
but the sights are made with an angle piece, so as to extend them to
a distance of about 12 inches apart for sighting. Fig. 211 is of one
cranked sight. The instrument illustrated Fig. 210 has parallel plates,
art. 193, p. 99, suitable for fairly level workings. A ball and socket
joint is sometimes fitted to this instrument in place of these.
[Illustration: Fig. 210.--_Hedley's dial with telescope._]
[Illustration: Fig. 211.--_Bracket sight._]
522.--_The Telescope_ is placed on Y's, and is of exactly the same
form as that described for a plain theodolite. The Y's in this
instrument offer a great convenience for reversing the telescope for
back sights in range when the vertical axis is fixed. The level under
the telescope is sufficiently good to convert this instrument into a
level for drainage, etc., when the rocking ring is locked with the
compass. _Its examination and adjustment_ are the same as those last
given, except for the telescope, which is the same in all particulars
as that of a 5-inch plain theodolite.
[Illustration: Fig. 212.--_Improved miner's dial._]
523.--=Improved Miner's Dial.=--The illustration given, Fig. 212, is of
the form of dial introduced by the author, a part of the arrangement
only being of his own design. The telescope with Y supports is the same
as that just described, and the sights, _not shown_, are cranked in
the same manner as shown Fig. 211. The horizontal circle, instead of
being in the interior of the box, is placed on the exterior rim, and
reads with two verniers--not for correction, but for convenience of
reading in different positions. The compass is divided upon the upper
surface of the step to degrees, and in the same manner on the interior
cylindrical surface of the step. This last often permits the compass to
be read in a close working when the upper surface could not either be
lighted or sighted. This plan was used on old circumferentors.[23] The
plane of the compass is divided to 10° as usual. The compass adjusts
by clamp and tangent motion. The axis of the instrument is supported
upon a ball and socket arrangement designed by the author for roughly
bringing the compass to level, and a parallel plate adjustment for
final setting. The ball is fixed by clamping a pair of plates together
by a thumb-screw. Each plate is hollowed in the centre to hold nearly
half the ball. When fixed, the instrument is found to be very rigid.
524.--A plan of clamping designed by the author to meet the conditions
of the tribrach system of adjustment of equal rigidity to that above
described, is shown in elevation, Fig. 213 _B_. In this the upper half
of the socket is screwed down outside the lower half socket by means
of three projecting handle pins. This is a somewhat neater arrangement
than that shown in Fig. 212. Either of the above-described ball
arrangements elevate the instrument, and are better omitted for close
working if there is a special adjustment in the tripod attached to the
instrument, as that to be described presently, which will be found
sufficient in most cases. The height of the instrument from the tripod
is about 6½ inches; weight, 11 lbs. for both parallel plate and
tribrach adjustments.
525.--_Adjustable Tripod for Dials._--The author's improved form of
tripod is adjustable to all heights between 30 inches and 57 inches,
Figs. 213, 214. Each leg is formed of two stiff bars of mahogany, shown
in detail, Fig. 214 G of section, about 1¼ inches by 5/8 inch, and
a third bar or leg _G′_ of about 1¼ inches square, which slides
between the other two. The sliding surfaces are grooved and tongued
together in V grooves in the solid. Two strap-pieces of brass _SS′_ are
fixed near the ends of the bars. One of these _S′_ is firmly soldered
to a boss-piece that takes a thumb-screw, which has quite sufficient
power to hold the leg _G′_ firmly at any position of extension. It is a
rigid stand, which may leave the tripod head nearly vertical upon any
inclination of the floor surface.
[Illustration: Fig. 213.--_The author's adjustable ball joint and
socket tribrach stand._]
[Illustration: Fig. 214.--_Adjustment to leg of tripod._]
526.--=Hedley's Dials, with Pastorelli's and Hoffmann's Ball
Arrangements.=--By either of these arrangements the ball and socket is
brought down close into the parallel plate adjustment so that the dial
is of less total height. Hoffmann's is now becoming the most popular
system, as practice has shown it to be the most perfect for mining
survey. By either of these arrangements the ball and socket is clamped
by the same screws that bring the instrument to final position. In
Pastorelli's arrangement[24] the socket is drawn down upon the ball by
the adjusting screws. In Hoffmann's[25] the ball is pressed up into
the socket, which is the exact mechanical equivalent. When the screws
are lightly clamped the ball can be moved with moderate force, or even
quite loosely by careful adjustment; and in either case, when the ball
is once set, care must be taken to keep pressure constantly upon it
during the final adjustment by the screws. The general arrangements
are shown in two Figs. 215, 216, which are taken from the drawings of
the respective patents. In Fig. 215, _va_, the axis of the instrument
terminates in a ball _e_ which works in a cup _f_. The axis has also
a portion of a ball of greater radius _b_ concentric with the lower
ball _e_. The upper parallel plate _d_ is cupped over this ball. When
the parallel plate is moderately free on _b_, the axis _va_ may be
set to any angle within the range of the central opening of _d_; and
as the friction upon _bd_ is greater than that upon _fe_, the axis
moves by the adjustment of the parallel plate screws _aa_. In Fig.
216 the action is precisely the same, except that the pressure is
upwards instead of downwards. In Fig. 215 there are springs _s_ under
the parallel plate screw heads to keep contact when the screws are
loosened. In Fig. 216 the spring is a plate under the screws _s_, the
action being the same in both cases.
[Illustration: Fig. 215.--_Pastorelli's ball and socket adjustment._]
[Illustration: Fig. 216.--_Hoffmann's ball and socket adjustment._]
527.--Some objections have been made to this class of arrangement, over
the simpler one of clamping the ball independently and then adjusting
by the screws, as being more complex. On the other hand this compound
arrangement has the merit in underground instruments of being lower and
more compact, which is very important. The author has somewhat modified
the arrangements of Hoffmann's head, as shown in the engraving on next
page, to render it still more compact for mining instruments.
[Illustration: Fig. 217.--_Improved Hedley's dial, mounted on
Hoffmann's head._]
528.--In Fig. 217 an improved Hedley's dial is mounted upon an improved
form of Hoffmann's head. The whole arrangement is very compact, rigid,
and rapid in action. The height of this dial is 9½ inches; the
weight 8 lbs. for a 6-inch instrument, in aluminium 5 lbs.
[Illustration: Fig. 218.--_Improved Hedley, with cradle ring._]
529.--=Hedley's Dial with Cranked Rocking Centre.=--One defect of the
Hedley's dial, which in certain cases makes Lean's preferred, is that
with the rocking ring the sights cannot be brought vertical for looking
up or down a shaft. The author has devised a means of getting over this
difficulty by making the ring of cradle form, thus throwing the bearing
surfaces to sufficient height to cause the ring, when the arc is raised
to about 90°, to fall under the compass-box and its adjustments, Fig.
218. This dial presents possibly the greatest refinements of the Hedley
principle at the time of its patent, No. 9134, 1898. Since this date
the reviser has introduced a few further refinements as illustrated at
Fig. 219.
[Illustration: Fig. 219.--_Stanley's improved dial._]
This instrument has tribrach levelling with quick-setting spherical
lower plate, a sliding tribrach for centring over any desired spot,
and full clamp and tangent motions to both horizontal centres. The
dividing is upon silver on a 6-inch covered limb reading by two
verniers to single minutes, folding sights interchangeable with
telescope Y's, and this dial may be used upon any staging without its
stand. The somewhat peculiar shape of the cranked rocking ring is
necessitated by the movement of the sliding tribrach, which it has to
clear in all positions for reading vertical sights.
530.--=Accessories Common to Hedley's Dials= are a vertical reflector
and a diaphragm illuminator.
_Reflecting Cap._--One of the disadvantages of Hedley's dials over
Lean's was pointed out to be the impossibility of vertical sight where
the two last described dials are not used. Some years ago the author
devised a plan of obtaining this vertical sight by reflection by means
of a reflecting cap, Fig. 220, placed over the end of the telescope.
The cap is formed of a tube which fits the outer surface of the object
end of the telescope. This is prolonged sufficiently to lock it by a
dowel in correct position against revolution when the points that are
used for index in the diaphragm of the telescope are vertical. The tube
is cut in two and hinged to turn up, as shown in two positions _H_
and _H′_. When turned up it leaves the tube open for direct vision. A
reflector _R_ is placed in the cap, and there is an opening below it
equal to the full aperture of the telescope. It is easy to see that
by this means a pair of lights or a line may be sighted up or down a
shaft, and the azimuth of its direction be reflected to follow a line
by slightly rocking the telescope upon its pivots. This may be done,
however, with more refinement if there is a clamp and tangent motion to
the vertical arc, which is placed only on first-class instruments.
[Illustration: Fig. 220.--_Reflecting cap to miner's dial._]
531.--_Illumination of the Diaphragm_ for observing the webs or a
point, may be conveniently effected underground by employing a conical
ring reflector in front of the object-glass. The aperture through the
cone leaves the field of the object-glass nearly free, as it is only
necessary that the cone should project in front of this for a very
small distance. This reflector is placed over the object end of the
telescope when it is required, just the same as the ray shade. The
vertical reflector, Fig. 220, goes on the same fitting. The reflector
Fig. 221 _R_ may be made of silver or platinum. A light placed anywhere
opposite this, and perpendicular to the axis of the telescope will
throw sufficient light to show the webs or point. Sometimes a simple,
plain mirror placed on an arm bent over to the centre of the front of
the object glass, in which the mirror stands at 45° to the axis, is
used; but this plan is not so good as that shown Fig. 221, as the light
has to be brought to face the mirror quite perpendicular to the axis of
the telescope, and this process is frequently difficult to accomplish
underground.
[Illustration: Fig. 221.--_Conical reflector to illuminate axis of
telescope._]
532.--=Continental Forms of Miner's Dials.=--On the Continent generally
sights have been abandoned for miner's dials. The telescopes are
usually of short form, with large object-glass and wide field of view.
The telescope is generally placed eccentrically, which permits the
instrument to be made of very low form. There is a certain amount of
disadvantage in the eccentricity of the telescope, as angles cannot be
taken direct from the centre of the instrument but this is compensated
for in the plotting by making each station a small circle equal to the
amount of the eccentricity of the instrument to scale, and setting
off angles tangentially to this, which may be done with a little more
trouble than that of plotting the angle from a point.
533.--=French Miner's Compasses.=--Fig. 222 shows the simpler form of
this instrument. The needle is open and quite free from obstruction.
The telescope is centred about level with the compass-box. The
vertical axis has clamp and tangent adjustment. The transverse axis is
set entirely by hand as with the plain dial. The instrument is set up
level by its tribrach adjustment. The height with 5-inch needle in a
level position, without tripod head, is about 5 inches; weight about
11 lbs. without the tripod table. The extremely squat form of the
instrument permits its use in very close workings, with a short tripod,
if the workings are fairly level. It is used also as a cheap form of
surface surveying instrument, consequently it is not generally very
carefully made. As a good instrument of the class it cannot compete
with that to be next described.
[Illustration: Fig. 222.--_French form of miner's dial._]
534.--It will be seen by Fig. 222 that the instrument has no direct
connection with its stand or tripod. This is general with all French
and German instruments, even with theodolites and surveying levels, it
being the rule that the top of the tripod should form a kind of table
upon which the instrument is set up. The table is almost uniformly made
of wood, and is somewhat bulky and clumsy in construction, therefore
not very well adapted to mining surveying, particularly in wet mines.
Neither is the tribrach system of adjustment, unless it is supplemented
by some form of ball and socket arrangement, or with adjustable stand.
This subject will be further discussed in the description of superior
instruments presently.
[Illustration: Fig. 223.--_French miner's transit survey instrument._]
535.--=Miner's Transit Instrument.=--This is the _théodolite souterrain_
of the French, and is of a construction very general throughout the
Continent--Fig. 223. The compass is placed clearly in view. The
vertical axis has a clamp and tangent motion to bring the compass to
exact bearing if desired, or to permit surveying with the compass only.
The axis has also a clamp and tangent screw to the exterior divided
circle, which reads with two verniers. The telescope is placed on the
side of the instrument, and has clamp and tangent motions to read
the vertical circle which the vernier traverses in transit. All the
divisions are made strong to be read clearly by lamp-light, either to
1′ or 3′ by the vernier, as desired. A second level is generally placed
on some part of this instrument at right angles to the one shown. The
instrument is balanced by a counterpoise weight to keep its vertical
axis in equilibrium. The height of an instrument with 5-inch needle
is about 6¼ inches; the weight without the tripod table is about
14 lbs. The tripod table is constructed in various ways by different
makers.
536.--The value of the transit principle applied to mining instruments,
for taking back and fore sights for hanging lines in undulating strata,
by simply turning the telescope over on its axis, cannot be overrated
for exact work such as the telescope alone can perform. Further, with
this construction the inclination and difference of hypotenuse and
base for correction of the chain measurements may be taken. But it
is important in the use of this instrument to observe the side upon
which the telescope is situated at the time of observation, _right_ or
_left_. For this a column should be placed in the field-book. As a rule
fore sights are taken with the telescope _left_; back sights with the
telescope _right_, remembering that in plotting all angles are taken
eccentrically from the axis of the instrument, that is, tangential
to a small circle which represents the eccentricity of the telescope
according to the scale used in plotting.
537.--_The Tripod Table_ of a superior class of Continental
instruments, whether this is used for surface or mining surveying, is
usually made with some form of adjustment to bring the upper surface
approximately level before setting up the instrument. In this case the
table is made a combination of wood and metal; and the only difference
between mine and surface tables is that in the former case there is a
jointed arrangement for shortening the legs, but not in the latter. The
table surface for superior work is generally adjusted to approximate
level either by a ball and socket joint or by a pair of knee joints
placed at right angles to each other, with clamps to hold it firmly
when adjusted. Radial V-grooves are commonly made for the points of the
tribrach, and a hole is sometimes made in the centre of the table for
suspending a plummet from the axis of the instrument. There are many
forms of tripod table in use, a modified form of one of which in metal
will be described further on in the chapter on plane tables. There are
certain merits in this table arrangement over connective stands, as the
table is convenient to set up fairly level, and the instrument need not
be exposed until the operation is complete. On the other hand there is
more risk of upsetting and injuring the instrument by accident when
loosely placed on the table. There are, however, schemes more or less
complicated to prevent this, as by a screw fixed in the tripod head
acting against a spring which draws the instrument constantly down when
attached, and other contrivances, none of which is perhaps equal in
simplicity to Everest's arrangement for the tribrach, Fig. 191, p. 273,
on this particular point.
[Illustration: Fig. 224.--_Stanley's improved mining survey transit._]
[Illustration: Fig. 225.--_Stand for the same._]
538.--=Improved Mining Survey Transit.=--The author has modified the
form of instrument last illustrated, retaining the general principles.
In Fig. 224 the compass is made larger and reads in the inside of the
step as well as upon the surface, which is the only way in many cases
that it can be read in a close working. The reading of the horizontal
circle is placed nearly vertical, so that it may be seen clearly when
the instrument is near the roof of the mine. The vertical circle is
made smaller than the horizontal, as this circle, as a rule, is of
less importance, and it can generally be read more exactly from its
convenient position. The arrangement also permits greater freedom for
the use of the tribrach. The telescope is made with a much larger
object-glass than is usual, to take a wide field of view; therefore it
forms a good level.
[Illustration: Fig. 226.--_Stanley's miner's dial sight._]
539.--Two pairs of sights are placed upon the telescope, either for
roughly sighting an object or station, or to be used in difficult
positions. These are made on a new principle, shown Fig. 226. The
sights are placed in two windows, each of which is formed of a needle
point of platino-iridium. In sighting, the points are brought over each
other, the distant lamp or object appearing between them. A sharp point
gives much clearer definition than a hair, as it subtends of itself no
angle to the axis of the eye. _ab_ represent the pair of sights, _c_ as
they appear superimposed. This instrument is very conveniently fitted
with subtense points in the telescope, by which distances may be taken
with the author's staff, Fig. 105, p. 158, without actual measurement,
for the particulars of which see next chapter. The subtense points
are arranged to measure the staff either vertically or horizontally.
As a rule it will be found with this instrument better to take rough
positions first with the points, and afterwards by the telescope. The
instrument cannot be recommended universally for underground surveying,
but it is valuable under certain conditions in close strata. Its height
is 6 inches and weight 13 lbs.
Fig. 225 is an ordinary tripod, like that used with a level. This is
preferred by many mining engineers as being firmer than any jointed
arrangement, and is sufficient for working in a seam of fairly equal
thickness. The legs vary from 9 inches to the full height, 5 feet 4
inches. An ordinary set of three tripods would be 1 foot 6 inches, 3
feet 6 inches, and 5 feet 4 inches.
[Illustration: Fig. 227.--_Stanley's underground theodolite._]
540.--=Mining Theodolite.=--This theodolite is of the most convenient
form for underground railways, Fig. 227. The telescope transits on
its axis to be brought to a vertical position. The vertical axis is
pierced so that about 10° of angle may read below the vertical most
conveniently by means of a diagonal eye-piece. The centre is supported
upon a sliding fitting so that it may be displaced about 1¼ inches
about the centre of the tripod and be clamped to its position. The
horizontal axis is pierced to permit the diaphragm to be illuminated
by a lamp. The tripod stand is fitted with sliding legs, if it is to
be used for mine survey, to adjust for irregularity of surface of
the ground and for low workings. The form of the instrument is very
compact, rigid, and portable.
[Illustration: Fig. 228.--_Stanley's prismatic mining compass._]
541--=Prismatic Mining Survey Compass.=--This arrangement is designed
by the author for very close workings. The entire depth of the
instrument being only 4 inches, any reading may be taken from one point
of view simultaneously with the observation. The 5-inch compass, Fig.
228, has a floating ring divided to half degrees, and the reading of
this is reflected through a prism so that it appears directly under
the fore sight, to be seen at the same time. The prism has a slight
magnifying power, so that by estimation a bearing may be easily taken
to ¼ degree or nearer. The principle of the compass is described art.
148, the prism art. 55; but in this case the prism is raised and has
a second lens under it, so that it forms a kind of prismatic Ramsden
eye-piece. This elevation of the prism permits sighting under a certain
amount of downward inclination, regulated by the height of the prism
and the length of the back sight, as well as the upward inclination
which is common to the use of prismatic compasses. The most important
feature in this compass is the mode of lighting, which is effected by
means of a large prism, Fig. 229 _R_, placed under the compass-box in
a square tube, and a small movable lamp to throw light into it, Fig.
228 _L_. The floating ring, Fig. 229 _C_, is made of celluloid, quite
transparent, so that the divisions upon it are clearly read through the
small window in the cover of the compass-box. The fore sight _W_ is
jointed in two folds _jj_, so that it extends the distance of sights
to about 10 inches apart in use, and yet folds away closely to the
compass for portability when out of use. On the near sight a cut is
made transversely to the slit. A second similar cut on the fore sight
is made level with this to take levels roughly. About 20° are set off
on each side of the cut on the fore sight, so that angles of altitude
may be approximately taken--although the instrument is not well adapted
to this. Two levels set at right angles to each other, to be used in
setting up the instrument, are fixed under the compass-box. Weight of
instrument, 4¼ lbs. without the tripod stand.
[Illustration: Fig. 229.--_Section of prismatic mining compass._]
542.--=Hanging Compass.=--A very general method of underground
surveying in mineral districts upon the Continent is by means of the
_hanging compass_; this instrument is therefore generally found in
catalogues of surveying instruments in France, Germany, and Italy.
The original hanging compass was invented by Balthasar Rössler about
1660.[26] It appears to the author to be a valuable instrument for
surveying in tortuous mineral veins where sighting is difficult. The
measuring line upon which it is used is either a hempen or copper
cord or a chain. The compass is hung upon the cord or chain, which
may be stretched to any point out of sight, and the compass will then
indicate the bearing of the line. In Germany two instruments are used
simultaneously--the hanging compass for taking the bearing, and a
clinometer, composed of a light brass semicircle graduated to degrees,
with a small plummet for taking the inclination.
[Illustration: Fig. 230.--_Stanley's hanging dial._]
543.--=Hanging Dial.=--Fig. 230 represents a modification of the
hanging compass designed by the author, by which inclination may be
taken simultaneously with bearing, if the dial can be suspended near
the centre of the line or chain where the catenary curve is parallel
with its points of support.
544.--In the construction of the instrument a circle of brass about 6
inches diameter, ½ inch wide, and 1/8 inch thick, has two arms
extended to 12 inches at the upper part, on the end of each of which a
hook is formed for hanging the instrument upon a cord or chain. Upon
the lower part of the circle a _fork-piece_, with a bearing clipping
the circle, is attached by two screws. The fork-piece is constructed
to support two axes concentric to the vertical circle, in which the
compass-box is suspended much above its centre of gravity, so that it
falls by its own weight in use to a level position. Upon the edge of
the compass-box an index is brought up nearly to the interior surface
of the vertical circle, which reads into graduations upon this circle
into degrees and half degrees.
[Illustration: Fig. 231.--_Hanging clinometer._]
545.--=A Light Hanging Clinometer=, Fig. 231, shows the kind that is
used in Germany, of 5 inches diameter, graduated to degrees, made
of thin brass. It is packed in the case with the hanging compass,
described art. 542. The ends of the semicircle are formed into hooks
for hanging on the line. The plummet has a horse-hair line, which cuts
the degrees. The clinometer may be used only when the hanging dial Fig.
230 cannot be suspended near the centre of the line, in which case
this light semicircle will cause less deflection of the line, and give
the inclination approximately. For further details of the use of the
hanging compass the reader is referred to Mr. B. H. Brough's admirable
work on _Mine Surveying_.
[Illustration: Fig. 232.--_French semi-circumferentor._]
[Illustration: Fig. 233.--_Tripod head._]
546.--=Semi-circumferentor.=--This simple instrument can scarcely be
enumerated with mining surveying instruments, as it is much more used
for surface work; but being of the class of circumferentors to which
miners' instruments generally belong, this is the most convenient place
for its description. It has very general use on the Continent. Its
construction is very simple, Fig. 232. It is supported on a ball and
socket joint. The socket is formed in two pieces, which are clamped
together to hold the ball by a winged-headed screw. One pair of sights
is mounted upon the extreme ends of lugs upon the limb. The limb is
divided to half degrees. When the ball is loosely clamped the fixed
pair of sights may be adjusted to cut any desired object. A second
pair of sights is jointed upon an axis to move centrally between the
first pair. These are made shorter to pass within the first pair to
any angle around the arc, except the small angles with which the
sights themselves interfere when they are superimposed. The movable
sights carry verniers to read on the limb to 2′. There is a small
compass attached to the limb. As a cheap instrument for taking angles
approximately it is very useful, particularly for workmen employed
in carrying out work from drawings plotted from a survey by a better
instrument. The weight of the instrument with 6-inch circle is about 2
lbs.; height above tripod, 7 inches.
547.--The tripod of this instrument is made of wood. The head is shown
Fig. 233. The legs are simply extensions of the upper parts, which are
shown attached with bolts. The point of each leg has a steel shoe to
prevent it slipping in use. The head is turned to a cone, which fits
into the socket-piece of the instrument and permits it to be rotated
with moderate friction. The head is made of triangular section that
the legs may be clamped firmly to it. When used for underground work a
separate set of short legs is provided, which attach to the head by the
same bolts.
548.--=Lighting Underground.=--The old underground station, formed of
a lighted candle or lamp, is not now considered good in practice where
surface land is exactly defined by boundaries held by legal clauses and
rights. The system of underground surveying now very generally followed
is that first recommended by Mr. Thomas Baker, C.E., and afterwards
fully developed by Mr. H. Mackworth,[27] by which a station taken for
angular directions is formed by the position of the centre of a tripod.
For this system three tripods are provided for each instrument, with
head adjustment complete. These tripods are made in such a manner that
the instrument can be placed on any one of them in a level position.
Two lamps are provided, the flame of either of which will take the
position of the vertical axis of the instrument when the lamp is placed
upon the tripod formerly occupied by it. It is easily seen that by this
system fore and back sights or angular positions can be extended with
all the accuracy that the uniformity of the flame of the lamp will
permit.
549.--=Mining Survey Lamp.=--The author constructed this lamp from an
idea given to him by Mr. Geo. Kilgour, C.E., Fig. 234. It is somewhat
different from the ordinary form. Its accuracy does not depend upon the
regularity of the flame. A vertical axis is formed under the lamp,
which is made to the same fitting on which the mining survey instrument
is placed. The lamp is placed entirely eccentric to the vertical axis
in such a manner that a vertical line formed by a wire upon its face
may stand central and linear with the axis. A cross line is also placed
at the same height above the tripod head as the centre of the axis of
the telescope or cross sight. By this means, although the lamp throws
its light broadly in one direction only, the cross is a perfectly
defined object, easily picked up and brought to exact bearing in the
instrument when placed upon another tripod. In converting this lamp
from a fore to a back sight it has simply to be turned half round
on its axis, which is done without any displacement of the relative
position of the cross in vertical or horizontal directions. Where this
lamp is required in mines liable to fire-damp, it is made on the safety
principle of the Davy lamp.
[Illustration: Fig. 234.--_Mining survey lamp._]
Electricity has been applied to lamps for surveying. This plan has
been found successful where a secondary battery is used that can be
charged by a dynamo upon or in the mine, or with some of the modern dry
batteries.
[Illustration: Fig. 235.--_Stanley's complete mining outfit._]
550.--=Mining Targets.=--The three tripod system has been much
improved by the introduction of accurate targets made specially for
the instrument used, and interchangeable with the instrument on
either stand. The reviser has designed several forms of these. They
are generally used with a mining theodolite for high-class mine
surveying, and the lower part is similar to the lower part of the
theodolite they are used with. Instead of a horizontal circle, they
simply support a plate carrying cross levels, and a pillar carried up
to bring the target level with the optical centre of the telescope of
the theodolite; this part is made to fit the outer centre of the lower
part into which it is held by a special clamp. The theodolite is made
with a double outer vertical centre, and this is held to the lower part
similarly clamped, so that the theodolite and targets all lift out of
their centres and interchange with each other. A complete mining set
of this description is shown at Fig. 235. This forms a very complete
mining outfit. It consists of a highest-class tacheometer with quick
setting spherical lower plate, mechanical centring stage, auxiliary
top and side telescope, illuminated axis, striding level, also two
targets with quick setting spherical lower plates, mechanical stages,
cross levels, and swivelled sighting crosses. All three are made with
lift-out centres, which are interchangeable, and all have base plates
permitting their use on any staging or fixing without their stands. The
targets are sometimes made to hold candles instead of the swivelled
cross, and sometimes with plain steel points only.
The auxiliary telescope is the special form designed by Mr. Dunbar
Scott, and it embraces all the advantages and eliminates all the
disadvantages of all other types.
The particular feature is its interchangeability with top or side
positions, and the means provided to ensure perfect adjustment with
the minimum of trouble, thus forming a mining transit which will
perform with exactness all the complex functions in mine surveying and
requiring no correction for eccentricity.
The auxiliary telescope is provided with a centre that may be screwed
to the threaded extension of either the transverse axis or the vertical
pillars of the main telescope. In either position it is clamped firmly
and ranged quickly into alignment with the main telescope by two
opposing screws. The diaphragm of the auxiliary telescope has one web
only, so placed that it is vertical when on the top and horizontal when
at the side.
[Illustration: Fig. 236.--_Stanley's Dunbar Scott auxiliary._]
The observation of steep horizontal angles is made only with the
auxiliary on top, and of precipitous vertical angles with the auxiliary
on the side. A counterpoise is provided, which exactly balances the
auxiliary, so that there is no strain upon the instrument.
For vertical sighting it is also most useful and accurate, as by
transferring the lines of both positions of auxiliary two lines are
transferred down a shaft, at right angles to each other, which, if
produced, will intersect each other exactly under the centre of the
instrument, and no allowance or calculation whatever has to be made to
ascertain the centre.
The whole attachment adds very little to the weight, the greater part
being of aluminium, and it is packed separately in the case so as not
to interfere in any way with the instrument when not in use.
In Fig. 235 the auxiliary telescope is shown at top; Fig. 236 shows it
attached at the side.
551.--=Pocket Instruments.=--A very light pocket instrument has been
designed by Mr. D. W. Brunton, which will be found useful; he terms
it a pocket mine transit, but of course it has nothing to do with a
transit. It is designed for roughly taking horizontal and vertical
angles, and answers the purpose of a prismatic compass, clinometer and
Abney level, and is very portable, made in aluminium, and weighing only
8 oz. It is shown at Fig. 237.
[Illustration: Fig. 237.--_Pocket mine transit._]
The cover is provided on its inside with a mirror, and this acts as a
back sight; it is opened out to an angle which reflects the fore sight,
and the object sighted and the reading of the needle is then taken. It
is necessary to hold the instrument firmly against the body and see
that it is level sideways by placing the spirit level across the box
and bringing the bubble to the centre of its run, while any turning
movement should be made by turning the body from the hips. For vertical
sighting the fore sight is used as the back sight, and the mirror in
the lid moved to reflect the bubble, the back sight being formed by
the hole in the mirror seen at the bottom of the centre line, the
clinometer bubble is then moved till the air bell is seen in the centre
of its run and the vernier reading taken.
552.--=Dip Compass.=--This consists of a magnetic needle suspended
between centres so as to move readily in a vertical plane, and is
shown at Fig. 238. When in use the ring is held in the hand and the
compass-box by its own weight takes a vertical position; it must then
be held in the plane of the meridian. In this position the needle when
unaffected by the attraction of iron assumes a horizontal position.
When brought over any mass of magnetic iron ore it dips, and thus
detects the presence of such ore with certainty.
[Illustration: Fig. 238.--_Dip compass._]
If held in a horizontal position it serves as an ordinary pocket
compass and thus indicates the magnetic meridian in the plane of which
it should be held when used to ascertain dip.
FOOTNOTES:
[19] Plate xiv., fig. 5. _Geometrical Essays_, Geo. Adams, 1803.
[20] _Proc. Min. Inst._, Cornwall, 1883, vol. i. p. 317.
[21] Patent No. 1592, April 1878.
[22] Patent No. 1857, J. L Casartelli, May, 1874.
[23] Illustrated plate xv. Fig. 1., _Geometrical Essays_, John Adams,
1803.
[24] Pastorelli's patent, No. 2714, 1863.
[25] Hoffmann's patent, No. 2084, 1878.
[26] _Geometria Subterranea_, Voitel, 1686.
[27] _Subterranean Surveying_, Thos. Fenwick, Lockwood.
CHAPTER XII.
INSTRUMENTS TO MEASURE SUBTENSE OR TANGENTIAL ANGLES TO ASCERTAIN
DISTANCES--HISTORICAL NOTES OF THE METHOD--PRINCIPLES INVOLVED--
STADIUM MEASUREMENT, DIRECT AND BY THE ORDINARY TELESCOPE--CORRECTIONS
FOR REFRACTION OF THE OBJECT-GLASS--STANLEY'S SUBTENSE DIAPHRAGM--
ANALLATIC TELESCOPE OF PORRO--TACHEOMETERS--STADIUM--FIELD-BOOK--
OMNIMETER AND ITS FIELD-BOOK--BAKEWELL's SUBTENSE ARRANGEMENT.
553.--=Direct Subtense Measurement of Distances=, _by an Instrument_,
depends upon our powers of measuring the image of a distant staff or
stadium, or the divisions marked thereon as they appear at the focus
of the telescope. If the stadium is placed at right angles to the
direction of one of two sight lines which subtend a given angle, the
number of units divided upon the stadium cut by these lines will be
proportional to units of length of base or cotangent for a constant
focus of the telescope; so that if we can measure at a fixed angle the
number of equal units of measurement of a stadium correctly, we can
obtain its exact distance; and whether this method is more or less
exact than chain measurement will depend entirely upon the perfection
with which either of these operations may be practically performed.
554.--_The Origin of the Invention of Subtense Surveying_ was thought
to be due to Wm. Green, an optician of Great Moulton Street, London,
who was awarded a premium for its invention by the Society of Arts
in 1778. He published a pamphlet giving a description of his method
in 1778.[28] This subject he pressed upon the notice of professional
men at the time, and his method has continued in use in this country
ever since. His refracting telescope, which alone has remained in use,
formed part of the theodolite. A micrometer was placed in the focus
of the eye-piece of the telescope, which revolved a quarter turn in
its axis to read angles vertically or horizontally. He constructed his
micrometer with lines fixed at a given distance apart, and by a second
method with the lines adjustable. For this adjustment a fine line
was ruled upon one side of two pieces of glass. The ruled sides were
placed face to face, so as to be at the same focus. One of the lines
was adjustable by a micrometer screw. His staff was 20 links in length
by 4 inches in width, divided decimally into 1000. His description of
the manner of using his instrument will give a general idea of working
the others which have been derived from it--tacheometers, omnimeters,
etc.--and this is worthy of note, as the invention, though generally
attributed to him, was not his:--
555.--"To find the contents of a field with either of the instruments
described, let the telescope be placed so that the observer may see
all its angles from his station. If near the centre of the field
the better. The person who carries the scale (_staff_) is to go all
round the field, stopping at every angle, and to place the scale at
right angles to the axis of the telescope (_passing_) from corner to
corner (from right to left if required) with the help of a signal
by the observer. After the distances all round the field are taken
(_by measurement of the image of the micrometer_) and all the angles
included betwixt them, with the theodolite, plot it out in the usual
manner, _e.g._, with a nonius protractor. Describe a circle, and on
this circle set off all the angles from the centre through each point
upon the circumference. Set off the length of every line by a scale
of equal parts. These points will give the limits of the field, which
may be laid out in trapeziums, triangles, etc., and measured from the
same scale of equal parts. The surveyor will comprehend how easily the
contents of the field are found by trigonometrical calculation, since
by this method there are two sides and one included angle given.
"The common method of measuring with the chain, besides the
inaccuracies to which it is liable, does only give the length of the
surface of the ground between two objects, and therefore not its proper
distance, unless the surface be straight and no object to hinder its
being measured from one end to the other. How often this is practicable
I leave to the consideration of those who are most accustomed to
measure lines, and doubt not that upon the whole they will find
the telescope method has besides ease, accuracy, and universality,
necessity itself to recommend it."
He points out the utility of the system for levelling, as "both
distance and inclination may be taken at the same time." He finds by
experiment that the accuracy of the method exceeds that which he could
reasonably expect by calculations deduced from theory, by several
circumstances in its favour being inseparable from it.
"The observer's station is the centre of circle whose radius is the
distance required, which is obtained by measuring the length, that is,
the tangent or subtense, of the small arcs whose limits are defined
by viewing their image in the focus of a telescope between two points
there placed, and moving them up and down until they appear to touch
the very extremities of said limits exactly. The manner of seeing is
natural and by practice will become habitual, and therefore continually
approach nearer to perfection.
"Thus may any surveyor in less than two hours take all the dimensions
of an irregular polygon necessary for obtaining its area, if it be as
much as 80 or 100 acres and limited by twenty or thirty unequal sides."
Green points out that if the subtense angle is taken horizontally,
atmospheric refraction error is eliminated. He proposes to use both
reflecting and refracting telescopes. With the reflector he possibly
obtained accurate results, but with the refracting telescope he does
not appear to have recognised a constant correction which is necessary
and important.
It has since been found that in 1778 the Danish Academy of Sciences
awarded a prize to G. F. Brander for a similar device, which he had
applied to his plane-table, six years before. Its real discoverer was
James Watt, who used it in 1771 for measuring distances in the surveys
for the Tarbert and Crinan Canals. In James Patrick Muirhead's _Life of
James Watt_, he gives a statement by Watt himself that he constructed
his instrument in 1770 and showed it to Smeaton in 1772.
556.--=Subtense Instruments=, as that originally made by Green, are
of some form of theodolite, the telescopes of which are constructed
to measure either the angle subtended by the chord of a small arc
or the tangent of the same. For convenience the tangent is more
generally taken upon a graduated stadium or staff, which is erected for
measurement perpendicularly to the horizon, the principle of which is
shown in the following scheme:--
[Illustration: Fig. 239.--_Diagram of tangential angle measurement._]
Let _AC_, Fig. 239, be a horizontal line; _BC_ a stadium set up
vertically. Then if the angle _BAC_ and the height _BC_ are known,
the distance of _AC_ can be easily calculated. For any intermediate
distance between _A_ and _C_ a vertical will be in length proportional
to this distance. Let _de_ be at one-third the distance from _A_; then
the line _de_ will be one-third the length of _BC_. If we divide _BC_
into three parts and place the stadium at _fg_ two-thirds the distance
from _A_, the angle _dAe_ given by an instrument subtending a fixed
angle will cut the staff at the second division, equal to two thirds
the staff, which demonstrates the principle of all tacheometers, Cleps,
etc.
If the tangent be made a constant equal to the length of the stadium
_BC_, and this stadium be placed at another position, say _de_ or _fg_;
then the angle subtended by its entire length will vary in a manner
that can only be estimated by trigonometrical calculation.
In case of reading two distant marks on the stadium only for the
subtense, the single central web of the telescope being directed first
to one and then to the other of these webs, the distance is calculated
as follows:--
Given the tangent _BC_ and the angle _BAC_, required the distance _AC_.
Let the angle _BAC_ be represented by _D_; then--
_CA_ / (_CB_) = cotan _D_, or _CA_ = _CB_ × cotan _D_.
Reducing by logarithms, we have--
log _CA_ = log _CB_ + _L_ cotan _D_ - 10.
For example, make _CB_ 14 feet, and the angle _D_ 2° 45′ 50″, thus:--
log _CB_ = 1·146128
_L_ cotan _D_ - 10 = 1·316265
----------
log _CA_ = 2·462393, or _CA_ = 290 feet.
The above gives the principles followed with instruments of the
theodolite class simply; but arrangements are made in omnimeters and
similar instruments to read the tangent directly and determine the
height _CB_ in equal parts, so that observation of the heights _BC_
gives rectangular co-ordinates and thus saves reduction from degrees of
arc.
In practice the staff or stadium is made of the greatest length
convenient for portability. With a telescopic staff, 14 or 16 feet is
commonly used. If a unit tangent be not employed, the foot is divided
into 100 parts, each of which parts, with the tacheometer, represents 1
foot of the base, and the whole staff 1400 or 1600 feet. The ordinary
Sopwith staff, art. 263, answers the purpose, but art. 268 better.
557.--_Measuring Distances by the Ordinary Telescope by Measurement
of its Focal Image._--When we apply a refracting telescope to measure
a subtense angle by webs fixed in the diaphragm, vision is not direct
as in the scheme Fig. 239, but subject to bending caused by the
refractive quality of the lens, art. 58, the telescopic focus varying
with the distance from the staff. Thus with a 12-inch telescope there
will be a difference of about ·25 inch in the focus, whether the staff
is held at 50 or 500 links from the telescope; and this difference
of focus is equal to a difference of base or cotangent between the
points _A_ and _C_ in the last figure, so that these distances do not
remain proportional to the fixed unit of the tangent or stadium. It is
important to go carefully into this subject of the use of subtense webs
in the ordinary telescope, as the necessary correction does not appear
to have been recognised by English writers on instruments, and no doubt
this is the principal reason that subtense measurement has not been
more practised in this country.
558.--At the commencement of the last century, Riechenbach, a Bavarian
engineer, pointed out a method still in use on the Continent. The
author is indebted to the kindness of Lord Rayleigh for the following
demonstration of Riechenbach's formula:--
[Illustration: Fig. 240.--_Subtense diagram._]
Let Fig. 240 _AB_ = _s_, _ab_ = _i_, _OA_ = _d_, _Ob_ = _r_. _O_ is the
optical centre of the object-glass; _ab_ a pair of webs at variable
distance _r_ from _O_ according to telescopic focus; _f_ focus for
parallel rays. Then by similar triangles _s_/_d_ = _i_/_r_ or _d_ =
_rs_/_i_, _r_ is found by optical laws to vary in the proportion of
1/_r_ + 1/_d_ = 1/_f_. We may therefore eliminate the variable _r_ by
substituting its value _r_ = _fd_/(_d_ - _f_), by which we find _d_ =
_sf_/_i_ + _f_, which gives the true correction; and the distance from
the axis of the instrument will be _d_ = _sf_/_i_ + _f_ + _c_ where
_c_ is the constant distance of the object-glass from the axis of the
instrument. It is usual to place the vertical axis of a theodolite
central between the object-glass and the diaphragm at solar focus, so
that the constant _c_ becomes _f_/2.
It is seen that _sf_/_i_ represents the direct subtense, whereas the
refraction, which is a constant, gives f and the position of the
object-glass _f_/2. Riechenbach's formula being true for parallel rays
is evidently also true for any subtense with refraction for the staff
at any distance. We may therefore adopt a plus constant of 1½_f_,
which added to the apparent subtense is found to produce no error. Thus
with a telescope of 1 foot solar focus, and using the decimal system
of notation, as before mentioned, if a stadium or distinct scale be
placed at 301½ feet distance from the centre of the instrument,
and the webs or points of the diaphragm be adjusted to read 3 feet =
300 divisions, every subtense may afterwards be taken as number of
divisions read + 1½ feet for distance in feet. If the subtense is
to be taken in links or metres the dividing of the stadium will be to
these measures, but the constant remains the same 1½ feet always.
559.--When the line of sight is inclined from the horizon and the
stadium is held erect--a convenient method commonly followed upon the
Continent--the reading becomes in excess of the true reading, in the
ratio of the cosine of the angle of the stadium, represented by a line
tangent to the sight-line subtended to the foot of the stadium, as
shown in the following diagram.
[Illustration: Fig. 241.--_Diagram of vertical stadium on an incline._]
Thus, Fig. 241, let the portion cut by the lines _AB_, _S′_ be the
reading of the stadium; then
_S′_(cos _a_) = _S_.
The inclined distance is then equal to
(_f_/_i_)_S′_(cos _a_) + _f_ + _c_
and the horizontal projection of that distance or
_a_ = ((_f_/_i_)_S′_(cos _a_) + _f_ + _c_)cos _a_;
or as _f_ + _c_ is small and the angle generally small also, _f_ + _c_
may be taken equal to (_f_ + _c_) cos _a_. Then
_a_=(_f_/i)_S′_ cos^2 _a_ + _f_ + _c_.
[Illustration: Fig. 242.--_Stanley's patent subtense diaphragm._]
560.--=The Subtense-diaphragm= of the author, Fig. 242, forms the
eye-piece of a theodolite. It has movable indices which are separated
according to a scale formed by calculation upon the data of the above
formulæ. By this, distances may be taken in the horizontal plane for
land of any inclination without after calculation. This result is
obtained by observing the angle of inclination upwards or downwards
on the theodolite and setting the micrometer to this angle before
reading the subtense distance. The reading is taken by points which
are arranged to measure the subtense 1 to 100, so that the ordinary
Sopwith staff may be used. The diaphragm at zero appears as an ordinary
subtense-diaphragm. It may be observed that this diaphragm may be used
as a good check, as distances may be taken over any irregularities of
intervening incline and give the true base for the entire distance.
561.--If the mean contour distance is required from station to station,
this may be taken directly by subtense from the staff-reading held at
right angles to the axis of the telescope. The means of doing this,
devised by the author, is to place a _sight director_ of a special form
upon the side of the staff, Fig. 243. This small piece of apparatus
is shown attached to the staff. It consists of a small telescope
three inches long attached at right angles to the staff by means of a
dovetail slide fitting when in use as shown. The staff-holder sights
the tacheometer through the short telescope, which can only be seen to
appear therein by moving the staff until it is approximately at right
angles to the direction of the tacheometer.
[Illustration: Fig. 243.--_Sight director for stadium._]
562.--=The Anallatic Telescope.=--In this telescope the focus is
constant, and consequently the tangential measurements indicated by
the numerical qualities subtended by a constant angle are directly
proportional to the base, so that there is no constant to be added. The
invention of this instrument and its modern application to subtense
measurement was due to Professor J. Porro, of Milan, who put it to
practical test in 1823,[29] in an instrument termed a tacheometer. The
telescope will be best understood by the following details:--
The object-glass _O_, Fig. 244, is made of a focus that falls well
in front of the axis of the instrument _CC′_, so that the rays cross
before falling upon the anallatic lens _A_, the optical arrangement
being such that if the rays fell direct without any refraction
they would reach the axis and subtend angles therefrom inversely
proportional to the distance of the stadium. The object-glass and
anallatic lens are of the same focus, so that the rays after crossing
from equal refraction may emerge parallel in the space _A_ to _M_.
The stop at _S_ and at the axis _CC′_ cuts off eccentric rays that
would otherwise give internal reflections from the telescope tube.
The eye-piece, represented by _MF_, may be made to pick up the image
of the stadium in front of it upon an ordinary webbed diaphragm or
upon ruled glass. The diaphragm webs are fixed, or the glass surface
engraved with three or five horizontal lines and one vertical. The
outer horizontal lines are used generally as the subtense lines, and
the central line for levelling and taking altitudes. The vertical line
is used for triangulating on the surface of the ground.
[Illustration: Fig. 244.--_Diagram of anallatic telescope._]
563.--There is an adjustment made by sliding tubes to bring the
object-glass and anallatic lens within mutual focus to ensure the
parallelism of the emergent rays and to adjust magnification. This is
commonly effected by means of a rack and pinion, moved by a separate
key kept in the instrument case, but which should not be touched after
the instrument is once adjusted by the maker, except in the case of
accident. It is much better made without this rack adjustment and
permanently fixed by the maker, as if it has the adjustment it is
likely to be tampered with and thus defeat its object. The eye-piece
adjusts to distance from the object-glass in the ordinary manner of the
surveying telescope--by rack and pinion.
564.--The eye-piece of the anallatic telescope is generally made
of much higher power than those ordinarily employed for levels and
theodolites--25 to 30 diameters is usual. Where a diaphragm is used the
subtense lines are commonly placed on a slip of glass in two or three
sets, so that greater magnitude of image may be taken for objects at
distances of from 2 to 7 chains with the 14-feet staff, or that the
staff may be read at greater distances than 14 chains. This series of
lines is distinguished as 50, 100, and 200, Figs. 245, 246 and 247; so
that with this as great a distance as 28 chains with a 14-feet staff
may be estimated, but this is beyond the safe power of the instrument.
The intermediate line, as shown Fig. 220, is valuable in all cases for
levelling. The advantage of the increased power of the eye-piece is
more than neutralized by the loss of light.
[Illustration: Figs. 245, 246, 247.--_Subtense lines ruled on glass._]
[Illustration: Fig. 248.--_Adjustable point diaphragm with stadia
points._]
565.--While many civil engineers are satisfied with a single percentage
pair of subtense lines the author much prefers using the point system,
arts. 237 to 239. In this case the diaphragm, as made by the author,
possesses two systems of adjustment; that shown Fig. 248 at a for the
single point for altitudes, and the pair of points separated by the
spring _ss_ for subtense angles. These points adjust by separate screws
top and bottom with a milled-headed key _f_. The two verticals are
fixed permanently. These points are all made of platino-iridium, which
possesses the hardness and elasticity of spring steel, and is at the
same time, as far as is known, perfectly non-corrosive. In case of any
light dust or moisture resting upon the points, it is perfectly safe to
brush them lightly with a soft camel-hair brush to clean them. Where
the 200 factor is required, a mean may be taken of two observations
above and below the central point. Where 50 is required, the vertical
points may be adjusted to this.
566.--In adjusting the lines, webs, or points to a given subtense, the
anallatic lens may be moved to give more or less angular displacement
or magnification of the image. Greater accuracy is obtainable when the
staff is held normal to the line of sight instead of vertical. If the
staff be held incorrectly in the inclined position at great angles of
elevation or depression, the resulting error is very much smaller than
in the case of an equal variation of the staff from the true vertical
position. When adjustment is made upon a distant stadium at small
angles of elevation or depression, the subtense of the small arc will
vary so little from a tangent to one of its radii that the one or other
may be taken without sensible error. The plan originally proposed by
Green of placing a sight tube through the stadium at right angles to
its face, as a means of keeping it in the chord of the arc, is as good
as any other, but is more cumbersome than that described art. 561. If
the vertical stadium be preferred, this may be set up by the small
level, Fig. 109, p. 163.
567.--It is well to note that with the anallatic telescope the stadium
must not be so near that the rays from the object-glass _do not
cross_ in front of the anallatic lens or the subtense will appear
much increased, so that there is a fixed nearness at which this form
of telescope can be used, say 50 feet. For this reason engineers
generally prefer an ordinary telescope, making use of the addition of
a constant. The author also prefers the plain telescope, as being more
correct according to his experiments where the constant is correctly
allowed. There are many advantages in the use of a plain open telescope
instead of the anallatic telescope for tacheometers, among them the
following may be mentioned. More light reaches the eye because there
are fewer lenses; there is no intermediate lens requiring adjustment
and which becomes dirty and bedewed and is inaccessible for cleaning,
and for the same dimensions of the telescope greater power can be
obtained. A larger telescope and of higher power is of great advantage
in subtense measurement, but the full advantage is not obtained in
the anallatic telescope. The idea which appears to be still common
that an ordinary open telescope will not give accurate results at
all distances by means of stadia readings, plus the distance of the
anterior principal focus of the object-glass from the axis of the
instrument, is entirely erroneous. When a staff is held at any distance
in front of the object-glass of an open telescope, an inverted image
of the staff is formed at the conjugate focus which subtends an angle
at the corresponding nodal point of the lens, equal to that subtended
by the staff at the other nodal point. If a diaphragm with two stadia
points or webs be placed at this conjugate focus the ratio _i_/_f′_ =
the ratio _l_/_D_; where _i_ is the space between the stadia points,
_l_ the height on the staff which these points appear to intercept
when viewed through the eye-piece accurately focussed on them, _D_ the
distance of the staff from the object-glass, and _f′_ the distance
of the diaphragm from the object-glass. Now in this equation _i_ is
a fixed space, _l_ is the observed height on the staff, and both f′
and D are variables, of which it is desired to find the value of D.
From the laws of optics it is also known that 1/_f′_ + 1/_D_ = 1/_F_
where _F_ is the principal focal length of the lens. Therefore _f′_
= _FD_/(_D_ - _F_) for all values of _D_. Substituting this value
of _f′_ in equation (1) we get _i_ × (_D_ - _F_)/_FD_ = l/_D_; and
multiplying both sides by _D_, _i_ × (_D_ - _F_)/_F_ = _l_. ∴ _D_ -
_F_ = (_F_/_i_)_l_ and _D_ = (_F_/_i_)_l_ + _F_ which is true for
all distances. But this distance is measured from the object-glass,
and the distance _S_ required by the surveyor is that from the axis
of the instrument, and it is therefore necessary to add that of the
object-glass from the axis _d_. ∴ _S_ = _D_ + _d_ = (_F_/_i_)_l_ + _F_
+ _d_, and _F_ + _d_ is the constant of the instrument = _c_. ∴ _S_ =
(_F_/_i_)_l_ + _c_.
When the range is greater than that at which the divisions of an
ordinary levelling staff can be clearly read with the stadia points,
target stadia rods or targets fixed to a levelling staff are used.
It is usual to use plain targets fixed with their centre lines at
exactly 10 or 20 feet apart or other convenient distance, and the
angle subtended by these is measured by a micrometer diaphragm. The
reviser, in conjunction with Mr. C. W. Scott, B.A.I., A.M.I.C.E., has
designed a micrometer diaphragm which has been proved to give very
accurate results. It is made to revolve, so that either horizontal or
vertical stadia rods may be measured, and it is fitted with fine fixed
platino-iridium points, which are much more satisfactory than webs or
lines engraved on glass. These are fixed on one side of the diaphragm,
two each 1/200 part of the principal focal length of the object-glass
above and below the axial point. On the other side of the diaphragm
is a movable point which can be traversed over the fixed points by a
micrometer screw, every complete turn of which moves the point over
a distance equal to 1/1000th of the principal focal distance and the
head of the micrometer being divided into 100 parts, it reads to the
one hundred-thousandth part of the same; while a small star-wheel
records the number of complete revolutions, five of which cover the
space between any two of the fixed points. In using this micrometer
with say a 10-foot target, let the lower target cross-bar be clamped to
the level staff at 2 feet, and the upper target cross-bar at 12 feet.
Direct the axial point to the centre between the targets at 7 feet and
read the angle, then bring the nearest fixed point to the top or bottom
mark by means of the tangent screw, and bring the micrometer point
to the other mark by the micrometer screw. The micrometer reading is
the reading on the divided head plus the hundredths indicated on the
star-wheel plus 500 for each included complete space between the fixed
points. See whether the micrometer reads up or down, and set the fixed
point to the lower or upper mark on target accordingly. To obtain the
distance from the axis of instrument, divide 100,000, multiplied by the
length of the target by the micrometer reading, and add the constant of
the instrument _S_ = 100,000_l_/_x_ + _c_ where _x_ is the micrometer
reading, and _l_ the length of the target. The tacheometer which the
author has lately made has a plain open telescope, but this is of the
same size as that used upon the Porro system, and consequently it gives
much more light and better definition.
568.--=Tacheometers= consist essentially of any form of theodolite that
is provided with means for reading distances by its telescope. Stadia
work is simply another name for tacheometry, which is derived from the
Greek _tacheos_ (quickly), and _metreo_ (I measure), and signifies the
art of measuring rapidly. The graduation of the arcs and circles of
these instruments is sometimes made upon the centesimal system, the
circle reading 400 grades, which are subdivided to half grades to read
with the vernier or micrometer to centigrade minutes of ·01 grade.
The centesimal system facilitates calculation, and permits a free
use of a logarithmic slide rule of a special kind. In France, where
working with this system at one time became more general, we have very
complete centesimal trigonometrical tables adapted to the tacheometer
published in stereotype,[30] but it has not gained favour, and very few
instruments are now so divided. A compromise which has found a certain
amount of favour is the decimal division of the ordinary degree of 90
to the quadrant; this greatly facilitates the calculation compared
with what is necessary with the sexagesimal division into minutes
and seconds and the reading of the verniers is much simpler and less
liable to errors. Moreover, the mental conversion of the sexagesimal
division into decimals of the same degree is much simpler than the
conversion into the centesimal degree of 100 to the quadrant. Any
instrument divided sexagesimally can be converted by simply changing
the vernier if the divisions on the limb are degrees or half degrees.
The theodolite, Fig. 169, the author made specially for a tacheometer.
Any theodolite may be converted into a tacheometer by fitting it with
a subtense diaphragm. A modern tacheometer should be a high-class
theodolite in which every possible refinement is included.
569.--The tacheometer, although manufactured for many years for export,
has been very little used in this country. The instrument to be
described, shown Fig. 249, is the author's latest pattern. It is made
with sexagesimal division or ingrades, to read by the verniers to 20″
or to centigrade minutes. The telescope is of much larger and of higher
power than that of the ordinary theodolite. For a 6-inch instrument the
telescope is of 11 inches focus, with an object-glass of 1¾ inches
aperture. The eye-pieces are of the Ramsden form of powers 18 and 25.
The points in the diaphragm are set to cut 100 divisions of the stadium
at 100 units + constant of the measurement intended to be taken, links,
feet, or metres. This precludes distant measures, say of over 15
chains, where a 16-feet stadium is used, but they are made adjustable
so that they may be set, if desired, for any other subtense, although
this is not recommended. It is doubtful whether the subtense method
can be considered as reliable at a distance of over 1500 links; or at
any rate we must assume that much greater accuracy can be obtained
by dividing distances greater than this into two by an intermediate
station for observation, independently of the additional convenience of
having the staff-holder within easy distance of communication.
[Illustration: Fig. 249.--_Stanley's 6-inch tacheometer._]
570.--Where points are not used in the diaphragm or where lines are
preferred, these may be divided upon glass in fine lines as Fig. 246;
or spider webs may be used, but these are more difficult to set exact
for stadia.
571.--=Stadium.=--Any accurate levelling staff will answer for the
stadium, but the ordinary Sopwith, Fig. 99, is slightly confusing. A
more open reading is generally recommended--that shown Fig. 102, p.
155, which the author designed for the purpose, answers perfectly. It
is better to read the stadium low, as there is less vibration; but it
is not often possible or at any time advisable to read it from the
bottom--1 foot up is generally most convenient. Readings are taken and
recorded of each subtense web, or point, separately, and the difference
of reading subtracted for the subtense of tangent. With a point
diaphragm for taking the subtense angle a fair certainty of accuracy
of measurement of distance within ·002 may be assured, which is much
nearer than can be attained by average chaining, taking six times the
labour.
572.--_The General System of Working the Tacheometer_, with sufficient
detail for practice, would take too much of our limited space to be
given here. We now have several good works published in Great Britain,
in addition to the able paper by Mr. Brough before mentioned, such
as _The Tacheometer: Its Theory and Practice_, by Mr. Neil Kennedy;
_Surveying_, by Whitelaw; _Aid to Survey Practice_, by L. D'A.
Jackson, &c. There is a small work published in New York giving some
details.[31] There are complete works in French, Italian, German, and
Spanish. In French, _Leves de Plans a la Stadia_, by M. J. Moinot,
engineer to the Paris, Lyons, and Mediterranean Railway, gives very
complete instructions for all conditions of country, upon surveys which
he has personally carried into practice with this instrument.
There are several tacheometers made upon the Continent, of more
complicated forms than those herein described, but they do not produce
better work.
573.--=Field-books= for the tacheometer are ruled in various ways in
columns, which vary in number in different books from twelve to twenty.
The French generally have fourteen columns, giving the number of the
station, time, heights of line of collimation above point levelled,
numbers of points selected, horizontal and vertical angles observed,
reading of subtense webs and their differences, height of staff by
reading central web, and columns for calculations and remarks; most
English forms are more simple.
[Illustration: Fig. 249_a_.]
574.--A convenient protractor in which the equivalent of surface
reading is taken from a scale upon its lower part directed from the
centre of the protractor is here shown.
[Illustration: Fig. 250.--_Perspective view of 5-inch omnimeter._]
575.--=The Omnimeter= is one of the class of instruments in which the
tangent to a radius proceeding direct from the axis of the telescope
is represented by the stadium made of constant length, the subtense
angle varying with the distance. The omnimeter is the invention of
Chas. A. C. Eckhold, a German engineer, described in the provisional
British patent[32] as "a person living in Alexandria." The instrument
as originally devised consisted of a kind of theodolite to which the
subtense tangential system was added as an entirely separate part.
The important part of the provisional specification shows that the
principle of the invention consists in the use of two sights to the
instrument, one a telescope to sight the object, and the other a
powerful compound microscope to read divisions upon a tangential scale.
The telescope and microscope are firmly united together in parallel
position with their axes exactly crossing the transverse axis of the
theodolite, so as to move together through the same angle by the motion
of the telescope in traversing the azimuth. A delicate level is placed
upon the telescope, and when the bubble is in the centre of its run
the scale is truly at right angles to the axis of the microscope. The
scale in the early instruments stood vertically at the extreme edge
of the instrument in a position lateral to the object-glass of the
telescope. It was finely divided to millimetres, and read the intervals
of the divisions by means of a micrometer screw with a vernier.
[Illustration: Fig. 251.--_Details of omnimeter, showing section of
microscope and scale._]
576.--With the instrument as originally constructed, it was found that
the delicate scale, protruding vertically to the extreme edge of the
instrument, was very liable to injury unless supported by heavy metal
work, which rendered the instrument cumbersome. A great improvement
was made in this instrument, which brought it to its modern form, by
placing the tangent scale in a horizontal position, where it could
be firmly fixed upon the vernier plate as shown Fig. 251 _S_, and
reading the scale by means of a reflecting prism _P_ in the eye-piece
of the microscope. In this improved instrument, as the microscope and
telescope are still united on one axis so that they move at equal
angles to each other, it is clearly indifferent whether the scale be
placed vertically or horizontally, provided it is placed truly at right
angles to the microscope when the axis of the telescope is horizontal.
The scale, which is 4 inches long, is placed in a sliding fitting to
adjust longitudinally to its position by means of a micrometer screw.
In the English instrument the scale is divided into 100 parts for
calculation. The divisions are subdivided by shorter lines, making the
actual division 200. The micrometer screw has 50 threads to the inch,
and moves over one of the divisions of the scale only. The micrometer
head is divided into 100, numbered at the tens; a vernier placed
against the head subdivides each of these divisions into 5, making the
total micrometer 500 for one complete revolution. The total division
of the 4-inch scale therefore becomes: 200 (divisions of scale) × 500
(micrometer) = 100,000 in 4 inches. The scale is placed centrally to
the instrument, so that when the telescope is level the microscope is
vertical, and reads 50,000 when in perfect adjustment.
[Illustration: Fig. 252.--_Details of prismatic eye-piece._]
577.--The general appearance of the instrument resembles the transit
theodolite, already described art. 368, in every way except for the
addition of the microscope and scale, shown in perspective in Fig.
250. The details of construction of the microscopic apparatus may be
followed in Fig. 251. _T_ telescope with sensitive level _B_ mounted
upon it; _R_ body of microscope connected solidly upon the same axis
as the telescope, shown in half section. The eye-piece is placed at
right angles to the microscope and telescope, and reads through the
reflection of a prism _P_ to the face of the instrument. The details
of the eye-piece are shown in section Fig. 252. The tangential scale
is shown in section Fig. 251 _S_ with the micrometer with edge reading
vernier at _M_. The compass of the instrument _C_ is of the trough
form, and placed on the opposite side to the level to be used after
transitting the telescope from the position in which it is shown in the
figure. The axis of the connected telescope and microscope is exactly 6
inches above the surface of the tangential scale _S_.
[Illustration: Fig. 253.--_Omnimeter webs; a telescope, b microscope._]
578.--The telescope diaphragm is generally webbed with one horizontal
and two vertical webs, Fig. 253 _a_, the altitude reading being
taken from the top of the horizontal web, and the horizontal angular
position from the centre of the interval between the vertical webs.
The microscope diaphragm _b_ has two horizontal webs, and reads from the
centre of the interval, which is judged by the eye. Observed in this
manner, there is no error due to covering angle subtended by the webs
themselves. The most exact reading is obtained with a fine point.
579.--_Reading of the Tangent Scale._--As the micrometer divides half
a principal division into 500, the complete _figured_ divisions are
therefore divided into 1000. This is done for the sake of decimal
notation. In reading it is only necessary to observe that the shorter
or half division is 500, which must be added to the micrometer reading
when it is past this division; as for instance 65½ reading is
65,500, and say the micrometer reads 234 past this, the reading is then
clearly 65,500 + 234 = 65,734, just as before described for reading
half degrees with the vernier.
580.--_Value of the Scale taken in Rectangular Coordinates._--The
radius from the transverse axis of the telescope to the tangent surface
of the scale is exactly 6 inches. The scale is 4 inches divided into
100,000 parts, as it is read with the aid of the micrometer and
vernier. The radius therefore in terms of the scale would be at 6 to
4, that is 150,000. By this we see that the divisions of the scale
by the angle subtended give tangents, the value of each division of
which is the reciprocal of this on 150,000 of the radius or base to
any unit we may select. If we make the unit 1 foot, then one division
represented by a unit of change of position of the vernier reading,
and consequently of equal angular change in the direction of the
axis of the telescope, would give a tangent of 1 foot upon a stadium
placed at 150,000 feet distance. If the stadium were made 10 feet, as
is usual, the same angular magnitude would be traversed in ten times
this distance, or over 280 miles, making the value of the units of the
vernier 1,500,000. This will give a general idea of the delicacy of the
instrument so far as constructive principles are concerned, and not its
performance.
581.--_The Stadium_ is marked off in a number of feet, links, or
metres, according to the unit taken for measurement of the surface
of the land. The English stadium is generally formed of a 14-feet
levelling staff, with the surface painted with a ground of plain
white. At 10 feet apart two black bands about 2 inches wide are
painted in, leaving in the centre of each band a clear white line of
about one-tenth of an inch in width. These white lines are carefully
set to 10-feet standard centre to centre. But a better plan is to
have two equilateral triangles painted, with their apices meeting to
the centre. An intermediate 5-feet line is drawn in black, which is
found convenient for near measurements, to avoid too great angular
displacement of the telescope. When the measurement is in chains, 15
links or 20 links may be taken for the distance of the lines apart to
give the tangent. For metre measurement 3 metres are commonly taken for
the stadium division. These are in each case subdivided. The lowest
stadium reading should be 1 foot at least from the ground to avoid
grass and other obstructions.
[Illustration: Fig. 254.--_Ruling of omnimeter field-book._]
582.--_Field-book._--The field-book as shown above, Fig. 254, was
recommended by the inventor.
583.--_Mode of Operating with the Omnimeter._--Carefully set the
instrument up at its station in perfect adjustment as a theodolite,
noting the departure point upon the scale reading through the
microscope. Place the stadium in a vertical position at the point to
which measurements are required. Direct the telescope so that the
horizontal web cuts the upper line of the stadium, and lightly clamp
it. Now read the microscope and record the reading as observed in
the field-book. Unclamp the telescope and take the reading of the
lower point of the staff and record this. Record the bearing of the
instrument on the horizontal circle as with a theodolite.
584.--_To Determine the Horizontal Distance in Feet._--Divide the
constant radius of 1,500,000 given before by the difference of the two
readings of the stadium mark, which are 10 feet apart. For example:--
First reading of scale 67,500, micrometer 235 = 67,735
Second " 64,000, " 450 = 64,450
Difference 3,285;
then 1,500,000/3285 = 456·6 feet distance.
The process is somewhat simplified by logarithms, as we have only the
log. of the difference to subtract from the constant, the 1,500,000
mantissa of which is 1,760,913. Thus--
log. 1,500,000 6·1760913
log. 3,285,000 3·5165354
---------
2·6595559 = 456·6 feet.
585.--_To Determine Horizontal Distance in Chains_ the stadium should
be marked as just described for feet, but at 20 links distance from
line to line. Then the radius 150,000 × 20 gives 3,000,000. Taking for
example, readings as before with difference of 3285 we have--
3,000,000/3285 = 913·2, or 9 chains 13·2 links distance.
_To Determine Horizontal Distance in Metres_, the stadium is divided
to 4 metres. Then radius 150,000 × 4 = 600,000. Taking, for example,
difference of reading as before 3285 then
600,000/3285 = 182·64 metres.
586.--_Levelling--Taking Altitudes._--To take the elevation of the
staff above the level of the instrument, subtract the reading of the
scale, when the axis of the telescope is level, from the lower reading
of the staff on the scale, and divide by the distance difference, as
found by the method discussed before, then multiply this by 10 feet.
Thus taking the lower reading as before 64,450 and the constant for the
level position of the instrument, say 50,010, we then have--
Lower reading 64,450
Level " 50,010
------
Difference 14,440
then 14,440/3285 × 10 = 43·96 feet nearly. The heights, in relation to
the position of the instrument, are _positive_ or _negative_ according
as the scale readings are greater or less than the constant level
reading or departure point.
587.--_Work of the Omnimeter._--The perfection of the principles of
the omnimeter would lead anyone to infer that work might be done with
it of the highest degree of accuracy. The testimony of the greatest
authorities show by comparison that it is unable to compete in this
respect with the best made tacheometers. A large number of these
instruments are employed in India. Colonel Laughton reports upon
it--"It has been found to give very accurate heights of buildings,
etc., also to be wonderfully accurate when used as a levelling
instrument; _but it is not so accurate for measuring distances over_ 600
_feet_, and even at this distance the error sometimes amounts to as much
as 1 _foot_. It is recommended as admirably adapted for city surveys
and traversing, also in hilly and jungly countries, and for railway and
similar purposes."[33]
588.--Wherein the instrument fails to give exact results is no doubt in
the difficulty of its manipulation. For taking two readings, which are
necessary for every operation in distance, the instrument has
necessarily to be set twice, the hand being placed upon the micrometer
for the second observation while the attention is upon the sighting of
the telescope; and even when the readings are taken by the telescope,
the microscope has to be separately adjusted to read the micrometer
scale. In the repetition of these processes it is almost impossible
to avoid some slight disturbance of centre by pressure. In distant
readings atmospheric changes giving difference of refraction occur
quickly, so that there is more risk of error from two separate
observations than if the observations of the subtense webs are
taken simultaneously, as with the tacheometer. Further, any defect
in workmanship or wear tells seriously against the readings of the
instrument. Its advantages are theoretically that a wide angle is
subtended by the stadium with the omnimeter in short distances which
must be in every way an advantage. Further, since the early general
use of the omnimeter, the tacheometer has been greatly improved,
particularly in providing it with a larger and better object-glass so
as to obtain greater field of view, that fairly near stations may be
taken with it that were formerly only possible of reading with the
omnimeter. The manufacture of omnimeters is now very limited; the
subject is only retained in this edition because there are still some
hundreds of these instruments in use.
589.--_Improvement in the Omnimeter._--One improvement in this
instrument by Mr. W. N. Bakewell, M.Inst.C.E., consists in turning
the body of the microscope to a right angle at the position of the
transverse axis of the omnimeter, and placing a reflecting prism at the
angle. By this means the eye-pieces of the telescope and the microscope
are brought side by side, greatly facilitating the joint readings. A
second improvement is in making the scale 1,000,000 instead of 150,000,
which much facilitates calculation, but it is doubtful if these
improvements will stay the declining popularity of the omnimeter.
[Illustration: Fig. 255.--_Bakewell's tangential arrangement to a
theodolite._]
590.--=Bakewell's Tangential Arrangement= _to a Theodolite for
Measuring Distances_.--This arrangement, which gives the distances by
direct reading without calculation, was devised by Mr. W. N. Bakewell
to extend the power of an ordinary 6-inch transit theodolite fitted
with subtense webs. The observations are made on marks at 3 feet and
13 feet on an ordinary Sopwith staff--a 10-feet base, as is usual with
the omnimeter. Any other base may be used if the distances registered
are proportionally altered, or the scale may be divided to suit. It
was first applied by the author to a theodolite that had been in good
service, without the necessity of making any structural alterations in
the instrument.[34] The measuring apparatus consists of a tangent screw
impinging upon a radial plane, with micrometer and vernier. The details
will be readily comprehended from the engraving, Fig. 255, and the
following full description.
591.--The transverse axis of a theodolite, upon the opposite side of
the telescope to that upon which the vertical arc is fixed, is turned
down to a cylindrical surface true with the pivots. A collar _A_,
which fits the cylindrical surface, is slit up on one side to enable
it to be clamped firmly to any position of the axis by a clamping
screw _B_. The collar is connected in the same gun-metal casting with
the radial arm _C_ that terminates at _T_ in a plane, which is made
truly radial with the transverse axis of the telescope. This radial
arm _C_ has a long German-silver spring _S_ at the opposite side to
the radial plane, which keeps it up firmly in contact with the point
of the micrometer screw. A screw is cut on the drum of the micrometer
_D_; on the spiral the scale of distances is engraved; and readings are
taken from a line on the index _I_ which slides on the bar _E_. The
scale being one of reciprocals the divisions are at unequal distances,
so a vernier cannot be used; consequently at long ranges where the
divisions are close, the subdivisions must be estimated. Where this is
too rough a method, resort must be had to calculation. The outer end
of the drum _D_ is divided into 200, and reads by vernier _V_ carried
by the arm _E_ in 5 or thousandths of a revolution. The micrometer
screw has twenty-five threads to an inch, and the radius of the arm
_C_ is 4 inches. One complete revolution of the screw is one-hundredth
of the radius, and using a base of 10 the radius factor is 1000 ×
100 × 10 or 1,000,000; consequently Barlow's or any other table of
reciprocals can be used, and the distances obtained, by inspection
with comparatively little labour. This additional part has not range
sufficient for altitudes, being available for about 2 degrees only.
The distance may be taken as a subtense or small tangential angle at a
radius which, with the azimuthal angle taken by the vertical arc of the
theodolite, will give altitude by its sine and horizontal distance by
its cosine in the usual manner. The principle is that of the omnimeter,
and it possesses the same objection for perfect performance, that the
theodolite has to be handled twice for the two observations necessary.
592.--=The Gradienter Screw.=--This is no doubt a simplified copy of
Bakewell's tangential arrangement and is shown at Fig. 256.
[Illustration: Fig. 256.--_Gradienter screw._]
It is a micrometer screw fitted to a tangent arm, which can be clamped
to the trunnion of telescope when the latter is in any position.
The screw is cut of a value that causes the web of the telescope to
move 50/100 of a foot at 100 feet distance for each revolution, and the
head of the screw is divided into 50 parts, consequently each division
upon the head represents a movement of the cross web of the telescope
of 1/100 of a foot upon a scale placed at 100 feet distance. The scale
on the arm over the gradienter screw indicates the number of complete
revolutions of the head, therefore, if the screw be revolved two whole
revolutions the two divisions covered on this scale indicate 50/100 × 2
= 1 foot to the 100 feet.
_To establish any grade with this screw._--Set the gradienter head to
zero, then level the telescope and clamp the gradienter arm. Suppose
grade required be 1·75. Turn the gradienter head through three whole
revolutions, which will equal 150, then go on turning through 25 of the
divisions on the head and the total movement will be 1·75, the required
grade.
_For Measuring Distance._--First with a staff for moderate distances.
Any space on the staff covered by two complete revolutions of head
is 1/100th part of distance, thus, if the difference between the two
readings be 3·475 feet the staff is distant 347·5 feet.
_Second Method._--For long distances with any rod of known length, such
as a 20-foot stadia rod. Send out a man with the rod which he holds
vertical at place to be measured. Then measure its length with the
gradienter screw; say it takes 2 revolutions and 45 divisions over,
thus 2 revolutions = 100 and 45 extra divisions = 145. Then--
20·00 feet/1·45 × 100 = 1379·3 feet.
Another instance.--Suppose the man at a distance has no stadia rod.
He simply holds up any stick, say a walking stick. Measure this in
telescope. Say it subtends 1 revolution and 28 divisions. This = 78.
When your man comes in with the stick, measure its length. Say it was
3·25 feet. Then--
3·25 feet/0·78 × 100 = 416·6 feet.
The above illustrations are for readings taken approximately level.
If there be much elevation or depression the angle must be read and
the difference of hypo and base calculated and the stadia rod or staff
must be inclined so that its face is at right angles to the line of
sight from telescope. This can be done by the rod man inclining the
staff or rod until the shortest reading is given if a staff be used, or
the longest measurement is recorded by the gradienter screw head if a
stadia rod be used. It is better in this case to have the staff fitted
with a director (see art. 561), so that the person holding the staff
may sight into the telescope of the instrument, thus ensuring the staff
being exactly at right angles to the line of sight.
No constant should be added with either this, Bakewell's, or omnimeter
measurements, as the angles are taken from the centre of the
instrument. This gradienter screw has the same fault as mentioned for
the two foregoing, viz., that all readings are taken by two movements
of the instrument.
FOOTNOTES:
[28] _Description and use of an Improved Reflecting and Refracting
Telescope and Scales for Surveying_, by William Green, 1778.
[29] _La Tachéomètre, ou l'Art de Lever les Plans et de Faire les
Nivellements_, Paris, 1858.
[30] _Tables Trigonométriques Centésimales_, by J. L. Sanguet, Paris.
[31] _Manual of the Theory and Practice of Topographical Surveying by
Means of the Transit and Stadia_, by J. B. Johnson. New York.
[32] Patent, prov., No. 1859, June, 1868; patent No. 3759, Dec., 1868.
[33] _Report on Omnimeter_, by Major G. A. Laughton, Superintendent,
Bombay Revenue Survey.
[34] _Proc. Inst. C.E._, vol. xcii. part ii. p. 248, 1887-1888.
CHAPTER XIII.
INSTRUMENTS CONSTRUCTED ESPECIALLY FOR OFFERING FACILITY OF TAKING
INCLINES--INCLINOMETER--THEODOLITE--GRADIOMETER--CLINOMETERS--ABNEY'S,
TROUGHTON'S, DE LISLE'S, STANLEY'S, BARKER'S, BURNIER'S, WATKINS'--
CLINOMETER SIGHTS--RULE CLINOMETERS--ROAD TRACER.
Certain instruments are constructed specially with the object of taking
inclines, where this is the predominant work to be performed with them.
They form an important branch of surveying instruments, and for their
special kind of work present many time-saving capabilities.
593.--=Lister's Inclinometer Theodolite.=[35]--This instrument is the
invention of Mr. James Lister, C.E. It was originally designed to set
out upon the surface of land the widths of slopes or batters by pegs,
as required in the execution of railway, canal, and other earth works.
In general construction it resembles a theodolite as before described,
arts. 370 to 391, with the addition of an extra vertical axis to the
telescope piercing the horizontal axis at right angles, Fig. 257. In
this construction the telescope upon the horizontal axis can be set
by the vertical supplementary axis to any inclination, so that if the
vertical axis be set to the slope of a railway cutting, any number of
points or pegs may be set out continuously with the same setting by
direct observation through the telescope across any irregularity or
inclination of the land surface. In this operation an immense amount of
labour is saved over the ordinary system of pegging by calculation with
the aid of a theodolite, where each peg requires a separate setting of
the instrument. When the inclinometer theodolite is used for surveying
purposes, the telescope is fixed by a spring catch which places it
firmly true to the reading of the ordinary vertical arc.
[Illustration: Fig. 257.--_Lister's inclinometer theodolite._]
The instrument is also fitted with a mechanical device for repeating
the tangential angles when operating on curves, which obviates the
necessity of reading them on the horizontal arc, thus facilitating the
work. This will be referred to in the following explanation of the
manipulation of the instrument as the "angle repeater."
The main difference between the method of taking cross sections by
the level and by the inclinometer theodolite is in substituting
inclined bases for horizontal ones, which will be clearly understood by
reference to the following diagrams, which illustrate somewhat extreme
surface inclination.
[Illustration: Fig. 258.]
[Illustration: Fig. 259.]
Fig. 258 shows the levelling method and Fig. 259 the method by the
inclinometer theodolite. In the first it will be seen that each section
requires to be taken singly with repeated changes in the position of
the instrument at each section, involving numerous readings on the
staff, booking, and reduction of the levels for changes only. Also
the sectional measurements require to be taken in short horizontal
lengths with the plumbing of the end of the tape at each length. By the
inclinometer method this unnecessary labour is avoided, there being no
changes in the position of the instrument, as from one setting a series
of sections may be taken on either side of it. There is no reduction
of levels, and the sectional measurements are taken on the surface to
which the base line is always approximately parallel.
The saving of labour is even more marked in the setting out of slope
pegs than in the taking of cross sections, for in addition to the
transference of level from the centre pegs to the outcrop of the slope
several approximate calculations have to be made before the exact
position of the slope peg can be found, while by using the inclinometer
theodolite it is only necessary to put in normal slope pegs at
intervals of a quarter of a mile, or at such distances apart that a
ranging rod may be seen from one point to the other, and by setting up
the instrument at each alternate peg, or at half mile intervals, the
whole of the intermediate pegs for a quarter of a mile on each side of
it can be "boned" as simply as ranging a straight line, the telescope
being inclined to, and revolving in the plane of the slope. In this
manner as much work may be done in a few hours as will take a week with
the levelling method, and this without the slightest physical or mental
strain to the operator.
594.--_Explanation of the Method of Operating with the Inclinometer
Theodolite._--For setting out a centre line of railway, etc., and
putting in level pegs the instrument may be used as an ordinary
theodolite, or even as a level, and the work performed in the usual
manner. It may also be used as a level when setting out the normal
slope pegs on slightly inclined ground surfaces, but when the
inclination is considerable it may be used in a special manner with
advantage as hereinafter explained.
595.--_To take Cross Sections when the Line is Straight._--It is
unnecessary to explain the use of the instrument when the ground
surface is comparatively level, so as to require no change in position
and resetting of the instrument, it being obvious that in this case
it may be used simply as a level with advantage; but when the surface
is inclined in the direction of the centre, and also at a right angle
thereto in the direction of the section lines, the method of procedure
is as follows:--
Assuming that it is desired to take a series of 15 sections (and this
is within the limit of the number that can be taken from one setting of
the instrument), set up the inclinometer, preferably over the centre
peg of the series, in such a position that the two front legs of the
tripod stand across the centre line, and the back leg (which has a
distinguishing mark) rests upon the centre line. Set the lower limb of
the tribrach stand upon which the instrument is supported to a level
condition in its lateral direction by manipulating the back leg, and at
the same time observing the bubble on the stand. This will enable the
instrument to be subsequently tilted to a certain extent in a perfectly
vertical position. Clamp the horizontal arc to zero and direct the
telescope to the centre line. Clamp the lower limb and bring the arc
round to an angle of 90°. The vertical arc is now at right angles to
the centre line and parallel with the section lines. Now release the
telescope from the vertical arc and turn it again on the centre line,
and by working the back adjusting of the instrument (or in case of
necessity manipulating the back leg) tilt the instrument until the
cross web of the telescope is elevated to a short distance above the
seventh or most distant peg of the sections, or site of the first
section to be taken. Now tilt the vertical arc until the cross web
assumes a position parallel to the general inclination of the ground
surface laterally. Clamp the arc to this inclination and note the angle
thereon, for this will be the angle of the inclined base from which the
whole of the sections will be taken and subsequently plotted.
Commencing at the seventh peg at this side of the instrument, the
sections may now be taken consecutively to the seventh peg on the other
side by taking readings on a level staff held in an inclined position
at a right angle to the cross web or base, as shown in Fig. 259, and
oscillated that the lowest reading may be taken. A reading must be
taken on the centre peg at each section to establish the height of the
base above the peg. The base may be raised or lowered at any section,
or part of a section, to meet any excessive elevation or depression
of the ground surface which might prevent the staff being read, but a
separate reading on the centre peg at each variation of the base must
be taken, thus:--Fig. 260.
[Illustration: Fig. 260.]
The bases being parallel the angle of inclination remains the same.
The tilting of the instrument produces a variation in the angle of the
vertical arc, but this is only to such an infinitesimal extent that
unless the tilt be excessive it may be disregarded. The correction,
however, may be simply made after the instrument has been adjusted for
any operation by ascertaining or simply noting approximately the angle
of the tilt, and setting off this angle on the horizontal arc towards
the tangent line, thus varying the chord or base line to this extent,
or it may be found by referring to a table of natural sines, etc.,
and multiplying the cosine of the angle of the tilt by the tangent of
the vertical arc angle, the result being the tangent of the corrected
angle, thus:--if the angle of the tilt be 10°, and the vertical arc
angle 25°--Referring to tables, cosine 10° = ·98481, tangent 25° =
·46631. ·46631 × ·98481 = ·45924 = tangent 24° 40′, the corrected angle
making a variation of 20′.