Improvements in and connected with Tacheometrical Instruments.
Year: 1895

page_text: Date of Application, 24th May, 1895
Complete Specification Left, 15th Oct., 1895-Accepted, 7th Mar., 1896
PROVISIONAL SPECIFICATION.
[Communicated from abroad by JAMES DONNAN, of Balaghat, in the Central
Provinces, British India, Assistant Engineer, Government of India, Public
Works Department.]
Improvements in and connected with Tacheometrical Instruments.
I, WILLIAM HENRY BECK of 115 Cannon Street in the City of London,
Consulting Engineer and Chartered Patent Agent, do hereby declare the nature
of the said invention to be as follows:-
The present forms of tacheometrical instruments are mostly made on one of the
following principles viz.; (1) the angle of deviation of the telescope being constant,
the height of the staff cut off varies with the distance or (2) the height of staff cut
off being constant, the angle of deviation varies with the distance. The staff
employed in both classes of instruments is divided into sections, painted or otherwise
marked on the wood.
The disadvantages of these devices are (1) that owing to the variations due to
focal lengths neither the angle of deviation nor the length of staff can be maintained
truly constant for all horizontal distances, hence causing inaccuracy in the result
obtained; (2) that owing to the divisions on the staff being difficult to make out at
any considerable distance work cannot be accurately done beyond say one thousand
feet. This calls for constant removal of the instrument, and requires a number of
places of observation thereby necessitating a great consumption of time in the
setting up, and the readjusting of the instrument. If the distance of observation
could be increased and the focal variatious eliminated it would minimise these
drawbacks.
The object of this invention is to construct an instrument whereby :-
(1) The horizontal distance of any point up to say three thousand feet from the
point of observation, (2) the total rise or fall of this point in relation to the point
of observation, and (3) the bearing of this line from the north (magnetic) or the
horizontal angle subtended between any two lines which meet at the instrument,
can be easily ascertained with accuracy at varying horizontal distances irrespective
of the focal variation.
With these ends in view the inventor has devised the instruments I now proceed
to describe.
An ordinary level or theodolite telescope is supported by two vertical supports as
in an ordinary theodolite, so that the telescope can move freely in a vertical plane
between them. The eyepiece of the telescope has cross wires or lines marked on
it which intersect each other in the line of collimation, and is provided with a
suitable focussing screw. A bubble tube or spirit level is also provided which can
be adjusted to the line of collimation of the telescope. An arm in the axis or
trunnion of the telescope can be moved freely in a plane parallel to that in which
the telescope itself moves and has a screw by means of which it can be clamped to
the said axis of the telescope at any desired inclination to the line of collimation
thereof. The said arm is rotated by means of a screw which moves in a segmental
groove fixed to one of the supports of the telescope. The arm is clamped at any
part of the groove by a clamping screw. The arm has a lengthening bar which
moves in and out of a slot therein, being actuated by a screw. The end of this

page_text: lengthening bar is provided with an indicator which is hinged to enable its point to
move in a plane at right angles to the lengthening bar. A horizontal scale is
provided, graduated to say the tenths and hundredths of an inch and having a
Vernier scale graduated so that say 99 of the 100 inch divisions of the
horizontal scale are equal to 100 of its divisions. This vernier is moved backwards
and forwards horizontally along the edge of the horizontal scale by means of a
suitable screw or otherwise. By means of this graduated scale and the vernier,
measurements to the Tobooth part of an inch can be taken. A bubble tube is
attached to the aforesaid scale. The instrument is supplied with two horizontal
circular plates the edges of which are marked in the manner usual to theodolites
for ascertaining horizontal angles. These are fitted with a vernier, magnifying
glasses, clamping and tangent screws as usual in most theodolites but these are not
features of the present invention.
The instrument has the usual stand of three screw legs.
The staff used in conjunction with the instrument, which the inventor calls a
Terrameter, is preferably about 15 feet long, 4 inches wide, and 2 inches thick, or
any other suitable size, with feet and inches marked on the back. Such divisions
are not however for reading off by the telescope, but as a guide to the placing of
two discs at any required height of the staff. The aforesaid discs may be about
two feet in diameter for example and made to slide up and down on the staff,
and they can be fixed at any desired height on the staff by screws or otherwise so
that a certain known distauce between the centres of the two discs exists. They
are divided into quadrants which are painted red and white alternately or in any
other distinctive manner to correspond with the lines on the glass of the eyepiece
of the telescope.
The end of the staff which is intended to rest on the ground may have a brass
shoe, and the other end may have a cap with three prongs for three guy ropes.
By means of these guy ropes and a short plumb fitted in the staff the latter may
be held perfectly vertical. Of course the guy ropes etcetera may be dispensed with
and the staff held by the staff-holder.
The principle of the invention is illustrated in the diagram annexed hereto.
Suppose the instrument be set up at O in the said diagram, and that
OX OY are a horizontal and vertical line respectively drawn through the
point O. At any point on the surface of the ground say A, let a staff AQR be
erected so that A Q is equal to the height of O above the ground. And let R be
any other point on the staff so that the distance R Q is a known quantity.
Through O draw OT and OV at right angles to OQ and OR respectively.
And draw S.T.V. parallel to the horizontal line O X.
Then to find the horizontal distance OP.

page_text: The value OS, that is the vertical distance from the centre of the axis of the
telescope to the centre of the horizontal graduated scale, is known for each
instrument, ten to six inches being a convenient size.
Hence O P, that is the horizontal distance of the staff from O, the centre of the
instrument is ascertained.
The method of working the terrameter is as follows:-The instrument having
been set up over any peg that marks a station in a survey the graduated scale is
adjusted so as to be perfectly horizontal by means of the three leg-screws
and the appropriate bubble. The arm on the axis or trunnion of the telescope is
then set at zero of the graduated scale and clamped in the segmental groove by
means of its clamping screw. The line of collimation is then adjusted horizontally
by means of its appropriate bubble and the telescope is clamped to the arm.
All horizontal angles that are necessary are read and results noted in the Field
Book.
The lower disc of the staff is set so that its centre is the same height from the
bottom of the staff as the central axis of the telescope is above the ground and
the upper disc of the staff is set so that the centres of the two discs are exactly,
say, ten feet apart. This will be found a convenient distance.
The staff is now sent to any point of the field at which an observation is
necessary, and is erected perfectly vertical.
The arm is now unclamped from the segmental groove and the inclination of the
telescope is altered until the cross marks on the glass of the eyepiece exactly
coincide with the quadrant lines of the lower disc; the arm is then clamped
again to the segmental groove and the lengthening bar is extended till the
point of the iudicator just touches the edge of the graduated scale.
The vernier is moved up to the point and the reading noted, using a
magnifying glass for this purpose. Let the reading be 0003 inches, or as the
scale shews 0.003.
The arm is again unclamped from the segmental groove and the reading of the
centre of the upper disc taken in a similar manner. Let this be 0035 inches,
or 0-035 in the scale.

page_text: Now the gradient of the rise from the instrument to the centre of the lower disc
was just found to be 003 that is 003 in 100 feet horizontal distance. Hence the
total rise:-
003 X 3125 feet = 0.9375 feet.
The angle subtended, the horizontal distance from the instrument, and the rise
or fall above any datum line can be ascertained in this manner for a series of
points which are visible from the instrument.
By means of another clamping screw fixed on the axis or trunnion of the
telescope on the opposite side to that on which the arm is attached, the vertical
range of observation can be greatly extended.
For example suppose the lower disc of the staff is at a height beyond the
range of the graduated scale the gradient can be ascertained in two or more
operations instead of one. After clamping the arin and the telescope to each
other, alter the inclination of the latter until the indicator reaches the division 50
on the scale and then clamp with the said clamping screw. Unclamp the arm
from the segmental groove and bring the arm to zero on the scale once more, and
then clamp it to the segmental groove again and release the other clamping
screw. The inclination of the telescope can then be altered till the disc is visible,
remembering to add to the reading given on the scale 50 for each shift of the
arm back to zero.
According to a modification of the instrument shorter distances can be ascer-
tained without the aid of a telescope thus reducing the cost of construction.
By this arrangement distances equal to those measured by the usual form of
tacheometers can be accurately measured.
In place of the telescope fore and back sights are provided (similar to the sights
ou a rifle) fixed in a suitable chamber; the other differences being that the
instrument is provided with a compass having two sighting vanes.
The divisions
on the rim of the compass are marked so that the divisions at which the north
end of the magnetic needle points is the magnetic bearing of the line.
The instrument is provided with three screw legs which fit into a stand of the
ordinary pattern or with any other suitable support.
The method of using this modification is similar to that described with reference
to that first above described save that the aforesaid chamber must be sighted_for
the middle of each disc by means of the sights in the same manner as a rifle. The
distance and levels are calculated in the same manner.
In cases in which the level is not required there is no need for the lower disc to
be set the same height from the ground as the telescope or chamber, but they may
be placed in any convenient position so long as the distance between the upper and
lower discs is ten feet or any other known distance.
Dated this 23rd day of May 1895.
W. H. BECK,
115 Cannon Street, London, E.C., Applicant.

page_text: Improvements in and connected with Tacheometrical Instruments.
I, WILLIAM HENRY BECK of 115 Cannon Street, in the City of London,
Consulting Engineer and Chartered Patent Agent, do hereby declare the
nature of the said invention and in what mauner the same is to be
performed, to be particularly described and ascertained in and by the following
statement:-
The present forms of tacheometrical instruments are mostly made on one of the
following principles viz., (1) the angle of deviation of the telescope being constant,
the height of the staff cut off varies with the distances; or (2) the height of staff
cut off being constant, the angle of deviation varies inversely with the distance.
The staff employed in both classes of instruments is divided into sections, painted
or otherwise marked on the wood.
The disadvantages of these devices are (1) that owing to the variations due to
focal lengths neither the angle of deviation, nor the length of staff can be
maintained truly constant for all horizontal distances, hence inaccuracy in the
results obtained; (2) that owing to the divisions on the staff being difficult to make
out at any considerable distance, work cannot be accurately done beyond say one
thousand feet. This calls for constant removal of the instrument, and requires a
number of places of observation, thereby necessitating a great consumption of time
in the setting up and re-adjusting of the instrument. If the distance of observation
could be increased and the focal variations eliminated it would minimise these
drawbacks.
The object of this invention is to construct an instrument whereby :-(1) The
horizontal distance of any point up to say three thousand feet from the point of
observation, (2) the total rise or fall of this point in relation to the point of
observation, and (3) the bearing of this line from the north (magnetic) or the
horizontal angle subtended between any two lines which meet at the instrument
can be easily ascertained with accuracy at varying horizontal distances irrespective
of the focal variation.
With these ends in view the inventor has devised the instruments I now proceed
to describe with reference to the accompanying drawings in which similar letters
of reference indicate like parts throughout.
Figure 1 is a side elevation of the terrameter.
Figure 2 is partly an end elevation, and partly a section on line X-X of
Figure 1.
Figure 3 is a modification of Figure 1.
Figure 4 is partly an end elevation, and partly a section on line Z-Z of
Figure 3.
Figure 5 is a front elevation of staff.
Figure 6 is a side elevation of same, and
Figure 7 is a diagram illustrating the principle of the invention.
A is an ordinary level or theodolite telescope supported by two vertical supports
as in an ordinary theodolite so that the telescope can move freely in a vertical
plane between them. The eyepiece of the telescope has cross wires or lines inarked
on it which intersect each other in the line of collimation, and is provided with a
suitable focussing screw B. C is a bubble tube or spirit level which can be
adjusted parallel to the line of collimation of the telescope. D is an arm on the
axis or trunnion of the telescope which can be moved freely in a plane parallel to
that in which the telescope itself moves, and has a screw E by means of which it
can be clamped to the axis of the telescope at any desired inclination to the line of
collimation thereof. The said arm D may be moved by means of the handle For
otherwise. The arm D is clamped at any part of a segmental groove G (fixed to

page_text: one of the supports of the telescope) by a clamping screw H. The arm has a
lengthening bar I which moves in and out of a slot therein being actuated by a
screw J. The end of this lengthening bar is provided with an indicator K which
is hinged to enable its point to move in a plane at right angles to the lengthening
bar.
M is a horizontal scale graduated to say the tenths and hundredths of an
inch
A Vernier scale N graduated so that say 99 of the Tb inch divisions of the
horizontal scale M are equal to 100 of its division is moved backwards and
forwards horizontally along the edge of the horizontal scale M by means of a
screw furnished with a head P. By means of this graduated scale and the
vernier, measurements to the 100th part of an inch can be taken. A bubble
tube Q is attached to the aforesaid scale M. The instrument is supplied with two
horizontal circular plates L the edges of which are marked in the manner usual to,
theodolites for ascertaining horizontal angles. These plates are fitted with a
vernier, magnifying glasses, clainping and tangent screws as usual in most
theodolites but these latter are not features of the present invention and are not
shown in the drawings.
The instrument has the usual stand of three screw legs.
The staff V (see Figures 5 and 6) used in conjunction with the instrument, which
the inventor calls a Terrameter, is preferaby about 15 feet long, 4 inches wide and
2 inches thick or any other suitable size, with feet and inches marked on the back.
Such divisions are not however for reading off by the telescope, but as a guide to
the placing of two discs W and Y at any required height of the staff. The
aforesaid discs may be about two feet in diameter for example and made to slide
up and down on the staff, and they can be fixed at any desired height on the staff
by screws or otherwise so that a certain known distance between the centres of
the two discs exists. They are divided into quadrants which are painted red and
white alternately, or in any other distinctive manner to correspond with the lines
on the glass of the eyepiece of the telescope.
The end of the staff which is intended to rest on the ground may have a brass
shoe, and the other end may have a cap with three prongs for three guy ropes.
By means of these guy ropes and a short plumb fitted in the staff the latter may
be held perfectly vertical. Of course the guy ropes etcetera may be dispensed
with and the staff held by the staff-holder.
The principle of the invention is illustrated in the diagram Figure 7. Suppose
the instrument to be set up at O in the said diagram, and that OY is a vertical,
and X a horizontal line drawn through the point O. At any point on the
surface of the ground say A let a staff A QR be erected so that AQ is equal
to the height of O above the ground. And let R be any other point on the staff
so that the distance R Q is a known quantity.
Through O draw OT and OV at right angles to OQ and OR respectively.
And draw S, T, V parallel to the horizontal line O X.
Then to find the horizontal distance O P.

page_text: The value OS, that is the vertical distance from the centre of the axis of the
telescope to the centre of the horizontal graduated scale is known for each
instrument, ten to six inches being a convenient size.
Hence O P, that is the horizontal distance of the staff from O the centre of the
instrument is ascertained.
The method of working the terrameter is as follows:-
The instrument having been set up over any peg that marks a station in a survey
the graduated scale is adjusted so as to be perfectly horizontal, by means of the
three leg-screws and the appropriate bubble Q. The arm D on the axis or
trunnion of the telescope is then set at zero of the graduated scale and clamped in
the segmental groove G by means of its clamping screw H. The line of collimation
is then adjusted horizontally by means of its appropriate bubble C and the
telescope A is clamped to the armi D by the clamping screw E.
All horizontal angles that are necessary are read and results noted in the Field
Book.
The lower disc Y of the staff V is set so that its centre is the same height from
the bottom of the staff as the central axis of the telescope A is above the ground,
and the upper disc W of the staff is set so that the centres of the two discs are
exactly a certain distance say ten feet apart. This will be found a convenient
distance.
The staff Vis now sent to any point of the field at which an observation is
necessary and is erected perfectly vertical.
The arm D is now unclamped from the segmental groove G and the inclination
of the telescope is altered until the cross marks on the glass of the eyepiece
exactly coincide with the quadrant lines of the lower disc Y, the arm D is then
clamped again to the segmental groove G and the lengthening bar I is extended till
the point of the indicator K just touches the edge of the graduated scale.
The vernier N is moved up to the point and the reading noted, using a
magnifying glass for this purpose if necessary. Let the reading be .0003 inches
or as the scale shews 0.003.
The arm D is again unclamped from the segmental groove G and the reading of
the centre of the upper disc W taken in a similar manner. Let this be 0035 inches.
or 0.035 on the scale.

page_text: Now the gradient of the rise from the instrument to the centre of the lower disc
was just found to be 003 that is 003 in 100 feet horizontal distance. Hence the
total rise
0.007
The angle subtended, the horizontal distance from the instrument, and the rise
or fall above any datuin line can be ascertained in this manner for a series of
points which are visible from the instrument.
By means of another clamping screw R fixed on the axis or trunnion of the
telescope on the opposite side to that on which the arm is attached, the vertical
range of observation can be greatly extended.
For example, suppose the lower disc of the staff is at a height beyond the range
of the graduated scale as shown in Figure 1 the gradient can be ascertained in two
or more operations instead of one. After clamping the arm D and the telescope A
to each other, alter the inclination of the latter until the indicator K reaches the
division 50 on the scale M and then clamp with the said clamping screw, R.
Unclamp the arm from the telescope and from the segmental groove, and bring the
arm to zero on the scale once more, and then clamp it to the telescope and to the
On again
segmental groove again and release the other clamping screw R.
releasing the screw H the inclination of the telescope can be altered till the disc
is visible.
It is obvious that when the indicator K stands at any division of the scale M the
reading on that scale is proportional to the tangent of the angle made by the
arm D and indicator K with the vertical. Let a represent that angle when
the indicator K is at the extreme end of the scale, and ẞ the angle at which the
indicator K stands with the vertical when the second inclination of the telescope
has been made then a +ẞ equal the total angular movement of the telescope
produced by the two separate inclinations, and tan (a + ẞ) is proportional to the
total reading that the indicator K would indicate on the scale were the said
indicator set to the angle a + ẞ and the scale extended far enough to be cut by
the indicator when in that position. The tan (a + ẞ) can be calculated by the
tan atan B
It is convenient to make the length
tan ax tan ẞ
formula-tan (a + ẞ)
=
-
=
b
of the scale M in either direction equal to half the distance from the centre of the
trunnion of the telescope to the edge of the scale M. If this length which
corresponds to the augle a be designated by a and the length on the scale
corresponding to the angle ẞ be designated by the tan a = 1, and tan B
Substituting these values in the above equation the above mentioned total reading
of the scale becomes ======
and a and b being known quantities the value of
a+b
b
4 a
the reading can easily be calculated.
=
-
2 a.
Or, if the length a of the scale be divided into 500 equal parts, the distance from
2 α,
the centre of the trunnion of the telescope to the scale will be equal to 1000
of those parts
radius, and the readings on the scale when the indicator K is set
to the angles a and ẞ respectively will represent the tangents of those angles, from
which the actual values of the angles themselves can be ascertained by means of
a table of tangents; then the tangent of the sum of these angles, found in the

page_text: same table, will represent the total reading that the indicator K would indicate on
the scale were the said indicator set to the angle a + ẞ, and the scale extended far
enough to be cut by the indicator when in that position.
If the inclination is so great that the disc cannot be observed with one movement
of the arm back to zero, it may be obtained with two or more such movements,
the total angles being in those cases 2a + ẞ, 3a + B etc., according to circumstances,
and the calculation modified accordingly.
According to a modification of this instrument shown in Figures 3 and 4
shorter distances can be ascertained without the aid of a telescope, thus reducing
the cost of construction. By this arrangement distances equal to those measured
by the usual form of tacheometers can be accurately measured.
In place of the telescope shown in Figures 1 and 2 fore and back sight are
provided (similar to the sights on a rifle) fixed in a suitable chamber S; the
other differences being that the instrument is provided with a compass T having
two sighting vanes U U. The divisions on the rim of the compass are marked
so that the divisions at which the north end of the magnetic needle points is the
magnetic bearing of the line.
The instrument is provided with three screw legs which fit into a stand of the
ordinary pattern or with any other suitable support.
The method of using this modification is similar to that described with reference
to the instrument first above described save that the aforesaid chamber S must be
sighted for the middle of each disc by means of the sights in the same manner
as a rifle. The distance and levels are calculated in the same manner.
In cases in which the level is not required there is no need for the lower disc
to be set the same height from the ground as the telescope A, or chamber S, but
they may be placed in any convenient position so long as the distance between
the upper and lower discs is ten feet or any other known distance.
Similar letters of reference indicate like parts in all the figures of the
drawings.
Having now particularly descubed and ascertained the nature of the said inven-
tion and in what manner the same is to be performed, I declare that what I
claim is :-
:-
First. In tacheometrical instruments the application of the principle of similar
triangles for ascertaining distances, substantially as described.
Second. In tacheometrical instruments the use of an arm with a lengthening bar
as described and illustrated.
Third. In tacheometrical instruments the use of a straight horizontal scale with
or without a vernier, marked as hereinbefore indicated or in any other suitable
manner as described, and illustrated in the accompanying drawings.
Fourth. In tacheometrical instruments the combination of an arm with a
lengthening bar and a straight horizontal scale substantially as and for the
purposes set forth and illustrated.
Fifth. In tacheometrical surveying the use of a staff having two movable discs
thereon the back of the staff being marked off in feet and inches or otherwise, the
discs being of a suitable diameter divided into quadrants or otherwise, the
alternate quadrants being painted in a distinct manner, substantially as specified,
and illustrated in the accompanying drawings.
Sixth. The combination of the various parts substantially as and for the purposes
described.
Dated this 15th day of October 1895
W. H. BECK,
115 Cannon Street, London, E.C., Applicant.