Diagrams for the Rapid Reduction of Readings taken in the Field with Tacheometers or Stadia and Telemetric Instruments.
Year: 1894

page_text: Date of Application, 27th Nov., 1894
Complete Specification Left, 8th Jan., 1895-Accepted, 22nd June, 1895
PROVISIONAL SPECIFICATION.
Diagrams for the Rapid Reduction of Readings taken in the Field
with Tacheometers or Stadia and Telemetric Instruments.
I, GUSTAVE GILLMAN, Civil Engineer, of Aguilas, Province of Murcia, Spain,
do hereby declare the nature of this invention to be as follows:-
-
This invention relates to diagrams for the rapid reduction of readings taken in
the field with tacheometers or stadia and telemetric instruments.
"
The diagram consists of two series of equidistant parallel lines ruled at right
argles to one another, any convenient scale being adopted for the spacing of the
same. The lines are numbered on the left hand and upper margins, those on the
left hand forming a scale of "generating numbers," that is, the difference between
the upper and lower staff readings," and those on the upper margin being a scale
of "heights," that is, the "difference of level between the axis of the tacheometer
and the division on the staff midway between the upper and lower staff readings."
On the lower and right hand margins a scale of "vertical angles" is formed in
the following manner. Taking the bottom line to represent the " generating
number" 500, to find the position on that line of the division corresponding to any
vertical angle A, multiply the square of the cosine of A by the tangent of A and
this product by 500. The number resulting will be that corresponding to the
required division measured along the bottom or 500 line by the scale of " “heights
marked on the upper margin of the diagram. Across the diagram a series of
curves are traced forming a scale, which represents the amount to be deducted
from the "generating number" to obtain the horizontal distance between the
tacheometer and the staff. The points for constructing these curves are obtained
in the following manner. To find a point in a curve representing a reduction
on the line corresponding to a generating number" g, the following formula is
employed
$6
"
=cosine a; tangent a x (g- x) = the distance to be measured by the
scale of "heights" along the horizontal line corresponding to the "generating
number" g.
To employ the diagram so constructed, a thin thread is attached to the upper
left hand corner of the diagram, preferably by means of a thin metal plate having
a fine hole drilled to receive the thread, the said hole coinciding with the origin of
the scales of "heights" and "generating numbers." The diagram is laid on
a table or other suitable plane surface, the thread is taken in the right hand
and applied to the division corresponding to the vertical angle read in the field,
care being taken to keep the thread stretched. By following the horizontal line
corresponding to the "generating number in the field book to where it is
intersected by the thread, the required "height" is obtained at the point of
intersection by means of the scale on the upper margin, and the nearest curve to
the said point of intersection gives the number to be subtracted from the
"generating number" to obtain the horizontal distance.
"
If the "generating number" exceeds 500, the half of the same can be taken and
the results doubled. In like manner for "generating numbers" under 50 the scale
on the left hand side may be taken as multiplied by 10 and one tenth of the results
taken

page_text: 66
The scale of vertical angles is preferably divided into centesimal degrees or
grades," but the principle is equally applicable to the sexagesimal or any other
division of the arc, thus permitting the use of any instrument provided with a
suitable telescope tacheometrically.
Dated this 27th day of November 1894
GUSTAVE GILLMAN,
By Harris & Mills,
23 Southampton Buildings, London, W.C., Agents.
Diagrams for the Rapid Reduction of Readings taken in the Field
with Tacheometers or Stadia and Telemetric Instruments.
I, GUSTAVE GILLMAN of Aguilas, Province of Murcia, Spain, Civil Engineer,
do hereby declare the nature of this invention and in what manner the same is to
be performed to be particularly described and ascertained in and by the following
statement:-
This invention relates to diagrams for the rapid reduction of readings taken in
the field with tacheometers or stadia and telemetric instruments.
A diagram constructed according to my invention is represented in the
accompanying drawings in which
Figs. 1, 2, 3 form the upper half of the diagram and Figs. 4, 5, 6 the lower half
of the same, the various parts being joined together on lines correspondingly
numbered. The fine divisions shown in Fig. 1 are used with all the other portions
of the diagram but they are omitted from Figs. 2, 3, 4, 5 & 6 for convenience.
Fig. 7 is a view of a complete diagram to a small scale, showing only the large
graduations.
Tacheometers and stadia instruments are surveying instruments provided with
pairs of horizontal wires placed at equal distances above and below the axial wire
in the diaphragm of the telescope, and so spaced that the number of divisions
intercepted between them on the graduated staff bears a fixed proportion to the
distance between the instrument and the staff when the telescope is level. The
staff is usually so graduated that the number of divisions intercepted gives the
distance in feet, yards or metres. When the point at which the staff is held is so
situated that the telescope must be inclined to take the reading, the number of
divisions intercepted by the wires no longer gives the exact horizontal distance,
but requires a correction in terms of the angle of inclination of the telescope with the
horizon. The number of divisions intercepted is usually called the "
number." To obtain from the "
generating
generating number" (g) and "the angle of
inclination (a), the "horizontal distance between the instrument and the
staf" (H) and "the difference of level between the axis of the instrument and the
point on the staff midway between where the upper and lower wires cut it" (h),
the following formulæ are employed:
دو
H=
h
These calculations if that had
:-
g x cosine² a.
= Hx tangent a.
2

page_text: angles to one another, any convenient scale being adopted for the spacing of the
same. The lines are numbered on the left-hand and upper margins preferably as
shown, those on the left-hand forming a scale of "generating numbers," that is the
"difference between the upper and lower staff readings," and those on the upper
margin being a scale of "heights," that is the "difference of level between the
axis of the tacheometer and the division on the staff midway between the upper
and lower staff-readings.
On the lower and right-hand margins a scale of "vertical angles" is formed in
the following manner. Taking, as in the accompanying diagram the bottom line
to represent the "generating number" 500, to find the position on that line of the
division corresponding to any vertical angle a multiply the square of the cosine a
by the tangent of a and this product by 500. The number resulting will be that
corresponding to the required division, measured along the bottom or 500 line,
by the scale of "heights" marked on the upper margin of the diagram.
"
Across the diagram a series of curves are traced forming a scale which
represents the amount to be deducted from the "generating number' to obtain the
horizontal distance between the tacheometer and the staff. The points for con-
structing these curves are obtained in the following manner. To find a point in a
curve representing a reduction on the line corresponding to a " generating
number" g, the following formula is employed :
=cosine a; tangent a x
=
:-
g
100 x
4
+ and
(g) the distance to be measured by the scale of "heights" along the
horizontal line corresponding to the "generating number" g.
Eliminating a from the above equations we obtain the equation / = √x (g- x),
which greatly facilitates the calculation of the co-ordinates of the curves.
The curves thus obtained are a family of parabolas, the vertex of each being
situated on the scale of generating numbers at the point where g = 2. The focus
of each curve is situated at the generating number corresponding to
its parameter = 100 x.
It will be seen in the diagram that the scale of his
chosen ten times that of 9.
In order to avoid having to note at each reading whether the vertical angle is
taken with the telescope looking up or down, the zero of the vertical circle is
placed at the top, 100% or 90° being horizontal according to whether the centesimal
or sexagesimal divisions are employed. Hence all angles less than 100% or 90°
are with the telescope looking up and those exceeding that figure are looking
downwards.
To employ the diagram so constructed, a thin thread T is attached to the upper
left hand corner of the diagram, preferably by means of a thin metal plate having a
fine hole drilled to receive the thread, the said hole coinciding with the origin of
the scales of "heights" and ", generating numbers." The diagram is laid on a
table or other suitable plane surface, the thread is taken in the right hand and
applied to the division corresponding to the vertical angle read in the field, care being
taken to keep the thread stretched. By following the horizontal line corresponding
to the "generating number" in the field book to where it is intersected by the
thread, the required "height" is obtained at the point of intersection by means
of the scale on the upper margin, and the nearest curve to the said point of inter-
section gives the number to be subtracted from the "generating number" to obtain
the horizontal distance.
If the "
generating number" exceeds 500, the half of the same can be taken
and the results doubled. In like manner for "generating numbers under 50,
the scale on the left hand side may be taken as multiplied by 10 and one tenth of
the results taken.
"
The accompanying diagram shows the scale of vertical angles divided into
centesminal degrees or "grades," but the principle is equally applicable to the
sexagesimal or any other division of the aic, thus permitting the use of any
instrument provided with a suitable telescope tacheometrically.

page_text: Examples of method of using the diagram as shown in dotted lines in Fig. 7 :-
Find H and h corresponding to g= 325 and A = 107. 93. Put thread (as
indicated by dotted line) to 1078. 93 (b). At point where it intersects 325 line (b¹), it
also cuts the vertical line corresponding to h = 40 and curve showing reduction
of 5. Therefore H = 325 - 5 = 320.
Find H and h for
300 and a =
9 =
888. 28.
Set thread (as per dotted line) to 888. 28 (c) and where it cuts 300 line (c¹) it
gives h
= 54 and H = 300 10 = 290.
Having now particularly described and ascertained the nature of my said inven-
tion and in what manner the same is to be performed I declare that what I
claim is-
1. In a diagram such as described a series of curved lines forming a scale for
reducing the "generating numbers to the corresponding horizontal distances.
2. In a diagram such as described an arrangement of the scale of vertical angles
so that it may be made suitable for reducing readings taken in the field with
tacheometers or other telemetric instruments whether with centesimal, sexagesimal
or other divisions of the vertical limb of the instrument.
3. The combination and general arrangement of the complete diagram sub-
stantially as described and illustrated in the accompanying drawings, whereby the
vertical and horizontal reductions are obtained at one operation from the
tacheometer field readings.
Dated January 8th 1805
By HARRIS & MILLS,
23 Southampton Buildings, London, W.C., Agents.