Year: 1886

page_text: I, GEORGE ANDERSON VETCH of No. 22 Grosvenor Street, Edinburgh, in the
County of Midlothian, North Britain, Gentleman do hereby declare the nature of
this invention to be as follows:-
This Invention, which relates to improvements in measuring distances, has for
its object to facilitate surveys in a rough country or wherever chaining is a difficult
operation, and by means of this Invention the use of the ordinary surveyor's chain.
is dispensed with and distances are determined or measured by direct observation
by the theodolite of the angles subtended by a horizontal bar or rod mounted on a
tripod or other convenient support.
In measuring distances with the horizontal rod or bar mounted as hereinbefore
described, the length of the rod is a constant quantity, and being known to the
observer it follows that when placed at any given distance from the theodolite say
for example at a chains distance, the angle subtended by the said bar at that
distance from the theodolite also becomes a constant or base for angle observations
from which the distance observation is immediately deducible for example, the
angles subtended by the aforesaid bar at a chain's distance being known it follows
that if the angle subtended by the said horizontal bar is found to be the half of
the angle which it subtends at a chain's distance that the bar is 'then at a distance
of two chains from the theodolite; similarly, if the angle subtended be a third or a
fourth or other division of the angle subtended by the said bar at a chain's distance
the distance measured is three chains or four chains or more. The theodolite
observations also similarly show fractions of chain's distance measured.

page_text: I, GEORGE ANDERSON. VETCH of No. 22 Grosvenor Street, Edinburgh, in the
County of Midlothian, North Britain, Gentleman do hereby declare the nature of
my invention for IMPROVEMENTS IN MEASURING DISTANCES AND IN APPLIANCES
THEREFOR, and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement :-
My Invention, which relates to improvements in measuring distances, has for its
object to facilitate surveys in a rough country or wherever chaining is a difficult
operation, and by means of this Invention the use of the ordinary surveyor's chain
when attended with difficulty, is dispensed with, and distances are determined or
measured by using the theodolite for direct observation of the angles subtended by
a horizontal bar or rod mounted on a tripod or other convenient support.
In measuring distances with the horizontal pole or bar mounted as herein before
described, the length on the rod is or may be a constant quantity, and being
known to the observer, it follows that when placed at any given distance from
the theodolite, say for example, at a chains distance, the angle subtended by the
said bar at that distance from the theodolite also becomes a constant or base for
angle observations from which the distance observation is immediately deducible,
for example, the angles subtended by the aforesaid bar at a chain's distance being
known, it follows that by the angle subtended by the said horizontal bar is found
to be the half of the angle which it subtends at a chain's distance, that the bar is
then at a distance of two chains from the theodolite; similarly, if the angle subtended
be a third or a fourth or other division of the angle subtended by the said bar at a
chain's distance, the distance measured is three chains or four chains or more.
The theodolite observations also similarly show fractions of chain's distance
measured.
In order that my said Invention may be properly understood and readily carried
into effect, I will now proceed to describe the drawings hereunto annexed.
Figure 1, is an elevation of a distance indicator constructed according to my
present Invention.
Figures 2 and 3 are views of detached portions, or portions to be used in
connection with the same.
Figures 4 and 5 are diagrams explanatory of the system of measuring embodied
under my present Invention.
--
The distance indicator, as constructed in accordance with my present Invention,
is an instrument specially designed to facilitate surveys in a rough country, or
wherever the obtaining measurements by means of a chain is a difficult operation.
In conjunction with the theodolite, the horizontal lengths of lines are determined
by direct observations, and are obtained with great ease, quickness and accuracy.-
The principle of my improvedi distance indicator is, that a constant base will
subtend angles greater or less as it is nearer or further removed, and so, the angle
subtended may indicate the distance between itself and the base. Thus it may be
explained with reference to the diagram at Figure 4, if the constant base B, C, at
the distance A, D, subtends an angle BA C, then, at a less distance it will subtend
an angle [B' A C', that is to say an angle greater than B A C, and at a greater

page_text: distance than A D it will subtend an angle B" A C" that is to say an angle less
than the angle BA C. Now, although these angles do not increase and diminish
in absolutely exact proportion inversely as the distance of the base from the angle,
yet, when the angles are small, it may, for all ordinary practical purposes of
surveying be assumed that they do so increase and diminish. If, for instance, the
constant base BC be constructed so as to subtend an angle of 2° at 2 chains,
then the error for a measurement of 20 chains on the supposed assumption would
be only about 1th of a link-this, of course would be quite immaterial. It is
assumed, then, that the distance of the base is inversely as the magnitude of the
angle it subtends, and thus the angle observed gives, by simple proportion, the
length of line.
The distance indicator as constructed in accordance with my present Invention,
and as shewn more particularly at Figure 1, of the annexed drawings, consists of
the wooden staff or pole a, which is mounted and free to rotate horizontally upon
the tripod b, and which may be clamped securely to or upon the said tripod in any
desired position by means of the clamping screw c, Figure 1. Upon the staff or
pole a, there are two marks e, and f, the distance between which is, say 5 feet
9 inches, this being a length such as enables the said pole to be also used as an
ordinary survey pole or, if desired, any other distance may be marked upon the
pole, such pole being either of a fixed length or capable of being extended
telescopically or otherwise. For facilitating these lines e, and f. being clearly
observed from a distance they are preferably defined by being the junction of a
bright colour such as scarlet, with white. For facilitating these lines e, and f.
being clearly observed from a further or greater distance, the discs or small
targets g, and h, also similarly painted scarlet and white, are capable of being
secured upon the staff or pole a, so as to define a distance between the lines of
juncture of the colours thereon, similar to the distance marked on the.staff a.
Figure 2, of the annexed drawings represents the pointed shoe i, of the staff or
pole a, detached therefrom, the position of the said shoe i, when secured upon the
said staff or pole being indicated in dotted lines at Figure 1. As shewn in full
lines at Figure 1, the shoe i, may be used as a plummet. At Figure 3, is
represented a sighting arrangement which may be temporarily secured to the staff
or pole a, at its centre, that is to say, above the tripod b, in order to place the said
staff or pole a, at right angles to the line to be measured, the said staff or pole a,
being rotated horizontally upon the tripod b, until the necessary position is attained
when it is clamped in such position by the screw c.
When it is desired to measure a line by means of the staff or rod a, herein before.
described the method of procedure is as follows:-While the theodolite is being set.
over the picket at one end of the line, the hereinbefore described indicator is sent
on to the other end and placed over the picket there, or vice versa. The horizontal
pole a, is in the manner hereinbefore explained brought into the position of right
angles to the line to be measured and the theodolite, with its horizontal vernier
set to any convenient degree, is directed to the line e, and clamped. The upper
plate is next released, and the telescope of the theodolite, directed to the line f, when
the upper plate is reclamped. "The angle subtended by e, f, will give the length of
the line by working out the simple proportion:
Angle subtended: A: : M: required distance, A and M being constant known
quantities that is to say, A-being a small angle and M the distance at which e, f,
subtend it. In practice, convenient values of A and M are:-A=2°; M = 250 links;
that is to say, the base e, f, shall subtend 2° at 250 links distance; and since,
practically, the angles diminish as the distances increase 4° or 30' will be subtended
at 1000 links. 30 and 1000 being figures easy to work with, we substitute them.
for A and M and get the very convenient formula-
30,000
Required distance = Inale enhanded (in minning)

page_text: length as to subtend 2° at 250 links, then the length of e, f, is about 5 feet 9 inches,
a length which can be marked off on a pole a, of convenient length to serve also
as an ordinary survey pole as herein before explained. It may also be here explained
that, as the chain-sticks will not be in use while a distance is being obtained by
means of the indicator, they may be so constructed as to allow of their being
screwed on, or otherwise attached to the ends of the pole a, and so form an extended
base three times the single length e, f, if desired. It frequently happens, in forest
and river surveys, that there is ample clear space on one side of a picket for
observing on a base, whilst the other side is densely obstructed. A provision is
made for such cases by taking the centre of the pole a, as an end of the base;
when, with a chain stick attached to the actual end of the pole a, on the clear side
of the survey line, a base is obtained equal to 14 of a single length. The formula
must of course be adapted to the length of the base used. Thus-
"
1 lengths-Required distance
+5,000
Augle.
"
3 lengths-Required distance
90,000
Angle.
I desire it to be understood that the pole a, may be constructed so as to lengthen
telescopically.
For accurate surveys the single length may be used up to about 20 chains; but
it is better, if convenient, to take shorter distances, or lengthen the base. With
this precaution, the only serious liability to error would rest with inaccuracy in
reading the theodolite. This liability to error may, however, be rapidly lessened
to any required extent by repeating the observations on e, and f, in continuity,
that is to say, after the first observation on f, redirect the theodolite (with its
upper plate remaining clamped) on e, and commence a second angle where the first
left off on the limb of the theodolite; in the same way commence a third where
the second left off, and so on, until a sufficiently large total arc has been laid off to
render the maximum possible error of reading the theodolite an admissible quantity.
It will be seen that whatever be the number of observations, only the original setting
of the theodolite vernier and its final position are absolutely necessary to be read-
they alone affect the accuracy of the reading of the total are turned off on the
theodolite and since the angle sought, is only a fraction of this total arc, the error
of reading affecting the angle is obviously reduced to a fraction also. This fraction
of error may be reduced ad infinitum by repeating the observations on e, and f,
an operation which can be performed very rapidly. In order to obtain an accuracy
equal to careful chaining over difficult ground, the observations should be continued
until a total arc of at least 4° has been turned off on the theodolite; and, since
on a single length of pole the base e, f, subtends 2° at 250 links, it will require-

page_text: The instrument of observation is supposed to be the ordinary 5-inch theodolite,
the vernier of which reads to minutes. Should the vernier, when the total arc has
been turned off, indicate a fraction of a minute, it may be estimated by the eye→
this will quite suffice. There is however, a graduation at f, for finding approxi-
mately the fractional part of a minute. It consists of two divisions, one of which
is subdivided into 5 parts-one full division subtends a minute at 10 chains-it
will, of course, subtend more if the indicator is at a less distance, and less if the
distance be greater, the formula being―
Distance of indicator: 10 chains: graduation subtended: fraction of minute
sought. The method of using this graduation is hereinafter explained.
As an example of the method of obtaining, by my Invention, a distance difficult
to measure with a chain, reference is now had to the diagram Figure 5.
The theodolite being at X, place the distance indicator at Y, adjusting it by
means of the tripod legs b, to a nearly horizontal position. Place the sighting
arrangement (Figure 3) over the centre of the pole a, and adjust and clamp the
latter at right angles to the line XY. If the line to be measured be a long one,
place the targets g and h, over the graduation lines at e, and f. Set the vernier of
the theodolite to any convenient degree, say 100°, and direct the telescope to e, or
to centre line of the target y; elamp under plate of theodolite, and releasing the
upper, direct the telescope to f, or to the centre line of the target h; reclamp the
upper plate and make a note of this angle (which let it be supposed is 24'); release
the under plate, and with the vernier still at 24', redirect on e, or g, and turn off a
further arc of the theodolite by directing on f, or h; continue this operation until
at least 4° (240') has been turned off in all. This would require 10 observations
one, and f, or their targets, supposing the first angle was correctly taken as 24';
but, the directing of the telescope is a simple and rapid operation, so, to make sure,
let 15 observations be taken. Now, suppose that the total are turned off be found
to be 5° 50' (350), then, in order to get the length of the line XY, there remains
only to work out the equation-
30,000 x 15
XY = 350
Where 30,000 is the constant quantity for a single length of pole, 15 is the number
of observations we have taken, and 350 is the total arc turned off (in minutes).
XY (the required distance) is thus found to be 1285-7 links. The decimal of links
may be discarded as a correction for any slight error arising from inaccuracies
in adjusting the indicator pole horizontally and at right angles to XY. Any
inaccuracies in these respects occasion errors of excess, but, with ordinary care,
they will be very trifling.
It will be observed that the angles taken by the theodolite being horizontal
angles the distance obtained is the horizontal value of the line XY. There is never
any reduction required as in chain measurements. If the vernier in this case had,
instead of giving the reading 5° 50' exactly, indicating a "fraction of a minute
over 50' then it would have sufficed to have estimated the fractional part by the
eye; or it may be obtained thus: turning back by means of the tangent screw
until the vernier comes to indicate exactly 5° 50'; read the divisions on the
pole from f to where the telescope wires now cut it; get approximately from the
first reading (24') the distance in chains (discarding links) thus = 12 chains,
and from the formula already given we may find the fractional part of the minute
sought. This, however, as already stated, is not necessary in the ordinary
operations of surveying, for which fractional parts of minutes may either be
discarded altogether, or estimated by the eye when reading the vernier.
80,000
24
The distance indicator method of obtaining distances is one which admits of
extreme accuracy, and might be used with suitable instruments for the measure-
ment of base lines, and with much less labour than is required for the usual
methods; nor would it be necessary to select a specially level or easy stretch of
country, as is the case under the methods in use,

page_text: Having now particularly described and ascertained the nature of my said
Invention and in what manner the same is to be performed, I declare that what
I claim is :-
.
First. Measuring distances by direct observation by the theodolite of the angles
subtended by the horizontal staff or pole a, all substantially as hereinbefore set
forth with reference to the annexed drawings.
Second. The staff or rod a, supported upon a tripod b, and marked at e, and f,
in the manner hereinbefore set forth and provided with the discs or targets g,
and h, shoe i, and the sighting apparatus shewn at Figure 3, and used in con-
junction with a theodolite or other equivalent angle-measuring instrument all
substantially as and for the purposes hereinbefore set forth with reference to the
annexed drawings or the mechanical equivalents of all or any of the parts thereof.
Dated this ninth day of Aust. 1886
J. H. JOHNSON, DAY & JOHNSON,
Applicant's Agents.