This little instrument was exhibited in a somewhat crude state at the
meeting of the British Association at Newcastle in 1889. It has since
been modified in several respects, and improvements suggested by
practical use have been introduced, bringing it into a practical form,
and enabling a much greater accuracy to be attained. The principle is
one which is occasionally employed for setting out circles with a
pocket sextant, viz., the property of a circle that the angle in a
segment is constant. The leading feature of the invention is the
arrangement of scales, which enables the operation of setting put
large curves for railway or other work to be carried out without
requiring any calculations, thereby enabling any intelligent man to
execute work which would otherwise call for a knowledge of the use of
a theodolite and the tables of tangential angles.
[Illustration: FIG. 1--PERSPECTIVE VIEW OF INSTRUMENT MOUNTED ON A
STAFF.]
The instrument is intended to be thoroughly portable; so much so,
indeed, that it is not necessary or even desirable to use a tripod. It
may be held in the hand like a sextant, or may be carried on a light
staff. The general appearance is shown in Fig. 1. It will be seen that
a metal plate, on which two scales are engraved, carries a mirror at
one end and an eye piece at the other. The mirror is mounted on a
metal plate, which is shaped to a peculiar curve. A clamp and slow
motion provide for rapid and for fine adjustment. The eye piece is set
at an angle, and contains a half silvered mirror, the upper portion
being transparent. This allows direct vision along the axis of the eye
piece, and at the same time vision in another direction, after two
reflections, one in the eye piece and the other at the adjustable
mirror. Fig. 2 is an outline plan of the instrument when closed. In
the first form of the instrument only one mirror was provided, but by
the double reflection in the improved pattern, any accidental twisting
of the rod or handle produces no displacement of the images, since the
inclination of one mirror neutralizes the equal and opposite
inclination of the other. No cross line is required with the new
arrangement, since it is only necessary that the two images should
coincide.
[Illustration: FIG. 2.--OUTLINE OF INSTRUMENT SHOWING THE PATH OF THE
DIRECT AND OF THE REFLECTED RAY.]
The dotted line A B represents the direct ray, and the line A C D the
reflected one. Fig. 3 shows the different geometrical and
trigonometrical elements of the curve, which can be read upon the
various scales, or to which the instrument may be set. An observer
standing at C sights the point B directly and the point A by
reflection. A staff being set up at each point, he will see them
simultaneously, and in coincidence if the instrument be properly set
for the curve. If any intermediate position be taken up on the curve,
both A and B will be seen in coincidence. If the two rods do not
appear superimposed, the operator must move to the right or the left
until this is the case. The instrument will then be over a point in
the curve. Any number of points at any regular or irregular distances
along the curve can thus be set out. One of the simplest elements
which can be taken as a datum is the ratio of the length of the chord
to the radius, AB/AO, Fig. 3. This being given, the value of the ratio
is found on the straight scale on the body of the instrument, and the
curved plate is moved until the beveled edge cuts the scale at the
desired point. The figure of this curve is a polar curve, whose
equation is _r_ = _a_ ± _b_ sin. 2 [theta], where _a_ is the distance
from the zero graduation to the axis of the mirror, and _b_ is the
length of the scale from zero to 2, and [theta] is the inclination of
the mirror. In the perspective view, Fig. 1, the curved edge cuts the
scale at 1. The instrument being thus set, the following elements may
be read either directly on the scales or by simple arithmetical
calculation:
[Illustration: FIG. 3]
The radius = 1.
AB, the chord, read direct on the straight scale.
AFB, the length of the arc, read direct on the back or under
surface of the plate.
FH, the versed sine, read direct on the curved scale.
ACB, the angle in the segment, read direct on the graduated
edge.
EAB, the angle between the chord and the tangent, read direct
on the graduated edge.
GAB, the tangential angle = 180 deg. - ACB.
AOB, the angle at the center = 2GAB.
AGB, the angle between the tangents = 180 deg. - AOB.
OAB, the angle between the chord and the radius = EAB - 90
deg.
AH_{2}
GF = --------- - FH.
HO
The foregoing elements are contained in a very simple diagram, Fig. 4,
which is engraved on the instrument, together with the following
references:
B = 180 deg. - A.
C = 2B.
D = 180 deg. - C.
E = A - 90.
Only one adjustment is necessary, and this is provided by means of the
screws which fix the inclination of the eyepiece. This is set at such
an angle that the instrument, when closed and reading 90° on the
divided limb, acts as an optical square.
It is not necessary, as in the ordinary method with a theodolite, that
one end of the curve should be visible from the other. If an obstacle
intervenes, all that part of the curve which commands a view of both
ends can be set out, and a ranging rod can be set up at any point of
the curve so found, and the instrument may be reset to complete the
curve.
To set out a tangent to the curve at A, Fig. 3, set up a rod at A and
another at any point C, and take up a position on the curve at some
point between them. Adjust the mirror until the rods are seen
superimposed. Then moving back to A, observe C direct, and set up a
rod at E in the line observed by reflection. Then A E is the tangent
required. Similarly, on completing the setting out of a curve, and
arriving at the end of the chord, the remote end being seen by
reflection, the direction observed along the axis of the eyepiece is
the new tangent.
Any of the angles or other ratios already mentioned may be used for
setting the instrument, but if no data whatever are given, as in the
rough surveys for colonial railways where no previous surveys exist,
it is only necessary to select points through which the curve must
pass, to set up ranging rods either at the extremities of the desired
curve, or at any points thereon, to take up a position on the desired
curve between two rods, and to adjust the instrument until they are
seen in coincidence. The curve can then be set out, and fully marked,
and the elements of the curve can be read on the scales and recorded
for reference.
[Illustration: FIG. 4.--DIAGRAM ENGRAVED ON THE INSTRUMENT.]
Various other cases which may occur in practice can be rapidly met by
one or other of the various scales. Suppose the angle A G B between
the tangents be given, together with the middle point F on the curve,
Fig. 3. Subtract this angle from 180 deg., the difference gives the
angle at the center A O B. Take half this, and set the instrument to
the angle thus found. Walk along the tangent until a rod set up at
some point in the tangent, say E, is seen in coincidence with a rod
set up at B. The position of the instrument then marks the point of
departure A. A rod being placed at A, the first half of the curve may
be set out; or, if B is invisible, the instrument may be reset for the
angle E A B, and the whole curve set out up to B. No cutting of hedges
is necessary, as with theodolite work, for a curve can easily be taken
piece by piece. Inclination of the whole instrument introduces no
appreciable error. If the eye piece be pointed up or down hill, the
instrument is thrown a little to one side or other of the tip of the
staff, but in a plane tangent to the circle. Errors made in setting
out a curve with the Trotter curve ranger are not cumulative, as in
the method of tangential angles with a theodolite. No corrections for
inaccurate hitting of the final rod can occur, for the curve must
necessarily end at that point. It should be observed that the
instrument is not intended to supersede a theodolite, but it has the
great advantage over the older instrument that no assistant or chains
or trigonometrical tables or any knowledge of mathematics are
required. The data being given, by a theodolite or otherwise, an
intelligent platelayer can easily set out the curve, while the trained
engineer proceeds in advance with the theodolite. No time is lost; as
in chaining, since the marks may be made wherever and as often as
convenient. In work where high accuracy is required this instrument is
well adapted for filling in, and where a rough idea of the nature of a
given curve is required, the mirror being adjusted for any three
points upon it, the various elements may be read off on the scales. A
telescope is provided, but the errors not being cumulative, it is
rarely required. The curve ranger weighs 1 lb. 10 oz., and is
manufactured by Messrs. Elliott Bros., St. Martin's Lane, London. It
is the invention of Mr. Alex. P. Trotter, Westminster.--_The
Engineer._
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