A New or Improved Instrument for Measuring Small Visual Angles, and for the Determination of Distances thereby.
Year: 1896

page_text: Date of Application, 15th Apr., 1896
Complete Specification Left, 15th Jan., 1897-Accepted, 10th Apr., 1997
PROVISIONAL SPECIFICATION.
A New or Improved Instrument for Measuring Small Visual Angles,
and for the Determination of Distances thereby.
I LEWIS KNOX BELL, Commander Royal Navy H.M.S. Barfleur, at present
on the Mediterranean Station do hereby declare the nature of this invention to
be as follows:-
My invention has for its principal object to provide a simple and efficient
instrument for the measurement of small visual angles in such a manner as to
ensure an exaggerated reading on an arc or scale and is primarily intended for
determining the distance of objects at sea or on land by observing from a known
height the angle subtended by the horizon and the water line of an object at sea,
or the angle of elevation of, or the angle subtended by, an object of known height
or dimensions, or by observing the depression angle or any other well known
method of determining distance by the measurement of visual angles, a graduated
arc or scale being provided to enable the distance corresponding to the angle
observed to be read off directly, as well as the angle measured.
For this purpose I employ a prism of known angle of minimum deviation so
mounted that it can be rotated in the plane of its axis perpendicular to the line
of sight, through an angle of 90 degrees. If a point or object on the horizon
be now viewed, the prism holder may be so held that the refracted image in the
prism will appear horizontally apart from the directly viewed image and at an
angular distance from it equal to the angle of deviation of the prism. If the prism
be then rotated in the same plane by turning the holder thereof through an angle
of 90 degrees, the refracted image will move on the circumference of a circle
described about the point or object until it appears vertically above or below the
directly viewed image and the portion of the horizon seen on either side of the
point or object will undergo displacement in a similar manner. When the refraction
takes place only in a horizontal direction (that is, when the axis of the prism is
vertical) the horizon as seen through the prism and by direct vision will appear in
an unbroken line, and when the holder of the prism is rotated through an angle
of 90° the directly viewed and refracted images of the horizon will be separated
vertically to an angular distance equal to the angle of deviation of the prism. If
the rotatory movement of the prism be arrested at any point between these positions
of only horizontal, and only vertical, displacement the vertical angle subtended by
the directly viewed and refracted images will be equal to the angle of deviation
of the prism multiplied by the sine of the angle rotated. For instance if the
minimuin angle of deviation of the prism be sixty minutes, then if the holder of
the prism be rotated in the manner described through an angle of thirty degrees
from the position of only horizontal displacement, the vertical angle subtended by
the directly viewed and refracted images of the horizon will be 60' x sine 30°,
that is 30 minutes. This rotatable prism is hereinafter referred to as prisin A.
Also, if a prism be fixedly attached to a support or frame the latter may be
so placed or held in the hand that the directly viewed and refracted images of
the horizon are seen in an unbroken line, that is when it is so held that refraction
in the prism only takes place in a horizontal direction, and if this position be lost it
may be recovered by moving the support in the same plane (ie. the plane of the

page_text: prism's axis perpendicular to the line of sight) until continuity of the horizon
is regained.
This fixed prism is hereinafter referred to as prism B.
For use at sea in measuring small visual angles for the determination of distance.
the instrument may consist of two principal parts capable of being rotated on the
same axis, one about the other, through an angle of 90 degrees.
One part forms the support or frame of the instrument and may be a disc of
metal or other suitable material having an axial bole, or aperture, in or about which
a tube can be rotated.
The other part consists of the said tube having attached to it circumferentially a
dise of a diameter smaller than that of the support or frame with which it is in
contact, the ring of the latter surrounding its circumference being used for
graduating the instrument, and the common axis of tube and support is the line
of collimation of the instrument.
In the tube I fix the prism A, whose minimum angle of deviation is approxi-
mately equal to, and not less than, the largest angle which the instrument is required.
to measure. This prism may be of semicircular form and is fixed in the position of
minimum deviation in a plane perpendicular to the axis of the tube.
In the hole or aperture in the support I fix the prism B which is of fairly large.
refracting angle (about three or four degrees) also in a plane perpendicular to the
common axis, and this prism is so placed that when the horizon is viewed through
the tube a portion of it will he seen by direct vision between the edges of the two
prisms, and also on the one hand through prism B and on the other hand through
prism A. The support can thus be held in such position that the horizon as seen by
direct vision and through the prism B is an unbroken line, and maintaining this
position of the support the tube can be rotated until the horizon as seen in the
prism A is continuous in the same line. Both prisms are then refracting only in a
truly horizontal direction, and this is the observing position of the support, and the
zero position of the tube which can be indicated by an arrow on the disc attached to
it coinciding with the initial point of graduation on that part or ring of the support
surrounding it.
If the support be maintained in this position the tube can be rotated until the
horizon as seen through the prism A touches the water line of an object at sea whose
distance it is desired to determine, and by the angle of rotation of the tube from the
zero position as described the vertical angle subtended between the direct and
refracted horizons is obtained and consequently the angle between the horizon and the
water line of the object from which angle the distance can be determined, the height
of the eye of the observer above the sea being known. In a similar manner angles
of elevation above the horizon, such as the altitude of distant land, ships' mastheads,
and the like can be measured..
A scale may be made on say each of the four quadrants of the support placing four
indices or arrows on the movable circle so that the instrument may be graduated to
read direct (1) the vertical angle measured (2) on the next quadrant the distance of
an object due to the angle measured at a certain height (3) on the third quadrant the
same at a certain other height and so on. Or the graduations may be so made as to
give the distance for all practical heights eitber of the observer's eye, or of the object
whose elevation is observed.
A telescope may be attached to the tube, and the prism A may be placed in the
manner described either before, or behind, the object glass, or it may be attached to
the said glass.
For land use the instrument may be constructed on the same principle, but the
prism B be dispensed with, and cross wires at right angles in the eye piece of a
telescope be substituted, the eye piece, or draw out, rotating in the tube of the
telescope to which the prism A is attached, in the manner hereinbefore described.
Thus if it be wished to obtain the angle subtended by a man standing at a distance the
instrument is directed towards him and two images are seen in the aperture, one by
direct vision, and one refracted. by the prism A. Both parts of, the instrument are

page_text: then turned independently until the two images are vertically disposed and on, or
parallel to, one of the cross wires held vertically. Retaining the eye piece and cross
wires in this position the part of the telescope which contains the prism A is rotated
until the upper part of one image and the lower part of the other image make contact
with the horizontal wire, and the angle of rotation thus made between the eye piece
and the part containing the prism A is a measure of the required angle as hereinbefore
described, and can be graduated in a similar manner. This instrument may also be
graduated to read directly the distance corresponding to the angular measurement of
objects of known and generally uniform dimensions, such as a man, a man on
horseback, a camel, a bell-tent, or other object.
The same principles can also be applied to the construction of similar instruments
in a binocular form.
A prism such as the prism B can be employed by rotation as described to obtain a
line vertical with the horizon or a line at any desired angle to a distant line.
Dated this 15th day of April 1896.
JOHNSONS & WILLCOX,
47 Lincoln's Inn Fields, London, W.C., Agents.
A New or Improved Instrument for Measuring Small Visual Angles,
and for the Determination of Distances thereby.
I, LEWIS KNOX BELL, Commander, Royal Navy H.M.S. Barfleur, at present on
the Mediterranean Station, 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:-
My invention has for its principal object to provide a simple and efficient
instrument for the measurement of small visual angles in such a manner as to
ensure an exaggerated reading on an arc or scale and is primarily intended for
determining the distance of objects at sea or on land by observing from a known
height the angle subtended by the horizon and the water line of an object at
sea, or the angle of elevation of, or the angle subtended by, an object of known
height or dimensions, or by observing the depression angle, or any other well
known method of determining distance by the measurement of visual angles, a
graduated are or scale being provided to enable the distance corresponding to the
angle observed to be read off directly, as well as the angle measured.
For this purpose I employ a prism of known angle of minimum deviation so
mounted that it can be rotated in the plane which bisects its refracting angle perpen-
dicular to the line of sight, through an angle of 90 degrees. If a point or object
on the horizon he now viewed the prism holder may be so held that the refracted
image in the prism will appear horizontally apart from the directly viewed image
and at an angular distance from it equal to the angle of minimum deviation of the
prism. If the prism be then rotated in the same plane by turning the holder thereof
through an angle of 90 degrees, the refracted image will move on the circumference
of a circle described about the point or object until it appears vertically above or
below the directly viewed image and the portion of the horizon seen on either sido
of the point or object will undergo displacement in a similar manner. When the
refraction takes place only in a horizontal direction (that is, when the axis of the
prism is vertical) the horizon as seen through the prism and by direct vision will
appear in an unbroken line, and when the holder of the prism is rotated through an
angle of 90° the directly viewed and refracted images of the horizon will be separated
vertically to an angular distance equal to the angle of minimum deviation of the

page_text: prism. If the rotatory movement of the prism be arrested at any point between these
positions of only horizontal, and only vertical displacement, the vertical angle sub-
tended by the directly viewed and refracted images will be equal to the angle of
deviation of the prism multiplied by the sine of the angle rotated.
For instance if the minimum angle of deviation of the prism be sixty minutes,
then if the holder of the prism be rotated in the manner described through an angle
of thirty degrees from the position of only horizontal displacement, the vertical angle
subtended by the directly viewed and refracted images of the horizon, will be :-
60'sine 30°, that is 30 minutes.
This rotatable prism is hereinafter referred to as prism A.
Also, if a prism be fixedly attached to a support or frame the latter may be so
placed or held in the hand that the directly viewed and refracted images of the
horizon are seen in an unbroken line, that is, when it is so held that refraction in the
prism only takes place in a horizontal direction, and if this position be lost it may
be recovered hy moving the support in the same plane (ie. the plane of the prisms'
axis perpendicular to the line of sight) until continuity of the horizon is regained.
This fixed prism is hereinafter referred to as prism B.
For use at sea in measuring small visual angles for the determination of distance,
the instrument may consist of two principal parts capable of being rotated on the
same axis one about the other, through an angle of 90 degrees.
One part forms the support or frame of the instrument and may be a disc of metal
or other suitable material having an axial hole or aperture in or about which a tube
can be rotated.
The other part consists of the said tube having attached to it circumferentially a
disc of a diameter smaller than that of the support or frame with which it is in
contact, the ring of the latter surrounding its circumference, being used for
graduating the instrument, and the common axis of tube and support is the line
of collimation of the instrument.
In the tube I fix the prism A, whose minimum angle of deviation is approximately
equal to, and not less than the largest angle which the instrument is required to
measure. This prism may be of semicircular form and is fixed in the position of
minimum deviation in a plane perpendicular to the axis of the tube, the base of the
prism being preferably towards the axis of the tube.
In the hole or aperture in the support I fix the prism B which is of fairly large
refracting angle (about three or four degrees) also in a plane perpendicular to the
axis of the tube, this prism being preferably arranged with its refracting edge towards
the axis of the tube, and so that when the horizon is viewed through the tube, a
portion of it will be seen by direct vision between the edges of the two prisms, and
also on the one hand through the prism B, and on the other hand through the
prism A. The support can thus be held in such position that the horizon as seen
by direct vision and through the prism B is an unbroken line, and maintaining this
position of the support the tube can be rotated until the horizon as seen in the
prism A is continuous in the same line. Both prisms are then refracting only in a
truly horizontal direction, and this is the observing position of the support, and
the zero position of the tube which can be indicated by an arrow on the disc
attached to it coinciding with the initial point of graduation on that part or ring
of the support surrounding it.
If the support be maintained in this position the tube can be rotated until the
horizon as seen directly and through the prism B, touches the water-line viewed
through the prism A, of an object at sea, whose distance it is desired to determine,
and by the angle of rotation of the tube from the zero position as described the vertical
angle subtended between the direct and refracted horizons is obtained and consequently
the angle between the horizon and the water-line of the object, from which angle the
distance can be determined, the height of the eye of the observer above the sea being
known. In a similar manner, angles of elevation above the horizon, such as the
altitude of distant land, ships' mastheads and the like can be measured.

page_text: A scale may be made on, say, each of the four quadrants of the support, placing
four indices or arrows on the movable circle, so that the instrument may be graduated
on one quadrant to read direct the vertical angle measured; on another quadrant the
distance of an object due to the angle measured at certain heights; on another
quadrant the distance at certain other heights, and so on. Or the graduations may
be so made as to give the distance for all practical heights, either of the observer's
eye, or of the object whose elevation is observed.
A telescope may be attached to the tube, and the prism A may be placed in the
manner described, either before, or behind, the object glass, or it may be attached to
the said glass.
Figure 1 of the accompanying drawings, represents in elevation, and Figure 2 in
horizontal section an instrument constructed according to this invention.
Figure 3 is a front elevation of a modified form of instrument and Figures 4 and 5
represent in front elevation and vertical section respectively another modification in
the form of the instrument and means for rotating the prism, the rest of the figures
are explanatory diagrams which will be hereinafter referred to.
Referring to Figures 1 and 2 C is the body or holder of the instrument of circular
form provided with a handle A' and carrying on one side a tube D having an
opening in its side through which projects to within a short distance of the axial
line of the tube a prism B the said prism being fixed in a case D connected by
screws to the body or holder C. On the side of the body or holder Copposite that
which carries the tube D is fitted, so as to be capable of rotation a tube É carrying
another prism A having a less angle than the prism B. The axes of the tubes D
and E are in line one with the other, and the tube E is shewn as being connected
to the body or holder C by screws passing through a flange d on the tube and
through slots in the body or holder concentric to the axes of the tubes E and D.
The prisms A and B when in their normal position have their edges a b parallel one
to the other as shewn in diagram Figure 1A so that on looking through the tube E at
the horizon for example with the edges a 6 of the prisms perpendicular to the horizon
the said horizon will appear as a continuous line, refraction taking place to the right
or left; but if the holder C be turned to the right or to the left the horizon will
appear to be twice broken as shewn for instance in the diagram Figure 1B the
prism B of larger angle throwing the portion of the horizon seen therethrough
considerably further out of the line than does the prism A of smaller angle. Now if
the instrument be held so that the horizon appears as shewn in diagramn Figure 14 and
then the tube E carrying the prism A be turned axially a portion of the horizon will
be refracted in the prism A and subtend an angle with the horizon seen through the
prism B and directly through the space between the edges a and b of the prisons. On
the base or flange d of the tube E is a pointer or index mark a¹ to indicate on the
scale marked on the holder C the angle through which the tube E and prism A is
turned. Each quadrant of the circular body or holder (the circle being struck from
the axis of the tube E) may be graduated, riz.-one quadrant for angles, one for
distances according to the height in feet of the observer's eye when observing from
the bridge of the vessel, one when observing from the conning tower, and the other
for observing from some other height, so that the same instrument can be used for
ascertaining distances at whatever height the observer's eye may be. The following
is a simple method of constructing the scales. Let a Figure 2A represent the axis of
the tube E which carries the prism A. xy radius of arc y z u to be graduated.
Erect a perpendicular eu on and divide the line cu into the same number of equal
parts as the angle of minimum deviation of the prism A contains minutes, say for
example 48'. Through these divisions draw lines parallel to the line y to the
arc y u then when the tube E carrying the prism A is rotated the mark on the arc
where the pointer on the flange of the tube reaches indicates on the arc the number
of minutes measured by the prism A. For example, suppose the line x u to be
divided into 48 divisions corresponding to the number of minutes in the angle of
minimum deviation of the prism A as before described and the tube E be rotated from
its zero position (that is when the edges ab of the prisms A B are parallel to each

page_text: other) till the pointer a¹ on the flange of the tube reaches the division 35 on the arc
(for instance at 2) the angle measured will be 35 minutes. The graduations for the
measurement of angles being found as described the other quadrants of the circle can
be graduated for measuring distances. The divisions should be made in the first
instance on a large scale and be reproduced on a scale suitable to the instrument; for
instance, if it be required to graduate on an arc y* *u* of say two inches radius, a
distance of 1000 yards the height of the observer's eye being 35 feet, the angle to be
measured is 34.69 minutes: Set off on the vertical or radius line of the arc au
34.69 minutes and draw a line parallel toy from this point through the large
are y z u and from the point of intersection on this are draw a line to a, then the
point where this line intersects the smaller are y* * * indicates the point of
measurement of 1000 yards on the said arc. Graduations for other distances are
similarly ascertained and marked on the are y* 2* u*. In like manner distances are
indicated and marked on arcs of other radii for different heights of the observer's eye.
The angles are calculated from the formula :-
The flange of the tube E is provided with radially adjustable pointers bone for
each of the three quadrants containing the scales for the different heights of the
observer's eye.
The instrument is provided with a telescope F as shewn in
Figure 2 screwed into the tube E.
In the apparatus illustrated by Figure 3 only one quadrant is provided the said

page_text: quadrant containing scales or graduations for indicating angles and also for
distances.
To the tube E carrying the prism A is connected an arm or radius bar El hy
which the tube and prism can be turned axially in the body or holder C. The
scales may be marked on the body or holder C itself, but it is preferred to mark
the scales on a separate piece and attach it to the holder so that it can be removed
and replaced by another scale when desired. The outer edge of the quadrant is
graduated for angles in minutes and the radius of the quadrant is graduated for
heights of the observer's eye say from 20 to 60 feet. The radius bar is fitted.
with an adjustable pointer which can be slidden along the radius bar to the
division on the radius line of the quadrant corresponding to the height of the
observer's eye and can be fixed in its adjusted position by a binding nat e.
The forward edge a' of the radius bar serves as a pointer to indicate on.
the graduations on the edge of the quadrant the angle in minutes measured.
The radius bar can be fixed by means of the clamping screw and nut d¹ in the
position to which it has been moved. For an instrument for general use at heights.
varying from 20 to 60 feet the angle of deviation of the prism A may be from
about 48 to 70 minutes but for an instrument intended for use at lower lieights say
from 20 to 80 feet, which would meet the requirements of the harbette, turret guns
and upper deck batteries of battleships, an angle of about 24 minutes will be
sufficient,
In the arrangement illustrated by Figures 4 and 5 the tube or holder E of the
prism A is arranged eccentrically to the centre of the disc and is provided with a
toothed segment E' with which gears a wheel H mounted on a stud in the centre of
the disc C. To the wheel H is attached a radius arm or bar E' carrying in bearings e
a screw threaded spindle I on which is fitted so as to traverse therealong a nut
provided with an index pointer to indicate on the scale the height of the observer's..
eye, the screw being rotated for the purpose of adjusting the index pointer &¹ by means
of a milled head [2.
The radius bar E is provided at its outer end with a depending lip d' between
which lip and the periphery of the dise C is interposed a spring f for the purpose of
causing sufficient friction between the radius bar and the disc C to retain the bar in
the position to which it is adjusted. The front edge a¹ of the radius bar serves as the
index to indicate on the scale the angle in minutes measured.
In constructing an instrument for use on land the movable prism B may be-
dispensed with and the prism A be fixed in front of the object glass of a terrestial
telescope the eye piece of the telescope being provided, inside, with crossthreads or
wires B as shewn diagrammatically in Figure 3A 3B and 3. The prism A is arranged
so as to cover about one half the field of view and its zero position is such that its.
refracting edge is parallel to one of the cross wires or threads and perpendicular to the
other cross wire or thread. To the tube of the telescope is attached a dise C having
one quadrant thereof graduated to angles. and another quadrant graduated for
distances corresponding to say 5 feet in height (about the height of a man) and the
eye piece carries a disc or index & which works in close proximity to the disc C.
Now if (for example) it be wished to obtain the angle subtended by a man standing
at a distance the tube of the telescope is adjusted so that the prism measures the-
maximum vertical angle and then the telescope is directed to the object (the man) and
turned bodily until the direct image and the refracted image of the object are in a
vertical line on or parallel to the vertical cross wire as shewn in the diagram.
Figure 3 the upper figure being the direct view and the lower figure the refracted
view of the object. Retaining the eye piece of the telescope and the cross wires
in this position, turn the tube containing the prism until the top of the lower figure
and the bottom of the top figure simultaneously touch the horizontal wire or thread as.
shewn in Figure 3C the rotation thus given to the prism measured from the zero
point on the scale indicates the angle and distance as hereinbefore described.
The scales for use with this instrument are similar to those shewn in Figures 1 and 3,
the oblique lines being, as before, lines of distance, whilst the radial graduations.

page_text: indicate heights of object observed. The angle, a, subtended at the eye by an object
at a distance, is given by the formula :-
and in constructing the scales a table of angles (in minutes) calculated by this formula
is to be used as before described. Before making an observation the adjustable
pointer or index is set to the height (known or estimated) of the object whose distance
is to be measured.
The same principle can be applied to the construction of similar instruments in a
binocular form.
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 an instrument for measuring visual angles the combination with a prism
of known angle of minimum deviation rotatable in a plane perpendicular to the line
of sight, of a fixed prism by means of which the instrument can be adjusted to
the correct position for making correct observation, substantially as hereinbefore
described.
2. In an instrument for measuring visual angles and distances the combination with
a prism of known angle of minimum deviation, rotatable in a plane perpendicular
to the line of sight, of a fixed prism, or cross wires or threads by means of
which the instrument can be adjusted to the correct position for making correct
observations, and a pointer or pointers, and a scale, or scales for indicating the
angle and distance measured substantially as herein before described..
3. The combinations and arrangements of parts constituting instruments for
measuring and indicating small visual angles and distances substantially as
herein before described and illustrated by the accompanying drawings.
Dated this 15th day of January 1897.
JOHNSONS & WILLCOX,
47 Lincoln's Inn Fields, London, W.C., Agents.