CERTAIN OPTICAL INSTRUMENTS FOR MEASURING ANGLES, AND ALSO CERTAIN IMPROVEMENTS UPON AND ADDITIONS TO TELESCOPES AND OTHER OPTICAL INSTRU- MENTS, FOR THE PURPOSE OF MEASURING ANGLES AND DISTANCES WITH FACILITY, AND OTHER PURPOSES
Year: 1811

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, we, DAVID
BREWSTER, of Edinburgh, North Britain, Doctor of Laws, and WILLIAM
HARRIS, of Holborn, in the County of Middlesex, Optician, send greeting.
WHEREAS His most Excellent Majesty King George the Third did, by
His Letters Patent under the Great Seal of the United Kingdom of Great
Britain and Ireland, bearing date at Westminster, the Twenty-first day
of May, in the fifty-first year of His reign, give and grant unto us,
our exors, admors, and assigns, His especial licence, full power, sole pri-
vilege and authority, that we, the said David Brewster and William
Harris, our exors, adññors, and assigns, should and lawfully might, during
the term of years therein expressed, make, use, exercise, and vend, within
England, Wales, and the Town of Berwick-upon-Tweed, our Invention of
"CERTAIN OPTICAL INSTRUMENTS FOR MEASURING ANGLES, AND ALSO CERTAIN
IMPROVEMENTS UPON AND ADDITIONS TO TELESCOPES AND OTHER OPTICAL INSTRU-
MENTS, FOR THE PURPOSE OF MEASURING ANGLES AND DISTANCES WITH FACILITY,
AND OTHER PURPOSES;" in which said Letters Patent there is contained a proviso
obliging us, the said David Brewster and William Harris, or one of us, by
an instrument in writing under the hands and seals of us, or the hand and

page_text: scal of one of us, to cause a particular description of the nature of our said
Invention, and in what manner the same is to be performed, to be enrolled
in His Majesty's High Court of Chancery within two calendar months after
the date of the said recited Letters Patent, as in and by the same, relation
being thereunto had, may more fully and at large appear.
NOW KNOW YE, that in compliance with the said proviso, I, the said
William Harris, do declare the nature of our Invention, and the manner in
which it is to be performed, to be particularly described as follows:-
No. 1. A Micrometrical Telescope. This instrument is intended to measuro
angles and distances, and is of great use in surveying and practical astronomy,
and for various military and naval purposes. The principle on which it is
founded is to encrease and diminish, by an optical contrivance, the angle sub-
tended by a pair of points or wires or any other two objects placed in the
anterior focus of the eyeglass of a telescope. By this means, the angle sub-
tended by any object or part of an object to which the telescope is directed
may be easily and accurately measured, and its distance from the observer
ascertained, as in other trigonometrical operations. The contrivance by which
this is effected consists in making a lens move along the axis of the telescope,
so that its distance from the object glass may be diminished till they come in
contact, or increased till their distance is equal to the focal length of the
object glass. When the lens and the object glass are in contact, the anglo
subtended by the. two points or wires, &c. is a maximum, and when their dis-
tance is equal to the focal length of the object glass, the angle is a minimum.
When the lens and the object glass are at any intermediate distance, the
angle has and intermediate valve, which varies with the distance. The maxi-
mum and minimum angles of the points or wires, &c. are ascertained in the
common way by experiment, and the intermediate angles are found upon a
scale of equal parts, which may ibe engraved on the tubes of the telescope, or
constructed in any other way, depending on the method which is employed to
give motion to the lens. The moveable lens and the object glass may bo
convex or concave, or a meniscus, or they may be achromatic or simple
lenses, and any or both of them may be made moveable; but they must
always be such as to have a positive focus lying between the moveable lens
and the eyepiece of the telescope. The same principle may-be-applied to the
Newtonian reflecting telescope, but particularly to the Gregorian and Casse-
grainian télescopes, where it is necessary only to give the eyepiece a motion
to and from the great telescope, by which means the angle subtended by two
points or wires, &c. is varied, and the variation is measured by the motion-of the
eyepiece, or by the revolutions of the pinion by which that motion is effected

page_text: This principle may also be employed in the compound microscope for measuring
the angles subtended by minute objects.
No. 2. Double Image Telescope.-This instrument is intended for the same
purposes as the preceding one, and resembles it in some measure in principle
and construction. The moveable lens in this case consists of two semilenses
having their centre at an invariable distance. Two images of the object are
thus formed, and these images are made to separate and to approach each
other, and are consequently brought into contact by varying the distance of
the semilenses from the fixed object glass. In order to measure with this
telescope the angle subtended by any object 'or part of an object, move the
lenses to or from the object glass till the two images of the object or of part
of an object are in contact, and the scale, which is the same as in the
preceding instrument, and constructed in the same way, will shew the angle
required.
The same contrivance may be applied to the reflecting telescope, by bisect-
ing the small mirror, and fixing the segments at an invariable distance. The
separation and approach of the images is then effected by varying the distance
between the eyepiece and the great speculum. A similar result may be
obtained by bisecting the third lens of an achromatic eyepiece, and separating
the images (formed by the fixed segments) by means of a moveable lens.
The double-image telescope forms an excellent coming-up glass for ascer-
taining whether a ship is approaching to or receding from the observer, and
is particularly useful for measuring angles at sea, or in cases where it is either
difficult or inconvenient to keep an instrument in a steady position.
No. 3. Rotatory Micrometer.-This instrument, which is of the same use
as the preceding, consists of a telescope, which has a sharp point in the ante-
rior focus of the eyeglass, and distinctly visible in the 'field of view. Another
point projecting into the field of view is fixed to the part of the eyepiece
which contains the first glass, and which has a motion of rotation about the
axis of the eyepiece. Hence, by turning the moveable part of the eyepiece,
the moveable point can be brought to coincide with the fixed one, and can be
separated from it in the circumference of a circle. The separation of the two
points, or the angle which they subtend at any given position, is measured by
a graduated circular head furnished with a vernier scale. By considering that
the distance between the points is always the chord of the circle which the
moveable point has described, the angle subtended by the points may be easily
found when the circular head is divided into 360°; or the angle may be found
directly, by inserting the minutes on the scale. An instrument on the same

page_text: principle may be constructed, by giving a rotatory motion to one of the lenses
of a divided object glass.
No. 4. Circular Micrometer.-This instrument is merely a circular piece
of mother-of-pearl, or of any other fit substance, fixed in the focus of the
eye-glass of a telescope, and having its interior circumference divided into
360°. The angle subtended by any object seen thro' the telescope is then
measured by observing how many degrees of the divided circumference it
occupies. The angle being always proportional to the chord of this arch it
may be easily found, after the angle subtended by the diameter of the divided
circumference has been ascertained by experiment.
No. 5. Luminous Image Micrometer. The object of this instrument is to
measure the angle subtended by two luminous points; for this purpose the
qbject glass and eyepiece of a common telescope or achromatic telescope arc
placed in a tube or tubes about ten inches longer than what is necessary for
common purposes. A scale, divided into equal parts, and having the zero in
the middle of it, slides in a groove in one of the tubes, so that the index points
to the zero of the scale, when the observer sees distinctly the luminous points
whose angle is to be determined. When the index is adjusted to zero by
the luminous points appearing very distinct thro' the telescope, shorten the
telescope by pushing in the tube which contains the scale, and the two
luminous points will swell into circular images of light till they appear in
accurate contact. The quantity by which the telescope has been pushed in,
pointed out by the index upon the scale, will be a measure of the angle sub-
tended by the luminous points. The same thing may be done by pulling out
the tube which contains the scale. As there may be some difficulty in ascer-
taining the exact zero of the scale, it would be preferable to place the zero,
not in the middle of the scale, but at the end next the eye. Let the tube
be then pushed in till the images come in contact; and in this situation put
the index at zero, draw out the tube beyond the principle focus till the circular
images are again in contact, and the index will point out the measure of the
angle. By this method of constructing the scale it becomes twice as long as
before, and will get rid of the difficulty of finding the zero.
No. 6. Klinometer.-This instrument for measuring with the naked eye
the apparent inclination of strata, the declivity of mountains, and the apparent
magnitude of angles when the eye is not at their vertex, is represented in
Fig. 1, where A, B, is a graduated arch fixed upon the base C, D. The arm
E, F, which carries the vernier F, moves round E, the centre of the arch
A, B. This arm likewise carries a frame G, H, enclosing a reflecting plane P

page_text: which move upon pivots A and B in a plane perpendicular to that of the
quadrant. When the instrument is to be used, it is adjusted to a horizontal
plane by the level L, and the finger screws S, S, S. The moveable arm is
then shifted along the graduated arch till the reflected image of the stratum,
&c., seen in the reflecting plane, is continuous with the direct image seen with
the eye. The arch intercepted between the index of the vornier and the
beginning of the scale will show the angle of inclination. The reflecting
plane P may be placed either at the centre E, or on the circumference A, B,
or on any part of the radius E, F. Greater accuracy might be obtained by
making the plane P very thin, so as to see the direct object both above and
below it. A level at right angles to the level L might also on some occasions
be requisite. The plane P might also be made to move in an opposite direc-
tion on pivots at p and q, in which case the scale would begin at 90.
No. 7. Goniometrical Microscope, Fig. 2.-This is nothing more than tho
preceding instrument applied to the microscope in Fig. 2. A, B, is the first
eyeglass; C, the small reflecting plane fixed to the graduated circle D, E, by
the worm O, which slides in the groove M, N. The plane C moves round
the axis A, B, so that it can easily be adjusted till the observer can at tho
same instant see the direct field of view and the reflected one in the plane C.
The vernier ff, is supported by an arm which rises from the tube T, T.
When an angular object is placed for measurement in the focus of the micro-
scope the mirror C is turned round its axis A, B, and moved in the groove
M, M, by means of the arm O, till the observer, by looking through the
eyeglass and into the mirror, perceives, at the same time, a distinct reflected
image of the field of view, and the angular object which it contains. The
graduated circle D, E, is then moved round its centre till the reflected image
of one of the lines which contains the angle is continuous with the line itself,
and the degree pointed out by the index is noted down. The circle is again
made to revolve till the image of the other line is continuous with the line
itself, and the place of the index is again marked. The arch of the circle
intercepted between these positions is the measure of the angle required.
No. 8. Goniometrical Telescope (Fig. 2).-The goniometrical telescope is
constructed in the same way as the microscope now described, with the addi-
tion of a small level L, L, fixed in such a manner to their graduated circle
D, E, that its axis is always in a plane parallel to that in which the mirror
C revolves about the pivot A, B. This instrument is employed to measure
the inclination of strata, and the declivity of mounts, &c., &c., when greater
accuracy is required, or when the object is too remote to be distinctly seen by

page_text: the naked eye. The optical principle upon which this and the two preceding
instruments may be applied with great success in the construction of other
instruments.
No. 9. Telescophical Klinometer (Fig. 3). This instrument, which is
intended for the same purposes as No. 8, is much superior to it in accuracy
and in the extent of its application. It may be employed to measure the
angle which a line joining two stars forms with the horizon, &c., or in general
any angle, when we have only two or more points in the lines by which the
angle is contained.
The instrument is represented in Fig. 3, where M, A, B, is a graduated
arch (which may be either a quadrant, a semicircle, or a circle) supported on
the base B, C, M.. The. arm E, D, carrying the vernier F, revolves round
the centre C, and a telescope G, H, with cross wires in the anterior focus
of its first eyeglass, moves upon two pivots E, R, in a plane perpendicular
to the plane of the arch. When the base B, C, M, is adjusted to a horizontal
plane by a level L, the arm which carries the telescope is raised into such a
position that during the motion of the telescope round the pivots E, K, the
intersection of the wires traces in the heavens the line which joins the two
stars. When this position is attained, the index will point out on the scale
the angle which the line joining the two stars forms with the horizon. This
instrument may be used for a variety of purposes.
No. 10. Angular Micrometer with wires or fibres, Figs. 4 and 5.-This
micrometer consists of two wires A, B, C, D, placed in the focus of the eye-
glass either of a telescope or microscope. One of these wires A, B, is fixed
at a little distance from the centre of the field, while the other C, D, moves
along with the tube which contains the eyeglass, and thus form every pos-
sible angle with A, B, sometimes crossing it, as in Fig. 4, and sometimes
inclined to it, as in Fig. 5. Now in order to measure with this instrument
the angle formed in any line seen in the field of view) with the horizon or
with any other line, turn the whole eyepiece till the fixed wire is horizontal,
which may be done by means of a level, or till it coincides with one of the
lines which contains the angle required, then turn the moveable part of the
eyepiece to which the other wire C, D, is fixed till the wire C, D, coincides
with the other line, or passes through two points in that line, then the angle
formed by the line A, B, C, D, will be the angle required. In order to find
this angle by the instrument, which has a graduated circular head with a
vernier like D, E, in Fig. 2, which moves along with the wire C, D, it must
be considered that the angle B, 0, D=arch B, D, arch A, C, when the

page_text: wires cross as in Fig. 4, and that B, O, D, arch B, D, E, arch A, C, when
they do not cross as in Fig. 5. Hence, by measuring the arches B, D, A, C,
which can be easily. and quickly done by the graduated head and vernier, the
angle of the wires may be instantly ascertained. In order to prevent the
division of the sum or difference of the arches by 2, the graduated head is
divided into 180 instead of 360°. If the two wires always crossed in the
centre of the field, the angle B, O, D, would be more easily measured; but
in that case we are limitted in the extent of our measurements to half the
field of view, whereas in the present instrument we have the command of the
whole field, besides other advantages. One of the wires might be placed
in the focus of the whole eyepiece, and the other in the focus of the first
eyeglass.
No. 11. Angular Micrometer with double images. In this instrument the
part of the telescope which contains the two semilenses must be turned round
till the two images of the line whose inclination to another line or to the
horizon is to be measured coincide or form one straight line; then the inclina-
tion of the line C, D, the common diameter of the semilenses A, B, is the
angle required, and it may easily be measured, as in the other instruments,
with a level and a divided circular head. When this instrument is joined with
No. 2, we may at the same time measure the angle subtended by the line
joining any two points and its inclination to the horizon.
No. 12. Giniometer for measuring the angle of chrystals (Fig. 7).-This
instrument is represented as Fig. 7, where A, B, is a circle divided into
360°, which moves round the centre O, and is supported by two upright
bars M, N, screwed into the stand S, to these bars is fixed the arm G that
carries the vernier E. This vernier remains stationary, while the rotatory
motion is communicated to the divided circle A, B, by means of the toothed
pinion Q, a rectangular piece of brass L is fixed by two screws to one of the
radii R of the graduated circle, so that the sliders s, s, may move upon it,
and be placed at different distances from the centre of motion. A thin
plate t, c, forming part of the cock in the top of this slider, carries the
chrystal K, and, by means of the handle T, has a motion round the centre O
in a plane perpendicular to that of A, B. Below this thin plate, and fixed
to it by the screw c, is another plate, part of which is seen at a, noveable
round the axis a, y, by means of the screw nut H, which works in another
plate of brass below, a, and thus raises or depresses the plate a, and
also the plate c which carries the chrystal K. These three plates forming
the projecting cock have a rotatory motion in the same plane with the
circle by means of the bandle II, which serves for a lever as well as for a

page_text: screw. By the combination of these motions the common section of the
surfaces of the chrystal is brought into a position parallel to the axis of tho
instrument. This adjustment is effected by placing the graduated circle in
such a position that a vertical window bar or any other straight line is nearly
in the plane of the circle. A motion of rotation is then given to the
chrystal, and if the reflected image of the window bar (from the surface of
the chrystal, from one straight line with the direct image when examined,
in cach surface of the chrystal the adjustment is complete, or the plane of the
graduated circle is parallel to a plane at right angles to the common section
of the surfaces of the chrystal. The instrument is then placed in such a
position that the plane passing through the eye of the window bar is perpen-
dicular to the plane of the divided circle, or that the common section of the
surfaces of the chrystal points to the bar of the window. The index is set
to the beginning of the scale by means of a stop at the 180th degree,
and the image of the vertical window bar or any rectilineal object formed by
reflection from the first or right-hand surface of the chrystal is brought to
coincide with the direct image by the vertical motion of the cock, the whole
graduated circle is then made to revolve by the pinion Q till the reflected
image of the vertical bar again coincides with the direct image when examined
in the other surface of the chrystal. When this position is attained, the
index of the vernier will point out in the divided arch the angle of the
chrystal. Any aberration arising from the distance of the chrystal from
the centre of motion may be removed by opening the centre of the circle A,
and placing the chrystal exactly in the centre. During the preceding operation
the instrument must evidently remain steady on its base, as the smallest
change in its position will affect the accuracy of the result. In order
to remove this inconvenience, and render the instrument portable and inde-
pendant of any object exterior to itself, a horizontal arm about 6 or 8
inches long projects from the base of the instrument, and carries the
vertical frame H, I. Across this frame three pair of parallel wires are
stretched in a perpendicular direction, and are used instead of the window
bars in the way already described. The angle of the chrystal may then
be determined when the instrument is held in the hand without the accu-
racy of the measure being affected by any agitation whatever. In the mensu-
ration of the angle the middle pair of silver wires may be employed when
the space described by the chrystal is not great; but when this space is con-
siderable, one of the extreme pairs should be used with the first surface of
the chrystal, and the other pair with the second. This instrument admits of
a variety of forms, and the cock at O may be constructed in various ways.

page_text: No. 13. Instrument for measuring angles and inaccessible distances at one
station.-Let A, B, ✗
see below, be two telescopes so fixed that their axis
may converge to a point one hundred yards before their object glasses. If the
telescopes thus fixed be directed to an object at a greater distance, their axis will
point to different parts of that object, and will comprehend a portion of it M, N.
Now if we know the angle A, R, B, at which the telescopes are fixed, we
have the equal vertical angle M, R, N, or that subtended by M, N, at a point
one hundred yards before the observer. If we suppose other two telescopes
so fixed that their axis converge to a point one hundred yards behind their
object glasses, and that these axis comprehend a portion O, P, of the former
object equal to M, N, then the angle at which the telescopes are fixed is the
angle subtended by the object O, P, or M, N, at a point one hundred yards
behind the observer. Hence we have the angle subtended by M, N, at the
two extremities of a base two hundred yards long, and can therefore find the
distance M, B, with R. These angles may be taken by one pair of telescopes
firmly fixed, having their axis or the intersection of the cross wire move-
able by
a micrometer screw, so that they may be made to converge to any
point before or behind the observer. The same thing may be done by one
telescope moveable along two concentric graduated arches. One extremity
of the telescope moving along one arch, and the other extremity along the
other. The telescope always pointing to the centre of the arch, or we may
obtain the same result by making the tube of the telescopo conical, and
causing it to revolve round a distant centre by rolling over a plain surface;
two telescopes fixed together so as to point always to the same place, may be

page_text: used with great advantage as a portable base, and the length of the base may
be varied by shifting the intersection of the wires.
In witness whereof, I, the said William Harris, have hereunto set my
hand and seal, the Thirteenth day of July, in the year of our Lord
One thousand eight hundred and ten.