A NEW MATHEMATICAL INSTRUMENT, TO BE TERMED THE HOROMETER,' FOR THE PURPOSE OF SOLVING PROBLEMS IN PLANE AND SPHERICAL TRIGONOMETRY, ONE FEATURE OF WHICH INVENTION IS OR MAY BE APPLICABLE IN THE CONSTRUCTION
Year: 1854

page_text: LETTERS PATENT to Auguste Edouard Loradoux Bellford, of 16, Castle
Street, Holborn (City), London, Patent Agent, for the Invention of "A
NEW MATHEMATICAL INSTRUMENT, TO BE TERMED THE HOROMETER,' FOR THE
PURPOSE OF SOLVING PROBLEMS IN PLANE AND SPHERICAL TRIGONOMETRY, ONE
FEATURE OF WHICH INVENTION IS OR MAY BE APPLICABLE IN THE CONSTRUCTION
"
PROVISIONAL SPECIFICATION left by the said Auguste Edouard Loradoux
Bellford at the Office of the Commissioners of Patents, with his Petition,
on the 20th September 1854.
I, AUGUSTE EDOUARD LORADOUX BELLFORD, of 16, Castle Street, Holborn
(City), London, Patent Agent, do hereby declare the nature of the said Inven-
tion for "A NEW MATHEMATICAL INSTRUMENT, TO BE TERMED THE 'HOROMETER,
FOR THE PURPOSE OF SOLVING PROBLEMS IN PLANE AND SPHERICAL TRIGONOMETRY,
ONE FEATURE OF WHICH INVENTION IS OR MAY BE APPLICABLE IN THE CONSTRUCTION
OF OTHER MATHEMATICAL INSTRUMENTS," to consist of a part of a circle marked on
a flat surface and representing the earth. The arc is divided into degrees and
half degrees, numbering from the point representing the pole. On one side
of zero is inscribed "south declination" & on the other "north declination."

page_text: Corresponding to the declination, the polar distance also is marked on the
A line is drawn to represent the equator, & is divided into a scale
of 100 equal parts. Parallel to this right line are drawn right lines from the
division of degrees on the arc. These lines are projections of latitude, and are
suitably numbered. Across these lines of latitude are drawn horizontal lines
of longitude.
The instrument has an arm of steel or other durable material, turning on a
centre, & extending to the arc of the circle, on which arm is a vernier reading
to any number of minutes of a degree. This arm has a straight edge on a
line with the centre around which it turns. There is also a straight-edged bar,
which, if the arm be made of steel or iron, is attached to a horse-shoe magnet,
which will attach it to the said arm at a right angle thereto, and allow it to
slide freely thereon; but if the arm be of other material, the bar must be con-
nected by mechanical means. On the side of the bar is a scale of co-sines &
co-altitude, for measuring angular distances, but compensating for refraction,
&, if necessary, may be made to compensate for semidiameter of the sun,
parallax, and "dip" on the other side is a scale of equal parts. If used to
take the altitude of objects, it has a pin at the centre projecting a little, on
which a plumb is suspended. At the pole is a piece of white leather attached,
to stand above the edge, on which to cast the shadow of the pin when the
altitude of the sun is taken.
A peculiar feature of this Invention is, that by the combination of projec-
tions of latitude and horizontal projections of longitude within an arc of a
circle on a plane, the instrument will, with or without a scale of co-sines
or co-altitudes, solve problems in spherical trigonometry without the usual
mathematical calculations.
SPECIFICATION in pursuance of the conditions of the Letters Patent, filed
by the said Auguste Edouard Loradoux Bellford in the Great Seal Patent
Office on the 19th March 1855.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I, AUGUSTE S
EDOUARD LORADOUX BELLFORD, of 16, Castle Street, Holborn (City), London,
Patent Agent, send greeting.
WHEREAS Her most Excellent Majesty Queen Victoria, by Her Letters
Patent, bearing date the Twentieth day of September, in the year of our Lord
One thousand eight hundred and fifty-four, in the eighteenth year of Her S

page_text: reign, did, for Herself, Her heirs and successors, give and grant unto me, the
said Auguste Edouard Loradoux Bellford, Her special licence that I, the said
Auguste Edouard Loradoux Bellford, iny executors, administrators, and assigns,
or such others as I, the said Auguste Edouard Loradoux Bellford, my execu-
tors, administrators, and assigns, should at any time agree with, and no others,
from time to time and at all times thereafter during the term therein expressed,
should and lawfully might make, use, exercise, and vend, within the United
Kingdom of Great Britain and Ireland, the Channel Islands, and Isle of
Man, an Invention of "A NEW MATHEMATICAL INSTRUMENT, TO BE TERMED THE
HOROMETER,' FOR THE PURPOSE OF SOLVING PROBLEMS IN PLAIN AND SPHERICAL
TRIGONOMETRY, ONE FEATURE OF WHICH INVENTION IS OR MAY BE APPLICABLE TO THE
CONSTRUCTION OF OTHER MATHEMATICAL INSTRUMENTS," a communication, upon
the condition (amongst others) that 1, the said Auguste Edouard Loradoux
Bellford, by an instrument in writing under my hand and seal, should par-
ticularly describe and ascertain the nature of the said Invention, and in what
manner the same was to be performed, and cause the same to be filed in the
Great Seal Patent Office within six calendar months next and immediately
after the date of the said Letters Patent.
NOW KNOW YE, that I, the said Auguste Edouard Loradoux Bellford, do
hereby declare the nature of the said Invention, and in what manner the same
is to be performed, to be particularly described and ascertained in and by the
following statement :-
Fig. 1 of the accompanying Drawing is a face view of the instrument.
A, B, C, D, is a part of a circle drawn, engraved, or otherwise inscribed upon
a flat piece of metal, wood, pasteboard, or any other material on which lines
can be drawn. This circle represents the earth. The arc A, B, C, D, is
divided into degrees and half degrees, numbering from the point C, which
represents the pole. On one side of zero is inscribed "south declination" and
on the other "north declination." Corresponding to the declination, the polar
distance also, is marked on the same are with 90° at the point C. From the
centre S a right line is drawn to the point B to represent the equator, and is
divided into a scale of 100 equal parts. Parallel to this right line are drawn
right lines, as many as may be necessary, from the division of degrees on the
arc, cutting the line S, C, at right angles, and extending to the line A, D.
These lines are projections of latitude, and are numbered on the line S, C, and
also on A, D. Across these lines of latitude on each side of the line S, C, are
drawn a horizontal projection of lines of longitude as far as is necessary;
these lines can be projected by measuring off the distance from the line S, C
of the several points of the line on the lines of latitude, and then drawing a

page_text: line through the several points. The distance of any point of the line of
longitude from the line S, C, may be found by the following formula, radius
being 1-Formula: Sine of longitude x co-sine of latitude distance from
the line S, C, on the given latitude.
The instrument has an arm S, K, of steel or other metal or durable mate-
rial, turning on the centre S, and extending to the arc of the circle, on which
arm is a vernier reading to any number of minutes of a degree. This arin has
a straight edge on a line with the centre S, around which it turns. There is
also a straight-edged bar F, G, which, if the arm S, K, is made of steel or
iron, is attached to a horse-shoe magnet E, which will attach it to the said
arm at a right angle thereto, and allow it to slide freely thereon; but if the
arm S, K, is of other material, the bar F, G, must be connected by such
mechanical means as are commonly employed for such purposes. On the side.
of the bar F, G, which is shown in Fig. 1, there is a scale of co-sines and
co-altitude for measuring angular distances, but compensating for refraction,
and if necessary may be made to compensate for semidiameter of the sun,
parallax, and "dip." On the other side, which is shown in a detached view
(Fig. 2), is a scale of equal parts H, I. If used to take the altitude of objects
it has a pin at the centro S, projecting a little, on which is suspended by a
thread a plumb P. At the point C of the arc is a piece of white leather b
attached, to stand above the edge, on which to cast the shadow of the pin when
the altitude of the sun is taken.
The instrument can be put to various uses. To measure the altitude of
objects, place the instrument vertically upon any convenient stand, and turn it
till its edge A, D, lies in the direction of the point whose height is to be
measured; observe what degree and minute is cut by the thread of the plumb
on the are; measure the distance of the object from the point of observation,
and find, on the plane scale S, B, which resembles the detached plane scalo
II, I, the number corresponding to that distance. From that point on the
scale S, B, and at right angles to it, measure with the detached plane scale
I, I, to the point where the thread of the plumb cuts the arc in taking the
altitude, and this will give the height of the object; or if the given distance
cannot be conveniently taken on the scale, assume any distance, and get the
comparative height to the assumed distance, and afterwards obtain the true
height by proportion.
If the altitude of the sun is to be taken, turn the instrument till the shadow
of the pin a falls on and along the line S, C, on to the piece of white leather b
at the point C, (the arm being placed at zero). The thread will cut the
co-altitude of the sun on the arc. These modes of taking the altitude and

page_text: measuring heights of objects are doubtless well known, substantially similar
devices having been employed for the same purposes, and being only added for
convenience to make the instrument servo a greater variety of purposes. For
nautical purposes especially, the altitude would be more accurately taken by a
sextant. What I regard as most peculiar about the instrument is, that by the
combination of projections of latitude and horizontal projections of longitude
within an arc of a circle on a plane, the instrument will, with or without a
scale of co-sines or co-altitudes, solve problems in spherical trigonometry
without the usual mathematical calculations. For example: to find the timo
of day by the altitude of the sun is a case where three sides of a triangle, viz.,
polar distance, co-altitude of the sun, and the co-latitudo of the place of
observation, are given to find the angle at the pole, which angle, turned into
time, gives the time from apparent noon. The way this can be solved mecha-
nically by my instrument is to set the zero of the arm S, K, at the polar
distance for the given time, and slide the scale of co-altitudes along the
straight edge of the arm and at right angles to it, till the co-altitude of the
sun on the scale meets the latitude at the place of observation. The degree of
longitude crossing the latitudo at that point will be the angle required; and
where the straight edge of the arm crosses, the latitude of the place will be the
time of the rising and setting of the sun, for it represents the line of illumina-
tion when the sun is at the given polar distance.
As the instrument is designed principally to solve those problems where
time is one of the elements, the longitudo is turned into time on the instru-
ment. The line of longitude S, C, corresponds to 6 o'clock, and the arc of the
circle B, C, corresponds to 12 o'clock, at noon. Any division of longitude
may be used. In the accompanying Drawing the lines are drawn one degree
and fifteen minutes apart, so that the time is in divisions of five minutes; but
it will, perhaps, be more convenient to use divisions of single degrees for the
several longitude lines, and these again subdivided by points of a minute cach
at the several latitude lines. It will be readily seen in the above problem,
where three terms are given to find a fourth, if three of either of the terms are
given the fourth may be found. So also the problem for finding the time of
sunrise is a case in right-angled spherical trigonometry, where two terms are
given to find the third. If two of either of the terms are given, the other can
be found. To find when the sun will be due east or west, place the arm
S, K, at the polar distance, as before, then slide the scale of co-altitudes over
the given latitude, and observe what co-altitude will give the same time on the
contiguous latitude each side of the given latitude; that co-altitude will be
the co-altitude when the sun is due east or west; and where that co-altitude

page_text: meets, the latitude of the place of observation will be the time when the sun is
due east or west.
I claim, first, an instrument upon which are delineated projections of latitude
and longitude, within an arc of a circle combined with the arm S, K, and
scale F, G, or their equivalent, substantially in the manner above described, for
the purpose of solving useful problems in spherical trigonometry, as above
mentioned, without the usual mathematical calculations.
Second, though I do not claim the Invention of any part of the apparatus
connected with the instrument for the purpose of taking altitudes of objects
or solving problems in plane trigonometry, I claim the combination of the
said apparatus with, and its application to, the instrument, substantially as
described, to make the instrument serve those purposes, as well as the more
important one of solving problems in spherical trigonometry.
Third, I claim the employment in this and other mathematical instruments
of magnetism to keep a slide at right angles, or any given angle to a straight
edge, and at the same time allowing it to slide freely upon the straight edge,
substantially as herein above set forth.
In witness whereof, I, the said Auguste Edouard Loradoux Bellford,
have hereunto set my hand and seal, this 19th day of March, in
the year of our Lord 1855.
A. E. LORADOUX BELLFORD. (L.B.)