AN INSTRU- MENT CONSTRUCTED ON UNERRING PRINCIPLES FOR EXPEDITIOUSLY CALCULATING TO A CERTAINTY WITHOUT REFERRING TO TABLES OF ANY KIND (MERIDIONAL TABLES EXCEPTED) THE VARIOUS CASES OR PROBLEMS IN NAVIGATION, PRACTICAL MATHAMATICS, AND TRIGONOMETRY, HEIGHTS AND DISTANCES, AND ALTOGETHER EMBRACING EVERY SCIENCE DEPENDING ON ANGLES
Year: 1813

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, WILLIAM
REID, of Foot Dee, Aberdeen, in that part of the United Kingdom of Great
Britain and Ireland called Scotland, send greeting.
WHEREAS His most Excellent Majesty King George the Third did, by
His Letters Patent under the Great Seal of Great Britain, bearing date at
Westminster, the Fifth day of May, in the fifty-third year of His reign, for
Himself, His heirs, and successors, give and grant unto me, the said William
Reid, my heirs, executors, administrators, and assigns, His especial licence;
full power, sole privilege and authority, that I, the said William Reid, my
executors, administrators, and assigns, or such others as I, the said William
Reid, my executors, administrators, or assigns, should at any time agree with,
and no others, from time to time and at all times during the term of years
therein expressed, should and lawfully might make, use, exercise, and vend,
within England, Wales, and the Town of Berwick-upon-Tweed, and also in all
His Majesty's Colonies and Plantations abroad, my Invention of "AN INSTRU-
MENT CONSTRUCTED ON UNERRING PRINCIPLES FOR EXPEDITIOUSLY CALCULATING TO A
CERTAINTY WITHOUT REFERRING TO TABLES OF ANY KIND (MERIDIONAL TABLES
EXCEPTED) THE VARIOUS CASES OR PROBLEMS IN NAVIGATION, PRACTICAL MATHAMATICS,
AND TRIGONOMETRY, HEIGHTS AND DISTANCES, AND ALTOGETHER EMBRACING EVERY
SCIENCE DEPENDING ON ANGLES;" in which said Letters Patent there is contained

page_text: a proviso, that if I, the said William Reid, by an instrument in writing under
my hand and seal, shall not particularly describe and ascertain the nature of
my said Invention, and in what manner the same is to be performed, and cause
the same to be inrolled in His Majesty's High Court of Chancery within two
calendar months next and immediately after the date of the said recited
Letters Patent, that then the said Letters Patent, and all liberties and advan-
tages whatsoever thereby granted, shall utterly cease, determine, and become
void, as in and by the same (relation being thereunto had, will more fully and
at large appear.
NOW KNOW YE, that in compliance with the said proviso, I, the said
William Reid, do hereby declare that the nature of my said Invention or
Instrument, and the manner in which the same is to be performed, are particu-
larly described and ascertained in the following Specification and by the
annexed Drawing, that is to say:-
The nature of my Invention consists in the application of mechanical means
to the practical construction and solution of triangles in all the various cases
which can occur in plain trigonometry, and which will more fully appear by a
particular description of those means, namely, the instrument itself, or the
various parts composing the same, which are as follows, and may be made of
any material fit for the construction of mathamatical instruments; I therefore
prefer brass, silver, or some other metal. The plane of the instrument is
rectangular, and may be made to any convenient dimensions. I generally make
a brass frame, about twelve or fifteen inches square, with its upper surface
reduced to a plane, the sides of which are about three quarters of an inch
wide, and about one-tenth of an inch thick, having their greater dimensions in
the said plane. The further explanation of the instrument will be better
understood by a reference to the Fig. in the annexed Drawing, where A, B,
C, D, represent the frame, the two opposite and parallel sides of which have
engraved upon each a scale of equal parts at a, e, and f, g. a, b, is a straight
ruler or index, moveable round a center at a, with a scale of equal parts
engraved upon its edge; j, c, d, is another ruler and index, also having a scale
of equal parts engraved upon its edge. It is necessary here to observe that
the sides of the frame a, e, and g, f, and the edges of the two rulers, are
divided with the same scale of equal parts. i, j, h, is a semicircle, with its
outside edge graduated with divisions, corresponding to the degrees of a circle,
and on the inside of which divisions are the points and quarter points, as
contained on the half of the mariner's compass; upon the under side of the
semicircle is fixed a piece of brass, of an appropriate shape, and fitted to a

page_text: groove in the side of the frame or instrument at m, n, in which it can be
moved or slid backward or forward either towards m or n; the ruler or index
j, c, d, moves upon a center at c, which is also the centre of the semicircle
i, j, h; the end of the ruler at j serves for an index to point out the number of
degrees contained in the angle a, c, d. Upon the two sides of the instrument
A, B, and B, C, are three lines of divisions, in the two outer lines are engraved
the degrees contained in a quadrant of the circle, the outmost one numbered
from g, g, to c, e; the other one numbered from e, e, to g, g. In the third or inner
line (numbered from e, e, to g, g,) are engraved the number of points and sub-
division of points usually contained in one quarter of the mariner's compass. The
requisites to be attended to in the construction of the instrument, and combining
the parts thereof, as above described, are that the divided edges of the rulers
be straight, and in a line with the centres upon which they respectively move;
that the line a, e, be also straight, and in a line with the centre of the ruler at
a; that the divisions upon the line g, f, should commence at g, so that the
angle e, a, g, be a right angle; that the centre at c of the semicircle be exactly
over the line a, e; and in order to secure this in all the situations into which
the semicircle and ruler may be moved, the groove m, n, must be parellel with
the line a, e; that the angular position of the semicircle be such, that when the
index at j is set to ninety degrees the divided edge of the ruler c, d, be at
right angles with the line a, e; that the scale of equal parts on the line a, e,
commence from the centre at a; that the divisions upon the ruler a, b,
commence also from the centre at a, and that the divisions upon the ruler c, d,
commence at the centre c. In order that the divisions upon the line a, e,
immediately below the centre of the ruler at c may be seen, the ruler is made
to move round upon a hollow or annular axis affixed to the semicircle, which
admits of the divisions being read off at the edge of the thin plate, bisecting the
ring at right angles with the line a, e, as represented in the Drawing. The
inspection of the Figure will render it sufficiently obvious to any one compe-
tently skilled in trigonometry that the edges of the two rulers will denote two
sides of a triangle, and that the third will be represented by the line a, e. It
is therefore unnecessary to give any further directions for its application and
use.
In witness whereof, I, the said William Reid, have hereunto set my
hand and seal, the Fifth day of July, in the year of our Lord One
thousand eight hundred and thirteen.
WILLIAM REID. (L.S.)

page_text: AND BE IT REMEMBERED, that on the same Fifth day July, in the
year above mentioned, the aforesaid William Reid came before our Lord the
King in His Chancery, and acknowledged the Specification aforesaid, and
all and every thing therein contained, in form above written. And also the
Specification aforesaid was stamped according to the tenor of the Statute
in that case made and provided.
Inrolled the same Fifth day of July, in the year above mentioned.