AN IMPROVED SPIRAL SLIDE RULE FOR WORKING ARITHMETICAL CALCULATIONS
Year: 1878

page_text: LETTERS PATENT to George Fuller, of Belfast, in the County of Antrim,
Ireland, Gentleman, for the Invention of "AN IMPROVED SPIRAL SLIDE RULE
FOR WORKING ARITHMETICAL CALCULATIONS."
COMPLETE SPECIFICATION filed by the said George Fuller at the Office of
the Commissioners of Patents on the 16th March 1878.
GEORGE FULLER, of Belfast, in the County of Antrim, Ireland, Gentleman.
"AN IMPROVED SPIRAL SLIDE RULE FOR WORKING ARITHMETICAL CALCULATIONS."
The object of the apparatus, forming the subject of the present Invention, is to
work arithmetical calculations in which multiplication, division, involution, and
evolution are either required singly or in combination.
The apparatus consists of a cylinder a of wood, paper, or metal, on the curved
surface of which a single logarithmic scale winds in a spiral. This scale may either
be engraved upon the material used for the cylinder, or printed upon cardboard or
paper and fixed round the cylinder.
The cylinder is made hollow so as to move up and down and turn round upon a
cylindrical axis of wood, metal, or cardboard b.
The friction between the axis and the cylinder to be such that whilst the
cylinder can be easily moved by hand it will not move by its own weight, even
when the axis is vertical.
Parallel to the axis, and fixed to the handle or stand that supports it, is a slip of
metal or wood c. This slip carries two indices d and e, and the scale f. In addition
to the above is a movable index g, which is fixed to a ring so that it can be easily
moved along and round the axis into any required position, and the friction between
it and the axis is sufficient to retain it in its place. The spiral scale makes a whole
number of turns round the cylinder, and the indices d and e are fixed so far apart
that when one is at the commencement of the logarithmic scale the other is at its
termination. The scale fis equal in length to the axial length of the spiral, and is
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page_text: divided into the same number of parts as there are turns in it, the index e being
the termination of the scale. At the bottom of the cylinder is a scale h, which is
merely the circular section of the cylinder divided into 100 parts.
The zero of the scale being the termination of the spiral, in the employment of
apparatus the following is the modus operandi:
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Multiplication. Find the number on the logarithmic scale that represents the
multiplier and place it to the index c, also the index g to 1000, that is, the com-
mencement of the logarithmic scale; then move the cylinder so that g points to the
number on the scale that represents the multiplicand, and the quotient is either read
off from the scale at the index e or d. From the mode of construction it will be
seen that the indices e and d can never both point to a number on the scale.
Division.―Find the number on the logarithmic scale that represents the dividend
and place it to the index d, also the index g to the number that represents the
divisor, then move the cylinder so that 9 points to 1000, and the quotient is either
read off from the scale at the index e or d
Involution and Evolution.-Find the number on the logarithmic scale that
represents the number whose power or root is required, and place it to the index e;
read the number of divisions on the scale fabove zero, also the number of parts
from the scale h. If the original number is in units, multiply or divide the sum
of these two readings by the power or root, and adjust the cylinder so that the top
line of the scale / makes this reading on the scales f and h. The indices d or e will
show the power or root required. If the number is in tens, the whole number of
the divisions of the scale fis to be added to the observed readings before multiply-
ing or dividing by the power or root; if the number is in hundreds, twice the
number of the divisions of the scale fare to be added; if it is in thousands, three
times the number, and so on.
If after multiplying or dividing by the power or root the quotient is greater than
the whole number of divisions on the scale f, then once, twice, three times, and so
on, the whole number of divisions must be deducted from the quotient and tho
remainder treated as shown above.
Having thus described my Invention, and the mode of carrying it into effect,
what I claim and desire to secure by Letters Patent is, the combination of the
logarithmic scale made into the form. of a spiral, and wound round a movable
cylinder with fixed and movable indices, as by this means I am enabled in a small
instrument to obtain a very extensive scale, and so make calculations more correctly
than with the ordinary slide rule.
It is not absolutely necessary that two indices should be fixed and one movable.
The apparatus may be made with one fixed and two on the movable arm, but I
prefer the method described in detail.
In witness whereof, I, the said George Fuller, have hereunto set_my_hand
and seal, this Thirteenth day of March, in the year of our Lord One
thousand eight hundred and seventy-eight.
GEORGE FULLER (T.α)