The Fascinating Tale of the Fowler Magnum Pocket Slide Rule
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Volume 20, Number 1, Spring, 2011
The Fascinating Tale of the Fowler Magnum Pocket Slide Rule
Bryan Purcell
The history of the Fowler Calculator line illustrates the connection of collegiate-minded yet practical engineering-skilled
types and their pursuit of a unique and special math tool, like
the Fowler Magnum (bear in mind, magnum means great).
William Henry Fowler (1853-1932) was an Assistant Engineer
to the Steam Users’ Association after years of engineering
training and winning a scholarship to study engineering at
Owens College in Manchester. In 1891, he turns from engineering to being the Editor of The Practical Engineer, a weekly
Manchester journal publication. In time, by 1898 he establishes the Scientific Publishing Company and publishes
Fowler’s Mechanical Engineer’s Pocket Book. In this same
year, Fowler’s The Mechanical Engineer carries an article
about a circular pocket-style calculator (slide rule), which
was also sold by the Scientific Publishing Company. This
calculator has a rotating face dial and fixed pointers moving
over a five scale face, so is very similar to the later models of
what becomes the trademark Fowler line of pocket calculators.
Harold Fowler (William’s son, born 1879) emulates his
father by winning a scholarship to the Manchester School of
Technology, then later attends Owens College and studies
engineering. Until 1905 he works as an electrical engineer
when he works as an editor for The Mechanical Engineer.
From 1905 to 1909 W.H. Fowler takes out three patents
on the Fowler Calculator. The first is for the double-sided
Long Scale version, which is the company’s main product for
the next 30 years. In this model, a milled nut moves one dial
while a knob turns the pointer on this face and moves the
opposing dial on the other side. By 1924 father and son take
out a patent on a second milled nut that is on the casing edge
so that the system’s operation can be done with one hand.
The first question, why a circular slide rule? In the
Fowler’s instruction manual they note that the scales are
always kept clean compared to a linear slide rule (as the scales
are under glass). There is never a need to switch slides or
worry about running over the index (since the index rotates
and is continuous). It is small and easier to carry. Like a
regular 10 inch linear model, the small circular calculator has
2-3 significant figure capabilities and with long scales, as on
the Magnum, up to 4 figures are possible. This classic question of circular versus linear is all a matter of one’s interests
and goals for the tool.
Through the 1930s and 1940s the company introduces
the 12-10 Calculator (1936) made for architects, builders, surveyors, and timber merchants, who not only used the decimal system, but the duodecimal system (12ths). In 1948 the
company releases the Jubilee Magnum, which has a 76 inch
(193 cm) scale along with a short scale (longer than 10 inches
in length) and an L (log) scale.
Despite the patents, new designs, and the classic style
of design the company never became very profitable. These
calculators, though precise and well made, had a large number of different parts (especially compared with linear slide
rules), and had to be assembled by hand (unlike the mass
production systems for the other slide rules). Both add considerably to the costs of manufacturing (up to four times);
hence, the high sale price.
The supreme design first appears in 1927 (and was manufactured into the 1940s) and is labeled the Fowler’s Magnum
Long Scale Calculator. It is 4 5/8 inches in diameter, glassfaced, nickel cased, and has the Fowler classic style. Like the
newest models in the line, the Magnum uses two screws to
control the functions. The screw over the fixed red line cursor rotates the scale while the other screw at 2 o’clock (given
the first screw is at noon) rotates the black imprinted cursor
line on a plastic strip or a plastic disc, with some variation
depending on the model.
FIGURE 1.
Fowler Magnum Long Scale Calculator
Like all other Fowler models, to multiply place the Index
under the red datum line and rotate the cursor to the multiplicand. Next rotate the disc with the top screw to the multiplier
and then read the product under the rotating cursor. For
division, place the numerator underneath the red datum line
and rotate the rotating cursor to the denominator. Now rotate
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Journal of the Oughtred Society
the disc so that the index is beneath the rotating cursor and
read the quotient under the red datum line.
The Magnum was produced in 2 models. The better of
the two is detailed here. This is an 8-scale design, as follows
(from the center out): T, S&T, S, long scale C (6 rings), L, two
ring A scale for square roots, C1, short C scale, and finally the
outer ring of Gauge Marks. Gauge Marks include: π, π/4,
radian, lbs-kg, km-mile, in-cm, gravitational acceleration (English) and many others. The other version has the L scale
inside the 6-ring long scale instead of outside it.
TABLE 1.
Fowler Magnum Long Scale
Ring
Outer Ring of Gauge Marks
Short C scale
C1
A (approx 3.1± 1)
A (1 – approx 3.1+)
L scale
Long C : 6th ring
Long C : 5th ring
Long C : 4th ring
Long C : 3rd ring
Long C : 2nd ring
Long C : 1st ring
Radius
(inches)
2.25
2.125
2.0
1.875
1.75
1.6875
1.625
1.5
1.375
1.25
1.125
1.0
Total Length
49.5
Sine 6o – 75o
Sine & Tangent 35’ – 5.5o
Tangent 6o – 45o
0.875
0.75
0.6875
Circumference
(inches)
14.4
13.4
12.6
11.8
11.0
10.6
10.2
9.4
8.6
7.9
7.1
6.3
5.5
4.7
3.9
From the chart, the one drawback is the relatively short
trig scales where the maximum lengths have the approximate
precision of a 6 inch slide rule. Still the lengths are effective
enough to obtain 2 significant figures when needed.
The first major strength is the short C scale, which is
longer than a conventional 10 inch slide rule scale. There is
greater space between marks such as those found between 9
and 1. This allows for a more precise reading of the values
when estimating.
For real power in this hand-sized slide rule, the inner
long C scale has an effective length of nearly 50 inches (more
than double a 20 inch slide rule!). The values between any
two secondary values, including 9 to 1, have tenths marked
off between them with a good span of distance making 3
significant figures the minimum for all calculations. An added
bonus is the fact that one can determine 6th power and 6th
roots as needed by reading the short and long C scales for a
given value.
The 2-line square root scale helps in finding square roots
effectively since it (like all the scales) are read in connection
to the outer short C scale. For values 1-10 (and all other odd
digit numbers) read the inner ring of the A scale, for values
10-100 (and all other even digit numbers) read the outer A
ring.
The L scale has 3 significant figures read very easily so
is invaluable as a math tool in determining powers and roots
as needed. The L scale outside the long C scale (compared to
the other version inside the long C scale) results in a high
degree of precision.
The really amazing power is that this tool has all of the
capability of a 9-scale slide rule! Looking at the table, one
finds the K scale is missing from the classic 9-scale model list
of scales. Taking cubes or cube roots would then appear to
be a task, since one would have to take the log of the number
in question, divide by three, look that back up on the L scale,
and find the corresponding answer on the short C scale.
Never fear, there is no need.
In order to perform a cube root, look up the number on
the A scale and find the cube root on the long C scale. The
reverse yields the cube of the value! This is the real genius of
the design.
I wonder if there are any other unique slide rules like this
where one can have the power of the classic 9-scale model
yet with creative forethought and innovation can lead to an
incredibly potent, portable, and yet analogous tool that even
has a very long scale special addition? This becomes the
mathematicians’ question – how to maximize the effectiveness of the tool yet minimize its number of requirements. I
find this one to be the epitome of pocket-watch style circular
slide rule design and consider the Fowler Magnum to be the
company’s magnum opus (great work). Why is a 9-scale so
important? Consider that Einstein and Von Braun used this
number of scales for their accomplishments. This range of
scales is capable of performing all the functions of a basic
scientific calculator and is only limited by one’s math skill
and imagination.
Could even a classic be improved? The only thing a
linear slide rule would calculate that this circular calculator
would not do as easily is where a linear rule has a fixed scale
and a moving scale so that when a ratio is arranged, all similar
ratios are arranged. As the Fowler has no fixed scale (perhaps an outer fixed ring with a C scale would solve this), so
to find all similar ratios one must turn the disc once the ratio
is arranged. I am looking forward to others to write about the
uniqueness of a classic slide rule and associated special attributes.