My Slide Rules Classification
I have divided my collection in three main classes:
These are the slide rules having only all or some of the next standard scales:
C-D. The simple log scales from 1 to 10, used for multiplication and division.
A-B. The double log scale from 1 to 10 to 100, designed to get the squares of numbers on scales C-D. Conversely, the square roots of the numbers on this scale, can be read on scales C-D.
S. The scale to find the value of sin(x) for angles 30' - 90o
T. The scale to find the value of tan(x) for angles 5.5o - 45o.
ST. The scale to find values of sin(x) and tan(x) for small angles: 34.9' - 5.4o
SRT. The scale to find values of sin(x) and tan(x) for small angles ( 34.9' - 5.4o) and to convert degrees into radians.
CI. Same scale as C but reversed, from 10 to 1. Used find the reciprocals of numbers on scales C-F, and used with C scale to perform also multiplications and divisions.
L. The scale to get the logs in base ten for numbers on scales C-D.
K. The Triple log scale from 1 to 10 to 100 to 1000, designed to get the cubes of numbers on scales C-D. Conversely, the cubic roots of the numbers on this scale, can be read on scales C-D.
DF-CF. These scales, called folded scales, are the same as scales C-D, but these folded scales begin in Pi and end in Pi, having their number one above the center of the C-D scaled. Folded scales are used to compute the product of Pi and numbers on scales C-D. and multiplications and divisions.
CIF. Same as scales DF-CF but reversed. Used find the reciprocals of numbers on scales DF-CF, and used with scale DF compute multiplications and divisions.
LL. The Log-Log scales in base ten, used to compute any power of the numbers from 1.001 or 1.01 to about 100000.
Some manufacturers decided to add to some of their all purpose slide rules other scales or make modifications to the above ones.
So many scales... and we can make this question? How these scales can be efficiently arranged on slide rules?
Mannheim Rules
Scales arrangements have been standardized during the many years slide rules were used. The first standardization was done in 1850 by the French Lieutenant Amédée Mannheim, then 19 years old only, with an arrangement of scales to perform operations involving multiplications-divisions, and squares-square roots: A [ B, C ] D. A slide rule with these scales was known Mannheim Rule.
Years later were incorporated other scales to calculate cubes-cubic roots, sine, tangent, logs in base 10, and a reverse scale to make multiplication operations more efficiently. This new scales set was known as Enhanced Mannheim, having the scales A [ B, CI, C ] D, K on the front face of the rule, and [ S, L, T ] on the back of the slider.
Rietz Rules
In 1902, the German engineer Max Rietz rearranged the Mannheim system, and added one extra scale to calculate with more precision sines and tangents of small angles. This new arrangement was called System Rietz, with the scales K, A [ B, CI, C ] D, L on the front face of the rule, and [ S, ST, T ] on the back of the slider.
Darmstadt Rules
In 1935 Alwin Walther, professor of the Technical University at Darmastdt, Germany, proposed an arrangement of the Enhanced Mannheim scales to make the calculation process in engineering more efficient, plus the addition of the Log-Log scales (invented by the British physician Peter Roget in 1815), and the Pythagorean scale P. This new array was known as System Darmstadt and it has the scales: L, K, A, [ B, CI, C ] D, P, S, T on the front face of the rule, [ LL1, LL2, LL3] and on the slider's back.
The three above standard scales settings were elaborated for single face slide rules, only the slider was double sided. In 1891 the British mathematician William Cox patented the Duplex Engineers Slide Rule, with scales in both faces and a double face indicator. This allowed to incorporate more scales and create more powerful slide rules, but there were not standard configurations like the above mentioned for duplex rules. Most of the All Purpose duplex rules include the basic scales A,B, C. D, K, L , Folded scales CF-DF, reciprocal scales CI, DI, CIF, trigonometric and Log-Log scales.
These are the slide rules having specially designed scales to compute solutions for specific tasks or problems, additional to the standard scales. Between 1900 and 1970 were produced hundred of different specialty rules, for many professional fields, from accounting, commerce or real state, to all science or engineering branches. It is not possible to include in this little space all the special scales created in those years, but here are some of the most common:
Sh. This is the scale to compute the Hyperbolic Sine function. This function is used in Civil and Electrical Engineering, as well as in Cartography.
Th. This is the scale to compute the Hyperbolic tangent function.
P1-P2. These scales are use in Engineering to compute vectors magnitudes using the Pythagorean Theorem.
Sr-Se. These scales are used to convert angles in radians to degrees and vice-versa.
Ge. This is the Gudermannian Hyperbolic scale. The Gudermannian function is very used in Cartography, and in some slides rules for electrical engineering, This scale allows to compute hyperbolic functions using the regular trigonometric scales.
Np or Ln. This is the Naperian scale. It gives the natural log of the numbers on C-D scales
2Pi. The 2Pi scale helped to solve problems of alternating and radio circuits whose formulas include the constant 2Pi, The quotient of numbers on scales C-D and 2Pi can read on this scale.
C%-R%. These are the Markup and Retail scales. These scales make simple to calculate markup and retail prices of selling items.
There are many more specialized scales, but they will be explained in the page of the corresponding slide rule.
Even though military slide rules could be considered as specialty rules, I put them apart of the ones used in business and industry, because most of them are devised for artillery fire, These rules have very special scales, and in many cases they do not include the standard scales . I am also including in this category the aerial and marine navigation slide rules.
