Slide rule scales and scale IDs

Scale IDs

The reason for use scale IDs instead of "common" name is that there is no consistency between manufactureres in labelling and naming scales. Also, same name (label) may be given to two slightly different scales, and sometimes to two completely different scales. For example, sine scale, usually called S has variations in what units (degrees and minutes, defgrees and decimal fractions of a degree) it is graduated. On the other hand, square root scales are called sometimes "R", sometimes "W" and sometimes "√". "P" may denote a "pythagorean" scale with formula $\log\sqrt{1-u^2}$ on Aristo rules or it may denote top variant of "vector" scale with formula $u^2$ from Hemmi 153.

When in the layout description, scale ID may be appended with a suffix that defines scale direction. "_" denotes "standing" scale, with tickmarks below the labels. Example of such scale is "C" scale. "~" denotes "hanging" scale, which tickmarks above the labels. Example: "D" scale. If suffix is not specified, \yasre{} will try to pick one style or another, depending on situation. If you do not like the choice, specify suffix explicitly.

Graduation of scales in this emulator is chosen to represent mathematical relationship to other scales and to be legible at low screen resolution. It is not chosen to accuratley portray individual scale of any specific slide rule. Variants of essentially the same scale on different rules may have different graduations, label placements and special tick marks.

Spacers and notches

-

horizontal rule one pixel wide;

notch

left and right notches

lnotch

left notch

rnotch

right notch

Analon scales for dimensional analysis

analon1

dimensional analysis scale from K&E Ananlon

analon1i

dimensional analysis scale from K&E Ananlon, inverted

analon2

dimensional analysis scale from K&E Ananlon

analon2i

dimensional analysis scale from K&E Ananlon, inverted

Common linear scales

l

decimal logs (linear)

cm

centimeters

in

inches, decimal subdivisions

inbin

inches, binary subdivisions

cel1

degrees Celsius, linear

far1

Fahrenheit, linear

cel2

degrees Celsius, logarithmic

far2

Fahrenheit, logarithmic

chem1

chem2

atomic weights of certain elements and common compounds

circ

pythgorean

deg

angular degree

gtheta

gudermanian scale from Hemmi 153 system

ISTd

Thornton differential trig scales (all 4)

kel2

Kelvin, logarithmic

ln

natural logs (linear)

Decimal keeper scales

ldk

logs, decimal keeper

log1dk

logarithmic, decimal keeper

log1dki

logarithmic inverted

log2dk

logarithmic half size decimal keeper

log2dki

logarithmic half size decimal keeper, inverted

log3dk

logarithmic, one third size, decimal keeper

log3dki

logarithmic, one third size, decimal keeper, inverted

Logarithmic scales

Common logarithmic

log1

This is the most ubiquitous scale. Pretty much every slide rule has it. It is often present at least twice -- once on a slide, once on body. Duplex rules usually have for copies of this scale -- 2 on one side, 2 on another. The pair of log scales allow multiplication and division. The scales are most commonly labeled "C" for slide-bound and "D" for body-bound. Most books use this notation when refer to these scales. Other scales, providing means to calculate special functions, often refer their values to this scale.

log2

logarithmic, half size, 2 decades. These are known as "A" and "B" scales. When referred to "C" and "D" scales they allow calculation of squares and square roots. The multiplicationa and division may also be performed on "A"/"B" pair, rather than "C"/"D" pair. Interesting enough, early Mannheim rules (with A[B,B]D layout) intened to use these scales as main calculation scales. Extra copy of B aligned wit single-decade scale "D" on body allowed squares and square roots without cursor line.

log3

3 decades logarithmic, one third size. Known as "K" scale, used to calculate cubes and cube roots. This site also describes fifth degree root algorithm where "K" plays prominent role.

log4

logarithmic, one quarter size