# Slide rule scales and scale IDs

## Scale IDs

Emulator refers to scales using their "scale IDs". Scale IDs are sequences of alphanumeric characters that uniquely define the scale layout for the emulator. IDs were chosen arbitrary and have no relation to common scale names, like "S" or "C". I tried to give scale IDs some mneumonic meaning, usually related to the scale formula, but this is not a hard rule.

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)
The following scales are not used for calculation, but are actual measuring scales. Most often these scales are located outside the scope of cursor, but some rules (FC) have them among regular scales, which allows to perform centimeters ↔ inches conversion lookups.
cm
centimeters
in
inches, decimal subdivisions
inbin
inches, binary subdivisions
Some FC rules have a pair of linear Celsius and Fahrenheit scales. They do not relate to any other scales and can only be use with each other to perform degrees conversion
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

With resolution traded for span, these scales allow to estimate order of magnitude of the result. These scales mimic operations with A,B,C,CI,D,K,L scales and their label is usually suffixed with asterisk.
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
log1i
logarithmic, inverted
log2i
logarithmic, half size, inverted
log1f10
folded at √10
log1f360
folded at 360
log1fM10
folded at ln10≈2.3
log1fME
folded at log10e≈0.43
log1fPI
folded at π
log1if10
inverted and folded at √10
log1if360
inverted and folded at 360 >
log1ifM10
inverted and folded at ln10≈2.3 >
log1ifME
inverted and folded at log10e≈0.43
log1ifPI
inverted and folded at π
log3i
logarithmic, one third size, inverted
loglg0
decimal log-log
loglg00
decimal log-log, negative exponent
loglg01
loglg02
loglg03
loglg1
loglg2
loglg3
logln0
natural log-log
logln00
natural log-log, negative exponent
logln01
logln02
logln03
logln1
logln2
logln3
logloga0
natural log-log, related to half-size log
logloga00
logr21
logarithmic, double size, left part
logr22
logarithmic, double size, right part
logr31
logarithmic, triple size, part 1
logr32
logarithmic, triple size, part 2
logr33
logarithmic, triple size, part 3
logr41
logr42
logr43
logr44
mix
small logarithmic and "mixture" scale from Hemmi 269
pctc
percent scale
pctr
negative percent
prop1
large mixture scale related to regular log
prop2
part2
prop3
part3
prop4
part4
pyth1
"vector" 1-10
pyth2
"vector" 10-14
rtheta
Degree in radians for Hemmi 153
sh1
hyperbolic sine
sh2
part 2
sin0dec
small sines, decimal fractions of a degree
sin0deci
small sines, decimal fractions of a degree, inverted
sin0min
small sines, degrees and minutes
sin0mini
small sines, degrees and minutes, inverted
sin1dec
sines, decimal fractions of a degree
sin1deci
sines, decimal fractions of a degree, inverted
sin1min
sines, degrees and minutes
sin1mini
sines, degrees and minutes, inverted
sinamin
sines, degrees and minutes, half-size
tan1dec
tangents, decimal fractions of a degree
tan1deci
tangents, decimal fractions of a degree, inverted
tan1min
tangents, degrees and minutes
tan1mini
tangents, degrees and minutes, inverted
tan2dec
large tangents, decimal fractions of a degree
tan2deci
large tangents, decimal fractions of a degree, inverted
tan2min
large tangents, degrees and minutes
tan2mini
large tangents, degrees and minutes, inverted
tanamin
tangents, degrees and minutes, half-size
th
hyperbolic tangents
theta
angle in degrees for Hemmi 153
ttheta
tangents for Hemmi 153
x

## Aliases

Aliassubstitution
A"A"log2
B"B"log2
C"C"log1
D"D"log1
K"K"log3
L"L"l
CI"CI"log1i
DI"DI"log1i
CF"CF"log1fPI
DF"DF"log1fPI
CIF"CIF"log1ifPI
DIF"DIF"log1ifPI
AI"AI"log2i
BI"BI"log2i
ST"S&T"sin0min
S"S"sin1min
T"T"tan1min
T2"T2"tan2min
SI"SI"sin1mini
TI"TI"tan1mini
L"L"l
LL0"LL0"logln0
LL1"LL1"logln1
LL2"LL2"logln2
LL3"LL3"logln3
LL00"LL00"logln00
LL01"LL01"logln01
LL02"LL02"logln02
LL03"LL03"logln03
N""notch
LeftN""lnotch
RightN""rnotch
P"P"circ

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