![==[]--](sr.gif)
Short notation for slide rule algorithms
Short notation for slide rule algorithmsScale is a line. Each point of a scale represents a real number. This number is sometimes called 'the name' of this point. Some points are marked with ticks and some ticks carry numeric and symbolic labels thus helping user to determine the name of the point. Distance between 2 ticks is choosen that way to allow linear approximation for points between them.
The formula that represents the distance from the begining of the
scale to a point with name x is often caled "formula of a scale".
Thus D scale has formula
What cursor essentially does, it finds the point on one scale that is
on the same distance from the scale beginning as point on another scale.
It is the toughest and the most important skill required for using
slide rule.
Generally this document does not give rules to determine digit count.
This topic is widely discussed in numerous slide rule manuals.
What constitutes "easy for human" depends a lot on a specific human in
question. It can be (in the order of increasing difficulty):
These steps are
considered elementary though they can lead to big errors.
The most often occuring relationship is equality. In this case
operation becomes "find such position of the cursor that it marks the
same numbers for two given scales".
This type of search is used to calculate square roots without A or
CI scale and also to calculate cubic roots without K scale. See (R.
Manely site).
Input values of algorithm usualy get names u, v, w, t etc.
Constants get names a,
b, c etc.
Values that should be found or intermediate values get names
x, y, etc.
Constants present on the scales denoted with their quoted names:
'pi', 'c1',
'rho'
Number followed by scale name represents point on the scale where
this number is located.
Index does not necessarily means "left edge" or "right edge", since sometimes scales have extensions that extend beyond index. Example would be LL scales, S scale, ST scale etc.
Informally, index of a stock scale is number that is aligned with 1 or 10 on
scale D and index of a slide scale is number that is aligned with 1 or 10 on
scale C.
There are two kinds of moving elements -- points on the
scales located on the slide and cursor. Arrow points
from moving entity to its position. Example:
[1CI->| means "move left index of CI
scale to cursor position".
Moving slide
By moving slide you change algebraic relationship between slide and
body scales. To be more specific -- if one of the scales is located on a
slide had formula d=f(x), then after the slide has been moved
l units right, then this scale has formula d=l+f(x).
Cursor
Cursor is used to set, read and store numbers.
The main part of cursor is its hairline (or hairlines)
that simultaneously intersects several scales, thus giving
correspondense between values on them.
Reading values
To read the number means "to determine the number represented by the
given point of given scale". This point can be defined by cursor
hairline, by tickmark
or by tickmark on another scale that touches this point.
Setting values with cursor
This means to put cursor in position that its hairline passes through the
desired point of the desired scale. If the value does not have tickmark
then you have to interpolate between nearby tick marks.
Digit count (or characteristic)
Each point of most scales represent not single number, but the whole
range of numbers that differ from each other by the power of ten factor.
Deciding which particular factor (the number of digits in it
is often called digit count of the number)
correspond to actual value should be decided by person making calculations.
Example
dc(45.12)=2
dc(3*109)=10
dc(0.7)=0
dc(0.0031)=-2
dc(1.9*10-4)=-3
Manual calculations
Some algorithms reference operations that are easy for
human but hard for slide rule. Example of such operation is addition: there
is no easy way to perform it with typical slide rule.
Searching
One very useful primitive operations is searching. Searching means the
following:
For any given pair of scales (usually one is on the stock, another
is on the slide) find the position of the cursor where numbers under
hairline satisfy given relationship.
Searching with a slide
Sometimes more complicated case of searching than above may be useful.
Put cursor into required position, then move slide,
while monitoring the value of one of the slide located scales under cursor
(a) and
and a value on the stock scale (this scale should be adjacent to slide)
pointed by slide index (or even by some constant, located on slide and
adjacent to its edge) (b).
When these a and b match the relation -- position of slide is found.
Short notation
Algorithms in this document are described in terms of elementary operations
defined above. The notation used was designed to be short rather than clear.
Notation decoder
This experimental feature will allow you to translate algorithm
written in slide rule notation into english. Most algorithms descriptions
on this site are 'clickable' -- this brings the window with translation.
However, if this is not working with your browser, you may try to
enter the algorithm description in this form and click 'Translate' button.
Links
http://www.howe.k12.ok.us/~jimaskew/askew/rules.htm
employs different "table" notation.