Slide rule

Before electric calculator was born, scientists, engineers, accountants and many people demand a tool for accurate calculation without paper and pencil.

After the discovery/innovation of log function. Slide rule was born.

The significant of log function is, it turns a multiplication/division into simple add/subtract. Because:

Log( m x n ) = log( m ) + log( n )

For example:

100 x 1000 = x

We can directly multiple and give the answer, but we can also take log from both side.

Log( 100 x 1000 ) = log ( 100 ) + log ( 1000 ) = log ( x )

2 + 3 = 5 = log ( x )

then, we inverse the log, which is 10^( ). More detail :

If : Log ( x ) = y

Then : x = 10^( y ) , by 10^( log ( x ) ) = x

Back to the topic,

5 = log ( x ) => 10^5 = x

See? For this simple illustration, the multiplication become intuitive adding!

If we have a ruler, on it, already marked the log of number. I. E., the numbers are not evenly distributed on the ruler, not same distance between 2 to 1 and 3 to 2, but marker of 2 is at length log (2) beyond marker of 1, marker 3 is at length log (3) beyond marker of 1, which is to say, a log scale.

Make 2 of such kind of ruler, then we are having a slide rule!

You can pick 2 ordinary rulers and try to do adding and subtraction, but it is naive and boring.

When you have 2 rulers in log scale, things are wonderful! When you adding length, "adding" number, you are actually doing multiplication!

Now aday, there are many function on a slide rule. And they no longer in ruler form but a circular form.

The simplest way to do calculation on slide rule is remember follow principle.

There are many rows on one slide rules. Basically C and D.

The number(x) in these row is read as C(x) = log (x) and D(x) = log (x), when you adding C row and D row, you are doing:

C(x) + D(y) = log (x) + log (y) = log (x * y) = D (x * y)

or

C(x) + D(y) = D(x*y)

The thing inside the log is the answer you want.

The actually step is for doing is, align D(x) by C(1), then read the D row on C(y). Simple!

There are other rows:

A(x) = B(x) = log(x^0.5)

K(x) = log(x^(1/3))

Cl(x) = log(1/x)

L(x) = log( 10^x ) = x

LL2(x) = log ( ln^(x) ), ln is natural log , x from 1.11 to e

LL3(x) = log ( ln^(x) ) x from e to 20000

S(x) = log ( sin(x) ) , x from 0 to 90 degrees

T1(x) = log ( tan(x) ) , x from 6 to 45 degrees

T2(x) = log ( tan(x) ) , x from 45 to 90 degrees

ST(x) = log ( tan(x) ) = log ( sin(x) ) , x from 40' to 6 degrees. Since sin and tan are almost the same in this small angle.

another way to read is :

A and B row is square of D row.

K row is order 3 of D row.

Cl row is inverse of D row.

L row is log of D row, which has a normal scale.

LL2 is exponential of D row in range of 0.05 to 1.

LL2 is exponential of D row in range of 1 to 10.

S row is arcsin of D row, in range of 0.105 to 1.

T1 row is arctan of D row in range of 0.105 to 1.

T2 row is arctan of D row in range of 1 to 9.5.

ST row is arcsin or arctan of D row in range of 0.0116 to 0.105.

See? The slide rule has every function!

and it has memory if there is a pointer!!

The last thing to keep in mind is, the digit has to keep in mind, for example, 2 x 6 = 1.2 in slide rule, but you knew that the 10 is missing.

or, you can use A row and B row. A(x)+ B(y) = A (x*y), and the range of A is from 1 to 100!

A wonderful thing on slide rule is, it is very good in calculating the form :

u x v / w

You just have to align D(u) with C(w) and read the D row on C(v)! One step, KO!

There are many fancy calculations on slide rule. Buy one now! ( interesting people can contact me and I send you one with price. ;P )