Scales (Slide Rule): Difference between revisions
Jump to navigation
Jump to search
Replace superscript tags inside of code blocks with their Unicode equivalents.
(Replace superscript tags inside of code blocks with their Unicode equivalents.) |
|||
| Line 47: | Line 47: | ||
Squares and square roots can be calculated using only the C and D scales with some practice, but are more easily performed with the D and A (or C and B) scales. The A and B scales are often called the "square scales" because they are half the length of the C and D scales, which results in any number on D having its square on A (and likewise C with B). This is because of the property of logarithms in which doubling the logarithm of a number (in this case having the scale grow twice as fast) results in the logarithm of its square. To make it more clear, here is an example: | Squares and square roots can be calculated using only the C and D scales with some practice, but are more easily performed with the D and A (or C and B) scales. The A and B scales are often called the "square scales" because they are half the length of the C and D scales, which results in any number on D having its square on A (and likewise C with B). This is because of the property of logarithms in which doubling the logarithm of a number (in this case having the scale grow twice as fast) results in the logarithm of its square. To make it more clear, here is an example: | ||
<syntaxhighlight> | <syntaxhighlight> | ||
3²=9 | |||
3(D) = 9(A) | 3(D) = 9(A) | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| Line 109: | Line 109: | ||
==== Scientific Notation ==== | ==== Scientific Notation ==== | ||
A more secure method of estimation is to begin by writing every number in scientific notation, that is, of the form X x | A more secure method of estimation is to begin by writing every number in scientific notation, that is, of the form X x 10ⁿ where X is greater than (or equal to) 1, but less than 10. Slide rules are particularly adept at this, since numbers such as 2, 200, and 0.0002 are all at the same position on the slide rule, it is easier to think of them as simply 2 with some multiplier power of ten. Most slide rule instruction books write the positions on the actual scales in this form, with 346 on the rule being described as 3.46. | ||
After all numbers are in the correct form, estimation can take place on the now one-digit numbers (called the mantissa), and simple addition and subtraction of the powers of ten (called the characteristic) can properly place the decimal. | After all numbers are in the correct form, estimation can take place on the now one-digit numbers (called the mantissa), and simple addition and subtraction of the powers of ten (called the characteristic) can properly place the decimal. | ||
<syntaxhighlight> | <syntaxhighlight> | ||
431 x 0.00085 = (4. | 431 x 0.00085 = (4.31x10²)x(8.5x10⁻⁴) ≈ 4x9x10²⁻⁴=36x10⁻²=0.36 | ||
4.31(D) | I → 8.5(C) ≈ 3.67(D) | 4.31(D) | I → 8.5(C) ≈ 3.67(D) | ||
therefore 431 x 0.00085 ≈ 0.367 (0.36635 exact) | therefore 431 x 0.00085 ≈ 0.367 (0.36635 exact) | ||
| Line 122: | Line 122: | ||
A peculiar feature of slide rules is the fact that the scales "wrap around" themselves quite often. This leads to a very nice tool in tracking any extra complications with the decimal point: the slide itself. When performing the standard multiplication procedure (starting at an index), any time the upper index is used, this represents using this "wrapping" feature, which in essence describes adding 1 to the characteristic at the end. With division, the operation is reversed, meaning that any time you reach the upper index, you have to subtract one from the characteristic. The actual rule takes more reasoning, but can be described as follows: if multiplying brings you ''down'' the rule, add one to the characteristic (using either method of multiplying). Likewise, if dividing (using either method) brings you ''up'' the rule, subtract one from the characteristic. This can be seen by using our previous example on scientific notation: | A peculiar feature of slide rules is the fact that the scales "wrap around" themselves quite often. This leads to a very nice tool in tracking any extra complications with the decimal point: the slide itself. When performing the standard multiplication procedure (starting at an index), any time the upper index is used, this represents using this "wrapping" feature, which in essence describes adding 1 to the characteristic at the end. With division, the operation is reversed, meaning that any time you reach the upper index, you have to subtract one from the characteristic. The actual rule takes more reasoning, but can be described as follows: if multiplying brings you ''down'' the rule, add one to the characteristic (using either method of multiplying). Likewise, if dividing (using either method) brings you ''up'' the rule, subtract one from the characteristic. This can be seen by using our previous example on scientific notation: | ||
<blockquote> | <blockquote> | ||
431 x 0.00085 = (4. | 431 x 0.00085 = (4.31x10²)x(8.5x10⁻⁴) which implies a characteristic of 2 - 4 = -2 | ||
4.31(D) | I → 8.5(C) ≈ 3.67(D), which is lower on the rule than we started (4 > 3), therefore we need to add 1 to the characteristic (-2 + 1 = -1). | 4.31(D) | I → 8.5(C) ≈ 3.67(D), which is lower on the rule than we started (4 > 3), therefore we need to add 1 to the characteristic (-2 + 1 = -1). | ||
thus, the result is 3. | thus, the result is 3.67x10⁻¹=0.367 | ||
</syntaxhighlight> | </syntaxhighlight> | ||