Slide Rules For Fun Part 3
In this third part of the Slide Rules posts, I realize there is not a huge demand for this type of information these days, unless someone is a collector, or gained a recent interest in slide rules, so this will be the last. However, there is one area I noticed from the first post that seemed a bit confusing, even to me. So this post will attempt to clarify.
The area I found required a bit of creative logic to figure out. In placing the decimal point in resulting calculations or answers, I had used something like the following.
- Multiplication with the C and D scales
– If the slide projects to the right of the stock, the digit count for the product is one less than the sum of the digit counts for the multiplicand and multiplier.
–If the slide projects to the left of the stock, the digit count for the product is equal to the sum of the digit counts for the multiplicand and multiplier.
- Multiplication with the CI and D scales.
– If the slide projects to the right of the stock, the digit count for the product is equal to the sum of the digit counts for the multiplicand and multiplier.
– If the slide projects to the left of the stock, the digit count for the product is one less than the sum of the digit counts for the multiplicand and multiplier.
- Division with the C and D scales.
– If the slide projects to the right of the stock, the digit count for the quotient is one more than the digit count for the dividend minus the digit count for the divisor.
– If the slide projects to the left of the stock, the digit count for the quotient is equal to the digit count for the dividend minus the digit count for the divisor.
- Division with the CI and D scales.
– If the slide projects to the right of the stock, the digit count for the quotient is equal to the digit count for the dividend minus the digit count for the divisor.
– If the slide projects to the left of the stock, the digit count for the quotient is one more than the digit count for the dividend minus the digit count for the divisor.
Attempting to depict the logic of those statements seemed a bit confusing. So hopefully, these additions will clear up the muddle.
An easy way to remember the above rules, using the C and D scales, is this chart, depending on whether the slide projects from the left or right end, respectively.
| Procedure | Formula | [] | Procedure | Formula |
|---|---|---|---|---|
| multiply | SUM | [] | multiply | SUM -1 |
| divide | DIFF | [] | divide | DIFF +1 |
When counting the number of digits (or span), decimal zeros are negative. For example, the below chart illustrates this concept.1
| Number | Span or Digit | | | Number | Span or Digit |
|---|---|---|---|---|
| 352.0 | 3 | | | 0.0352 | -1 |
| 35.2 | 2 | | | 0.00352 | -2 |
| 3.52 | 1 | | | 0.000352 | -3 |
| 0.352 | 0 | | | 0.0000352 | -4 |
These examples illustrate the above notes.
Example: \(\frac{755}{0.0272} = \frac{7.55_{E}^{\; \; \; 2}}{2.72_{E}^{\; \; \; -2}}\). The slide projects to the right, so we add 1 to difference: 3 - (-1) + 1 = 5. So the quotient of 278 is 27800. Using scientific notation, the 2 - (-2) = 4, so 2.78 becomes 2.78E4.
Example: \(\frac{0.0000215}{24600}\) The digits (span) are (-4) - 5 = -9 and the slide is left. So 0.875 becomes 0.000000000875, or 8.75E-10.
Example: \(.023 \times 14\). the digits are (-1) + 2 -1 = 0. So 322 becomes 0.322.
For combined operations, note the slide end’s direction during each calculation to add or subtract digits (or span) for the final answer.
Example: \(\frac{6 \times 0.35}{81 \times 0.005} = 52\). Set 81 (C scale) over 6 (D scale), move HL to 3.5 (C scale), move slide to place 5 (C scale) under HL. Read 5185 (D scale) at index. Digits for each operation (slide all to left end) are: (-1) +0 - (-1) = 1, giving the result of 5.185.
Example: \(\frac{0.015 \times 4}{2.5 \times 1.2} = \frac{0.06}{3}\) Set 2.5 (C scale) over 1.5 (D scale) (slide left), slide HL to 4 (C scale), move slide to place 1.2 (C scale) (slide right) under HL, read 2 at index (D scale). Digit placement: (-1) -1 +1 -1 = -2, so final answer is 0.02.
Hopefully, this makes the rules a tiny bit clearer, for those that are interested in using slide rules. Actually, it can be fun to use this old bit of technology in today’s world, especially when the calculator batteries die!
There are many books available, both in book stores and online, that go into much greater detail, for those that just have to know more! And here is my small contribution, recently updated using Xie, Dervieux, and Riederer (2020), from the 2015 version done in LibreOffice. I use this for my own procedural refreshment. Any errors found are my own.
As always, we thank the Lord Jesus for all things, for without Him, we would be struggling with the world and its sin all around us! Have a great day and God Bless!
References
Footnotes
See “Slide Rule, How to use it, Third Edition” by Calvin C. Bishop, 1955, Barnes & Noble.↩︎