For now, just notice that A and B are also laid out logarithmically, so it's possible to perform multiplications on them too. Since these are half-length copies, there are two instances for each span of D and C. Therefore, you'll find a 3.5, say, appearing twice. In this case, for simple multiplications, just use the leftmost one, and you'll be guaranteed to stay on scale regardless of the second multiplicand. (As usual, you'll be interpreting the order of the magnitude appropriately at the end anyway).
Example 2.1: Find the product of 3.5 and 2.7:
- Set the cursor at the leftmost 3.5 on the A scale.
- Align the left index with the hairline.
- Move the cursor to 2.7 on the B scale.
- Read the result under the hairline on the A scale: 9.45.
 |
| Left index on A:3.5, cursor on B:2.7, result at A:9.45 |
Did you notice in step (3) that you had a choice of which 2.7 on the B scale to use? That won't always be the case, but the good news is that you'll always have at least one and won't have to swap indices. Let's try the troublemaker from Method #1 (which used the C and D scales) and see.
Example 2.2: Find the product of 4.2 and 6.5:
- Set the cursor at the leftmost 4.2 on the A scale.
- Align the left index with the hairline.
- Move the cursor to 6.5 on the B scale.
- Read the result under the hairline on the A scale: 27.30.
 |
| Left index on A:4.2, cursor on B:6.5, result at A:27.30 |
In this instance, you get no choice for 6.5, but at least you had it on scale!
Wrap-Up: Let's recap the virtues and otherwise for using the A and B scales for multiplication.
- Advantages: With two copies of the mantissas available, you'll never be forced into index swapping. Also, the A and B scales are available on most (but not all) slide rules.
- Disadvantage: Because these are half-length scales requiring some real eye-squinting, it's hard to achieve the same accuracy you would with the D and C scales.
Next installment: Multiplication -- Method #3