Powers of 10 and Scale Jumps
For measurements that are off the scales, or to shift calculations to scale ranges with finer logarithmic divisions, it is possible to move the decimal point or to achieve greater precision by multiplying (or 'jumping' scales).
This means that if a value does not fit on a scale -- either the left (MIL) scale or the right (s) scale -- divide it by any number and multiply the result by the same number.
As sample input values we have:
- 5 MIL measured angle size
- 18 m known object size
If the input is off the scale: shift power of 10
18 m isn’t part of the scale, so we have to use 1.8 m (18/10) to read the result:
- We connect 5 MIL and 1.8 m (18/10) and read 250-400 m on the medium scale.
- 5 = 5 × 100
- 18 / 10 = 1.8
- = 18 × 10-1
- So we have to append a zero to the result.
- = 2,500-4,000 m
If the input is too low or high on a scale: shift power of 10
5 MIL is too low to read since the string is almost parallel to the scale, so we use 50 MIL (5 × 10):
- We connect 50 MIL (5 × 10) and 1.8 m (18/10) and read 36 m on the center scale.
- 5 × 10 = 50
- = 5 × 10-1
- 18 / 10 = 1.8
- = 18 × 10-1
- So we have to append two zeros to the result.
- = 3,600 m
If powers of 10 are impractical: divide or multiply by an arbitrary factor on one side to jump scales
Should the input numbers be impractical to shift by powers of 10, it’s possible to multiply or divide a scale value by an arbitrary factor that shifts the values on that scale.
We take the 1.8 and multiply it by 2 to move down and further to the center of the scale:
- We connect 50 MIL (5 × 10) and 3.6 m (18/10 × 2) and read 72 m on the center scale.
- 5 × 10 = 50
- = 5 × 10-1
- 18 / 10 × 2 = 3.6
- = 36 × 10-1
- We therefore add two zeros and divide by 2.
- = 3,600 m
If powers of 10 are impractical: divide or multiply by an equal factor on both sides
If the input values are inconvenient to shift by powers of ten, it is possible to either multiply or divide both input values by any value (the same on both sides) that shifts the values on the scale.
Now we take the 50 and multiply it equally by 2 to move up, further into the center of the scale:
- We connect 100 MIL (50 × 10 × 2) and 3.6 m (18/10 × 2) and read 36 m on the center scale.
- 5 × 10 × 2 = 100
- = 10 × 10-1
- 18 / 10 × 2 = 3.6
- = 36 × 10-1
- Equal factors on both sides can be ignored, but we need to append two zeros to the result.
- = 3,600 m