1. The Form of the CI Scale

The CI scale is identical with the C scale except that the CI scale reads from right to left for this reason great care should be taken in reading the CI scale. Note, by the term ‘reciprocal of a number ‘N’ we mean .

2. Reciprocals (Numbers between 1 and 10)

For numbers between 1 and 10 on the C scale, its reciprocal is read directly off the CI scale as a number between 1 and 0.01. We can also find reciprocal by working from the CI scale to the C scale.

Fig 7-1

Example 1: (Fig. 7-1)

1. Set the hair line over 6 on the C scale.
2. Under the hair line read off 0.167 on the CI scale.

1. Set the hair line over 6 on the CI scale.
2. Under the hair line read off 0.167 on the C scale.

Example 2:

1. Set the hair line over 2.44 on the C (or CI ) scale.
2. Under the hair line read off 0.41 on the CI (or C) scale.

1. Reciprocals (Numbers outside the range 1 to 10)

For numbers less than 1, their reciprocals will always be larger than 1.

e.g.

For numbers greater than 10, their reciprocals will always be smaller than 0.1.

e.g.

Example 1:

1. Set the hair line over 42 on the C (or CI) scale.
2. Under the hair line read off ‘238’ on the CI (or C) scale as the answer.

To locate the decimal point, the following procedure is possibly the easiest

Note:

(As the reciprocal of a number between 1 and 10 is always between 1 and 0.1.) The answer is therefore 23.8.

Example 2:

1. Set the hair line over 420 on the C (or CI) scale.
2. Under the hair line read off ‘238’ on the CI (or C) scale as the answer.

Note: Some modern Slide Rules have a DI scale located on the body. This scale can be used in conjunction with the D scale to obtain recprocals.

Note that instead of multiplying 2 by 7, we could divide by the reciprocal of 7.

i.e. ¸

Example 1: (Fig. 7-2)

1. Set the hair line over 2 on the D scale.
2. Place the 7 of CI scale under the hair line.
3. Below the left index of the C scale read off 14 on the D scale as the answer.

Note: When we place the 7 of the CI scale under the hair line (step 2 above), this brings 0.1428 on the C scale immediately above the 2 on the D scale. Thus we are dividing 2 by 0.1428.

(i.e. 2 ¸ 0.1428 = 2 ¸ = 2 x 7)

Example 2: 4.15 x 1.35 = 5.6

1. Set the hair line over 4.15 on the D scale.
2. Place the 1.35 of the CI scale under the hair line.
3. Below the right index of the C scale read off 5.6 on the D scale as the answer.

Note: Using the D and CI scale to multiply, we never run off the end of the scale for the answer as we did when using the C and D scales. The answer is always found on the D scale under the left or right index of the C scale.

1. 1.5 x 4.7 =
2. 2.2 x 2.4 =
3. 2.258 x 3.1 =
4. 1.95 x 5.05 =
5. 7.6 x 1.25 =
6. 6.88 x 1.09 =

Instead of dividing, say, 108 by 7.5, we could simply multiply by the reciprocal of 7.5.

i.e. 108 ¸ 7.5 = 108 x

Example 1: 108 ¸ 7.5 = 14.4

1. Place the left index of the C scale over 108 on the D scale.
2. Set the hair line over 7.5 on the CI scale.
3. Under the hair line read off 14.4 on the D scale as the answer.

Note: In the above procedure we have effectively multiplies 108 by 0.1335, or , (i.e. the value on the C scale under the hair line.)

(108 x 0.1335 = 108 x = 108 ¸ 7.5)

Example 2: 96 ¸ 149 = 0.644

1. Place the right index of the C scale over 96 on the D scale.
1. Set the hair line over 149 on the CI scale.
2. Under the hair line read off 0.644 on the D scale as the answer.

Note: When we divide with the CI and D scales, sometimes we use the left index (example 1 above), while on other occasions we use the right index (example 2 above). This is dictated by the numbers involved, and if one index does not bring the numbers we are dividing by onto the scale, the other index will.

1. 43 ¸ 5.5 =
2. 5.7 ¸ 1.9 =
3. 77 ¸ 35 =
4. 675 ¸ 326 =
5. 196 ¸ 14 =
6. 6.6 ¸ 14.2 =