marked 1 at the beginning, center, and the end. These marks are called indexes and are known as the left, center, and right A indexes.

FIG. 101.-A-scale from 1 to 2.

The distance between the graduations numbered 1 and 2 is divided into how many large graduations?

Each of these large graduations is divided into how many parts?

If the left index is taken as 1, the first large graduation will denote what?

Each small graduation therefore denotes how many hundredths?

Set down the reading for each graduation from 1 to 2 inclusive.

If the left index is taken as 10, each of the smallest graduations therefore denotes how many tenths?

Set down the reading for each graduation from 10 to 11 inclusive.

If the left index is taken as 100, the first graduation will be read what instead of 11? (If unable to answer, notice what it must be in order that the graduation numbered 2 or 20 may be read 200.)

Write the reading for each graduation from 100 to 200 inclusive.

2

3

FIG. 102.-A-scale. from 2 to 5.

Examine the A scale from 2 to 5.

Is the number of the large graduations the same as from 1 to 2?

Are the small graduations the same?

Write the reading for each graduation from 2 to 3 inclusive; from 3 to 4; from 4 to 5; from 20 to 30 inclusive; from 400 to 500 inclusive.

Examine the A scale from 5 to the end.

Is the number of the large graduations the same as in other parts of the scale?

Are the small graduations the same?

Write the reading for each graduation from 7 to 8 inclusive; from 70 to 80 inclusive; from 800 to 900 inclusive.

FIG. 104.-B scale showing left and middle indexes.

Examine the B scale. This is the second scale on the

rule, being the upper scale on the slide.

Is it the same as the A scale? How is it read?

284. Graduation of the C and D Scales. Examine the D scale.

This is the fourth scale on the rule, being the scale on the lower stock.

By reference to the U. S. linear scale on the edge of the rule state the relation of the distance from 1 to 2 on the D scale, to the distance from 1 to 2 on the A scale.

What is the relation of the number of graduations on the D scale from 1 to 2, to the number of graduations on the A scale from 1 to 2?

Write the reading for each graduation on the D scale between the following limits inclusive:

Examine the C scale. This is the third scale on the rule, being the lower scale on the slide.

FIG. 106.-Section of C scale.

Is it exactly the same as the D scale? How is it read?

§ 2. SINES

285. Graduation of the S Scale. The S or sine scale on most rules is the lower scale on the reverse of the slide when the rule is held in position for reading the face scales. When the rule is turned over without reversing ends the S scale therefore is the upper scale, the lower scale being a tangent scale, with a scale of logarithms between the two.

Draw the slide to the left and examine the left end of the S scale. Looking back from the first numbered graduation which is 40', observe that the scale begins at slightly less than 35', or at 34′ 18′′.

Write the readings for each graduation from 35' to 2°, disregarding the irregularly placed graduations which may immediately follow the 1° 10' and precede the 2° graduations; these are gage-points as explained in paragraph 290.

FIG. 107.-Back of slide, showing the first 10° of the sine scale.

What is the graduation unit from 35' to 10°? From 10° to 20°? From 20° to 40°? From 40° to 70°? From

From 80° to 90°?

70° to 80°? Observe that the S scale is a scale of angles and not of sines.

286. How Sines are Read with Unreversed Slide. On all rules sines are read on the B or the A scale. When the back of the rule has a notch at the end, sines may be read by moving the slide so as to bring the given angle on the S scale directly under the index mark on the edge of the notch in the right end of the rule.

The rule is then turned over, and the numerical value of the sine of the angle is read on B, directly under the right A index.

287. Rule for Pointing off a Sine Reading. (1) Place .0 before all sines which are read on the first B scale.

(2) Place decimal point only, before all sines which are read on the second B scale.

Thus sin 24° 15' is read as follows:

(1) Set 24° 15' under the right notch index.

(2) Turn the rule over.

(3) Move runner to right A index, and read .411 on B.