Understanding Scales in Drafting and Measurement

Scales are essential tools used in drafting, engineering, and surveying to represent objects or distances with a specific ratio relative to their actual size. Different types of scales are designed for various purposes and levels of precision.

Identifying the Scale for Three Successive Dimensions

The question asks about a specific type of scale that allows for the measurement of three successive dimensions. Let's examine the options provided:

1. Vernier scale
2. Engineer’s scale
3. Diagonal scale
4. Scale of chords

We need to determine which of these scales is designed to measure three successive units of measurement, such as meters, decimeters, and centimeters, or yards, feet, and inches, or even units, tenths of units, and hundredths of units.

Analyzing the Different Scale Types

Diagonal Scale Explained

A Diagonal scale is constructed in a way that allows for the measurement of a main unit, its tenth part, and the tenth part of the tenth part (i.e., hundredth part of the main unit). This is achieved by dividing the smallest main divisions into tenths vertically and then using diagonal lines to further subdivide these tenths horizontally along specific lines. This construction effectively provides a way to measure three successive dimensions: the main unit, the first subdivision (tenths), and the second subdivision (hundredths).

For example, on a diagonal scale representing meters, decimeters, and centimeters:

• The main divisions represent meters.
• The primary subdivisions represent decimeters.
• Using the diagonal lines, you can read measurements down to centimeters (hundredths of a meter, or tenths of a decimeter).

Thus, a diagonal scale is capable of measuring three successive units of measure.

Other Scales in Comparison

• Vernier scale: This scale is used to measure fractional parts of the smallest division on a main scale with high accuracy. It is typically used for precise measurement of a single dimension, not three successive ones.
• Engineer’s scale: An engineer's scale is usually divided into decimal units (e.g., 10, 20, 30, 40, 50, or 60 parts to the inch). It is used to draw or measure objects according to a specific scale factor (like 1:100 or 1:50). While useful for converting distances, it doesn't inherently provide measurement of three successive standard units simultaneously in the same way a diagonal scale does.
• Scale of chords: This is a graphical scale used primarily for setting out or measuring angles, not linear distances or successive dimensions.

Based on the function and construction of each scale, the Diagonal scale is specifically designed to measure three successive dimensions.

Therefore, the scale capable of measuring three successive dimensions is the Diagonal scale.

Revision Table: Scale Types

Additional Information: Applications of Diagonal Scales

Diagonal scales are particularly useful in technical drawings, surveying plans, and maps where accurate measurements involving units, tenths, and hundredths are required. They allow draftsmen and engineers to transfer dimensions from a drawing to scale or to take measurements from a scaled drawing with greater precision than a simple plain scale.

The principle behind the diagonal scale's ability to measure hundredths relies on the geometric principle of similar triangles. As the diagonal line crosses equally spaced horizontal lines and equally spaced vertical lines, it creates a linear variation that corresponds proportionally to the subdivisions.