Drawing a graphical scale

Drawing a graphical (bar) scale. By convention, a metric bar is about 15 cm long and an English one about 6 inches.

Steps:

• Find what ground distance the conventional length represents.
• That figure is rarely round, so choose a round number near it.
• Work out the exact line length for that round number.
• Draw the line, divide it into equal primary divisions, and number them from 0, moving right.
• Split the extreme left division into smaller secondary divisions for fine readings.

The book's metric example (1 : 50,000): 15 cm represents 50,000 × 15 ÷ 1,00,000 = 7.5 km, not a round number. Choose 5 km: its line is 15 × 5 ÷ 7.5 = 10 cm. Divide the 10 cm line into 5 parts of 1 km; split the left part into 10 parts of 100 m (or 2, 4 or 5 parts of 500, 250 or 200 m).

The book's English examples:

• 1 inch to 1 mile: 6 inches show 6 miles; divide into 6 parts of 1 mile, and split the left part into 4 parts of 2 furlongs.
• 1 : 50,000 in miles: 6 inches represent 50,000 × 6 ÷ 63,360, about 4.73 miles; choose 5 miles, whose line is about 6.34 inches.

Dividing an awkward length into equal parts. A line of 6.34 inches cannot easily be split into 5 equal parts with a ruler. Instead:

• From each end of the line, draw a slanting line at about 40° or 45°, on opposite sides.
• Mark 5 equal steps (say 1 inch each) along each slanting line.
• Join the matching marks with dotted lines; where they cross the main line, it is divided into 5 equal parts.

Example (new): for a map at 1 : 25,000, a 15 cm line represents 25,000 × 15 ÷ 1,00,000 = 3.75 km. Choose 3 km: its line is 15 × 3 ÷ 3.75 = 12 cm, divided into 3 parts of 1 km, with the left part split into 4 parts of 250 m.