Draw a scale with R.F. 1:63360 to read miles and furlongs.

We assume a convenient maximum length to be measured, for example, $6 \text{ miles}$.
The formula for the Length of the Scale (LOS) is:

$$\text{LOS} = \text{R.F.} \times \text{Maximum length}$$

Given R.F. = $1:63360$ and Maximum length = $6 \text{ miles}$.
We know that $1 \text{ mile} = 63360 \text{ inches}$.

$$\text{LOS} = \frac{1}{63360} \times (6 \times 63360 \text{ inches})$$ $$\text{LOS} = 6 \text{ inches}$$

To convert this to centimeters for drawing on paper, use $1 \text{ inch} = 2.54 \text{ cm}$:

$$\text{LOS} = 6 \times 2.54 \text{ cm}$$ $$\text{LOS} = 15.24 \text{ cm}$$

So, the total length of the scale to be drawn on paper will be $15.24 \text{ cm}$.

The $15.24 \text{ cm}$ line represents $6 \text{ miles}$.

• Primary Divisions (for miles): Divide the $15.24 \text{ cm}$ line into 6 equal parts. Each part will represent $1 \text{ mile}$. Length of each primary division = $\frac{15.24 \text{ cm}}{6} = 2.54 \text{ cm}$.
• Secondary Divisions (for furlongs): The leftmost primary division represents $1 \text{ mile}$. Since $1 \text{ mile} = 8 \text{ furlongs}$, this $2.54 \text{ cm}$ segment needs to be divided into 8 equal parts. Length of each secondary division = $\frac{2.54 \text{ cm}}{8} \approx 0.3175 \text{ cm}$. Each of these will represent $1 \text{ furlong}$.

1. Draw a horizontal line segment $15.24 \text{ cm}$ long.
2. Divide this line into 6 equal main parts, each $2.54 \text{ cm}$ long.
3. Mark the main divisions starting from the second mark from the left as $0, 1, 2, 3, 4, 5 \text{ miles}$. The first main division (to the left of 0) is reserved for furlongs.
4. Divide the leftmost main division (the $2.54 \text{ cm}$ segment to the left of 0) into 8 equal sub-parts, each approximately $0.3175 \text{ cm}$ long.
5. Mark these sub-divisions as $0, 1, 2, ..., 8 \text{ furlongs}$.
6. Draw a rectangle around the scale and add text labels: "R.F. = 1:63360", "Miles" below the main divisions, and "Furlongs" below the sub-divisions.

The final scale will be a $15.24 \text{ cm}$ line representing $6 \text{ miles}$, with main divisions of $2.54 \text{ cm}$ for miles and sub-divisions of approximately $0.3175 \text{ cm}$ for furlongs.