Whether a fractional portion of a secondary division is necessary, that is too small to be sub-divided, and a diagonal scale may be employed along with ease. This scale can read meter, decimeter (dm) and centimeter (cm) or kilometer (km), decameter and hectometer. Hence, along with the using of a diagonal scale, single can measure up to the second position of decimal.
Principle for Diagonal Scale
(a) Draw a rectangle ABCD.
(b) Divide it into ten equivalent parts with horizontal lines.
(c) Draw the diagonal BD line, intersecting the above lines.
(d) Draw perpendiculars from the above points to form a sequence of steps.
Like single moves along with the diagonal BD, while a fresh line is crossed, so the movement is 1/10 AB to the left.
PQ is 3/5 AB.
During constructing of a diagonal scale, it should be remembered such the similar number of equidistant parallel lines should be drawn above AB, like there is a third dimension in single secondary division.