Protractor on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way. Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and to the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved. Reading the Vernier scale: The bevel protractor Vernier scale may have graduations of 5′ (minutes) or 1/12°. Each space on the Vernier scale is 5′ less
Schema for vertical declining dials graphical techniques were used to derive formula_1 and formula_2 and from it formula_3. There are four basic angles that are needed to construct a vertical declining dial, Waugh described them such: The four basic calculation have a certain symmetry. At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor). Before the protractor became ubiquitous, compasses and the Scale of Chords were used for laying out an angle. This method originally used them. At this point only three lines matter, the vertical, the substyle length