File:Wigham-Richardson vertical decliner method (2)-(final).svg

Before the protractor became ubiquitous, compasses and the Scale of Chords were used for laying out an angle. This method originally used them.

• A large cross is drawn, ACB being the vertical line and PCQ horizontally.
• Two arcs are drawn to the right - AQ, and CT.
• Two triangle are drawn ACT- with the co-latitude (90- Φ) at the top, and CWX- with the declination 'D' at the centre. For the example these will be 38° and 20°

Finding SD

• A line is drawn from X through C to a point that will be eventually named S. Take compasses and using the radius CD swing an clockwise arc to this line, where it cuts is the point S. In otherwords CS is equal in length to CD.
• Drop a perpendicular line (RS) from line PQ to cut through S. To fix the point Y: copy the length RS, from C onto the line PQ. This is CY. RS=CY.
• Join A to Y. This is the substyle distance SD.

Finding SH and the centre of the equinoctial

• A long line, perpendicular to AY is drawn- it will take the points G,Y,P and M. YG is equal in length to CR. Join AG and the angle YAG is the substyle height.

Drawing the hourlines

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).

• A perpendicular line through Y is dropped from the sub-style line- the crossing is marked 'g '.
• Compasses are used to transfer this length onto the substyle line. The point is called 'O' ', this is the centre of the equinoctial circle- a long line F F' is drawn perpendicularly.
• Centre the circular protractor on O', with one line passing through P- call this XII.
• From A the actual hour-lines through each of the points (stars) where the protractor lines cross G,Y,P and M.