This method first appeared in Peter Nicholsons A popular Course of Pure and Mixed Mathematics in 1825. It was copied by School World in Jun 1903, then in Kenneth Lynch's, Sundial and Spheres 1971. It starts by drawing the well known triangle, and takes the vertices to draw two circles at radius (OB) sin φ and (AB) tan φ. The 15° lines are drawn, intersecting these circles. Lines are taken horizontally, and vertically from these circles and their intersection point (OB sin t,AB cos t) is on the hour line. That is tan κ = OB sin t/ AB cos t which resolves to sin φ. tan t.

• 1: Draw the NS line, and the EW line crossing at the origin O. At a convenient point in the first quadrant join the axes with a line set at the target angle. This forms the basic triangle OAB.
• 2:Set the compasses at length OB and inscribe a circle. Set the compasses on AB and inscribe a concentric circle.
• 3:On both of these circles mark out the 15° angles.
• 4:Taking the lines vertically from the inner circle, and horizontally from the outer circle, Mark each of the intersections. These are on the hour lines.
• 5:Connect the intersection points to the origin.