On the Apparent Magnitude of the Sun when Low and High

of the rod, and between the pinnacidia: sights or vanes on an astronomical instrument used for alignment placed at its ends, I found a length of 22 Royal feet, 2 digits, 0 lines, and 4 parts, totaling 38,308 parts in all. The Royal foot, or pied de roi, was a standard French unit of length roughly equal to 32.5 centimeters. It was divided into 12 inches (digits) and 144 lines. Measuring the sights themselves, which were of the required height, I found the width to be 5 digits, 6 lines, and 4 parts, totaling 796 parts. For this setup, I had a small beam erected near a window so that, by blocking light from other sources, the shadow of the upper sight would be cast more darkly and clearly onto the lower one. I always took account only of the darkest shadow, which you and Aquilonius: François d'Aguilon (1567 to 1617), a Belgian Jesuit mathematician and physicist rightly call the perfect and full shadow. This is because that faint, imperfect, or diminished shadow seen at the edges, which Kepplero: Johannes Kepler (1571 to 1630), the German astronomer who first coined the term penumbra calls the penumbra: the partially shaded outer region of a shadow, is not produced by the entire diameter, or if you prefer, the full disk of the celestial body.

I also employed special precautions regarding the Moon, because it casts a shadow with a softer outline, no matter how dark the room is. For while the Sun's shadow can be defined by faint or dotted lines on the lower sight, or even on a piece of clean paper placed upon it, using the sharp points of a compass, the distance between those points can then be transferred to a steel ruler divided in the manner described. However, the same cannot be done for the Moon. This is especially true because of its swift movement, as the shadow continually slips away due to the constant motion of the sky.

Therefore, I always have at hand several small white sheets of paper to be applied to the lower sight. Since two parallel lines are marked on each sheet, with different spacing on each one, it eventually becomes clear from applying many in succession which spacing between the lines matches the Lunar shadow, and which...