The measurements made thanks to the Meridian consisted of determining the positions of the upper and lower edges of the solar image along the demarcated line. Roughly speaking, the position of the center of the solar disk was obtained by half the sum of these measurements; it is therefore vital that the spot of light accurately represents the image of the Sun, projected onto a perfectly horizontal plane.
This is achieved only if the diameter of the gnomonic hole is small enough. This is the principle of the camera obscura - according to terminology introduced by Kepler - known since antiquity but only fully explained by the great Arab astronomer Ibn al-Haytham (965-1040). From the sixteenth century to the eighteenth century, the camera obscura benefited from a revival of interest, not only among astronomers in their observations of the Sun, but also among artists like the painter Johannes Vermeer (1632 - 1675): make the hole too small and the effects of light diffraction will occur such that the dimensions of the solar image are artificially increased; make the hole much larger and the spot of light will be only the oblique section of the tube of light based on the contours of the gnomon. Jean-Dominique Cassini, before being invited by Colbert to come and be the head of the Paris Observatory in 1667, had been able to determine at Bologna - in the church of San Petronio, where, in 1655, he carefully built a great meridian line twice the size as that of Paris - the optimal value that the diameter of the gnomon should have. This was equal to a thousandth part of its height (in the course of the nineteenth century, various formulae were proposed so as to gauge the size of the optimum diameter of the gnomon; in the case of Cassini's meridian, these formulae yield an optimum value of 6.6 mm in order to get a clear image in the end, which is fairly close to that given by Cassini's own rule).
In Paris, during the summer solstice, which occurs around June 21, the sun is in the sign of Cancer and culminates in an altitude of 64.6°, while in the winter solstice (December 21) it is found in the sign of Capricorn and its meridian altitude will be only 17.8°. At the equinoxes, around March 21 and September 21, the zenithal angle of the sun at noon is equal to the latitude (48°50'). The size of the image thus varies between 11cm in summer and 1m in winter. The image of the Sun takes just a little over 2 minutes to cross the meridian line.
