Note the time of transit of the Sun over the meridian line. It is expressed in UTC (Universal Coordinated Time) which, since 1972, is the successor of the old Greenwich Mean Time or GMT. For the sake of simplicity, UTC is Greenwich Mean Time, Greenwich being a suburb of London whose meridian, in relation to which all others are measured, is located 2°20' west of the meridian of Paris, as determined by the meridian line of the Paris Observatory.
It is customary to say that it is noon when the Sun is at its highest point in the sky, that is to say, when its image crosses the meridian line - which is not strictly true, since the culmination of stars in close proximity to Earth such as the Moon and the Sun, does not occur, in general, when passing the meridian. However, we can see for ourselves that not only is it not noon by our watch, whether in Universal Coordinated Time or in local time, but also from one day to the next, this moment which we now call true noon, will change. In reality, the Sun, or at least its image, which we observe by its bisection of the meridian line, is not the sun by which our watches are aligned. Time, in our daily lives, must have a uniform flow, regular and predictable, and this corresponds to the time as measured by our watches. In order not to disturb the daily rhythm of the succession of days and nights, it is necessary to connect this mechanical time to the one given by the motion of the sun in the sky. Yet this motion is only apparent. It refers, in essence, to the rotation of the Earth around its axis; but it also suffers small variations that come from the Earth's motion around the Sun, this being non-uniform motion along a slightly elliptical orbit which causes acceleration and deceleration in accordance with the laws of motion set forth by Kepler in the early seventeenth century. This irregular orbital motion, as well as the tilt of the spin axis of the Earth on its orbital plane, is responsible for the irregularities of solar time, i.e. the time defined solely by the apparent diurnal motion of the Sun. The difference between this perfectly uniform time - as measured by UTC which is arrived at by averaging out the Sun's movements and is thus a purely mathematical entity - and true solar time is called the equation of time, which, when plotted against the time of year, has the appearance of an oscillating curve spanning values up to ± 15 minutes.
In the course of the year, these two suns, the real and the virtual, will coincide exactly four times, on April 15, June 13, September 1 and December 25, which means that the equation of time is zero at these dates. However, universal time displayed is still - despite the correction to conventional time of one or two hours depending on the time of year - not noon by the Sun. Why? It is important simply to remember that Universal Time is Greenwich Mean Time, so on these four dates, it will be exactly 12:00 Universal Time in Greenwich, but only for other days is there the need to correct time as related to the difference in longitude from Greenwich. Thus, in Paris, located 2°20' east of Greenwich, the Sun moves across the meridian slightly earlier, exactly 9mn 20.9s earlier, which is the time the Earth takes to rotate through an angle equal to the difference of longitude from Greenwich, 2°20' (since the Earth rotates 360 degrees in 24 hours). Therefore, on the dates when there is no need to allow for the equation of time on the meridian of Paris, at the moment of passing, as expressed in universal time, the Sun will be below the meridian of 9mn 20.9s at true noon.
The equation of time can be drawn on the ground by a figure of eight, oscillating around the meridian line. It is called the meridian of mean solar time, or the "analemma" - in order to distinguish it from the true meridian of time, that is to say, the meridian itself - because at each point of this curve the Sun passes every day exactly at noon of average time ; in other words it is the crossing point of the meridian of a false Sun whose motion is uniform. This curve generally appears on many sundials. The first person who came up with the idea of this curve is Jean-Paul Grandjean de Fouchy (1707-1788) around 1730, at the home of the Comte de Clermont in the Hôtel du Petit Luxembourg, of which nothing remains today. On this point, it is worth noting that Fouchy came to live at the Royal Observatory of Paris on April 4, 1744, shortly after taking up his office on January 8 of that same year as permanent secretary of the Academy of Sciences - a position he held until 1776 - where he occupied the second floor apartment, directly overlooking the meridian in the great room. He left in 1757 when water leaking into his apartment as a result of the poor condition of the vaults above, had rendered it uninhabitable. However, it was never intended that a a meridian line of average time be drawn on the floor of the hall.
