Urbain Le Verrier in 1859 on the perihelion precession of Mercury
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While of the Sun we only have meridian observations subject to great objections, we have, over the space of a century and a half, a certain number of observations of Mercury possessing great precision - I want to speak of the internal contacts of Mercury's disc with the Sun's disc, when the planet comes to pass in front of this star. As long as the place where the observation was made is well known, and as long as the astronomer had a reasonable refracting telescope and his clock was accurate to within a few seconds, the knowledge of the instant when the internal contact happened must allow us to estimate the distance between the centre of the planet and the centre of the Sun without an error of more than one arcsecond. We possess, from 1697 until 1848, twenty-one observations of this type, for which we have to be able to satisfy in the most stringent manner whether the irregularities of the movements of the Earth and of Mercury were well calculated, and if the values attributed to the perturbative masses are correct.
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But what is remarkable is that increasing the secular movement of the perihelion by 38 arcseconds was enough to show all the observations of the transits to within one second, and even the majority of those to within one half-second. This result, so clean, which immediately shows in all comparisons a greater precision than achieved until now in astronomical theories, clearly shows the increase in the movement of the Mercury's perihelion is indispensable, and that therefore the Tables of Mercury and of the Sun have all the desired precision.