The angle thus represented is what is called the "horizontal parallax" of the sun. By this amount--the breadth of a halfpenny at 2,000 feet--he is, to a spectator on the rotating earth, removed at rising and setting from his meridian place in the heavens. Such, in other terms, would be the magnitude of the terrestrial radius as viewed from the sun. If we knew this magnitude with certainty and precision, we should also know with certainty and precision--the dimensions of the earth being, as they are, well ascertained--the distance of the sun. In fact, the one quantity commonly stands for the other in works treating professedly of astronomy. But this angle of parallax or apparent displacement cannot be directly measured--cannot even be perceived with the finest instruments. Not from its smallness. The parallactic shift of the nearest of the stars as seen from opposite sides of the earth's orbit, is many times smaller. But at the sun's limb, and close to the horizon, where the visual angle in question opens out to its full extent, atmospheric troubles become overwhelming, and altogether swamp the far more minute effects of parallax. There remain indirect methods. Astronomers are well acquainted with the proportions which the various planetary orbits bear to each other. They are so connected, in the manner expressed by Kepler's Third Law, that the periods being known, it only needs to find the interval between any two of them in order to infer at once the distances separating them all from one another and from the sun. The plan is given; what we want to discover is the scale upon which it is drawn; so that, if we can get a reliable measure of the distance of a single planet from the earth, our problem is solved. Now some of our fellow-travellers in our unending journey round the sun, come at times well within the scope of celestial trigonometry. The orbit of Mars lies at one point not more than thirty-five million miles outside that of the earth, and when the two bodies happen to arrive together in or near the favourable spot--a conjuncture which occurs every fifteen years--the desired opportunity is granted. Mars is then "in opposition," or on the _opposite_ side of us from the sun, crossing the meridian consequently at midnight.[749] It was from an opposition of Mars, observed in 1672 by Richer at Cayenne in concert with Cassini in Paris, that the first scientific estimate of the sun's distance was derived. It appeared to be nearly eighty-seven millions of miles (parallax 9·5"); while Flamsteed deduced 81,700,000 (parallax 10") from his independent observations of the same occurrence--a difference quite insignificant at that stage of the inquiry. But Picard's result was just half Flamsteed's (parallax 20"; distance forty-one million miles); and Lahire considered that we must be separated from the hearth of our system by an interval of _at least_ 136 million miles.[750] So that uncertainty continued to have an enormous range.