Then I tried to remember what was the parallax of this star. I recalled that a friend of mine, a Russian astronomer, had made a calculation, which had been confirmed, of this parallax. It was proved to be 0,″046.—When I had thus solved the mystery my heart beat with joy. Every geometrician knows that parallax indicates mathematically the distance in units of the magnitude employed in the calculation. I sought then to recall exactly the distance which separated this star from the Earth, in order to prove the accuracy of the calculation. I only needed to find out what number corresponded to 0,″046.[2]
The velocity of light.
Expressed in millions of leagues, this number is 170,392,000, and so, from the star on which I was, the Earth was distant 170 billions 392 thousand millions of leagues. The principle was thus established, and the problem was three parts solved. Now, here is the main point, to which I call your special attention, for you will find in it an explanation of the most marvellous realities. Light, you know, does not cross instantaneously from one place to another, but in successive waves. If you throw a stone into a pool of tranquil water, a series of undulations form around the point where the stone fell. In the same way, sound undulates in the air when passing from one point to another, and thus, also, light travels in space—it is transmitted in successive undulations. The light of a star takes a certain time to reach the Earth, and this time naturally depends on the distance which separates the star from the Earth.
How the heavenly bodies are seen.
Sound travels 340 metres in a second. A cannon shot is heard immediately by those who fire it, a second later by persons who are at a distance of 340 metres, in three seconds by those who are a kilometre off, twelve seconds after the shot at four kilometres. It takes two minutes to reach those who are ten times farther off, and those who live at a distance of a hundred kilometres hear this human thunder in five minutes. Light travels with much greater swiftness, but it is not transmitted instantaneously, as the ancients supposed. It travels at the rate of 300,000 kilometres per second, and if it could revolve, might encircle the Earth eight times in a second. Light occupies one second and a quarter to come from the Moon to the Earth, eight minutes and thirteen seconds to come from the Sun, forty-two minutes to come from Jupiter, two hours to come from Uranus, and four hours to come from Neptune. Therefore, we see the heavenly bodies not as they are at the moment we observe them, but as they were when the luminous ray which reaches us left them. If a volcano were to burst forth in eruption on one of the worlds I have named, we should not see the flames in the Moon till a second and a quarter had elapsed, if in Jupiter not till forty-two minutes, in Uranus two hours after, and we should not see it in Neptune till four hours after the eruption. The distances are incomparably more vast outside our planetary system, and the light is still longer in reaching us. Thus, a luminous ray coming from the star nearest to us, Alpha, in Centaurus, takes four years in coming. A ray from Sirius is nearly ten years in crossing the abyss which separates us from that sun. The star Capella, being the distance above mentioned from the Earth, it is easy to calculate, at the rate of 300,000 kilometres the second, what time is needed to cross this distance. The calculation amounts to seventy-one years, eight months, and twenty-four days. The luminous ray, therefore, which came from Capella to the Earth, traversed space without interruption seventy-one years, eight months, and twenty-four days before it was visible on the Earth. In like manner, the ray of light which leaves the Earth can only arrive at Capella in the same period of time.
Time occupied in the transmission of light.
Quærens. If the luminous ray which comes from that star takes nearly seventy-two years to reach us, it follows that we see the star as it was nearly seventy-two years ago?
Lumen. You are quite right, and this is the fact that I want you take note of specially.