Man's Place in the Universe. Alfred Russel Wallace

same observer after an interval of nine or ten hours, may examine the moon from positions six or seven thousand miles apart, and by accurate measurements of its angular distance from a star, or by the time of its passage over the meridian of the place as observed with a transit instrument, the angular displacement can be found and the distance determined with very great accuracy, although that distance is more than thirty times the length of the base. The distance of the planet Mars when nearest to us has been found in the same way. His distance from us even when at his nearest point during the most favourable oppositions is about 36 million miles, or more than four thousand times the earth's diameter, so that it requires the most delicate observations many times repeated and with the finest instruments to obtain a tolerably approximate result. When this is done, by Kepler's law of the fixed proportion between the distances of planets from the sun and their times of revolution, the proportionate distance of all the other planets and that of the sun can be ascertained. This method, however, is not sufficiently accurate to satisfy astronomers, because upon the sun's distance that of every other member of the solar system depends. Fortunately there are two other methods by which this important measurement has been made with much greater approach to certainty and precision.

      Diagram illustrating the transit of Venus.

      The first of these methods is by means of the rare occasions when the planet Venus passes across the sun's disc as seen from the earth. When this takes place, observations of the transit, as it is termed, are made at remote parts of the earth, the distance between which places can of course easily be calculated from their latitudes and longitudes. The diagram here given illustrates the simplest mode of determining the sun's distance by this observation, and the following description from Proctor's Old and New Astronomy is so clear that I copy it verbally:—'V represents Venus passing between the Earth E and the Sun S; and we see how an observer at E will see Venus as at v', while an observer at E' will see her as at v. The measurement of the distance v v', as compared with the diameter of the sun's disc, determines the angle v V v' or E V E'; whence the distance E V can be calculated from the known length of the base-line E E'. For instance, it is known (from the known proportions of the Solar System as determined from the times of revolution by Kepler's third law) that E V bears to V v the proportion 28 to 72, or 7 to 18; whence E E' bears to v v' the same proportion. Suppose, now, that the distance between the two stations is known to be 7000 miles, so that v v' is 18,000 miles; and that v v' is found by accurate measurement to be ¹/₄₈ part of the sun's diameter. Then the sun's diameter, as determined by this observation, is 48 times 18,000 miles, or 864,000 miles; whence from his known apparent size, which is that of a globe 107¹/₃ times farther away from us than its own diameter, his distance is found to be 92,736,000 miles.'

      Of course, there being two observers, the proportion of the distance v v' to the diameter of the sun's disc cannot be measured directly, but each of them can measure the apparent angular distance of the planet from the sun's upper and lower margins as it passes across the disc, and thus the angular distance between the two lines of transit can be obtained. The distance v v' can also be found by accurately noting the times of the upper and lower passage of Venus, which, as the line of transit is considerably shorter in one than the other, gives by the known properties of the circle the exact proportion of the distance between them to the sun's diameter; and as this is found to be the most accurate method, it is the one generally adopted. For this purpose the stations of the observers are so chosen that the length of the two chords, v and v', may have a considerable difference, thus rendering the measurement more easy.

      The other method of determining the sun's distance is by the direct measurement of the velocity of light. This was first done by the French physicist, Fizeau, in 1849, by the use of rapidly revolving mirrors, as described in most works on physics. This method has now been brought to such a decree of perfection that the sun's distance so determined is considered to be equally trustworthy with that derived from the transits of Venus. The reason that the determination of the velocity of light leads to a determination of the sun's distance is, because the time taken by light to pass from the sun to the earth is independently known to be 8 min. 13¹/₃ sec. This was discovered so long ago as 1675 by means of the eclipses of Jupiter's satellites. These satellites revolve round the planet in from 1³/₄ to 16 days, and, owing to their moving very nearly in the plane of the ecliptic and the shadow of Jupiter being so large, the three which are nearest to the planet are eclipsed at every revolution. This rapid revolution of the satellites and frequency of the eclipses enabled their periods of recurrence to be determined with extreme accuracy, especially after many years of careful observation. It was then found that when Jupiter was at its farthest distance from the earth the eclipses of the satellites took place a little more than eight minutes later than the time calculated from the mean period of revolution, and when the planet was nearest to us the eclipses occurred the same amount earlier. And when further observation showed that there was no difference between calculation and observation when the planet was at its mean distance from us, and that the error arose and increased exactly in proportion to our varying distance from it, then it became clear that the only cause adequate to produce such an effect was, that light had not an infinite velocity but travelled at a certain fixed rate. This however, though a highly probable explanation, was not absolutely proved till nearly two centuries later, by means of two very difficult measurements—that of the actual distance of the sun from the earth, and that of the actual speed of light in miles per second; the latter corresponding almost exactly with the speed deduced from the eclipses of Jupiter's satellites and the sun's distance as measured by the transits of Venus.