Very few stars appear brighter than Saturn at its brightest; it looks about as bright as Altair, the eleventh brightest star in the sky. Yet Saturn shines only by the light it reflects from the sun, and its distance from the sun is such that it receives only about one part in 2500 million of the total light emitted by the sun. And, as the surface of Saturn only reflects back about two-fifths of the light it receives, it follows that Saturn shines with only a 6000 millionth part of the light of the sun. If, as Kepler and others had maintained, Altair was essentially similar to the sun, it would probably be of about the same candle-power as the sun, and so would give out about 6000 million times as much light as Saturn. The fact that Altair and Saturn appear about equally bright in the sky can only mean that Altair is 80,000 times as distant as Saturn[1]. This argument is essentially identical with one which Newton gave in his _System of the World_ to shew that even the brightest stars, such as Altair, must be very distant indeed. [1] For the apparent brightness of an object falls off as the inverse square of its distance, and the square of 80,000 is approximately equal to 6000 million. And such has proved to be the case. All efforts to discover the apparent swinging motion of the stars—“parallactic motion,” as it is technically called—which results from the earth’s orbital motion failed until 1838, when three astronomers, Bessel, Henderson, and Struve, almost simultaneously detected the parallactic motions of the three stars, 61 Cygni, α Centauri and α Lyrae respectively. The amount of their parallactic motion made it possible to calculate the distances of the stars, so that the inhabitants of the earth were not only placed in possession of definite ocular proof that they were swinging round the sun, but from the visible effects of this swing they were able to compute the distances of the nearer stars. The calculated values were not accurate when judged by modern standards, but they provided the first definite estimates of the scale on which the universe is built. Let us pause for a minute to consider how this scale is built up. The first step is to select a convenient base-line a few miles in length on the surface of the earth, and to measure this in terms of standard yards or metres. Starting out from this base-line, a geodetic survey maps out a long narrow strip of the earth’s surface, preferably running due north and south. The difference of latitude at the two ends is then measured by astronomical methods, as for instance by noticing the difference in the altitude of the pole-star at the two places. As the length of the strip is already known in miles, this immediately gives the dimensions of the earth. According to Hayford (1909), the earth’s equatorial radius is 6378·388 kilometres, or 3963·34 miles, its polar radius being 6356·909 kilometres or 3949·99 miles.