Catalogues of the stars have, of course, led to other minor catalogues of various classes of stars, binary, variable, and the like. In the later years catalogues of stars according to their spectra have enriched science. The first extensive catalogue of stellar spectra was published by Vogel. It dealt with four thousand and fifty-one stars, and appeared in 1883; it has since been followed by the Draper catalogue, based upon photographs of the spectra, which contains a much larger number. With regard to nebulæ, Herschel published his third catalogue in 1802. The last catalogue of this nature is by Dreyer (1888), and contains seven thousand eight hundred and forty of these objects. In the time of Tycho they could be counted on the fingers of one hand. INVESTIGATIONS OF SOME IMPORTANT ASTRONOMICAL CONSTANTS The nineteenth century was fruitful in the determination of many numerical values which are all important in enabling us to determine the distance and masses of the heavenly bodies, thereby giving us a firm grasp not only of the dimensions of our own system, but of those scattered in the celestial spaces. To take the distances first. We must begin with the exact measure of the earth; for this we must measure the exact length of an arc of meridian or of parallel—that is, a stretch of the earth’s surface lying north and south or east and west, between places of which the latitudes are accurately known in the former case, and the longitude in the latter. In either case we can determine the number of miles which go to a degree. Beginning at the opening of the nineteenth century with an arc of meridian of two degrees measured by Gauss, from Göttingen to Altona, the arcs of meridian grew longer as the century grew older, till, at the close, the measurement of an arc of meridian from the Cape to Cairo, embracing something like sixty-eight degrees of latitude, was mooted. The measurements of arcs of parallel have been developed by the rapid extension of telegraphic communications, which now permit the longitude of the terminal stations to be determined with the greatest accuracy. Thanks to this work, we now have the size of our planet to a few miles. The polar diameter is 41,709,790 feet, but the equator is not a circle: the equatorial diameter from longitude 8 degrees 15 minutes west to longitude 188 degrees 15 minutes west is 41,853,258 feet; that at right angles to it is 41,850,210 feet—that is, some thousand yards shorter. The earth, then, is shaped like an orange slightly squeezed. Knowing the earth’s diameter, we can obtain the sun’s distance by several methods, the old one by observing transits of Venus, one of which Cook went out to observe in 1768, and two of which recurred in 1874 and 1882; new ones by observations of Mars or one of the minor planets at a favorable opposition, and by determining the velocity of light.