opened: Ceres, the first asteroid, was found on the first day of the nineteenth century. Bode's law, therefore, appeared to have found confirmation here, for, though there was no single great planet, as elsewhere, nevertheless the small army of fragments seemed to point to some abortive attempt of Nature to form a world in the usual order, or else to an explosion of one already formed. In either case the distance of the 'mean asteroid' might be expected to follow the law, which it was found approximately to do. It seems a pity that the law, having survived so many tests, should go to pieces at last on what was perhaps the final test which remained to be applied. When Neptune was discovered, however, in 1846, it did not conform to the law at all. The following table gives a comparison between the true distances and those which result from Bode's law, the distance of the earth being taken as unity:
| Planet. | Distance. | Bode. | Difference. | Period. | ||||
| Mercury | 0 | .39 | 0 | .4 | -0 | .01 | 3 | months. |
| Venus | 0 | .72 | 0 | .7 | +0 | .02 | 7 | .4" |
| Earth | 1 | .00 | 1 | .0 | 0 | .00 | 1 | .0 years. |
| Mars | 1 | .52 | 1 | .6 | -0 | .08 | 1 | .9" |
| Mean Asteroid | 2 | .65 | 2 | .8 | -1 | .15 | .... | |
| Jupiter | 5 | .20 | 5 | .2 | 0 | .00 | 11 | .9 years. |
| Saturn | 9 | .54 | 10 | .0 | -0 | .46 | 29 | .5" |
| Uranus | 19 | .18 | 19 | .6 | -0 | .42 | 84 | .0" |
| Neptune | 30 | .05 | 38 | .8 | -8 | .75 | 164 | .8" |
The discovery of asteroids has been much simplified by the increase of star maps, and especially by the advances in celestial photography. One feature, which is incidental to the duration of the photographic exposure, renders the detection of such objects comparatively easy. When a photographic plate is exposed to the sky in a camera or telescope, if there is no clockwork, so that the instrument remains at rest, the images of the stars are drawn out into lines or trails. Ordinarily, however, the instrument is kept in motion by a driving clock, so that it exactly follows the stars in their apparent daily motion, and the images of the stars result as circular dots on the plate. An asteroid, however, from its nearness has so rapid an apparent motion among the stars that, if an exposure is made of an hour or more, its image is spread out in a line, while the images of stars remain circular. On some of the plates, for example, made with the great Bruce photographic telescope at Arequipa, several hundred thousand stars appear. On one of these plates, which had an exposure of four hours, seven asteroid trails were found. If these asteroids had formed circular images, similar to those of the stars, their detection among the several hundred thousand images on the plate would have been an enormous labor and would have required other
