Nor are the difficulties encountered by the meridian observer due solely to his instrument. He has to contend against his own imperfections; he has often to allow for personal peculiarities of an unexpected nature; the troubles that the atmosphere can give are notorious; while the levelling of his instrument warns him that he cannot even rely on the solid earth itself. We learn that the earthquakes, by which the solid ground is sometimes disturbed, are merely the more conspicuous instances of incessant small movements in the earth which every night in the year derange the delicate adjustment of the instrument. When the existence of these errors has been recognised, the first great step has been taken. By an alliance between the astronomer and the mathematician it is possible to measure the discrepancies between the actual meridian circle and the instrument that is ideally perfect. Once this has been done, we can estimate the effect which the irregularities produce on the observations, and finally, we succeed in purging the observations from the grosser errors by which they are contaminated. We thus obtain results which are not indeed mathematically accurate, but are nevertheless close approximations to those which would be obtained by a perfect observer using an ideal instrument of geometrical accuracy, standing on an earth of absolute rigidity, and viewing the heavens without the intervention of the atmosphere. In addition to instruments like those already indicated, astronomers have other means of following the motions of the heavenly bodies. Within the last fifteen years photography has commenced to play an important part in practical astronomy. This beautiful art can be utilised for representing many objects in the heavens by more faithful pictures than the pencil of even the most skilful draughtsman can produce. Photography is also applicable for making charts of any region in the sky which it is desired to examine. When repeated pictures of the same region are made from time to time, their comparison gives the means of ascertaining whether any star has moved during the interval. The amount and direction of this motion may be ascertained by a delicate measuring apparatus under which the photographic plate is placed. If a refracting telescope is to be used for taking celestial photographs, the lenses of the object-glass must be specially designed for this purpose. The rays of light which imprint an image on the prepared plate are not exactly the same as those which are chiefly concerned in the production of the image on the retina of the human eye. A reflecting mirror, however, brings all the rays, both those which are chemically active and those which are solely visual, to one and the same focus. The same reflecting instrument may therefore be used either for looking at the heavens or for taking pictures on a photographic plate which has been substituted for the observer's eye.