A mathematical proof admits of no doubts or contingencies. A man may calculate the force of the wind, but he cannot tell how long it will continue to blow in that direction, whether it will increase to a hurricane or subside to a calm. He may count the revolutions of an engine, but he cannot test its extreme power, or prove its continued {39} existence for a single hour. How many of the most important affairs of life can be demonstrated by means of the multiplication table? It would be safe to say not one in ten. Again, mathematics frequently deal with purely ideal figures, which never did or never can exist. There is not a mathematical line--length without breadth--in all the universe. On careful examination, we find that there are no mathematical figures in nature. We speak of the earth as a sphere, but it is a sphere pitted with hollows as deep as the ocean, and crested with protuberances as high as the Andes or Himalayas, in every conceivable irregularity of form. There is not an acre of absolutely level ground on the face of the earth; even its waters pile themselves up in waves, or dash into breakers, rather than remain perfectly level for a single hour. The microscope reveals the fact that the pearl is proportionally rougher than the surface of the earth, and the dew-drop is no nearer round than a pear. When we speak of the orbits of the planets as elliptical or circular, it is only in a general way; just as we speak of a circular saw, the outline of its teeth being regularity itself, as compared with the motions of the planets in their orbits. So also with _Astronomy_, it is far from being an exact science. From the comparative simplicity of the forces with which it has to deal, and the approximate regularity of the paths of the heavenly bodies, it may be regarded as the science in which the greatest possible certainty is attainable. {40} It opens, at once, the widest field to the imagination, and the noblest range to the reason; it has attracted the most exalted intellects to its pursuit, and has rewarded their toils with the grandest discoveries. Lest we should ascribe to the discoverers of the laws of the universe, the glory due to their Creator, let us glance at some of the errors of astronomy. Sir John Herschel, than whom none has a better right to speak on this subject, devotes a chapter to the "Errors of Astronomy." "No philosophical observation or experiment is absolutely accurate. The error of a thousandth part of an inch in an instrument, will multiply itself into thousands and millions of miles according to the distance of the object."