Sidereal science is, on its geometrical side, of modern development; on its physical side, of modern origin. The places of the stars, as referred to certain lines and points on the surface of an imaginary hollow sphere, are obtained now on essentially the same principles as by Hipparchus, only with incomparably greater refinement. And refinement is everything where the stars are concerned. Significant changes among them can only be brought out by minute accuracy. To a rough discernment their relative situations are immutable; and systematic inquiries into their movements hence became possible only when the grosser errors were banished from observation. Bessel's discovery of Bradley's exactitude gave the signal for such inquiries. It became worth while to re-observe stars already so well determined that discrepancies might safely be interpreted to mean real change.

Thus it is only within the last sixty or seventy years that the stars have been extensively catalogued for their own sakes, and no longer in the undivided interests of planetary or cometary astronomy. The scope of such labours now widens continually. For the objects of them are all but innumerable, and the nineteenth century has brought to bear on its large schemes of scientific ambition heretofore undreamt-of facilities for executing them by combination.