PHYSICAL AND MATHEMATICAL SCIENCES. 73
in modern Europe until a comparatively late period,and was obstinately retained as long as the increasinglight of inductive truth still left a dark nook where itspartisans could find refuge in congenial obscurity.
Of the instruments commonly employed by the an-cient astronomers, the gnomon was at once the simplest,and probably the most accurate for its purpose. Besidesthis, we find them, especially in these later ages, usingastrolabes, and armillary spheres of various constructions,which being fixed with their circles in the actual posi-tions of the real sphere, the equinoxes were observed bythe coincidence of the plane of the circle representingthe equator with its own shadow. Altitudes were mea-sured by a circle in the plane of the meridian, and theshadow of a small projecting piece at the extremity ofa revolving diameter, made to fall exactly on a corre-sponding projection at its other extremity. Ptolemy him-self contrived a quadrant with a similar apparatus. Healso used an instrument of a similar principle, but ofwhich all the parts were rectilinear: he thus measuredthe chord of the angle observed; and found the angleby a table of chords. The great defect in all theseinstruments was that want of certainty in fixing uponthe precise position of any celestial object, which couldnot be remedied without a knowledge of the telescope.Their graduation also, probably, was but of a very in-ferior degree of accuracy. Another fundamental defi-ciency in their observatories was in the accurate meansof measuring time. The clepsydra was open to manifestobjection. Upon the whole, it is rather matter of asto-nishment that, in the department of actual observation,the ancients should have done so much, considering thelimited means at their command, than that they shouldnot have effected more.