been done. [Illustration: FIG. 110.—Crystals of Iceland Spar showing, A A´, the optic axis. ] It is obvious that a Barlow lens, cut in the same manner as the object-glass of the heliometer, will answer the same purpose; the two halves are of course moved in just the same manner as the halves of the divided object-glass. Mr. Browning has constructed micrometers on this principle. [Illustration: FIG. 111.—Double Image Micrometer. FIG. _a_, _p q_, single image formed by object-glass. FIG. _b_, _p_{1} q_{1}_, _p_{2} q_{2}_, images separated by the double refracting prism. FIG. _c_, same, separated less, by the motion of the prism. ] There is yet another double-image micrometer depending on the power of a prism to alter the direction of rays of light. It is constructed by making two very weak prisms, _i.e._, having their sides very nearly parallel, and cutting them to a circular shape; these are mounted in a frame one over the other with power to turn one round, so that in one position they both act in the same direction, and in the opposite one they neutralise each other; these are carried by radial arms, and are placed either in front of the object-glass or at such a distance from it inside the telescope that they intercept one half of the light, and the remaining portion goes to form the usual image, while the other is altered in its course by the prism and forms another image, and this alteration depends on the position of the movable prism. ----- Footnote 10: Grant’s _History of Physical Astronomy_, p. 454. Footnote 11: More accurately the time of transit is to be multiplied by the cosine of the star’s declination. Footnote 12: So called because the contrivance was first used to measure the diameter of the sun. BOOK IV. _MODERN MERIDIONAL OBSERVATIONS._ CHAPTER XVI. THE TRANSIT CIRCLE. We are now, then, in full possession of the stock-in-trade of the modern astronomer—the telescope, the clock, and the circle,—and we have first to deal with what is termed astronomy of position, that branch of the subject which enables us to determine the exact position of the heavenly bodies in the celestial sphere at any instant of time. Before, however, we proceed with modern methods, it will be well, on the principle of _reculer pour mieux sauter_, to refer back to the old ones in order that we can the better see how the modern instruments are arranged for doing the work which Tycho, for instance, had to do, and which he accomplished by means of the instruments of which we have already spoken. First of all let us refer to the Mural Quadrant, in which we have the germ of a great deal of modern work, its direct descendant being the Transit Circle of the present time.