THE goniometer-as the instrument used for the measurement of the interfacial angles of crystals is called-has gradually developed from a simple and crude piece of apparatus to a refined and somewhat complex optical instrument, and the measurements made with it have become increasingly more accurate as the form improved, while on the other hand the methods of investigating the morphological characters of crystals have on the whole become simpler. Nicolaus Steno, who (in 1669) was the first to study the angles between the plane surfaces of crystals, laboriously determined them by slicing the crystals perpendicular to the edges bounding the faces in question, and outlining the sections on paper. The first instrument used for the purpose of measuring the interfacial angles is that known as the contact-goniometer, and was devised by Carangeot in 1783; it is used to this day for measuring large rough crystals. This type consists essentially of two arms, one movable with respect to the other, which are laid on the faces in question at right angles to their common edge; the position on a graduated scale of the end of the movable arm beyond the pivot gives the angle required. A cheap form of this type made in cardboard or celluloid was designed by S. L. Pen-field in 1900. Accuracy to single degrees of arc is the utmost that can under the most favourable conditions be expected of the contact-goniometer. To the ingenuity of W. H. Wollaston, in 1809, is due the reflective form of goniometer. In this type the common edge of the pair of faces under measurement is set in line with the axis of a rotatable graduated circle, and the position of the circle is read when some distant signal is reflected by the particular face in a predetermined direction; the circle is rotated, and the reading taken corresponding to the second face. The difference betwen the pair of readings gives the interfacial angle required. In the original form the graduated circle was vertical, and no means existed for fixing accurately the direction of reference. In a goniometer described shortly afterwards, in 1810, by E. L. Malus, a telescope of low power was used for receiving the reflections, and assuring, therefore, the constancy of the direction of reference, and in 1839 J. Babinet designed an instrument with a horizontal circle. E. Mitscherlich introduced many improvements and accessories in 1843; ne added a colli-mator in place of a distant signal, and his screw arrangements for centring and adjusting the crystal are in principle the same as those generally used now. The horizontal-circle form of goniometer is extensively used at the present day, and the optical features and accessories have been brought to a high standard of perfection by the well-known firm of R. Fuess, of Berlin, who have devoted considerable attention to crystallo-graphical instruments. Spider-lines were first used in the collimator, and afterwards the ordinary spectroscope-slit, but neither are satisfactory for goniometer work owing to the diffusion of the image on reflection at the tin.y faces such as often occur on crystals. The difficulty was investigated by C. F. M. Websky, and in 1878 he described a slit, the jaws of which consisted of coplanar circular discs in contact, or nearly so, at the middle. This slit allows plenty of light to pass at the top and bottom, and the constriction at the centre admits of refined readings. In its original form, or slightly modified, this slit is universally used in modern goniometers. For the purpose of viewing the crystal while in position and determining what face gives a particular reflection, the telescope is usually supplied with a lens which is applied in front of either the objective or the eyepiece for converting it into a microscope of low power. In a well-made instrument, if the crystal reflections admit, readings may be made to 30 minutes of arc.