NOTE.—In dealing with optical formulæ look out for the algebraic signs. Writers vary in their conventions regarding them and it sometimes is as difficult to learn how to apply a formula as to derive it from the start. Also, especially in optical patents, look out for camouflage, as omitting to specify an optical constant, giving examples involving glasses not produced by any manufacturer, and even specifying curves leading to absurd properties. It is a good idea to check up the achromatization and focal length before getting too trustful of a numerical design. CHAPTER V MOUNTINGS A steady and convenient mounting is just as necessary to the successful use of the telescope as is a good objective. No satisfactory observations for any purpose can be made with a telescope unsteadily mounted and not provided with adjustments enabling it to be moved smoothly and easily in following a celestial object. Broadly, telescope mounts may be divided into two general classes, alt-azimuth and equatorial. The former class is, as its name suggests, arranged to be turned in azimuth about a vertical axis, and in altitude about a horizontal axis. Such a mounting may be made of extreme simplicity, but obviously it requires two motions in order to follow up any object in the field, for the apparent motion of the heavenly bodies is in circles about the celestial pole as an axis, and consequently inclined from the vertical by the latitude of the place of observation. Pointing a telescope with motions about a vertical and horizontal axis only, therefore means that, as a star moves in its apparent path, it will drift away from the telescope both in azimuth and in altitude, and require to be followed by a double motion. Alt-azimuth mounts may be divided into three general groups according to their construction. The first and simplest of them is the pillar-and-claw stand shown in Figure 69. This consists of a vertical pillar supported on a strong tripod, usually of brass or iron, and provided at its top with a long conical bearing carrying at its upper extremity a hinged joint, bearing a bar to which the telescope is screwed as shown in the illustration. If properly made the upper joint comprises a circular plate carrying the bar and held between two cheek pieces with means for taking up wear, and providing just enough friction to permit of easy adjustment of the telescope, which can be swung in altitude from near the zenith to the horizon or below, and turned around its vertical axis in any direction. When well made a stand of this kind is steady and smooth working, readily capable of carrying a telescope up to about 3 inches aperture. It needs for its proper use a firm sub-support for the three strong hinged legs of the pillar. This is conveniently made as a very solid stool with spreading legs, or a plank of sufficient size may be firmly bolted to a well set post. [Illustration: FIG. 69.—Table Mount with Slow Motion.]