The vertical inclination of the telescope and the consequent aberration of the ray, was then measured by a graduated arc, with an adjusting spirit-level, moved by a rack and pinion. The accompanying figure (fig. 78) shews the arrangement just described. E is the small flame in the focus; ABC is the zone; TT is the telescope; and R a graduated limb, on which is read the angular deviation θ of the axis of the telescope from the horizon. In the figure, the ray emergent from the centre of AC is shewn dipping below the _true level_, to which the line TC is supposed to be parallel. I have succeeded by this method in detecting the inaccurate position of some of the zones in the frame; and the error has been reduced by carefully resetting them, so as to diminish considerably the error of a great proportion of the emergent rays. Another mode, and that which, owing to its convenience, was chiefly employed in preference to that just described, was to measure the vertical inclination (given in the Table in the Appendix), of each surface of the zone, and more especially the reflecting surface, by means of the instrument, shewn in figures 79 and 80, after the zones were fixed in their place. The figure (No. 79) shews the mode of gauging the reflecting side AB of a zone of the upper series; and the second (No. 80) shews the position of the instrument in gauging the reflecting side AB of a zone of the under series. In those figures, L is a spirit-level; R, a graduated limb for reading the angular deviation from the true inclination of the tangents to each surface; and SS are studs which rest on the convex surfaces AB and BC of the zones, so as to make the ruler parallel to the tangents of those sides. I have only to add, that I have restricted the error, in the position of the reflecting side of the zones, to 50′ as an extreme limit; and I have invariably endeavoured, in altering the position of the zone in the frame, to throw any error on the side of safety, by causing the rays to _dip_ below the horizon, rather than to rise above it.[70] [Illustration: Fig. 79.] [Illustration: Fig. 80.] [70] In connection with the use of the clinometer, I determined the inclinations of the tangents or chords of the three curve surfaces AB, BC, and AC of each zone with NP, the axis of the system, by means of the obvious relations of the known angles about C, A, and B. Those inclinations (fig. 81) are shewn by the angles BNO, BON, and CPF; and are given in the Table of the Zones in the Appendix. [Illustration: Fig. 81.] ~Framing of Zones.~