ON DRAWING, WRITING AND MEASURING. 81 



being fixed on the revolving plate of the engine, its arc is made to advance 

 under the cutting tool by very minute steps, regulated by the turns of a 

 screw, of which each revolution is divided into a considerable number of 

 equal parts. The largest and finest instruments are, however, still usually 

 divided by hand ; that is, by means of compasses. Some artists have first 

 divided a straight plate, and then made a hoop of it, which has served as 

 a standard for further processes. An arc of 7 10', of which the chord is 

 one-eighth of the radius, may be employed as a test of the accuracy of the 

 work. A micrometer screw is often used in large instruments as a substi- 

 tute for the minutest divisions ; * a moveable part of the index being 

 brought to coincide with the nearest point marked in the arc, by turning 

 the screw through a part of its revolution, which is measured by means of 

 a graduated circle. But a simpler method of reading off divisions with 

 accuracy in common instruments, is the application of a vernier, an appa- 

 ratus so called from its inventor. The space occupied by eleven divisions 

 of the scale being divided into ten parts on the index, the coincidence of 

 any of the divisions of the index with those of the scale, shows, by its 

 distance from the end, the number of tenths that are to be added to that of 

 the entire divisions. (Plate VII. Fig. 92.) 



There are several ways of measuring the angular elevation of an object 

 above the horizon ; at sea, the apparent horizon, formed by the surface 

 of the water, affords the most convenient determination ; but since the 

 spectator is somewhat elevated above the convex surface of the sea, the 

 apparent horizon is necessarily lower than the true horizon, and a correc- 

 tion is therefore required according to the height. In the open sea this 

 correction may be determined by measuring the whole angle above and 

 below the apparent horizon [respectively], and taking one fourth of the 

 difference for the dip or depression. On shore,- a plumb line is the simplest 

 instrument for determining the situation of the horizon, and its accidental 

 vibrations may be prevented by suspending the weight in water or in oil. 

 For small instruments, a spirit level, of which the operation depends on 

 hydrostatical principles, is capable of greater delicacy than a plumb line. 

 It readily indicates, when well made, an error of a single second ; but it 

 requires some attention to avoid inequalities of temperature, which would 

 tend to disturb its figure. Well rectified ether is found, on account of its 

 perfect fluidity, to be the best liquid for a spirit level. An artificial hori- 

 zon is a reflecting surface employed for obtaining an image as much below 

 the horizon as the object is above it, and for measuring the angular dis- 

 tance of this image from the object: sometimes a plane speculum of glass 

 or metal is used for this purpose, being previously adjusted by a spirit 

 level ; and sometimes the surface of mercury, treacle, or tar, protected from 

 the wind by a vessel with holes in it, or by a glass cover, either detached, or 

 simply floating on the mercury, when this liquid is employed. 



It is in many cases simpler and more convenient to estimate angles, not 

 by the arcs subtending them, but by their sines, or the perpendiculars 

 falling from one leg on the other. Thus, it is usual among miners, to say 



* Hooke's Lectures, Lambert iiber die Branderschen micrometer, 12 Aug. 1769. 

 Hornblower, in Nich. Jour. vi. 247. 



