MEASURING THE EARTH'S SURFACE. 251 



any two directions in which the glass may be pointed. The glass may 

 be turned toward any point on the horizon, and also in an upward or 

 downward direction. The scale on the circle is read by means of two 

 microscopes, diametrically opposite to each other. Spirit-levels, mi- 

 crometric arrangements, etc., are provided, and the observer has to be 

 very careful about placing his instrument in the right position before 

 he can actually begin operations. Although the stations are not at 

 the same altitude, the angles between any two directions have to be 

 so measured as if the stations were all on the same level, on a per- 

 fect plane. This plane is supposed to be vertical to the earth's radius 

 which crosses that particular station — that is, a plane tangent to the 

 earth's circumference and perfectly horizontal. The movement of the 

 field-glass has, therefore, to be such that, although two stations may 

 be situated lower or higher, the angle between the two directions can 

 be read as if each of them had been raised or lowered vertically to 

 the level of the station from which the observations are being made. 

 The circle of the theodolite represents this horizontal plane ; its cen- 

 ter is supposed to be mathematically "the point," and the theodolite 

 has, therefore, to be so placed that the center of this circle is in a per- 

 fect perpendicular to the point, while the surface of the circle itself is 

 perfectly horizontal. The field-glass is situated on a support in the 

 form of a double column, and the central axis of this support is ver- 

 tical to the circle, and passes through its center. Delicate and exact 

 mechanical arrangements permit of the glass being turned toward all 

 points of the compass, and also of its being turned in an upward or 

 downward direction ; but each movement is either in a horizontal or 

 a vertical direction to the circle. This enables the observer to obtain 

 the angle desired — that is, the angle which any two directions would 

 give if all the stations were at the same level. 



The length of the sides of the triangles varies according to the 

 facilities for extending a good net which the ground offers. From 

 twelve miles upward is a suitable distance, the distance being in some 

 cases only limited by the visual power of the glass. 



The scale on the circle is divided into degrees, minutes, and possibly 

 seconds, the latter and their fractions being read with the microscope. 



The angles are measured as follows : When the theodolite is placed 

 in its exact position, and the circle is perfectly horizontal, the glass is 

 pointed successively at each of the surrounding stations, and for every 

 direction the scale on the circle is read and noted on the field-book. 

 Supposing the scale reads 56° IS' 12-075" when the glass is pointed 

 toward one station, and 115° 56' 18-850" when pointed in another di- 

 rection, the angle between the two directions is equal to the difference 

 between the two readings, which is in this case 59° 38' O'TTS". These 

 readings are repeated several times, the circle being every time moved 

 around its center in order not to have all the readings on the same 

 divisions of the scale. "When a complete set of observations has been 



