MEASUREMENT OF ANGLES. 



This mode of sighting is far from giving the same degree of 

 accuracy as the use of verniers. With a circle 16 centimetres in 

 diameter it is difficult to sight to less than i'; this is about the case 

 with Gambey's dip circle. In the same conditions a vernier would 

 give 5". 



A very ingenious arrangement has been used by MM. Brunner 

 for dip circles. The vertical divided circle is movable about an axis 

 which coincides with that of the needle, and carries a small concave 

 mirror, the centre of curvature of which describes the same circum- 

 ference as the end of the needle. When the point of the needle is 

 near the centre of curvature of the mirror, a reversed image is 

 produced in the same plane as the needle itself, and the adjust- 

 ment consists in bringing these two images in the prolongation of 

 each other. It is easy to estimate the degree of accuracy of which 

 this method is capable. If the diameter of the mirror is i'6 cm., its 

 angle of penetration is 10", which, for a curvature of 5 centimetres, 



Fig. 128. 



corresponds to an absolute length of 0*0025 mm. ; the approxi- 

 mation is virtually the same as with the verniers. 



662. MIRROR METHOD. In order to improve the mode of 

 measuring rotations, PoggendorrT* conceived the ingenious idea of 

 attaching to the movable body itself a mirror by which the displace- 

 ment of the image of an external body is observed. This method 

 came rapidly into general use in consequence of the beautiful 

 researches of Gauss and Weber. 



Let us suppose that the movable part turns about a vertical axis, 

 and carries a plane mirror passing through the axis. 



Let M be the mirror (Fig. 128), MN the direction of the per- 

 pendicular at its centre, when the movable system is in equilibrium, 

 or in that position which is taken as the initial one, and CC'DD' 

 the vertical plane through "this normal and the axis of rotation. A 



* POGGENDORFF. Pogg. Ann., Vol. VII., p. 121. 1826. 



