126 Mr. F. L. 0. Wadsworth on a 



to the optical axis of the telescope T. These two adjust- 

 ments are made simultaneously in the same manner as 

 described in a previous article*; i. e. by bringing the reflected 

 image of the cross-wires into coincidence with the wires 

 themselves, revolving the mirror through 180° and correcting 

 one-half of the resulting vertical displacement by means of the 

 adjusting screws b, b, b, against the heads of which the mirror 

 rests, and the other half by means of the screw e, which forms 

 part of the geometrical clamp E. The level is then adjusted 

 until it is perpendicular to the axis of rotation by means of 

 the screws /, /, in the usual manner. 



Lastly, the telescope is set at the height of the object to be 

 measured and clamped in position, and the axis C adjusted to 

 vertically by the screws I and H (or the levelling-screws in 

 the base of this support) , the level being placed first parallel 

 to the telescope-tube and then at right angles to itf . The first 

 of these adjustments is made once for all ; the second is tested 

 at the beginning of each day's work; and the third only is 

 necessary at each setting of the telescope. 



It is important to notice that a small error in levelling has 

 the same effect in this new form as in the ordinary form ; L e. 

 the error is not doubled by reflexion from the mirror, because 

 the telescope and the latter move together, so far as any move- 

 ment in a vertical plane is concerned. Let us consider the 

 effect of a small error in levelling, first, in the vertical plane 

 parallel to the axis of the telescope ; second, in the vertical 

 plane at right angles to that axis. Let 6 be the angle which 

 the line of sight to the object makes with the first plane con- 

 sidered, and a the angle which the axis of rotation c makes 

 with the vertical in that plane. Then, if e denote the difference 

 in reading produced by this inclination from the vertical, and 

 r the distance of the object from the axis of rotation, we have 

 evidently 



e=rsin «cos# ; 



for the difference produced by an inclination a in a plane 

 at right angles to this 



* " A Simple Method of Determining the Eccentricity of a Graduated 

 Circle with only one vernier," F. L. O. Wadsworth, Amer. Journ. of 

 Sci., May 1894, vol. xlvii. p. 373. 



t The mounting shown in figs. 1 and 2 is especiallv convenient in per- 

 forming this last operation, as the screws H, I, and the third pivot-point 

 bear respectively in a slot, plane, and conical hole at the three vertices of 

 a right-angled triangle, and the motion of either screw, therefore, affects 

 the position of the axis C only in the vertical plane passing through that 

 screw and the pivot-point. 



