Wadsworth — Simple and Accurate Cathetometer. 43 



previous article in this Journal,* i. e. by bringing the reflected 

 image of the cross wires into coincidence with the wires them- 

 selves, revolving the mirror through 180° and correcting one- 

 half of the resulting vertical displacement by means of the 

 adjusting screws h, &, 5, against the heads of which the mirror 

 rests, and the other half by means of the screw 6, 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 f,f, in the usual manner. 



Last 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 leveling screws in 

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

 to the telescope tube and then at right angles to it.f 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 leveling has 

 the same effect in this new form as in the ordinary form, i. e. 

 the error is not doubled by reflection 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 leveling, first in the vertical plane 

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

 at right angles to that axis. Let d be the angle which the line 

 of sight to the object makes with the first plane considered 

 and a the angle which the axis of rotation c makes with the 

 vertical in that plane. Then if e denote the difference in read- 

 ing produced by this inclination from the vertical, and r the 

 distance of the object from the axis of rotation, we have evi- 

 dently 



€ = r sin a cos 6 



and for the difference produced by an inclination a in a plane 

 at right angles to this 



e'= r sin a sin 6 



and for the corresponding errors in comparison of object and 



scale 



A =z £ — s / = r sin a (cos 6— cos 6 x ) (1) 



A' = e' — sj = r sin a:'(sin0— sin dj (2) 



* A Simple Method of Determining the Eccentricity of a Graduated Circle with 

 only one vernier, F. L. 0. Wadsworth, this Journal, May, 1894, vol. xlvii, p. 3T3. 



t The mounting shown in figs. I and 2 is especially convenient in performing 

 this last operatiou, as the screws H, 1, and ihe 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. 



