The clamping arm of the gradienter, described in connection 

 with the alidades on page 57, however, is short enough so that 

 the pitch of the thread can be cut 1:100 and the drum divided into 

 100 parts. Some transit instruments have been constructed with 

 half length tangent clamps for the purpose just explained, but the 

 plan is neither necessary nor desirable. 



ADJUSTMENT 



The gradienter drum is held in any required initial position 

 by a circular spring and clamping nut. If it is desired to begin 

 with the zero at the index for any particular position of the telescope, 

 grasp the knurled head with one hand, so that the screw may not 

 turn, and revolve the graduated drum on the shank until the desired 

 relationship has been secured. 



To measure distances with the gradienter, level the tele- 

 scope, set the index to zero as above and turn a certain number of 

 revolutions, up or down, until the central cross wire strikes the 

 rod. Turn two more revolutions and read the intercept for use in 

 the subsequent calculation. 



Let UG be perpendicular to TR and let LG be perpendicular 

 to TG. Let(n 1) revolutions equal a and let the angular value of 

 the last revolution be equal to b. Then 



UGR a + b and cos (a + b) GU -*- GR 



LGR = GTF a 



LRG = 90 (a + b) and RLG =c 90 + b, but 



LG : RG : : sin LRG : sin RLG, then 

 LG _ ( (os a cos b ) - - ( sin a sin b ) 

 RG cosb 



GL = GR cos a (sin a tan b) 

 Dist. TG =100 GL 



= 100 GR cos a (sin a tan b) 



T /"* 1 



tanb = TG == Yoo ;8ubstituting ' 

 Dist. TG GR (100 cos a sin a) 

 Dist. TF = TG cos a 



= GR (100 to* 2 a Y* sin 2a) 



If a were an angle of depression, the vertical angle should be 

 measured to the upper leg of the nth revolution. The angle b, 

 representing 1 double revolution of the screw, is 34' 23". 



To obtain the vertical coordinate, FG, let KG = H.I. Meas- 

 ure one more complete revolution of the gradienter above G, then, 

 Dist. FG - - GR (100 cos a sin a sin-a), 



One of the principal objections with reference to the accuracy 

 of the gradienter is the conceivable lost motion, or back lash, in the 

 screw incident to continued wear. Our screw shanks are of German 

 silver operating in a bronze encasement. While the pitch of the 

 thread remains unaltered, the Deration of the screw, ought to be 

 accurate. To take up lost motion we provide a set screw, as shown 



