40 



a value of a single revolution, as to cause the horizontal cross-line of the telescope 

 to move over a space of jjg of a foot, placed at a distance of 100 feet, when the 

 screw is turned through one of the smallest spaces on its graduated head ; and 

 since there are fifty such spaces on the head, it follows that one revolution of the 

 screw is equivalent to ^ ot a foot, at a distance of 100 feet. The numbered gradua- 

 tions on the screw head are then, each equivalent to ^ of. a foot in 100 feet ; and two 

 entire revolutions of the screw would be twice ^, or 1 foot to the 100. It is readily 

 seen that grades can be established with great rapidity with this screw. It is only 

 necessary after setting the gradienter screw to zero, and leveling and clamping the 

 telescope, to move it up or Sown as many spaces of the head of the gradienter screw 

 as there are hundredths of feet to the hundred, in the grade to be established. 

 Thus, to establish a grade of 1 * 85, the screw head is turned through three whole 

 spares of the scale, wnich corresponds to l. ft 50,, and through three of the numbered 

 divisions:, and five of the shortest ones to make up the entire reading of 1 ." 85. 



For measuring distances this screw takes the place of stadia lines, and is more 

 convenient ; since for any approximately horizontal distance, the space on an ordi- 

 nary leveling rod expressed in hundredths of feet, included in two revolutions of 

 the screw, will be the number of feet the level rod is distant from the center of the 

 instrument. Th'us the difference between two readings of the level rod was 2" . 965 

 when the telescope was moved in altitude through two revolutions of the screw. 

 The rod therefore was distant 296.5 feet. 



It is unnecessary even that a leveling rod be used. A ranging pole or walking 

 stick, or any arbitrary length which can afterwards be measured, will suffice. Thus 

 n stick, which was afterwards measured and found to be 3". 38 long, was found to 

 be subtended by 3^ revolutions of the screw at an unknown distance. 



In this case the distance was 



- 

 1 . 58 



In case, however, the distance to be measured is not approximately in the same 

 level plane with the transit telescope, it is necessary to compute the distance, from 

 the readings of the rod. In taking such readings at an altitude, it is customary to 

 incline the rod towards the telescope, and by trial find the least space subtended by 

 two stadia lines. A skilful rod-man will plumb a rod more readily than he can 

 incline it at the proper angle, and a reading of the plumb rod can be taken with 

 greater accuracy, and in less time than with the inclined rod ; but it ordinarily 

 involves some additional computing to reduce such vertical readings to horizontal 

 distances. With the view of reducing the computation to a simple multiplication, 

 the following table is appended with the trignometrical argument on which it 

 depends. The engineer will notice the solution is not rigorously exact, but is suf- 

 ficiently so for all cases in practice. 



