Stadia Rods have !> i-d in extensive variety. While 



no one pattern may be best suited to all classes of work, the saw- 

 tooth or diamond point designs ha 1 , e b-rn widely adopted so that 

 fractional readings can be made by estimating the position of the 

 wire against a diagonal line. Simplicity rather than multiplicity 

 is the chief requisite. Ideal conditions provide for an unchange- 

 able wire interval of exactly 1:100 and a rod that will answer for 

 stadia work as well as for leveling. 



Beaman Stadia Arc 



This device was designed by W. M. Beaman, U. S. G. S., for 

 the mechanical indication of those angles which are simple multiples 

 of the differences in elevation, expressed in rod intervals. Mr. 

 Saegmuller made the first model for Mr. Beaman in Washington 

 in June, 1904, to carry out the rapid instrumental execution of the 

 "Stepping Method". 



The first stadia interval above the horizon, as in field B, Fig. 64, 

 has an angular value of 1:100, or 34' 23". As the gradient becomes 

 more precipitous and the number of intervals increase, the angular 

 value of the interval increases as the cord of the stadia angle, or %, 

 sin 2^, as previously deduced, so that when the tenth interval is 

 reached, for instance, the value of that interval is 35' 01" and the 

 total angle is 5 46' 07" instead of 10 X 34' 23". 



In this manner we may graduate a supplementary arc, known 

 as the V-scale, in which the spaces gradually increase both sides of 

 a center line, arbitrarily nvimbered 50, so that the notes will show, 

 beyond doubt, whether the vertical angle was one of elevation or 

 depression. V 42, for instance, would be an 8-interval angle of 

 depression while V 58 would be an 8-interval angle of elevation. 



To Utilize the V-Scale for determining elevations, turn the 

 telescope up or down until a full stadia interval can be measured on 

 the rod when the index coincides with some division on the V-scale. 

 Note the interval, also the position of the central wire as well as the 

 division indicated on the V-scale. 



l.-t it be assumed that the interval was 8.45, that the central 

 wire cut 6.30 above the peg and that the V-scale indicated 57. This 

 being an angle of elevation, the computation would be: 

 57 50 = 7 X 8.45 = 59.15 6.30 = 52.S5 

 which is the elevation of the peg above the H. 1. 



To test the accuracy of the V-scale, we append a table of 

 equivalent values. Set the principal arc, if an alidade, at 

 the Beaman Arc at 50. As we*make them, this will place the scales 

 in proper relative position. 



113 



