44 
SURVEY OF IDAHO-MONTANA BOUNDARY LINE. 
[BULL. 170. 
supposition that the rods were graduated arbitrarily into regular 
divisions, which were sufficiently small to admit of reading distances 
approximately to a foot, and that the stadia wires were set at some 
fixed interval. The fact that the rods were actually graduated so as 
to be read, as nearly as might be, to feet, tenths, and hundredths, 
and that the wire interval was approximate in the ratio of 1 to 100, 
does not enter at all into the theory of this condition. In fact the 
rod might be graduated in any systematic manner and the wires 
placed at any fixed interval without affecting the results after the 
proper corrections had been applied. An analogous case would be 
one in which certain distances were measured with a chain or tape the 
exact-length of which was not known at the time the measurement 
was made but which was afterwards determined and the correction 
applied. The tape might prove to be 99 feet in length, but this would 
not affect the ultimate results after proper allowance had been 
made. The fourth section of the boundary line furnished a means 
by which the relation between the distances determined by the stadia 
and careful measurements with a steel tape, in other words, the stadia 
factor, might be ascertained. 
Table of comparisons of stadia and steel-tape measurements from transit station 
949 (post S) to the international boundary (post 0), section 4. 
Location. 
Station 949 
Post? 
Post 6 
Post 5 
Post 4 
Post 3 
Post 2 
Post 1 
PostO 
Steel tape. 
Feet 

4,618.6 
8,606 
13,760.5 
18,148.3 
23, 596. 2 
27, 153 
31,106 
33, 219 
Stadia. 
Difference. 
Feet. 
Feet. 


4,601.5 
17.1 
8,572 
34 
13, 698 
62. 5 
18,077 
71.3 
23,512 
84.2 
27,062.5 
90. 5 
31,000 
106 
33, 103 
116 
Discrepancy. 
1 in 270 
1 in 253 
1 in 220 
1 in 254 
1 in 280 
1 in 300 
1 in 293 
1 in 286 
Au inspection of the foregoing table will develop the fact that the 
ratio existing between the results from the steel-tape and the stadia 
measurements is fairly constant. The steel-tape measurements were 
carefully made with a 100-foot steel tape, under conditions approxi- 
mating those under which the other portions of the line were meas- 
ured independently by the stadia, except that the surface was probably 
not so broken and the change of elevation not so great, thus favoring 
the accuracy of the tape measurement. The steel tape was after- 
wards compared with the United States Coast and Geodetic Survey 
standard, and the values in the table are affected by a small correc- 
