TRANSIT AND STADIA WORK, 
45 
tion necessary to reduce them to the standard. Thus the comparison 
maybe considered as determining the stadia factor, or the amount by 
which each stadia distance should be corrected in order to reduce it 
to a true measurement. 
It appears from the table that in a distance of 33,219 feet the stadia 
measurement was 33,103 feet, or a difference of L16 feet, which cor- 
responds to 1 in 286 ; this correction to be added to the stadia results. 
It might be argued that it would be preferable to obtain the stadia 
factor by direct comparison with the computed Lengths of the lines in 
sections 1, 2, and 3; and so it would if the rods were to be used for 
other purposes, but for the present purpose, which is to make a com 
parison between the computed distances and the direct stadia meas- 
urements, the other method is adopted. 
Table showing discrepancies between stadia distances corrected for stadia factor 
and computed distances. 
Section. 
Stations. 
Stadia dis- 
tance 
reduced to 
mean 
sea level. 
Correc- 
tion for 
stadia 
factor, 1 
in 286. 
Corrected 
stadia 
distance. 
( Iqmputed 
distance. 
Discrep- 
ancy; add 
distance. 
I >iscrepancy. 
1 
2 
3. 
0-154 
154-800 
800-949 
Feet. 
62, 061 
227, 967 
49, 119 
Feet. 
+217 
+797 
+172 
Feet. 
62, 278 
228, 764 
49, 291 
62,276 
228, 734 
49, 190 
i: ■ / 
o 
— 30 
— 101 
1 in 31, 139 
1 in 
1 m I8*j 
A combination of the figures in the foregoing table indicates thai 
in a total distance of 340,200 feet, or about 65 miles, there was an 
apparent error of 133 feet, or 1 in about 2,565. It Mould not , of course, 
be proper to claim any such accuracy for the stadia work, and in 
fact the figures themselves do not justify such a claim, as the range 
between them is too great to admit of any general deduction from the 
three combined results. For the purposes of this discussion it would 
have been better if the line could have been divided into more numer- 
ous sections and if more than one comparison for the determination 
of the stadia factor could have been made. 
A second condition is represented by the supposition that the rods 
were originally accurately subdivided so as to read to feet, tenths, 
and hundredths and that the stadia wires were at a fixed interval of 
1 to 100. A correction inherent to this condition, from the theory of 
stadia measurement, is that of /+ c, f corresponding to the distance 
from the plane of the cross wires to the objective, and c being the 
distance from the center of the instrumen I to the objective. In order 
to obtain a correct distance. the measurem mi i should, then, be from a 
point which is/+c, or, in the instrument used, 0.95 feet, ahead of 
the center of the transit. In other words, this amount should be 
added to the distance obtained at each transit station. 
