134 
KIRTLEY F. MATHER 
through 200, 300, etc., divisions, reading the arc at each hun- 
dred until the screw has reached the farther limit of its play. 
Usually 9 or 10 hundred divisions will suffice. Repeat the opera- 
tion at least five times and take the average value in minutes 
for each hundred divisions. Determine the corresponding dif- 
ference in elevation for each of these angles by interpolation of 
the regular stadia tables or from a table of natural sines by the 
formula: Difference of elevation = J sine of twice the angle. 
The first value thus determined divided by 100 is the difference 
in elevation corresponding to each Stebinger division between 
0 and 100. The second value minus the first and divided by 
100 is the difference in elevation corresponding to each Stebinger 
division between 100 and 200. The third minus the second and 
divided by 100 is the value for Stebinger divisions between 200 
and 300, etc. Carry the quotients in each case to the fifth 
decimal. With an adding machine set at the difference in 
elevation for one division between 0 and 100, print 100 addi- 
tions for the factors corresponding to the first 100 Stebinger 
divisions. Then with the machine set at the difference in eleva- 
tion per division between 100 and 200, print 100 additions for 
the factors corresponding to the second 100 Stebinger divisions. 
Complete the table in this manner, changing the addition figure 
after each 100 additions. Number the divisions, strike out the 
extra decimals beyond the third for the first 50 divisions and 
beyond the second thereafter, and typewrite into tabular form 
in parallel columns; the number of divisions in one column, the 
corresponding factors in another. Brief tables for correction 
because of curvature and refraction as well as for conversion of 
observed to horizontal distances should be added at the margin. 
The whole, if properly planned, will occupy a sheet about 5x7 
inches in size when photographed to one-half reduction for field 
use. 
A slight modification^® of the above method will give a still 
more accurate series of factors. Read the vertical arc at each 
50th division of the Stebinger drum instead of each 100th; deter- 
Suggested by K. C. Heald of the U. S. Geological Survey. 
