TRIANGULATTON AND COMPUTING. 69 
at 0.05 n/ D feet, in which D represents the length of the line or cir- 
cuit in miles. 
The instruments in general use are 20-inch engineer's levels and 
New York rods, the latter furnished with plumbing levels and with a 
specially constructed foot plate. The only respect in which the rods 
differ from those regularly furnished consists in making the foot plate 
a truncated pyramid of brass, the bottom of which is but one-half inch 
in width. This is in order to keep it freer of dirt and to compel its 
being placed more accurately on the top of the steel turning peg. 
The only change from the regular form made in the instrument is in 
increasing the sensitiveness of the level bubble so that 1 division on 
the tube equals 10 seconds of arc. All turning points must be on steel 
pegs at least 12 inches in length and driven firmty into the ground. 
In addition to the ordinary primary and flying levels, the Geolog- 
ical Survey has run several lines of precise levels, most of which form 
elements in the precise-level net extending from the Atlantic coast 
to the Mississippi River and the Gulf of Mexico, which comprises in 
addition the work of the Corps of Engineers of the Army, the Coast 
and Geodetic Survey, the Lake Survey, and the Pennsylvania and the 
Baltimore and Ohio railroad companies. 
The precise- leveling instruments used by this Survey differ from 
the ordinary spirit levels in many particulars, the effect of which is to 
make them high-grade instruments of precision, 8-inch and 4-inch 
bubble tubes being used. The rods are of special design, 10 feet long, 
double-faced target reading and nonextensible, and are made from 
selected white pine and treated with boiling paraffin or linseed oil. 
The lines are run with two rods and rodmen, an umbrellaman, and 
a laborer. Instructions for the conduct of the work differ from those 
for primary work in the following essential points: 
The instrument is at all times shaded from the wind and the sun; 
fore and back sights are of exactly equal lengths, and no sight over 
300 feet in length is permitted except in special cases. The instru- 
ment is undamped from the tripod after the legs have been firmly set. 
Four steel turning points are used at the same time, two for each rod- 
man, and they are so used that those employed for backsights are 
not withdrawn until the foresight pegs have been set; thus the line 
depends at no time on the stability of the instrument, as there are always 
two turning points in the ground. The limit of apparent error in the 
work is fixed at .03 ^distance in miles, which represents the allowable 
difference, in feet, in the elevations of any bench mark as determined 
by the duplicate lines. 
Office work. — The office work of triangulation consists in reduc- 
tion to center, station adjustment, computation of spherical excess of 
triangles, and adjustment of figures by the method of least squares; 
also the computation of distances and azimuths between and the geo- 
