An Experimental Study of Field Methods. 
555 
objective, y the distance from the outer focus e to the rod, and D the 
distance from the instrument to the rod. 
From the principles of optics, we know that all rays of light which pass 
through e are parallel to each other after emerging from the objective. 
Therefore, there is some point q which will emit a single ray of light that 
will pass through e, and, after traversing the objective, will strike the cross 
wire a. If the telescope is focused for the point q, the objective will bring 
all rays emitted by q to a focus at a; and hence it is immaterial whether 
we consider the real course of the rays, or assume that all the light from q 
passes along the line q e a. 
Similarly, we may assume that all the rays from p pass along the line 
peh. 
In Fig. 21 we have from similar triangles, s : y = i: f from which 
y = [ s = Ks (1) 
Notice that K, (■= J ^ is a constant co-efficient peculiar to each instru¬ 
ment; and also that the intercept s on the rod varies as y , the distance 
of the rod from the outer focus of the objective. 
Since the two rays from p and q are parallel after entering the telescope 
it is immaterial where the cross hairs are; and, therefore, the distance of 
the rod from e is always proportional to the intercept s. 
The distance of the rod from the plumb-line is y -f- f + c or 
D = Ks + f + c (2) 
Equation (2) is the fundamental one of stadia work. The values f and c 
can be measured directly on the instrument, and K is determined by ob¬ 
serving a number of values of s on known distances. 
In this paper getting the value of K is called determining the stadia in¬ 
terval. 
The explanation here given applies only to those measurements made 
with horizontal sights. Only a slight modification is necessary, however, 
for extending the discussion to inclined sights. 
