STANDARD - Survey Instrument Antique Center!

From the center of the instrument to the rod the distance is
c being the distance from the objective to the center of the instrument.
Since (c -f/) is practically a constant it is usually denoted by the single letter c
and is known as the " constant of the instrument."
When the line of sight is not level, but the stadia held at right angle to it, the
formula for the horizontal distance is :
D = fc.a.cos n ~\- c -j- om.
(2)
The member om -- sin n ; for a = 24', n 45 the value of om is but 8.4', and for
o = 10' , n = 10 it is 0.86' ; this shows that om in most cases may safely be omitted.
Some engineers let the rodman hold the staff perpendicularly to the line of sight ;
they accomplish this by different devices, as, a telescope or a pair of sights attached
at right angle to the staff. This method is not practicable, as it is very difficult,
especially in long distances, and with greater vertical angles for the rodman to see
the exact position of the telescopes, and furthermore, in some instances it is entirely
Impossible, when, for instance, the point to be ascertained is on a place where only
the staff can stand, but where there is no room for the man. The only correct way
to hold the staff is vertically.
In this case we have the following : (Fig. 4)
MF = c + GF = c + &.C.D.
CD must be expressed by AB.
AB = a. AGB = 2m.
And finally, after many
CD = 2GF tan.m.
transformations :
D=c.cos n-f-a.A;.cos 2n a.fc.sin 2 n tan jrn. The third member of this equation may safely be neglected, as it is very small
even for long distances and large angles of elevation (for 1500', n = 45 and k= 100,
it is but 0.02'). Therefore, the final formula for distances, with a stadia kept ver-
tically, and with wires equi-distant from the center wire, is the following :
(3)
D = C.POS n-\-a.k.cos*n.
The value of c.cos n is usually neglected, as it amounts to but 1 or 1.5 feet ; it is
exact enough to add always 1.25' to the distance as derived from the formula
(3a)
D = a.&.eos'n
without considering the different values of the angle n.
In order to make the subtraction of the readings of the upper and lower wire
quickly, place one of the latter on the division of a whole foot and count the parts