STANDARD - Survey Instrument Antique Center!

and
In the above figure,
47
TH=the transit horizontal sight line.
The angle HTB = the angle of elevation of the telescope to the foot of the rod
= E.
" " BTA=the angle subtended by any number of revolutions of the
gradienter screw= G.
AB = the length of the rod included by the angle G, when the rod
is vertical = R.
CB is drawn perpendicular to TB.
Then, CBA=BTH=E TAH = 90 (E + G)
J5= ( 90 - CE + G)
) cog E cos G - ~~ sin E sin G.
:
AB sin (904- G)
cos G.
.-. BC=R (cos E tan G sin E.)
tan G= - where h is the height above a horizontal line, subtended by
one revolution of the gradienter screw at a distance a.
n is the number of revolutions made in any given case.
BT= ^rBC=
nh R4-(cosE nh sinE)
^
a
.-.BT=R cos E sinE ........ I.
HT=BT cosE
.-.HT=R rCos'E ^sin2E ....... II.
Formulas I and II are general formulas for any gradienter screw. In C. L.
Berger & Sons' transits the screw is cut and placed so that when a= 100, for
n =2 and A= i, by substitution these formulas become,
BT = R (100 cos E sin E.)
HT = R (100 cos 2 E y2 sin 2 E.)
Where BT = the direct distance from the center of the horizontal axis of the
transit to the foot of the vertical rod.
HT = the horizontal distance from the center of the horizontal axis of the
transit to the plumb line dropped from the foot of the vertical rod.
R=the space included on the vertical rod by two revolutions of the
gradienter screw.
E = the elevation of the foot of the rod above the horizontal sight line
of the telescope.
When the angle E becomes an angle of depression instead of elevation, then the
point B is the upper end of the part of the rod used,A B. The distance B T in
this case is the direct distance between the center of the horizontal axis of the telescope
and the upper reading of the vertical rod in the valley.
The distance H T is, as before, the horizontal distance between the center of
the horizontal axis of the telescope, and the plumb line prolonged in this case
upwards from the upper end of the vertical rod. The plumb line in all cases coin-
cides with the direction of the rod.
By means of the following table, it is only necessary to multiply the factor
opposite the angle of elevation, by the space included upon a vertical rod by two
gradienter screw revolutions, to obtain either the direct or horizontal distance of
the center of the horizontal axis of the telescope from the foot of the rod ; or the
game distance from the upper reading of the vertical rod in the case of an angle of
depression.