he
ns
telescope is rendered anallatic.
the interposition of the anallati
end-wires to the staff, form an angle o with its vertex at O, the centre
of the telescope (Fig. 2). The an
angle, and O the anallatic point.
distance of the anallatic lens from the object-glass. If this distance
increases, o decreases, and conversely, whilst if the distance remains
constant, is invariable. It can easily be seen that the distance
from O, the centre of the telescope, can be deduced fro:
A B intercepted by the wires.
Papers.] BROUGH ON TACHEOMETRY. 7
a+ (f+ ¢) cos a. But since (f 4- c) is, at most, equal to 2 feet, and
the angle a is so very small, c' may be taken as equal to its hori-
zontal projection. The horizontal distance will then be equal to
100 s cos? a + (f + ©).
In Germany it is usual to hold the staff perpendicular to the line
of sight. The inclined distance is then equal to 100 s 4 (fF + e),
and its horizontal projection is equal to {100 s 4 (f + c)} cos a, or
approximately, 100 s cos a + (f +e).
The most effectual method of remedying the variability of r is
that proposed by Porro, a Piedmontese officer, afterwards professor
at Milan, who in 1823 modified the construction of the telescope
in such a way as to remove all necessity for adding constants, and
the distances measured from the centre of the instrument are then
directly proportional tos. He introduced between the object-glass
and eye-piece a third lens, the focus of which coincided with
Fic. 9.
that of the object-glass. Consequently the rays after passing
through this third lens become parallel, whilst the sizes of objects
subtending the same angle at the centre of “anallatism,” or un-
changeableness, are proportional to their distance from that point.
This point being placed in the vertical axis of the instrument, the
In other words, in consequence of
c lens, the rays coming from the
gle v is termed the diastimometric
The angle o varies with the
n thelength
In fact the sides of the diastimo-
REL p T x
N a ES RS
Su
a
