CROSS-STAFF, a mathematical instrument used to take the sunís altitude.
consists of a staff and four crosses, viz. the tenth cross, the thirtieth
cross, the sixtieth cross, and the ninetieth cross.
The staff is a
square piece of wood on which the crosses slide, each side being graduated
into divisions: the first side has from about three degrees to ten
delineated on it; the second from ten to thirty; the third from twenty to
sixty; and the fourth from thirty to ninety.
The tenth cross,
so called from its belonging to that side of the staff, which is numbered
from three to ten degrees, is the shortest of the four crosses, and is to
be used when the sunís altitude is under ten degrees. Sometimes the
breadth of the thirtieth cross supplies its place.
cross is longer than that of ten, and belongs to that side of the cross
which is numbered from ten to thirty, whence it has its name: when the
sunís altitude is between ten and thirty degrees, this cross is to be
The third, or
sixtieth cross, so termed from belonging to that side of the staff, which
is numbered from twenty to sixty, is longer than the former, and is to be
used when the sunís altitude is between thirty and sixty degrees.
cross is called the ninetieth cross, because it belongs to that side of
the staff which is numbered from thirty to ninety degrees. This cross is
used when the sunís altitude is between sixty and ninety degrees.
divisions on the staff are constructed after the following manner.
Let AB (plate
LXIV. fig. 7.) represent the side of the staff to be
any convenient radius, setting one foot of the compasses in A, with the
other describe the semicircle DEC, and draw the diameter DAC, at right
angles to AB: divide each quadrant into ninety equal parts or degrees; at
the distance of half the length of the cross, draw the lines Ff, Gg,
parallel to AB, and from the center of the circle draw right lines through
the several divisions of the quadrants; and, from the intersections of
those right lines with the two parallel lines Ff, Gg, draw
right lines intersecting the staff AB, which will give the several
divisions: thus the line FG, intersecting the staff AB, in the point a,
will give the division of twenty degrees, because the angle FAG = twenty
degrees: and after the same manner, and by making use of the length of the
several crosses, may the four sides of the staff be divided.
To take the
sunís altitude with the FORE-STAFF. -
Having adapted the proper cross to the staff, apply the flat end of the
staff at A, (fig. 8.) to the outside of the
eye, the face being
turned towards the sun; look for the object at the upper end of the cross
at C, and at the lower end B for the horizon; but, if the sky appear
instead of the horizon, slide the cross nearer to the
eye; if the sea appear, remove it farther from the
eye, till the object appear at the end C, and, at the same time, the
horizon at the end B; then will the cross cut, on the side of the staff
proper to it, the degree and minute of altitude. But if the meridian
altitude be required, the observation must be continued, and as the object
approaches the meridian, the sky will appear at the end B, instead of the
horizon; but, when the object begins to descend, the sea will appear at
the end B, and then is the observation finshed, and the cross will cut the
degrees, &c. of altitude.