+ⵏ–
⟵ⵏ⟶
–ⵏ+
found at both ends of the A scale is of general application but of
questionable utility. It is assumed to represent a fraction, the
vertical line indicating the position of the decimal point. If the
number 455 is to be dealt with in a multiplication on the lower scales,
we may suppose the decimal point moved two places to the left, giving
4·55, a value which can be actually found on the scale. If we use this
value, then to the number of digits in this result, as many must be
added as the number of places (two in this case) by which the decimal
point was moved. If the point is moved to the right, the number of
places must be subtracted. Similarly, in division, if the decimal point
in the divisor is moved _n_ places to the left, then _n_ places must be
subtracted at the end of the operation; while if the point is moved
through _n_ places to the right, then _n_ places must be added. The sign
referred to, which, of course, applies to all scales, completely
indicates these processes and is submitted as a reminder of the
procedure to be followed by those using the method described.
The signs π, _c_, _c′_, and M are explained in the Section on “Gauge
Points,” p. 53.
On some rules additional signs are found on the D scale. One, locating
the value (180 × 60)/(π) = 3437·74 and hence giving the number of
minutes in a radian, is marked ρ′. Another, representing the value (180
× 60 × 60)/(π) = 206265, and hence giving the number of seconds in a
radian is marked ρ″. A third point, marked ρ_{˶}, placed at the value
(200 × 100 × 100)/(π) = 636620, is used when the newer graduation of the
circle is employed.
These gauge points are useful when converting angles into circular
measure, or _vice versa_, and also for determining the functions of
small angles.
A gauge point is sometimes marked at 1146 on the A and B scales. This is
known as the “Gunner’s Mark,” and is used in artillery calculations
involving angles of less than 20°, when, for the purpose in view, the
tangent and circular measure of the angle may be regarded as equal. For
this constant, the angle is taken in minutes, the auxiliary base in
feet, and the base in yards. The auxiliary base in feet on B is set to
the angle in minutes on A when over 1146 on B is the base in yards on A.
The value (1)/(1146) = (π × 3)/(180 × 60).