_To the logarithm of the number of minutes in the difference of
longitude add the constant logarithm[29] -4.1015105, and to their sum
the logarithm sine of the mean latitude, and let this last sum be_ S.
_The cotangent of the mean latitude being_ T, _and an arithmetical mean
between half the difference of latitude and its tangent being called_
m, _from the logarithm of_ T + m _take the logarithm of_ T - m, _and
let the logarithm of their difference be_ D; _then shall_ S - D _be
nearly the logarithm tangent of the angle, in which the ship’s course
cuts the meridians_.
_Note_, We ought, in strictness, to use the ratio of _tx_ + _x_R to
_tx_ - _x_R instead of T + _m_ to T - _m_; but we substitute this
last as more easily computed, and very little different.