Doubling the Angle on the Bow
This is a refinement of the running fix which takes advantage of the properties of isosceles triangles.
As we know that the angle on the bow when the first bearing is taken is 35°. The time of this bearing is noted and the bearing then carefully watched until the angle on the bow doubles to 70°. The triangle formed by the two position lines and the course line is isosceles, therefore the range at the time of the second bearing is equal to the distance run between bearings.
The Four-Point Bearing
This is a further refinement of the running fix in which the first bearing is taken when the object is at four points (45°) on the bow. When the object is on the beam the range will be the same as the distance run since the first bearing was taken. The disadvantage of the four point bearing is that the range of the single object is not known until it is abeam. This is of little help in passing at a safe distance.
The Transit Bearing
When two charted objects come into line they are said to be in transit. It has already been shown how a transit can be used to check the compass error. A transit can also be used to obtain a fix in conjunction with another position line such as a range (or be used to obtain a fix in conjunction with another position line such as a range (or even a sounding) without use of the compass.
