There are certain special cases that come under the method of obtaining a running fix from two bearings and the intervening run which do not require the use of tables. Two of these cases are when the multiplier is equal to unity, and the distance run is equal to the distance from the object.
If the second difference is double the first difference, triangle is isosceles. Which means the run is equal to the distance off at the time of the second bearing. This is called doubling the angle on the bow.
If the first angle is 45° and the second 90°, the distance run equals the distance when broad on the beam. These are called bow and beam bearings.
If bearings of the fixed object are taken at two (2) and four (4) points on the bow (22.5° and 45°) seven-tenths (0.7) of the distance run between bearings will be the distance at which the point will be passed abeam, and (0.7) of the time run added on to the time of second bearing will be the time abeam. This is known as the seven-tenths rule.
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