SPECIAL CASES - There are certain special cases using 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. 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.
When the first bearing is 26.5° from ahead, and the second 45°, the distance at which the object will be pass abeam will equal the run between bearings, and the time run added on to the time of the second bearing will be the time abeam.
If bearings of the fixed object be taken at two (2) and four (4) points on the bow (22 1/2 and 46°) 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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EXAMPLE OF 22.5 -45 or .7 rule
Course 315 T
Speed 12 kts
Time 1st Brg 1230
Bearing 337.5
Course 315
Diff 22.5
Time 2nd Brg 1300
Bearing 000
Course 315
Diff 45
Time x Speed = Distance Run
30m x 12kts = 6.0 miles x .7 = 4.2 miles abeam
Time run 30m x .7 = 21m (1300 + 21 = 1321) time abeam
