Calculations convergence

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The difference in direction between the grid and graticule lines is known as convergence; the value of the convergence is zero along the meridian 2° W but varies over the rest of the projection (see figure, right).
It may occasionally be necessary to know the angle at any point in the projection from the meridian to the grid line (that is from true north to grid north). To calculate this accurately requires special tables; but the following formula gives the convergence to within ¼ minute of arc:

C'=sin

where

C' = convergence, in minutes, of the meridian at a point., It is positive when measured clockwise and negative when anticlockwise, from true north.
= longitude difference, in minutes of arc, between the point and the central meridian (2° W). It is positive when east and negative when west of the central meridian.
= latitude of point.
Note:  should be measured to ¼ minute of arc. If it is less accurately known then the accuracy of the result will be of the same order as that to which is measured.
should be measured to five minutes of arc.

Example

At a point in Norfolk 1° 10' E, 52°40' N. = 190' sin 52° 40' = 0.79512
C'= 190 x 0.79512 =  151 minutes = grid north is 2° 31' east of true north.