= 16° ch.long × sin 42.5° = 10.8° — Page 247, Lesson 228

Let’s pick this up right where the numbers left off. We’ve just calculated that the convergency between two meridians, for a change of longitude of 16° at a latitude of 42.5°, is 10.8°. That came from the formula: convergency equals change of longitude multiplied by the sine of the latitude — so 16° times sin 42.5° gives us 10.8°. Now, what does that convergency value actually represent? There are two ways to think about it, and both are equally valid. The first way: convergency is the change in great circle track angle as you move from one meridian to the other. So if we’re tracking westwards, and the great circle track angle at the starting meridian is, say, 260.8° True, then the convergency of 10.8° tells us that the track angle at the far end — let’s call that point G — is also 260.8° True going westwards. The reciprocal, the track back from G to the starting point, would then be 080.8° True. The second way to think about convergency is as the angle of inclination between the two meridians. That’s a geometric view: the meridians are not parallel; they converge towards the poles, and the angle between them at a given latitude is exactly that convergency value. To work out the track angle from one meridian to the other using this second idea, we can draw in a parallel construction line. Imagine we have a line drawn parallel to the starting meridian, passing through point G. That construction line gives us a reference direction. The reciprocal track from G to H, measured from that parallel construction line, is 070°. Now, the convergency between that parallel construction line and the actual meridian at G is 10.8°. So to get the true track angle from True North — that is, from the meridian itself — at G back to H, we add that convergency to the 070° reference. That gives us 080.8° True. So either way — whether you think of convergency as a change in great circle track angle, or as the angle between the meridians themselves — you arrive at the same answer: 080.8° True.