NavList:

Hi Christian,
You are right, Mills did drop a minus sign in equation (3).
Getting to step 4 is not hard (I'm thinking you are going to think, "Duh"). But it's just not easy to always be clear when writing about math.

Here's one way to see what he did:

cos(alt).d(alt)= cos(lat).cos(dec).sin(HA).d(HA) (3)

Divide both sides of the equation by d(HA).cos(dec):

cos(alt).d(alt)/(d(HA).cos(dec))= cos(lat).sin(HA)

so that we can replace d(alt)/(d(HA).cos(dec)) on the left-hand side
with sin(x) (from equation 2). This gives us

cos(alt).sin(x)= cos(lat).sin(HA)

or, solving for sin(x):
sin(x)= cos(lat).sin(HA)/cos(alt)

and, by equation 2,
sin(x)= d(alt)/(d(HA).cos(dec))

so we have two different expressions for sin(x), and that
is what Mills is indicating with (4).

Robert Bernecky
Mystic CT

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