Now we will look at Chichester's illustration of the old method on page 234 to compare it with the short method already discussed.
What he is doing with this example is using the traditional Haversine- Cosine method of calculating Hc and azimuth. The formulas used for this were derived from the standard Sine - Cosine formulas and, in fact, uses the same method and formula for calculating azimuth.
The formula for calculating Hc is:
hav ZD = hav LHA cos Lat cos Dec + hav (Lat ~ Dec)
(Lat ~ Dec means the difference between latitude and declination, subtracting the smaller from the larger if of the same name and adding if of different names)
(ZD is zenith distance)
so Hc = 90º - ZD
For calculating azimuth we use
sin Z = (sin LHA cos dec ) / cos Hc
usually rearranged into the more convenient form of
sin Z = sin LHA cos dec sec Hc
Since csec ZD is the same as sec Hc
we can rearrange this formula to
sin Z = sin LHA cos dec csec ZD
Chichester used these formulas and solved them using logarithms by using this format:
Hc Az
LHA ___________ log hav LHA ___________ log sin LHA ______________
Lat ___________ log cos Lat ____________
Dec __________ log cos Dec + ___________ log cos Dec ______________
______________
hav _______________
(L ~ D) ___________ hav (L~D) + ____________
89-60
ZD - ___________<<<< inv hav _____________>>> >>>>>>log csec ZD +___________
Hc ____________
Ho-_____________
A______________ Z ______________<<<>>>>>>>> log csec ZD +_10.16166____
Hc __46-26_____
Ho-__46-23___________
A____3 away___ Z ___57_________<<<<<