Dear All,
An intriguing question has been raised on the
Italian Sundial list by Fabio Savian. Slightly
re-expressed he is asking...
When specifying the orientation of a plane
dial, is your order:
A) Declination then Inclination
B) Inclination then Declination ?
This is important because rotations are not
commutative: R1.R2 does not equal R2.R1.
My own answer is firmly (A) and (slightly
simplified and avoiding using either word)
I think as follows:
1. Start with a vertical plane facing
due north (sic).
2. Rotate about a vertical axis until
it has the correct azimuth.
3. Rotate about a horizontal axis until
the tilt is right.
I use this order because both rotations are
about axes IN THE PLANE being used. This
keeps rotation matrices simple and so on.
An alternative is:
1. Start with a vertical plane facing
due north.
2. Rotate about a horizontal axis until
the tilt is right.
3. Rotate about a vertical axis until
the azimuth is right.
This is fine but the second rotation is not
about an axis in the plane being used.
Here I quote a delightful observation by
John Davis in the BSS Glossary referring
to a definition of inclination:
Beware: this convention is not followed
by all authors.
He could be referring to a host of other
definitions :-)
OK. Which way do you all do things:
Dec then Inc or Inc then Dec ?
There is no right answer but it would be
interesting to hear who does what!
Frank King
Cambridge, U.K.
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