[ATM] Gregorian Secondary Size

[saundby at foothill.net (Mark Graybill)]

I'm designing a Gregorian, and I'd like a check--or correction--on the method 
I'm using to get secondary size. Initially I came up with this estimation 
method on my own:

d=(a/F)*(D+i)

where:

d is the diameter of the secondary, 
a is the first focus of the ellipsoid,
F is the focal length of the primary,
D is the diameter of the primary, and
i is the fully illuminated diameter at the image plane.

Then, looking at Gerald North's book, I found his equation for sizing a 
secondary for a Cassegrain (classical type), and I modified it for the 
Gregorian by changing the term (f-a) to an (f+a) to get:

d=a((D/F)+i(f+a)/bf)

where b is the second focus of the ellipsoid. Since I'm getting numbers pretty 
close to what I got with the first equation it leads me to think that I've 
modified it properly to account for the geometry changes in a Greg vs. a 
Cass.

Is this an appropriate equation to use for sizing Gregorian secondaries, or is 
there a different equation I should be using?

Thanks,

Mark G.