One last thought on the subject.
Since part of the work that a gamma match does is introduce inductance and capacitance to change the input impedance, and since the inductance and capacitance of the antenna in relation to the earth also affects it's input impedance (and point of resonance), positioning the gamma horizontally to earth will increase that the antenna's interaction with the earth (ground) to some extent (also assuming that the antenna is horizontal to ground to start with). The areas of 'exposure' being equivalent to the area of the plates of a capacitor determining it's total capacitance. If part of the gamma was 'hidden' from ground that interaction would be reduced. (You see where I'm going with this?) So, the placement of the gamma ~could~ make some difference in the efficiency of the antenna due to it's interactive reactance with earth/ground!
- 'Doc
PS - Now, having said all that, the placement of the gamma will make absolutely NO practical difference in the 'real world' with the typical antenna at anything close to 'normal' operating conditions. The only 'areas' of the gamma that I can think of off hand that would make any difference would be the area of the connecting strap on the outer end of the gamma. What's that, something like 1" x 3", or 3 square inches of 'plate' area? A capacitor's plates of 3 sq.inches, with a distance between plates of anything over just a few inches just doesn't make for much capacitance... more like an open circuit, right? Well, maybe at SHF or EHF, sort of. Naaw, forget it, not even at 'light' frequencies... Wait a minute! If the velocity factor of the material used to make the gamma match could be such that the VF was a double digit whole number, it would mean faster than light propagation! OMG! That would mean that antennas for cell phones would have to be several yards long just to account for the gamma match! No wonder those stinking little antennas make the cellphone loose signal every now and then. I am a genius!
(and this is so much B.S. that the Sahara would turn green over night)