Generally, in a three-card series, the center card is the Principal, or focus card, and the two cards on either side are Modifiers. The most useful idea is to analyze the energy flow through the sequence, as discussed in Liber Theta. My understanding is that elemental dignity doesn't change the nature of the focus card, just its potency. I like to think of it in terms of natural forces: Air bounded by Fire on both sides would get super-heated; it reminds me of the Santa Anna winds in California that fan tremendouly destructive wildfires.
Here is a quote from Israel Regardie's Complete Golden Dawn System of Magic:
"A card is strong or weak, well-dignified or ill-dignified, according to the cards which are next to it on either side. Cards of the same suit on either side strengthen it greatly either for good or evil, according to their nature. Cards of the suits answering to its contrary element, on either side, weaken it greatly for good or evil. Air and Earth are contraries as also are Fire and Water. Air is friendly with Water and Fire, and Fire with Air and Earth." (He missed that Water and Earth are friendly to one another.)
This is OK as far as it goes, but it's notable for what is left unsaid; there are some gaps in the logic that have to be worked through to make sense of it.
A Fire card surrounded by cards that are friendly to Fire and mutually friendly to each other would strengthen the Fire card. So Fire/Fire/Fire, Fire/Fire/Air, Air/Fire/Fire, Air/Fire/Air, Fire/Fire/Earth, Earth/Fire/Fire and Earth/Fire/Earth would all strengthen the central Fire card.
A Fire card surrounded by cards that are unfriendly to Fire and mutually friendly to each other would weaken the Fire card. So Water/Fire/Water would weaken the central Fire card; all other mutually friendly Water pairings would be at least half-friendly to Fire (Water/Fire/Air and Water/Fire/Earth and their mirrors), so the negative effect would be mitigated. The same would be true for the remaining mutually-friendly Air pairings: Air/Fire/Water and Water/Fire/Air would marginally weaken the central Fire card.
Supposedly, surrounding cards that are mutually unfriendly regardless of their relationship to the focus card would have no effect on the latter. So with Water/Fire/Fire and Air/Fire/Earth and their mirrors, the contrary bounding cards would neutralize one another. I have some trouble swallowing this, since the first combination is half-friendly and the second one is fully friendly to Fire, so there should be a middling favorable effect with the first (two Fires would seem to trump one Water) and a completely supportive influence with the second (cards helpful to Fire fore and aft). This is where the Liber Theta idea of "energy flow analysis" comes into play:
"Energy Blocks and Flows
Analysis of the three-card combinations gives you the opportunity to see whether the energy is blocked, flows easily, is enhanced or diminished, or even transformed. You can see if the Subject (Principal) is supported by the Modifiers, or whether the Modifiers are working together or against themselves."
This seems to offer the possibility of letting a little rational light and air into the rigid rule structure. I like to use a "two-thirds" model: two cards in series that are mutually friendly and supportive in a three-card combination would outrank a third card that is friendly to neither, regardless of where they fall in the sequence. If they are at the end, they would carry on as if the opposition didn't exist, while if they are at the beginning they should be able to overpower the blocking emphasis, or at least moderate it.
