Good job with the diagrams, Light- thanks!
Let's see if I can come up with some more words to help with this. We all know that sound waves are really just a series of disturbances in the pressure of the air: the air is compressed (positive pressure), and then rarefied (negative pressure), as the waves pass any given point in space. Let's take an identical pair of SM57s. And just for argument, let's say that both of them put out a positive voltage (on pin 3 with respect to pin 2) when they experience a positive pressure on their diaphragms.
Now, let's hang our pair of SM57s on a snare drum: one 5" above the top head, and one 5" below it. And we'll hit the snare once, nice and hard. What happened?
Let's model the behavior of the snare as putting out a single pressure pulse when the stick hits the head, and let's ignore the contributions of the bottom head and the snares (and reverb from the floor, and son on...!) for the moment. That's horribly oversimplified, but for the purposes of illustration we'll go with it. The two mics are symmetrically 5" away from the top head, one above, one below.
The head on top experiences a negative pressure pulse: the stick moves the head away from the mic, creating a lower pressure above the head than below. So the upper mic sees a negative pressure pulse, and the lower mic sees a positive pressure pulse: they see essentially the same signal, but with opposite polarity.
Let's say the top mic puts out -1V when we whack the snare- then the bottom mic will put out +1V. Identical mics, but the pressure environment is different, because they are on opposite sides of the head. Sum their outputs, and you get zero, because they are equal, opposite polarity, and not delayed with respect to each other. Good so far?
This is the really simple case: a single head, mics identical distances away from it on opposite sides. In the real world it is _never_ that simple... Just for grins, let's take that bottom mic and move it 3" further down: top mic is 5" off the head, bottom is 8" off the head. We'll still get about +1V from the bottom mic, but we'll get it 3/1100*12 seconds or .22 milliseconds later. It's now no longer purely the opposite polarity: it's now delayed, and that delay may cause some problems if we sum the outputs of the two mics, some of the components will cancel, and some will reinforce. 3" is the wavelength of a 4400Hz signal- so we'll exactly cancel out everything at 4400Hz (because the two mics see opposite polarity signals, remember), creating a huge upper midrange suckout. Maybe we need that effect, maybe we don't: but the distance between the two mics controls where the first cancellation occurs. It's basically an EQ knob!
Here's a fun trick: if you have a polarity switch for the lower mic, switch it now, without touching anything else. And you'll find that the suckout moves from 4400Hz to 2200Hz (one half wavelength of the signal gives us the opposite polarity, instead of one full wavelength with the _mic_ giving us the opposite polarity).
Clear as mud, probably: I wrote it, but I doubt that that will help clear up much...
Anyway, if you are having phasing issues with a multiple mic setup, by all means play with the polarity switches at the preamp. Changing the polarity of one or more mics may change an awful comb-filtered sound into a *pleasant* comb-filtered sound: creative use of interference is the order of the day. Changing the polarities can move those notches and peaks around, and sometimes that's exactly what you need (for example, to tame a "pingy" underdamped snare sound...).
Multiple mics on a single source _will_ create cancellations and reinforcements, and it is a game of inches. That's why everybody always says "experiment with placement": a move of 6-8 inches can move the first comb filtering notch right down to 1kHz, and that's in the most sensitive part of your hearing range. Little moves make _big_ differences. And hopefully, all this verbiage will help explain why...
Light, back to you at the studio!