Hello,
If the coil-membrane junction of the 2 loudspeakers are vertically aligned then for a 2nd order Butterworth crossover (12dB*octave) you have to invert the polarity of the mid-high loudspeaker. It is the same with a 2nd order Linkwitz-Riley.
With perfect loudspeakers the Butterworth 2nd order gives theorically a +3dB bump in the frequency response and a flat response with the 2nd order Linkwitz-Riley.
If you use the Butterworth 2nd order,eventually you can move the mid-high loudspeakers forward on one inch (26millimeters) the response will be a bit better and the impulse response improved.
If you use a non inverted polarity for the mid-high loudspeaker then for both the 2nd order Butterworth and Linkwitz-Riley you'l have a deep hole in the frequency response around 2500Hz.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Either it is mid or woofer(as in the picture) doesn't make any difference.
The question is about connection polarity. Whether to reverse for woofer or not?