What can anyone say about Quarter Wavelength transmission line enclosure design ?

I built a pair (in 1981), per Roger’s design, to go with a customer’s Acoustat Model IIIs. He wanted something that could match the speed and definition, of his electrostatics. They worked so well, powered by a Halfer DH-500 and crossed over via a Dahlquist DQ-LP1, I duplicated the system for myself(and my Acoustats) and another customer. Back then, I used a 10" woofer that Milo Nestorovic employed in his woofer systems. In answer to the OP’s original query; TLs(at that time), were the only woofers systems around, that many of us had experienced, able to blend well with electrostatics. I used bi-amped TLs, in concert with various planars, for 36 years. Now, with an Emerald Physics system. The trusty DQ-LP1 was replaced by a modded TacT RCS 2.2X(and Hafler Trans-Nova 9505), about 12 years ago. The TacT’s DSP(time-alignment/room correction/EQ) was the finishing touch, to an already stellar bottom end. Guess I’m a TL believer!

I am very fortunate to have a pair of T+A Criterion 210 speakers that are transmission line designs that are done right!  They have exceptional response from top to bottom and absolutely no overhang in the bass. They are very heavy speakers due to the transmission line enclosure, but that is a small price to pay for wonderful sound. 

Fried, and his IMF(Irving M Fried) designs, got me interested in TLs.  Man; that's been awhile(I'm dating myself).

Bose has used transmission lines many times. Not these inverted horns stuffed with fiber that some call TL's, which really aren't. They have the problem of limited bandwidth and size. It's why the Bose Wave Radio was huge.  Not a technology I personally take too seriously.