I believe a couple of very, very old timers (early 1900's I believe) developed this high rep squat method. Either Mr Ellis or a Mr Berry, not sure which, wrote an article about it in a physical culture magazine to start it off. The original verson had the trainee use only bwt (a 100lb BB was popular also) on the bar and nothing more. Never advancing or adding on extra weight. This concept, with the 3 or more breaths between reps, was to expand the rib box, not so much for gaining muscle size. With bwt only on the bar a lot of guy's worked up to 30,40,50 reps or more. There was an old theory than that the more oxygen forced into the body the more the body would grow. The core of the idea was more oxygen taken in by the muscle cells (blood, chemicals produced by the body, etc also) the larger the tissue would grow. Good Luck.
Side Bar: If any heavy squater's out there would like to experiment with just bwt squats for 20 reps or so than please pass the results alone to us here. That would be 3 deep breaths (no shallow one's...deep) at the start and between each rep. Thank you.