Now, imagine doing a degage in second while turned in. There willcome a point when the trochanter is going to interfere with thepelvis (look at that book again), & you can't get your leg anyhigher. But if you turn your thighs out, this will rotate thatneck so it's pointing back-to-front instead of outside-to-in. Nowthe trochanter will remain roughly stationary & how high you canget your leg will be limited by flexibility & your ability tostretch instead of by those bones. (This is what I've read,anyway; DancingDoc will, I hope, correct me if I've gotten anyimportant detail wrong.) Turnout is how people like Allegra Kentcan get their legs up next to their ears.
I must add that in order to get good extension to the side, youdon't need a full 180 degrees of turnout--or so my kinesiologybook tells me. But there's aesthetics as well as mechanics, & 180degrees, for those who can manage it, is the aesthetic aspect.
I personally believe that turnout first became important whenballet moved to the proscenium stage. Before that, it was viewed"in the round," as you can see from surviving engravings of earlyballets. But ballet lost a dimension when it went to the stage, &movement to the side became a much more important aspect of dance.This meant that degages, & in fact most movement in secondposition, were much more important than they had been before, &greater extension was sought after. Since greater extensionrequires turnout, turnout became an important feature of ballet.
Many dancers also feel that turnout also has a general opening-outeffect on the dancer. The critic Andre Levinson thought that thiswas what made ballet ballet, in fact. But the bottom line for thedancer is twofold (1) turnout must be from the hip joint, not thefeet & (2) if you can manage 180 degrees, do what you can & don'trepine.
Tom Parsons