Persistance meets with success.
I believe I can put a proper name to the this type of photography. It's not a style of photography as I had originally thought. It's simply the subject of the photographs, which in this case turns out to be Dance and Modern Dance. And more specifically, Dance and Modern Dance from the late 1800's and early twentieth century. One notable photographer in this area would have been Arnold Genthe, who's "The Book of the Dance" even goes as far as to depict the Bubble Dance mentioned earlier. Now that was a lucky find. I had seen these types of images many years ago.
Thanks to all for the suggestions and help provided on this daunting puzzle. I can now search out other photographers who worked in this area.