The threading is shown below. Treadling varies. Most of the time, if using a jack loom, you will treadle the opposite of what is shown.
Most of the patterns require two shots of weft (as evidenced in the photos of finished fabric in the books), but the weaving directions may not specify that.
Some of the photos of the fabrics in the books do not appear to match the treadling instructions given, when weaving or after washing.
The original material called for was 4-8 cotton, but I am using 16/2. This weight and fiber would make *excellent* towels from some of these patterns!
I am sampling the following patterns from the following O.B. sources...
Module de Tissus & Le Metier a Quatre Lames, (early 1930's?) both French editions
> Gaufre, page 117
> Gaufre, page 159
Home Weaving (1947 edition) English
> Broken Twill, page 120
> Honeycomb, page 160
> Waffle Weave, page 166
> Reversed Serge, page 207
> Reversed Serge, page 208
> (Unnamed), page 229
In trying to come up with a treadling that matches the illustration on page 117 of the Module de Tissus, Leslie M pointed out a Davison threading and treadling on page 118 of her book comes close. (New Canaan Check, under "block weaves", treading XVI.)
I will post more results as I get a chance to take more photos. I have woven 11 samples to date (6/6/12)