Hey Umut,
It's not a gum print, but a form of imbibition (dye transfer) printing. The dyes were...
Bayer's alizarin blue A S, 1 gram to 1 quart of water, with 1 gram of citric acid and 1 to 3 grams of citrate of potash. For magenta pink, equal parts of Bayer's alizarin rubinol R and rubinol 3 G, with 1 gram of citric acid and 1 to 3 grams of citrate of potash. For yellow, Bayer's sulphon yellow R, with 1 gram of citric acid and 1 to 3 grams of citrate of potash.
These dyes are cyan: CI Acid Blue 47, magenta: CI Acid Red 80 & CI Acid Red 82, yellow: CI Acid Yellow 42., from (there was a url link here which no longer exists)
The filter arrangement isn't so simple, as it was a bi-pack set up. There was a rose colored compensating filter behind the lens, a yellow reflector that reflected "white" (all) light towards the blue-sensitive plate and simultaneously transmitted the light (minus blue) to the green & red emulsions, which didn't really use filters but were instead spectrally sensitized to the right regions.
The lenses were pretty lousy actually, and the process itself introduced a lot of diffusion.