In the early - mid '20's, Victor switched to sprayed, tinted lacquer finishes ("pyroxylin lacquer", also known as nitro-cellulose), which dried much faster.
This is the finish found on Orthophonic Victrolas.
The earlier Victrolas used a base finish of shellac, and then top-coat of varnish to give it water resistance ( prevent white rings from damp glasses, flower-pots, etc. ).
As it ages, and is exposed to heat, sunlight, UV, the oils gradually evaporate from the varnish layer, causing it to shrink, first showing as a fine web of "crazing" where you see crackles, but the finish layer is still smooth, and then it advances to "alligatoring" where the varnish continues to shrink, and the crazing lines become cracks, and the finish becomes rough and dull. Many pre-Depression pianos look like this.
I believe Edison and Columbia used the same basic techniques.
While shellac and lacquer finishes can sometimes be "re-amalgamated" with application of the appropriate solvent, allowing the surface to "flow-out", once varnish has cured, the original solvent (turpentine) will no longer soften it.
Many forum members have good results improving an alligatored finish using Howard's "restore-a-finish" products.
The very first recommendation is to give the piece a thorough cleaning, removing years of dead wax, tobacco / nicotine funk / dirt, and get down to the finish itself. A favorite approach is to use GOOP cream hand-cleaner (non-gritty), and paper towels, and perhaps 0000 steel-wool.
Once you get the piece de-gunked, you can better evaluate the condition of the finish itself, and go from there.
This is just scratching the surface ( if you'll pardon the expression )...
