The barrels are usually not marked. Supposedly, they were machine barrels or those from other rifles (Winchester 95s are often mentioned). Some of the parts have a S in a circle.
Keep in mind that these rifles were different than those rifles that have Sedgely barrels. Sedgely did supply barrels and certain other parts as replacements during WWII for use by military M1903s. Two types of barrels were used - those marked USMC, which were (at least initially) used by the Marines and those marked with just a "circled S" which were for use by the Army.