Basically nothing? Goddard didn't really work on solid rockets as far as I know, he was focused on liquids mostly. Quite rightly, too, because liquids, at the time, could offer interesting performance, whereas solids were still basically black powder or a little bit better, with utterly atrocious specific impulse (and hence performance). The solid work that Archibald is referring to took place at JPL beginning around 1940--maybe a few years earlier, maybe a year or two later--and involved the invention of composite solid propellants that could (eventually) match liquid-fuel ISPs.
Ok. All i remember of Goddards work in this is in 1918 he provided the US Army with a rocket motor to propel a standard rifle grenade out of a shoulder held tube. That was a solid or dry fueled rocket.
Col L Skinners bio states he was assigned to Aberdeen Proving Ground in 1932 & soon started experimenting with rocket motors. Not clear if he was working with solid fuel or both solid and liquid. Circa 1940 he proposed a weapon very similar to Goddards 1918 weapon for antitank use. The proposal was sucessfully tested in 1941 & went into production in 1942. Skinner is suposed to have been interested in rocketry as a teenager & experimenting with rockets as early as 1915. Perhaps he had been familar with Goddards work.