The information on the kinds of matrices Goudy engraved is incomplete. In Typologia , he appears to be quite specific: "My matrices are of three forms: first, the sort used in the Monotype caster; second, the form used in the Thompson type caster; and third, the form employed in the automatic type casters of the type foundries." (p. 118) But this information isn't quite as precise as it appears.
We may assume that by "the sort used in the Monotype caster" he means a Lanston Monotype display matrix. He does illustrate such a matrix just below the statement quoted above. 
Here's a public domain image of an equivalent matrix. It's from the Lanston Monotype Machine Company "Matrix Information" section of their specimen book. 
However, this type of matrix was used only for casting display type for the cases, typically in sizes from 14 to 36 points. (The Monotype Type-&-Rule caster could cast up to 36 point. The Thompson could cast up to 48 point using similar matrices. The Lanston Monotype Giant Caster could cast larger types, but typically used a matrix of a different style in these large sizes.)
Goudy's types were also cut in composition sizes, and the matrix used for the Monotype Composition Caster is quite different. I don't know if Goudy ever cut these, or if he left this to the Lanston Monotype Machine Company. (My guess - just a guess - is that he did not.)  Here is an illustration of a Lanston (= American) Monotype composition matrix (aka "cellular" matrix), from the same "Matrix Information" section of a Lanston specimen book.
The reference to the Thompson is imprecise because the Thompson, with proper equipment, can cast any style of matrix ever made from 5 to 48 points in size.  The Thompson was designed to cast with Linotype matrices and an original "native" Thompson matrix format (ultimately in two variations), but by the time Goudy started casting in the 1920s the "native" thompson matrices must have been less common. I do not know if he meant that he made matrices specifically in the native-Thompson format or rather in other formats which would fit the Thompson. A matrix of the same external dimensions as a Lanston Monotype display matrix but without the corner-cuts required for use in the Monotype Type-&-Rule Caster will fit in a standard Lanston display matrix holder on the Thompson. Such plain rectangular matrices are shown at various points in the Kellerman film.
Goudy's third reference, to the "foundry automatics," must refer to ATF Barth casters (as I'm not sure that he had access to any foundries using European automatic casters such as the Stempel or Küstermann). Although foundry-style matrices all have a certain general similarity, there is a great variation in dimensional detail among them.
We know from a photograph in the Library of Congress' Goudy collection, reprinted on p. 62 of Bruckner's biography that Goudy owned a Nuernberger-Rettig Type Caster (also known as a Universal Automatic Type Casting Machine) Whether he actually cast with this machine is as yet unknown, but it was right there in his studio. 
2. As a point of trivia, it happens to be for 36 point Series No. 63 as well, which strongly suggests that Goudy was just recycling a Lanston illustration. Curiously, it does not appear in my mid-century Lanston specimen; I have to go back to at least my 1926 specimen, where it is shown by number without name. The drawing of a matrix from "Matrix Information" almost actually resembles Latin Antique; the one from Typologia doesn't even come close.
3. Beilenson, in The Story of Frederic W. Goudy , says that Goudy had "Monotype" casting machines (plural, but models unspecified) at Deepdene (before the fire) (p. 57 of the 1965 reprint of the 1939 edition).
5. If you happen to own any type known to have been cast by Goudy, you can help. In regular typecasting, the typemetal enters the type mold through a sort of a funnel or cone. In order that the type be fully formed, the caster (human or machine) has to inject more metal than is minimally necessary for the type. This means that a newly cast type will have a cone-shaped bit of metal sticking out of it (this is called the "jet"; it would be a "sprue" in regular metal casting terminology). This "jet" must be broken off, which leaves a rough surface on the bottom of the type. This rough area is subsequently plowed away, leaving a groove in the foot of the type. An examination of (nearly) any type will show this. One of the patented features of the Nuernberger-Rettig was a method of casting type so that the middle of the bottom of the type was recessed. The jet could then be broken off above the foot of the type, eliminating the need to plow a groove. So a type cast on a Nuernberger-Rettig machine will have a semicircular recess where the groove would be, with a rough spot in the middle of this recess where the jet was broken off but left unplowed. If we could find even a single type known to have been cast by Goudy which has these features, we'd know that he did, in fact, cast on his Nuernberger-Rettig.
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