I just added the caption and diagram below to the Alto Trombone Timeline and the Alto in Treatises page. Another alto trombone primary source. Notice that the alto trombone is not merely a tenor trombone with an extra-small mouthpiece, but a smaller trombone in a clearly different key.

1853—New York: Allen Dodworth shows position charts for alto trombone in F, tenor trombone in C, tenor trombone in B-flat, and bass trombone in G, in his book, Dodworth’s Brass Band School (see below image; public domain).