"He [Beeler] is also the inventor of a simple and accurate form of pantograph, which changes the proportions of the letters according to taste, isntead of following the one fixed templet from six-point to seventy-two point, as is usually done. He has also invented a combined routing and ruling machin e- which is a great time-saver and capable of doing wonders - and is about completing a machine for engraving type which will not only alter the proportions of letters from the one fixed templet, but will also cut back-slope or italic from the same templet." (417)
We know nothing of the mechanical details of this pantograph. Neither, strictly speaking, do we know whether it engraved patrices, engraved matrices, or simply altered drawings or patterns. However, it is in my opinion most likely that it was a patrix-engraving machine. (The passage notes that his back-slope/italic machine was "a machine for engraving type". The use of "not only" to describe this machine suggests that his earlier machine was also an engraving machine. While the first pantograph used in type-making in America (the Central Type Foundry machine, in 1882), and while the machines of Schroeder and Werner were derived from this matrix engraving machine, other remarks in Loy suggest that in his view direct matrix engraving was in 1898 a relatively new development.)
We do not know for whom he constructed it, although he was employed primarily at MacKellar, Smiths and Jordan and, after the 1892 amalgamation, American Type Founders. If any patent for this pantograph was issued, I have not located it.
Beeler went on to direct the "Special Matrix Department" at the Lanston Monotype Machine Company. At one point (probably 1921), he engraved the Lord's Prayer, presumably on a patrix. Matrices were electroformed from this and distributed; many types have been cast from it. (I have three identical examples of the type, but no matrix.)
One online source claims that he engraved this type "on a pantograph machine of his own invention and making" ( http://www.holoworld.com/holo/worlds_smallest_lords_prayer.html) However, this site offers no evidence in support of this and no source for this claim. By this time the Lanston Monotype Machine Company had been commercially engraving both patrices and punches first on a Benton pantograph and later on machines of their own manufacture (probably Pierpont machines, though the details of Lanston's matrix department are obscure).
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