What's established so far:
Going back to Muley Gil's SCSW p158-159 reference it states "Pre-production TL in 45 Special caliber, serial # 09, actually thought to be chambered in 45 Frankfor[d] caliber built for U.S. government tests in 1906...The 45 Frankford was an experimental cartridge before the 45 ACP."
Smith & Wesson 1857-1945, by Neal & Jinks. Page 208 states:
"In 1908 or 1909 [S&W] seriously considered introducing a model that was to be called the "45 Special." This cartridge was designed for use in the 44 Hand Ejector 1st Model [New Century]. The cartridge was a revolver cartridge developed for military use at the Frankford Arsenal."
In 1909 the Frankford Arsenal produced .45 Revolver Ball Cartridges Model 1909. They were never made commercially.
REF:
.45 Colt - Wikipedia, the free encyclopedia
Box for sale here:
WTS: Pristine Frankford Arsenal Box Of Model 1909 .45 Revolver Ball Cartridges
Essentially these were 45 Colt cartridges with standard primers, same overall length with a larger diameter rim made to between .536" and .540" to more reliably eject in DA revolvers. 'Balloon' head 45 Colt rims of the time were .500" -.505" and 45 Schofield rims were .522".
Both pictured in the below link and referred to as 45 Frankford Cartridges that were not involved in the Army Trials of 1906-7. And neither of which are the 45 S&W Special/45 Frankford. This also answers the correct Frankford spelling issue.
File:Colt .45 LC Cartridges.JPG - Wikipedia, the free encyclopedia
In 1906 various experimental 45 auto rounds were being developed as were the pistols for them. Both rimless and SEMI-RIMMED rounds were developed. REF:
The Frankford Arsenal experimental 1906 FA 4 06, .45 caliber round.
Question:
Considering the above established facts, which then was "The 45 Frankford [that S&W referred to as the 45 Special] was an experimental cartridge before the 45 ACP" as stated in the SCSW?
The Frankford Arsenal 1909 .45 Revolver Ball Cartridge was certainly not produced in 1909 without prior experimentation and seems to be the most likely candidate chambered in the Triple Lock (as the 45 special) and used in the 1906-7 U.S. Trials.
Maybe someone who owns one of the TLs in 45 Spl or that can communicate with someone who does, could confirm the chamber dimensions.