Gobrecht 3-cent design?

To which Gobrecht design does this letter refer?
"Mint of the United States
Philadelphia
March 25, 1851
Sir,
I have the honor to transmit herewith (enclosed in the paper marked No. 1), specimens of a three-cent piece, made conformably to the design of Mr. Longacre, the present Engraver of the Mint.
In the paper marked No. 2 will be found specimens of the same coin, struck from dies made by Mr. Gobrecht, the predecessor of Mr. Longacre.
In compliance with the course heretofore adopted, on similar occasions, I submit these coins, through the Department, for the examination of the President, with the request that I may be informed if either, and if so which, of them meets his approval. Without presuming to indicate my own judgement in the matter, I respectfully suggest that if no marked inferiority is found in the design of Mr. Longacre his present official position makes it manifestly desirable that it should be accepted.
Very respectfully,
Your faithful servant,
R. M. Patterson, Director
Hon. Thomas Corwin,
Secretary of the Treasury"
Comments
Presumably this one:
http://uspatterns.stores.yahoo.net/j125p147.html
The 1850 Trime J-125 unless this is a trick question.
R.I.P. Bear
No tricks, just a question Meaning this one?
Why the "1850" date rather than "1851?"
I'd guess that the ones in the letter attributed to Longacre would be the 1851-dated proofs of the adopted design (unattributed as a pattern today, although it would stand to reason that the handful of 1851 proofs would be these coins, particularly given the absence of compelling proofs that year for the H10C, 10C, 25C and 50C and original S$1).
The ones attributed to Gobrecht could be the Cap and Rays style pictured above - it is early enough in the year that it is imaginable that the Gobrecht-style pieces were struck a few months earlier, hence the 1850 date.
What is now proved was once only imagined. - William Blake
Having recently won the Mexican-American War, it would have been ironic if we had adopted the Mexican-inspired Gobrecht Trime.
Doggedly collecting coins of the Central American Republic.
Visit the Society of US Pattern Collectors at USPatterns.com.
Of the three-cent silver, too.