Judd 1150 is an 1871-dated version of Longacre's Seated Liberty obverse combined with a normal eagle reverse as used on the regular With Motto Silver Dollar Proofs. Saul Teichman suggests a known population of half a dozen examples, but the PCGS CoinFacts APR lists eleven different auction appearances since 1992. Undoubtedly, some duplication appear in those listings, but the overall population is probably closer to a dozen pieces.
Nothing was going on in 1871 that required a new Silver Dollar, so these were probably made at the Mint to have something new and unusual to sell to collectors. These were sold as part of complete, off-metal sets of patterns; few, if any, of those sets remain intact today.