Science on the Farther Shore
Rediscovery and Reappraisal
We have no Science Citation Index for the early 19th century, but it seems a safe bet that the works of Gauss and Legendre were more widely noted than those of Robert Adrain. Indeed, Adrain's papers seem to have gone almost entirely unnoticed for 60 years, until Cleveland Abbe and Mansfield Merriman reprinted some excerpts in the 1870s, both in American journals. The republication finally attracted some attention on the other side of the Atlantic: J. W. L. Glaisher wrote a stern critique. Thereafter, Adrain dropped out of sight again for another 50 years, until Julian L. Coolidge and M. J. Babb wrote appreciative biographical articles in the 1920s. There have been a few more re-appraisals since then, such as those of Dirk Struik, E. R. Hogan and Jacques Dutka. Most important, Stephen M. Stigler has included three of Adrain's papers in a compendium of early sources on mathematical statistics in the U.S., making readily available what might otherwise be a very rare item of incunabula.
Modern judgments of Adrain range from warmly sympathetic to glacially cool. Anders Hald, in a vast work on the history of statistics, praises Adrain's "intuition and common sense." But Stigler describes Adrain's arguments in support of the normal distribution as "more wishful thinking than proofs."
Adrain's priority and originality have also been questioned. The article on least squares appeared in an issue of The Analyst dated 1808, but Stigler has found evidence it was not actually printed until 1809, so that it may not have preceded Gauss's publication, which came out in the spring of that year. The doubt here is strictly about priority, not borrowing: Adrain could not possibly have seen Gauss's book before writing his own paper. On the other hand, Adrain could very well have seen Legendre's 1805 description of the least-squares method. Babb found a copy of Legendre's book in Adrain's library, although there is no way of telling when it was acquired. Adrain never mentions Legendre's work.