  in the case of a quaternion q. Peirce wrote an extensive survey (Peirce 1870), determining the numbers of all algebras with from two to six elements obeying also various other laws (Walsh 2000, ch. 2). To two of those he gave names which have become durable: ‘idempotent’, the law xm = x (for m≥2) which George Boole had introduced in this form in his algebra of logic in 1847; and ‘nilpotent’, when xm = 0, for some m. The history of the publication of this work is very unusual (Grattan-Guinness 1997). Peirce had presented some of his results from 1867 onwards to the National Academy of Sciences, of which he had been appointed a founder member four years earlier; but they could not afford to print it. Thus, in an initiative taken by Coast Survey staff, a lady without mathematical training but possessing a fine hand was found who could both read his ghastly script and write out the entire text 12 pages at a time on lithograph stones. 100 copies were printed (Peirce 1870), and distributed world-wide to major mathematicians and professional colleagues. Eleven years later Charles, then at Johns Hopkins University, had the lithograph reprinted posthumously, with some additional notes of his own, as a long paper in American journal of mathematics, which J.J. Sylvester had recently launched (Peirce 1881a); it also came out in book form in the next year. This study helped mathematicians to recognise an aspect of the wide variety of algebras which could be examined; it also played a role in the development of model theory in the U.S. in the early 1900s. Enough work on it had been done by then for a book-length study to be written (Shaw 1907). 