authored source, as well as its dissemination through printing, would yield to the ‘untiring action and unerring certainty of mechanical agency'/
Before being handed over to the printers, the tabulations were checked for accuracy using various verification techniques. This chapter first describes verification processes. It then discusses the generic processes of typesetting, proofreading, stereotyping, and printing, with special reference to the needs of the table makers, specifically the management of errors and attempts to increase readability through improved typography.
Verification by Double Computation
One of the main techniques of avoiding errors of calculation was for the same calculation to be performed by different computers, and then for the independently computed results to be compared for discrepancies. The principle of the method was that two computers, working without collaboration, are unlikely to make the same mistake. The practice appears to have been well-established by the nineteenth century. Nevil Maskelyne, Astronomer Royal, used the system in the preparation of the Nautical Almanac, first published in 1767.^ The Almanac
tabulated the distance of the moon from the sun and the bright stars at intervals of a few hours and allowed mariners to determine ship’s longitude at sea using the method of lunar distances.^ In Maskelyne’s scheme one computer was called the ‘computer*, the second computer was referred to as the ‘anticomputeri and the
^ The phrase is Lardners. See Lardner (1834), Works, Vol. 2, p. 169.
^ Maskelyne (b. 1732), was the fifth Astronomer Royal and served from 1765 to until his death 1811. For an admiring biography of Maskelyne see Howse (1989).
® Forbes (1965), pp. 391-401. For an account of the importance of astronomical navigation to colonisation and trade see Ronan (1967), Ch. Ill, pp. 47-9.
checker was called the ‘comparer’/ The computer and anticomputer worked separately, usually from their own homes, in a ‘cottage’ network, and their results were sent to the Astronomer Royal who sent them to the comparer for consistency checking. The effectiveness of the technique relies in part on the absolute
independence of the computers. Two computers, Keech and Robbins, were instantly dismissed when, hired to assist in the preparation of the Almanacs for 1771 and 1772, they were found to be ‘acting collusively’.®
The technique of double computation was not foolproof. It was not unknown for computers to produce the same incorrect result despite insulation from each other. Such errors would avoid detection by a comparer and Lardner moralised with characteristic puff that ‘falsehood in this case assumes that character of consistency, which is regarded as the exclusive attribute of truth’.® Lardner cited three instances of discovered errors being first masked by their agreement.^ He reported that de Prony on occasions found ‘three and even a greater number of computers, working separately and independently, to return him the same numerical result, and that result wrong’ It seems that de Prony was not alone. Lardner reports that Lieutenant W. S. Stratford had similar experiences preparing the Nautical Almanac in the 1830s.® In the third instance cited by Lardner, Francis Baily, suspecting an error in a newly published set of astronomical tables which
^ Ibid., p. 85. For use of the term 'anticomputer' see Croarken (2002, unpublished).
® Ibid. Also Forbes (1965), p. 394. Forbes does not cite the date of the dismissal. Croarken (2002, unpublished) gives the date as 1770. Croarken also reports that in addition to firing the two miscreants Maskelyne demanded that they pay for the additional work of the comparer. ® Lardner (1834), Works, Vol. 2, p. 134.
^ Lardneris views are discussed in more detail in Chapter 3. ® Ibid. Emphasis.
® Lardner refers to one 'Mr Stratford, the conductor of the Nautical Almanac’ with no further identification. Works, Vol. 2, p. 134. This is evidently L t W . S. Stratford, Superintendent of the Nautical Almanac, 1831-1853. See Superintendents o f The Nautical Almanac & Heads o fH M Nautical Almanac Office [<http://www.nao.ri.ac.uk>].
Chapter 2: Verification, and generic processes 76
had already been verified by comparison ‘with great care and attention’ by
Stratford, recomputed the position of the star, and himself ‘obtained precisely the
same erroneous numerical resulf.^° The occurrences could have resulted from the
same flawed procedures being correctly followed by different computers, or from the same incorrect starting values or erroneous auxiliary tables being used by the independent computers. However, Lardner does not offer any explanation for these coincidences. In drawing attention to the unreliability of verification by double computation he appears to be more concerned to advertise the deficiencies of non mechanised methods than to analyse possible causes.^^
To further reduce the risk of error the separate computers were sometimes given computationally different but mathematically equivalent formulae to find the same result.''^ If mathematical relationships are expressed in different but equally valid ways, the process of evaluation follows a different computational process: the order of operations may be different as might the specific arithmetical functions used. Babbage gave an example in which an algebraic expression arranged one way required thirty-five multiplications and six additions. Arranged differently, the same result was produced using five multiplications and one addition.^^ The context of his observation was computational efficiency rather than psychology. In the context of error detection, the purpose of using different arithmetical
procedures helped to disrupt shared mental and operational patterns that might lead to the same incorrect result. The technique reduced the risk of error but could
Lardner (1834), Works, Vol. 2. p. 134. Italics original.
Chapter 3 argues that it was in Lardner*s interests to magnify the problem of tabular errors.