¹ The writer’s article (“Francis Walking(h)ame and The Tutor’s Assistant” (subsequently referred to as FWTA) in the June 1956 Notes and Queries, pp. 258-61, tried to fill in some of the gaps in our knowledge alluded to by De Morgan in his 1847 Arithmetical Books, p. 80, and only partially answered in Sir Ambrose Heal’s standard history of writing-masters, The English Penman, 1945, p. 111. Although mentioned by Florence A. Yeldham in her 1936 The Teaching of Arithmetic Through 400 years, 1535-1935, p. 105, Walkingame was strangely and unjustifiably neglected.

² Mathematical Gazette xlv, no. 351, Feb. 1961, pp. 1-8.

³ Many of the rules and examples are exactly the same or very similar to those in Walkingame. The two bills given by Dr. Flett had been printed verbatim in many editions, usually with a current date and sometimes with local addresses.

⁴ Mathematical Gazette xlvi, no. 355, Feb. 1962, pp. 27-9, and in a private letter to the writer. Scottish measures were used by Stewart, so it is possible that he used an unknown Scottish edition of Walkingame; these may, however, have been additions dictated by the Dundee master.

⁵ Ibid, p. 68. In a letter to the writer, Dr. Mary Hartley states that her great-uncle graduated at Owen’s College and then lectured in classics before going to Madagascar as a missionary.

⁶ Mathematical Gazette xlvi, no. 356, May 1962, pp. 170-2. Decimals only appear in Part III. Kersey was responsible for separating Fractions and Decimals from Integers. Some who have seen exercise books based only on part of Walkingame have been misled as to the extent of the work done by students using his book.

⁷ Earlier editions did not mention francs, gave Rouen instead of Bordeaux, and stated a livre was worth 1/6, again without alteration from year to year.

⁸ The early Fraser editions carry the date on the title page. Mrs. Townley has kindly enabled the writer to inspect her copy, which is the latest now known. The date can be fixed by comparing the dates of the books advertised with the information from Messrs. Longmans’ Impressions and Copyright books, which were consulted through the kindness of Mr. C. Blagden.

⁹ R. S. Williamson, “Grammar School Arithmetic a Century Ago,” Mathe matical Gazette, xiv, no. 194, May 1928, pp. 128-33, quoted by Yeldham, op. cit. pp. 128-30. See also FWTA, note 60.

¹⁰ Francis Walkingame’s grandfather, also John, wrote his will on June 9th, 1691 and it was proved at the Commissary Court of London on August 13th, 1691, by his relict Anne. Their son John was left a brewhouse; the family house in Monmouth Street, and other property were given to his sisters Frances, Ann and Elizabeth.

¹¹ See Chancery Proceedings for 1724 and 1739 (P.R.O. C.11/1328/44 and 2737/57) on behalf of Charles, Duke of Somerset. I am indebted to the Westminster Reference Librarian, Mr. G. F Osborne for information about the water works, briefly described in H. W Dickinson, Water Supply of Greater London, 1954, pp. 51-2. The technical work was done by George Sorocold and John Hadley and attracted the interest of Sir Godfrey Copley, so it would seem as if John Walkingame would have known some leading engineers and scientists. The name was often spelt Merchant.

¹² Hugh Merchant’s will, dated October 29th, 1714, and proved at P.C.C. (29 Fagg) February 22nd, 1714/5 by his relict Mary, mentioned their unmarried daughter Elizabeth, and apparently feared legal action “concerning the nonpayment of my Rent Charge payable out of Merchant’s Waterworks.”

¹³ His will was dated 10th March, 1751, and proved at P.C.C, the next month, Francis being the executor.

¹⁴ For the general educational background see N. Hans, New Trends in Education in the Eighteenth Century, 1951. R. C. Archibald has listed many of the periodicals in the Mathematical Gazette xiv, no. 200, April 1929. See also the writer’s article in the Oct. 1953 North Carolina Historical Review, xxx, pp. 561-3 and the sources quoted there.

¹⁵ A Wapping Schoolmaster who issued The Schoolmaster’s Assistant … in 1743 with a Preface to Schoolmasters and an Essay On the Education of Youth to Parents … See below for a discussion of this popular Arithmetic book.

¹⁶ There were several Coffee Houses of this name in London. Like other houses this was a centre for many activities and in particular for the Hand-in-Hand Society and Westminster Fire Office, two early insurance companies. E. A. Davies, An Account of the Formation of the Westminster Fire Office, 1952, reproduces Rocques 1746 map in which it is called the Fire Office. The latter company moved in 1751 and may then have vacated the rooms used by Walkingame for his School.

¹⁷ Dated November 4th, 1774, and proved April 15th, 1778 (P.C.C. 172 Hay), it refers to his business “in money taking for some Salesmen and others in Smithfield Market.”

¹⁸ P.R.O. C.12/472/80.

¹⁹ Proved March 6th, 1783 (P.C.C. 153 Cornwallis).

²⁰ Mentioned in the will of his sister Martha (FWTA p. 259).

²¹ These are the figures given for nineteenth century editions in Messrs. Longmans’ books.

²² The dates of successive editions were 1751, 1752, 1757, 1760, 1765, 1766, 1768, 1770, ?, 1771 (10th), ?, ?, 1775, 1776, 1777, 1779, ?, 1782, where the question marks indicate editions which have not been traced.

²³ The details given in the different editions supplement the information in H. R. Plomer … A Dictionary of the Printers and Booksellers Who were at Work in England from 1728 to 1775, 1932. Dod(d) may have taken over the business of Reeve (s) as he was himself succeeded in turn by Johnson and Scatcherd. See FWTA p. 260.

²⁴ Another edition by Taylor was published by Swinney and Hawkins of Birmingham in 1800, and Daniel T. Sheridan edited that issued by Swinney and Ferrall in 1804.

²⁵ Unfortunately the York series is not numbered so it is impossible to know how many editions have been issued but editions for the following years have been traced: 1797, 1799, 1800(2), 1802, 1804, 1805, 1806, 1808, 1809, 1811, 1814, 1818, 1823, 1828, 1836, 1840, 1841.

²⁶ From 1798 until 1824 Crosby was Master of York Blue Coat School. Subsequently described as a gentleman, he lived at 14, St. Saviourgate and died on November 18th 1847 (this information kindly supplied by the York City Librarian from a notice in the Yorkshire Gazette four days later). He wrote his will in August 1844 and dated a codicil in January 1846; it was proved at York on January 11th 1848. It mentions his wife Ann and sons, the Rev. Joseph and Thomas Crosby; Ann was to have his furniture and books but nothing specific was mentioned about his editions of The Tutor’s Assistant.

²⁷ See FWTA p. 259.

²⁸ Editions are known to have appeared in 1844, 1845, 1846, 1848, 1851, 1854, 1856, 1858, 1860(2), 1863, 1864, 1865, 1867, 1870, 1874, 1876, and 1882, the latest known of any edition. These were printed by Spottiswood.

²⁹ Maynard edited Arithmetics by Joyce, Keith, Goodacre, Morrison, Greig, Taylor, Saul and Bonnycastle in the period 1808—53.

³⁰ See FWTA p. 259 note 19 and J A. Harrison, Private Schools in Doncaster … Part II, 1960, chapter 4.

³¹ Gainsborough editions appeared in 1808 and 1810. Mozley moved to Derby in 1815 and after the start in 1827 five others had appeared by 1830, another in 1831 and that in 1838 is described as the thirty-sixth. Birkin’s 51st edition appeared in 1843, his 59th and 60th in 1846 and the last known in 1851.

³² Birkin was a Schoolmaster in Derby and Dronfield. See Journal Derb. Arch. Soc. lxxv, 1955, pp. 153-5.

³³ Rev. Thomas Peacock was curate of Denton chapelry, near Darlington, from 1780 until the end of 1835. He had a boarding school at Thornton Hall and also published The Practical Measurer, 1st edition in 1798. From 1839, until his death in 1851, aged 96, he was Rector of North Tuddenham, Norfolk. His son, George Peacock, Fellow of Trinity College, Cambridge, Professor and Dean of Ely was very influential in the development of Mathematics and probably owed his interest in the subject to his father. The Librarians at Newcastle and Darlington have kindly provided information about Peacock.

³⁴ Guy’s editions are known in 1826 (fourth), 1837 (eleventh) and 1855. He and his son issued many other school books.

³⁵ Details of American editions are given in J M. Greenwood and A. Martin, Notes on the History of American Textbooks, 1899, and L. C. Karpinski, Bibliography of Mathematical Works Printed in America through 1850, 1940. English editions also circulated in America and Dr. Harriet C. Jameson of Ann Arbor Library kindly sent details of two editions not located in this country.

³⁶ Many details are given by De Morgan and Yeldham in the books already cited but the former concentrated on a description of particular books more than an account of their connection, and the latter is very incomplete for the period about 1750. The dates after the authors’ names show the earliest date of publication but not the period of popularity with numerous re-issues and editions.

³⁷ Op. cit. p. 111.

³⁸ See FWTA p. 261.

³⁹ The books are very similar but Walkingame is a little clearer in a number of respects and this slight difference seems to have given it much greater sales. Nonetheless even a brief comparison of the two books and the similarity in title, apart from the direct quotation from Dilworth’s Preface, shows that Walkingame’s book owes much to Dilworth’s.