[1]
See, for example, L. J. Comrie, in B.A.A.S., Mathematical Tables, v. 1, p. xi-xii, London, 1930; Interpolation and Allied Tables, reprinted from the Nautical Almanac for 1937, p. 928-929, London, 1936.  In these accounts the term 'modified differences' is given a special meaning, now accepted fairly widely.  This use is not the same as that of Herget & Clemence, who use the term in place of the more familiar first divided differences (first used by A. De Morgan, Differential and Integral Calculus, p. 550, London, 1842); A. C. Aitken has suggested the symbol for these (see H. Freeman, Mathematics for Actuarial Students, Part II, Finite Differences, Probabilty & Elementary Statistics, Cambridge, 1939, p. 41. 

See, for example, L. J. Comrie, in B.A.A.S., Mathematical Tables, v. 1, p. xi-xii, London, 1930; Interpolation and Allied Tables, reprinted from the Nautical Almanac for 1937, p. 928-929, London, 1936.  In these accounts the term 'modified differences' is given a special meaning, now accepted fairly widely.  This use is not the same as that of Herget & Clemence, who use the term in place of the more familiar first divided differences (first used by A. De Morgan, Differential and Integral Calculus, p. 550, London, 1842); A. C. Aitken has suggested the symbol for these (see H. Freeman, Mathematics for Actuarial Students, Part II, Finite Differences, Probabilty & Elementary Statistics, Cambridge, 1939, p. 41.