rett's method.
(It is also called the commutation method and the columnar method.)
Barrett's method of calculating annuities was explained by him to
Francis Baily in the year 1811, and was first made known to the world in
a paper written by the latter and read before the Royal Society in 1812.

By what has been universally considered an unfortunate error of
judgment, this paper was not recommended by the council of the Royal
Society to be printed, but it was given by Baily as an appendix to the
second issue (in 1813) of his work on life annuities and assurances.
Barrett had calculated extensive tables, and with Baily's aid attempted
to get them published by subscription, but without success; and the only
printed tables calculated according to his manner, besides the specimen
tables given by Baily, are the tables contained in Babbage's
_Comparative View of the various Institutions for the Assurance of
Lives_, 1826.

In the year 1825 Griffith Davies published his _Tables of Life
Contingencies_, a work which contains, among others, two tables, which
are confessedly derived from Baily's explanation of Barrett's tables.

Those who desire to pursue the subject further can refer to the
appendix to Baily's _Life Annuities and Assurances_, De Morgan's paper
"On the Calculation of Single Life Contingencies," _Assurance
Magazine_, xii. 348-349; Gray's _Tables and Formulae_ chap. viii.; the
preface to Davies's _Treatise on Annuities_; also Hendriks's papers in
the _Assurance Magazine_, No. 1, p. 1, and No. 2, p. 12; and in
particular De Morgan's "Account of a Correspondence between Mr George
Barrett and Mr Francis Baily," in the _Assurance Magazine_, vol. iv.
p. 185.

The principal commutation tables published in England are contained in
the following works:--David Jones, _Value of Annuities and
Reversionary Payments_, issued in parts by the Useful Knowledge
Society, completed in 1843; Jenkin Jones, _New Rate of Mortality_,
1843; G. Davies, _Treatise on Annuities_, 1825 (issued 1855); David
Chisholm, _Commutation Tables_, 1858; Nelson's _Contributions to Vital
Statistics_, 1857; Jardine Henry, _Government Life Annuity Commutation
Tables_, 1866 and 1873; _Institute of Actuaries Life Tables_, 1872;
R.P. Hardy, _Valuation Tables_, 1873; and Dr William Farr's
contributions to the sixth (1844), twelfth (1849), and twentieth
(1857) _Reports_ of the Registrar General in England (English Tables,