llation, the principal
operations having been effected in 1863, 1867, 1870, 1874, 1883 and
1899. Annuities of this class do not affect the public at all, except of
course in their effect on the market for government securities. They are
merely financial operations between the government, in its capacity as
the banker of savings banks and other funds, and itself, in the capacity
of custodian of the national finances. Savings bank depositors are not
concerned with the manner in which government invests their money, their
rights being confined to the receipt of interest and the repayment of
deposits upon specified conditions. The case is, however, different as
regards forty millions of consols (included in the above figures),
belonging to suitors in chancery, which were cancelled and replaced by a
terminable annuity in 1883. As the liability to the suitors in that case
was for a specified amount of stock, special arrangements were made to
ensure the ultimate replacement of the precise amount of stock
cancelled.

_Annuity Calculations._--The mathematical theory of life annuities is
based upon a knowledge of the rate of mortality among mankind in
general, or among the particular class of persons on whose lives the
annuities depend. It involves a mathematical treatment too complicated
to be dealt with fully in this place, and in practice it has been
reduced to the form of tables, which vary in different places, but which
are easily accessible. The history of the subject may, however, be
sketched. Abraham Demoivre, in his _Annuities on Lives_, propounded a
very simple law of mortality which is to the effect that, out of 86
children born alive, 1 will die every year until the last dies between
the ages of 85 and 86. This law agreed sufficiently well at the middle
ages of life with the mortality deduced from the best observations of
his time; but, as observations became more exact, the approximation was
found to be not sufficiently close. This was particularly the case when
it was desired to obtain the value of joint life, contingent or other
complicated benefits. Therefore Demoivre's law is entirely devoid of
practical utility. No simple formula has yet been discovered that will
represent the rate of mortality with sufficient accuracy.

The rate of mortality at each age is, therefore, in practice usually
determined by a series of figures deduced from observation; and the
value of an annuity at any age is found from these numbe