^{page 289 note *} (1) The incidence of tax is assumed to be appropriately allowed for, e.g. tax is deducted separately from expenses and interest in the U.K. (2) Surrenders are gnored, the assumption being that the values granted are kept within the amounts vailable.

^{page 290 note *} By analogy with equilibrium in statics we could describe a fund as immunized if the first derivative is zero, and the immunization as stable stable or unstable according the second derivative is positive or negative.

^{page 300 note *} It may be that with-profit premium rates are left unchanged for many years, and that the nominal formula employed becomes obsolete and out of step with current experience. It is desirable, however, to re-express the premium rates actually charged in the light of the actuary's assessment of the future experience at the time of issue. The re-cast formula expresses the plan or intention at the time a policy is issued, and it is a valuation on the basis of this original plan which earns the title of a ‘natural valuation’.