76   Life Contingencies

The amount of labour involved in the formation of all the elementary functions in a complete select table would be prohibitive. If for example the ages at entry were from 15 to 60 there would be 46 separate tables. It is however generally assumed that the effect of selection "wears off" in a definite number of years called the period of selection; so that, after this period has passed the mortality may be taken as a function of the attained age regardless of the duration. The result is that a "trunk" or "ultimate" table is formed into which run the different branches covering the period of selection for the different ages at entry.

4. The English Life Table No. 8 is an aggregate table formed from population statistics. So is the Carlisle Table. The HA" Table is an aggregate table formed from assured male lives. This table is based upon the experience up to 1863 of some twenty Assurance companies in Great Britain. The American Experience Table is an ultimate table mainly based upon the experience of one of the oldest American companies. It was published about 1868.

The O[`r ir] is a select table based on assured male lives who had taken out whole-life, non-participating assurances in English companies. The experience covered the period 1863-1893. The period of selection was taken as 5 years. The ages at entry for the select portion of the table were from 20 to 75 inclusive.

5. In order to distinguish the age at entry in our symbols, a bracket [ 1 is written around this age in the suffix. The duration is then added until the ultimate part of the table is reached when a single suffix can be used.

Thus q[x] represents the rate of mortality between ages x and x+l for a person selected at age x.

q[251+3 represents the rate of mortality for a person who is aged 28, having been selected at age 25.

If the period of selection is 5 years, then

q[25]+n -q2,+n where n 5, and this symbol represents the rate of mortality for a person who is aged 25+n and who had been selected at an age younger than 21+n.