VALUE OF COPYHOLDS. XXI 



of the value of the life in one year. Multiplying by 

 dQ, the chance of this occurrence,, and integrating from 

 6=0 to 6 = 1, we find 1 +-| rar for the mean sum, 



and P i^P-f^AP for the mean life. If the time 

 allowed for renewal be more than six months, the rule 

 (without this correction) gives an advantage to the lessor; 

 if six months, to neither ; if less than six months, to the 

 lessee. Substitute 1 + -J- r a,r and P A P -j- a A P 

 for II fine and a life P, and we have 



E-A 



{l+ir-ar ]; 



which I believe to be the most correct rule that can be 

 given for the present value of all the fines upon a single 

 life renewable for ever, the value of the present life 

 being A, the tabular value of the best life P, that of 

 a life one year older P AP, the fraction of a year 

 allowed for renewal a, r the interest of one pound for 

 one year, and E the perpetuity. By substituting nE 

 (A + JB + C-h ---- ) for E-A, the value of all the fines 

 from an estate held on any number of lives is found. 

 Similar considerations apply to the present value of IL 

 to be received in a of a year after the death of a life A. 

 The offices frequently pay in three months after the 

 death is proved, whereas the tables are calculated for 

 the end of the year of death. Again, they rate all lives 

 as they will be at the next birthday, the parties being 

 one with another half a year younger. To a party who 

 dies at the end of of a year, the office has paid by the 

 end of the year 1+ ( 1 a 0) r which, treated as be- 

 fore, gives 1 -{--J- r ar. And the present value of I/., 

 which is computed by the office from 



(where Jc is the proportion of profit demanded) may be 

 more strictly computed from 



E-A IAA ,_ , . 



- Ir _ f JL x (] +lr_,) 

 Y 4 



