EXPECTATION VALUE. 135 



Thinning in the year n = --- - -*j 



_ T xl'op r 



~ 



_ T 

 ~ 



~~ 



Expenses : 



(1) Annual expenses to be incurred from the year m to the 

 year r ; their present Value amounts to : 



00 /> 



- + - ~ + . . . + - - = (according to Formula VI.) 

 I'op I'op- l'op r ~' 



e d'm/~ TO "h 

 = e (l'op r - m -l) = 'op V _ = E (l'op r - m -l) 



l-op r ~ m x'op l'op r ~ m l'op r ~ m 



(2) Eent of soil to be paid from the year m to the year r ; 

 its annual amount may be denoted by S X 'op ; the total 

 present value of the rent of the soil during r - m years amounts 

 to: 



Sx'op tS_x^op_ , _, Sx-op _ S X'op (I op r ~ m 1) 



l- op Top 7 " i-op r ~ m ^^ 



= S (l'op r - m -l) 



The formula for the expectation value of a wood stands 

 therefore as follows: 



r . _ Y r + T n x l-op r - n + . . . + T q x l-op r - - (S + E) (l- 



-- 



Example. A fully-stocked Scotch pine wood, worked under 

 a rotation of 80 years, is feloniously burned when 45 }^ears 

 old ; what compensation per acre should be paid to the owner, 

 if the expected returns are those indicated in the table at 

 page 122. 



/t,-H 



.*. c , I ,, A * 



^ ^ 



-- 3 0. 



*$</ i '->T AN ^ J ~ " ( ' ' ^' ; - ;X? ^ P ^ 



