41 



is necessary tnat the number of trees per unit of area should be one 

 and tht same for all the age-classes. For let v^, n^, v-^ be res- 

 pectively these numbers for the several classes^ then 



^1 = «i "i ;.% = ^2 "2 ; % = l^S^S' 



and by formula (vii) 



7 _ «1 "l yi + «2 "2 ^2 + «3 ''8^3 . 



«! Vl + «2 "2 + S'S'S ■•■■■• 



by formula (vi)' 



■ r also = "l^l + «^^2 + "3^3 . 



"l + "2 + "S 



and we must hence have 



"l = "2 = "3 = 



It has now been shown that formula (vii) holds good only on 

 condition (a) that the mean annual increment is one and the same 

 for all the girth classes, and.(i) that the number of trees per 

 acre is one and the same at all ages, assumptions that are incom- 

 patible with actual facts. Hence the employment of this formula 

 should be avoided. 



If in formula (vii; we assume that n^ = «2 = ^s = " j 



that is to say, that the number of" stems in each age-class is the 

 same, we have 



Y - Vx + Vi + Vz 



n 

 =. the arithmetical mean of the ages of the sample trees. Now, in 

 Urich's method of valuation survey each sample tree corresponds 

 to one and the same number of trees in the crop. Hence if, in 

 working according to thatmethod, we deduce the mean age of the 

 crop by taking the menu of the ages of the sample trees, we obtain 

 the same result as if we had adopted formula (vii), which has just 

 been shown to be incorrect. 



Nevertheless, as by far the easiest way of determining the meau 

 age of a crop is to take the simple arithmetical mean of the ages of 

 the sample trees, let us examine under what conditions such a 

 procedure wonld give correct results. 



Let us then suppose that in this special ease the mean age of 

 the crop is equal to the arithmetical mean of the ages of the sam- 

 ple trees. Hence 



yi + Vi + y% ■■■ .y° = y = "i + «'2 + ^s + t'n--- ^^ poj.. 



« ■?!i_4.£2.^.3 ^.J^n mula 



i\ Vi ys '" yx. (v)J 



