FRENCH FIR MANAGEMENT IN THE VOSGES 543 



the growing forces. We feel that the normal spacing for the fir is that 

 between these two conditions — that is to say, when the soil commences 

 to become covered with vegetation, when seedlings grow but do not 

 develop. At this limit, moreover, the trees are well balanced and 

 vigorous. 



From the result of our experiments, extending over areas of suffi- 

 cient size and diversity of conditions, we found that when the space 

 separating the crowns exceeds fifteen times the diameter of the bole, 

 the soil is more or less covered with grass or with advance regenera- 

 tion ; on the other hand, when this spacing is less, the soil being either 

 bare or covered with seedlings which cannot develop, all conditions of 

 the height of cover are about equal. 



With this explanation, this is how we proceeded to determine the 

 average spacing of the trees in the stand appearing "fully stocked" : 



Let X be the average relation between the diameters of the crowns 

 and the diameters of the bole d, d' , d" , d'" of the boles; S the surface 

 of the ground experimented with ; .y the basal areas. 



The diameters of the crowns are dx, d' x, d" x, d'" x . . ., and if one 

 considers that the crowns are irregular, but that, the stand being com- 

 plete, their projection will occupy the entire soil surface, one can then 

 admit, without making an appreciable error, that the surface of each 

 crown is equal to that of a square having for the sides the diameter of 

 the crown ; the total area of the crowns will then equal d~x^ -\- d'-x- -f- 

 d"-x-, an amount equal to the surface of the soil, or d'X- -\- d''^x- -j- 



d"-x- -f . . . = 5; from which .r = \ -— -; — ~- — ^ — -— ,- , or, the 



basal area .9 being the sum of the sections of the boles at breast height, 



one lias — -[- 1 \- . . . = S , or d- -\- d^ -\- d^ -\- . . , = ^-^ ■ 



4 4 4 T ' 



6" 



hence .^-= > 4. c = -\/ _ = a/ ?:Z_5l:? ; for example, with a surface 



TT 



of 3.18 hectares and a basal area of 21.813 square meters, we would 



^ 2t.8t3 

 With this very simple formula, one can then easily determine this 

 average relation by careful stock-taking (on the carefully chosen ex- 

 perimental areas), including all diameter classes. From our experi- 

 ments, we have concluded that with a relation over 20, the trees have 

 their individual shape and not their "forest" form. 



