Periodical Literature 341 



The proof for the approximate correctness of the formula is given. 



A niimber of approximation formulae for giving contents of 

 logs are elaborated. 



To these mathematical considerations is added a discussion on 

 ''Anschauung,'' "conception," or the ability of securing a mental 

 picture of the meaning of measurements ; for instance if a larch is 

 given as containing 15 cubic feet, can we picture it and have an 

 idea of its linear dimensions. Having been accustomed to go to 

 tables, this ability remains undeveloped, a condition which is 

 medieval as compared with other sciences ; progress in mensuration 

 can be expected only from methodical cultivation of "Anschaiiung." 



To develop this ability, it is necessary first to have conceptions 

 of the unit measures and their relations. Starting with a Christ- 

 mas tree of 20 dm (80 inch) height, we may realize that it represents 

 a cube of 1 liter ( = cubic decimeter = 61 cubic inches). This 

 conception can be extended to stouter and higher trees and grad- 

 ually by practice an eye is developed. Finally, however, there 

 is a limit even for the practised eye, beyond which the conception, 

 on account of the many liter, is not any more clear, when the ap- 

 proximate calculation must help out. Then, we can secure a 

 conception that the tree asstimes the form of a cylinder with the 

 diameter at breasthigh and the form height. One can, then, 

 mentally calculate the basal area with that height and get a 

 conception of the size of the tree. Or we can apply formula (2) 

 and come to the conception that it is possible to change the normal 

 tree body into 40 cubes of the side of d. b. h. The eye learns not 



h 

 only that normally (when — = 100, /=5) these 40 cubes represent 



d 



actually the tree volume, but also that when there is a deviation 



from these normal conditions, a complement is necessary. By the 



conceived change of the tree body into elementary unit bodies the 



estimate becomes siu-er. 



Again formiila (3) tells that normally the tree volume represents 



a cube of side. This side of the cube would exceed the d. b. h. 



3 



2 Vs times or 1 Vec? on each end ; to secure a conception in comparison 



with the tree, we would have to move out this side so that there 



develops a cube which on all sides symmetrically encloses the 



tree like a cuff. The practised eye also recognizes at once that, 



for instance, a long spruce pole can be represented by a body, the 



