ALINEMKNT CHARTS IN FOREST MENSURATION 777 



In practice, in such cases it is not necessary to locate the position of 

 the final axis or calculate its scale by analysis. It is often simpler first 

 to locate its position by drawing two straight lines, each connecting a 

 pair of values on the initial axes which gives the same result on the 

 final, as, for instance, 2, 6 and 5, 3. Since 2-^6 = 8 and 5 + 3 = 8, 

 these must intersect on the 8 point on the final axis, which can then be 



10 



8 



7 



-6 



-4 



_3 



-2 



JOO 



■ 90 

 BO 

 10 



■ 60 



■ SO 



30 



20 



./O 

 <? 



8 



. 7 



6 

 -5- 



-4 

 -3 



-2 



/O 

 9 



d 



.7 

 .6 



■ S 



-4 



-J 



-2 



Fic. 4. — Elementary chart for multiplication. 



drawn parallel to the other axes through that point. A third pair of 

 values, such as 2, 5, will determine a straight line which intersects this 

 axis at the 7 point, thus determining the graduating unit interval, which 

 may then be applied to the remainder of the axis. Or the other gradua- 

 tions may all be supplied by intersections, taking some convenient value 

 of .r and varying successively the values of y and hence of z. 



