MECHANICAL AIDS IN STEM ANALYSIS 683 



is readily solved on the adding-machine or on the slide-rule and adding- 

 machine combined. There are three operations : First, work out the 

 parenthetical quantity on the machine. Second and third, calculate the 

 stump and tip volumes with one setting of the slide-rule for each, for 

 either the Bn or Ji^ may be divided by 3 mentally. For example, on a 

 cordwood operation with 4- foot sections, take the basal areas from a 

 table such as that in the Appendix of Graves' Mensuration. List these 

 values in turn on the machine and take a subtotal. Then, with the 

 repeat key on, pull the lever twice after setting up the subtotal ; then 

 once and take another subtotal. This gives the used volume. It fre- 

 quently happens that the stump height is .5, .75, i.o foot, or some other 

 fraction easy to handle. If so, the stump volume is obtained mentally 

 and set in the machine. Otherwise, set the basal area on the D scale 

 of the slide-rule, set i of the C scale over it, and under the height of the 

 stump on the C scale read the volume on the D scale. The volume of 

 the tip is obtained similarly and added. 



If one wishes to correlate age and diameter or height and diameter, 

 the ordinary method is to arrange the sheets according to diameter 

 classes, transfer the values desired, average and then plot the average 

 values. The listing, totaling, and averaging may all be done in one 

 operation on an adding-machine. With a machine like the Burroughs 

 or Wales, use the left side for one set of figures and the right side for 

 the other set. Leave enough columns between the sides to take care of 

 extra figures in the totals. The same work is performed by the use of 

 the split-key device on the Dalton machine. By the use of a table of 

 reciprocals, figure the averages. This is easily done on a Dalton. Then 

 plot the averages in the ordinary manner. 



If one wishes to determine the average rate of growth of an uneven- 

 aged stand, the adding-machine is again helpful. The following 

 method was used in an investigation made during the summer of 1918 

 on a cordwood operation where the second cut closely approximated the 

 breast-high point: 



First. Lay oflf a scale on cross-section paper twice as large as is 

 desired for the finished graph. Let the horizontal scale be units of 

 radius and the vertical scale units of radial growth for ten years, inside 

 bark. The field measurements show that when a tree had a certain 

 radius, the radius had increased to a certain length during ten years. 

 Then on this first radius plot the increase; plot for each radius the 

 corresponding increases ; list and add the values ; average and plot and 

 draw in a finished curve ; then convert the scale of the graph to diameter 



