Stem Analyses. 165 



stem analyses could thus be removed by tabulating the data in 

 the manner described. The advantages of recording the data and 

 measurements in this form are obvious, and at the same time the 

 whole arrangement is much more logical, since the measurements 

 for any particular decade all fall in the same column. 



The second point, — namely, the recording of diameters directly 

 instead of radii, which will necessarily be doubled later, has al- 

 ready been sufficiently explained, and the advantages are self- 

 evident. 



For the determination of the dimensions of the several "tips" 

 or "tops" or "cones," which appear as we trace the history of 

 the tree from decade to decade, (which was the third source of 

 trouble mentioned), it is recommended that the graphic method 

 be employed. It is a simple matter to plot the height on age by 

 taking the values given in columns "b" and "c"; and once a 

 curve has been drawn connecting the several points plotted, the 

 height of the tree at an age of 10 years, 20 years, 30 years, etc., 

 etc., can be read directly from the curve. For example, the data 

 in columns "b" and "c" give the curve shown in Figure 2, (page 

 — ), and from this curve it is easily learned that the height of the 

 tree at the age of 50 years was 60 feet. The top of the tree, 

 then, at the age of 50 years, fell between sections 5 and 6; and 

 the length of the cone which had a base of 0.9 inches diameter 

 (column 5, under "h," and opposite section 5) at that period, is 

 obtained by subtracting the height of section 5 from the total 

 height of the tree at that age,— that is, 60-57.8 feet, or 2.2 feet 

 In like manner, the heights of the other small tips, or cones, can 

 be just as readily found for any and all other decades. 



As a test of the accuracy of this method when compared with 

 the old method, the calculations were carried out for the volume 

 of the tree at every decade, by both methods, and the results 

 are shown graphically in figure 3. It will be observed that the 

 plotted values fall at different ages, — those by the new method 

 falling at the ages of 10, 20, 30, 40, 50, 60, 70, 80 and 85 years, 

 while by the old method they occur at the ages of 5, 15, 25, 35, 

 45. 55» 65, 75 and 85 years. When the two curves are drawn, 

 they are found to coincide throughout their whole course. This 

 proves the accuracy of the new method, and its adaptability to any 

 age tree. 



