FUNDAMENTAL PRINCIPLES 17 



enclose it within a small circle or square. Opposite the average 

 point enter the number of trees that the point represents. 



Note. — The following short cut in averaging saves a great deal of time. Instead of adding 

 the actual values represented by the plotted points, let the first heavy line below and a similar 

 one to the left of the group of points to be averaged represent zero lines. Now find the value 

 of each point in terms of the number of spaces it is located from the new zero. Average, 

 and locate the new point accordingly. 



(c) Draicing the Curve. 



6. Connect the average points by fine straight hncs. This will help 



to show the general direction of the curve. 



7. Next locate the direction of the curve by eye. In doing this 



imagine the curve as a flexible steel band so placed that the aver- 

 age points, which are considered as magnets of a strength 

 dependent on the number of trees represented, are about equally 

 located on either side of it. The band will then take a position 

 nearest the points with the greatest attractive force. After 

 locating the direction of the curve by the eye, sketch in it free- 

 handed as smoothly and regularly as possible, and finally smooth 

 off the irregularities by means of a spline or adjustable curve. 



8. From this curve construct a table of heights for each diameter in 



whole inches by noting the points where the respective perpen- 

 dicular lines from the co-ordinate axes meet the curve. 



C. Discussion. 



1. Supposing that the method of first averaging and then plotting the 



averaged points were used instead of that described above, explain 

 in detail how the method of proced\ire would be varied. 



2. Why can not the data be averaged in the above problem just as well 



without plotting values and drawing a curve? 



