438 ESTIMATION OF INCREMENT 



periods, when, provided no thinnings have taken place, the 

 difference in the total contents will give the increment over 

 the period taken. To be of any real value, the measurements 

 must be very accurate ; and to avoid complications the con- 

 tents just after a thinning should be known and compared 

 with measurements taken before another thinning is made. 

 Now, suppose that a crop, after being thinned, contained 

 1500 cubic feet of saleable timber, and that 10 years after- 

 wards the saleable contents were computed at 2200 cubic 

 feet. Then the increment for the period will have been 700 

 cubic feet, and the average annual increment for that period 

 will have been 70 cubic feet. 



Possessed of these data, it is quite easy to show at what 

 rate of interest the volume of the crop has been increas- 

 ing; this information of course being most valuable. It is 

 most important to reckon the rate of compound interest (and 

 not simple interest), for the result is the same whether one is 

 reckoning in cubic feet or in s. d. 



The easiest way to find this rate of interest is to find the 

 proportionate amount to which I cubic foot has increased in 

 the 10 years, and then to refer to interest tables l showing 

 the amount of I () at different rates per cent, for different 

 periods. 



Now, 1500 amounts to 2200 in 10 years. 



Therefore, i - = 1-46. 



1500 



Hence, on referring to tables, it is found that I amounts to 

 1-46 in 10 years at 3f per cent, or 3-75 per cent. 



It is, of course, absolutely fallacious to argue that 



On 1500 the gain is 700 in 10 years 

 ,,ioo 46-6 10 



Therefore, in I year the gain per cent, is 4-66. 



The true rate of compound interest as already found by 

 reference to tables, can also be found in the following way, 

 which is given here, because it will help to explain some of 



1 Vide Appendix C. 



