6O NO TES ON FORES TR Y. 



loss of 22 per cent, by taking the quarter girth, and 

 nearly 4 per cent, by taking the area at the middle 

 of the log. 



Either of the three following methods may be 

 substituted for the rule given above, and one of 

 them should always be had recourse to when accu- 

 racy is required : 



Formula 1. To the square of the diameter at the 

 middle, add one- twelfth the square of the difference 

 of the extreme diameters, and multiply by *7854 

 for the mean area, and by the length for the cubic 

 contents. Thus, with the log above measured 



Formula 2. From the mean of the squares of the 

 two extremes deduct one-sixth the square of their 

 difference, and multiply the product by *7854 and 

 by the length. Thus, proceeding with the same 





Formula 3. To the square of the mean add one- i 

 third the difference between it and the mean of the 

 square of the extremes ; multiply by "7854 and by 

 the length. Thus- 



Square of the mean, 81. Mean of the squares of 

 the extremes, 144 + 36 = 90; difference 9, one-third 



