— 161 — 



heavier the thinnirgs, the greater is the mean when the age of the stand 

 is the same. 



I will now discuss the nature of frequency using the notation of 

 Pearson's memoir^ on Skew Variation. 



The following tables give the chief analytical constants of the skew 

 curves. The second column gives the sum of the percentage number of 

 trees in a stand on which the calculation is based; the third shows the 

 unit in terms of which the 2nd, 3rd, 4th moments {f/^, p^ and i\) are 

 calculated; after the moments follow columns giving ^,, ^^, the diffe- 

 rence between ^^ and the number 3, i. e. 3— jj^ and the "criterion" 

 (iCi=2j32— 3^1 +6) ; the next three columns given the mean, the amount of 

 skew and the distance from mean to mode. 



The amount of skew was calculated from the moments directly by 



the formula SK= ?'^^ '--, and from this the distance from mean 



2 5po-6p,-9 



to mode was obtained by multiplying by . 



Age 



in 

 years 



No 



32i 



37| 

 41 

 47i 

 52 



32 

 37 

 41 

 47 

 52 



Unite 



Ha 



\H 



V-\ 



3-fe 



Mean 



100.1 

 99.9 

 100.2 

 100.0 



99.9 

 100.2 

 100.2 



99.0 

 100.0 



1cm. 

 1cm. 

 1cm. 

 1cm. 



99.8 1cm- 



1cm. 

 1cm. 

 1cm. 

 1cm. 

 1cm. 



Stand with " a " grade. 



11.1791119.3217 

 12.4068121.7493 

 12.8511 19.5214 



I6.108ll35.4888 



347.1585 

 422.5860 

 441.2438 

 771.2744 



16.670234.8887 784.5014 



0.2672 

 0.2477 

 0.1796 

 0.3013 

 0.2714 



0.5170 

 0.4971 

 0.4238 

 0.5491 

 0.5210 



+0.2221 

 + 0.2547 

 + 0,3282 

 + 0.0275 



-1.2458 

 -1.2525 

 -1.1952 

 -0.9589 



+ 0.1770-1.1682 



Stand with " b " grade. 



10.2683 

 9.7688 

 11.1452 

 14.3912 

 15.4624 



22.2901 

 17.5817 

 19.6651 

 24.1016 

 14.2331 



367.8495 

 320.4697 

 402.7196 

 572.1703 

 686.2946 



0.4589 

 0.3316 

 0.2793 

 0.1949 

 0.0548 



0.6774 

 0.5758 

 0.5285 

 0.4414 

 0.2341 



-0.4888 

 -0.3582 

 -0.2421 

 + 0.2373 

 +0.1295 



-0.3991 

 -0.2784 

 -0.3537 

 -1.0593 

 -0.4234 



Skew- 

 ness 



The dis- 

 tance 

 from 



mean to 

 mode 



7.568 

 9.577 

 11.397 

 13.62 

 15.470 



11.196 

 12,061 

 12.589 

 14.660 

 16.517 



0.4545 

 0.4422 

 0.3663 

 0.4044 

 0.4351 



0.3862 

 0.3155 

 0.2980 

 0.3490 

 0.1368 



1.5198 

 1.5574 

 1.3128 

 1.6233 

 1.7765 



1.2374 

 0.9862 

 0.9947 

 1.3243 

 0.5380 



Dealing first with the skewness, we observe that in all the cases it 

 is positive, or the mean is greater than the mode. We will next examine 

 the constants (3i and ^2. If ^i=0 and ^2 = 3, the curve representing the dis- 



