MATHEMATICAL CONTRIBUTIONS TO THE THEORY OP EVOLUTION. 295 



'818 gland with a probable error of '157. It is, therefore, clear that our 

 method gives the start of the range with very considerable accuracy. The whole 

 length of the range runs to 17*227 glands, with a probable error of 2'536. We may, 

 accordingly, conclude that the maximum possible number of glands is hardly likely 

 to be less than 16 or more than 20. We consider that this example is a good 

 illustration of the accuracy with which the principal "physical" characteristics of a 

 distribution may be obtained by aid of skew curves, and how they provide much 

 information which is not given by the use of the normal curve. 



The next point is the determination of the umbral equations giving the error 

 correlations of the " physical " constants. They are, if Antl. stands for antilogaritlun : 



X mean = Antl. 792,415Gx/ 1 Antl. 1-380,2040x6 Antl. 1-153,9020 

 + Antl. l-508,1033x,,, 



X range = X&> 



X, jo = Antl. l-011,7885x 4 Antl. 248,2856x,, li + Antl. I'097,6534x,, l3 , 

 X, = Antl. 1-109,9660x6 + Antl. -168,8507x,,,, - Antl. 1-151 ,0582x W3 , 

 Xd = Antl. '397,2701x6 - Antl. 274,1702 x ,, il - Antl. I'S 10,31 80 x ,,,,, 

 x , 4 . = Antl. -381,5919x,,, + Antl. > 367,7012x,, li . 



Multiplying these out pair and pair, we found 



ERROR Correlation Table. 



Hence, proceeding to multiply rows and divide columns by the corresponding 

 standard deviations, we have, after altering the units, the following 



