MR. K. PEARSON ON- THE MATHEMATICAL THEORY OF EVOLUTION. 393 
so as to get a series of tints in arithmetical progression 1, 2, 38, 4, 5, 6, 7, 8, and 9. 
These tints were then placed in non-consecutive order, and 231 persons asked to guess 
a tint by affixed letters lying between 1 and 9. The results were as follows :— 




| Tint. | Frequency of Tint. Frequency of 
| | guess. guess. 
d 0 | 6 54 
es 8 | 7 94. 
2 7 | 8 40 
5 22 | | 
! | 


Now, obviously, the number of tints and the number of persons guessing were far 
too limited to draw any definite conclusions as to the distribution of tint guesses.* 
I propose here merely to use these statistics to illustrate the calculation of a skew 
frequency curve with a given limited range. I do not wish to propound any theory 
of tint guessing, nor to assert that these guesses actually distribute themselves 
according to the curves dealt with in this paper. 
Calculating the moments about the centroid in the usual manner, we have 
ie Py ie 3 7 | 
ttg= — 3°70067 Centroid lies at a distance of 5°376624 units 
is a 19°6255 from the tint 1. 
4 “a 
We easily find 2p (39? — wy) + 3p,” = 15°96335, or the observations fall into a 
curve of Type L, that is to say, have a limited range. 
We obtain 
[si == UBIOEMOT, B, = 427862, 
(AOE oA ie e= 6°443186. 
hence the range 
(DD == WB Ee, 
Further 
m, = 4°858705, My O99KGD, 
a, = 11°08997, d= ‘22769, 
dono: Skewness = 1:06666. 
Thus the range of the theoretical curve runs from a point 4°15233 units before 
tint 1, and concludes at a point ‘734674 unit before tint 9. The curve is, however, 
* I hope later to deal with the subject of tint guesses falling within a limited range, as my material 
increases in bulk. I would only note here, that the geometrical mean frequency curve does not seem to 
give results according well with experiment. 
MDCCCXCV.—A. 3 E 
