MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 413 
frequency—we obtain results which, although more complex in form, are not as satis- 
factory as those given by the generalised curve.: 
For example, Dr. THIELE gives the following series (p. 12) :— 

feebvealucseceiesere NSH ae [ecole Or l/a10y eT) 12 
| | 
Frequency. . . .| 3 7 30 | 101 | 89) 94 
13| 14 | 16) a7 48 19 

70 | 46) 30 


His “ Faktiske Fejllove ” gives 
y = °12218,, (a) + 278 AB,, (x) + -600 A°B,, (x) 
+ 216 A%8, (w) + °278 A%B, (w) — 318 AB, (w) 
+ +574 A®B, (x) + -596 A7B, (x) + +499 A8B, (x) 
+ +259 AB; (a) — 0645 AYB, (x) — 0303 AUB, (a) 
— 0088 APB, (2). 
He tells us that 6 terms practically suffice, the additional terms merely accounting 
for the individual irregularities of this particular 500 observations. Without speci- 
fying what the observations are, he tells us that the possible values run from 4 to 28, 
or that the range is really limited. 
If we fit our generalised curve of Type I., we find for its equation : 

8 xv 3°89708 2 1727285 
ee (1 te un (1 = icone) , 
the origin is at 11°191, or the range runs from 6°6715 to 31°1202, we., is a range of 
24-5487 instead of 25, but is shifted some 2 to 3 units. Considering the small 
number of observations, this is not a bad approximation to a marked feature of the 
distribution not indicated on the surface by the observations, nor discoverable from 
the “ Faktiske Fejllove.” 
Comparing our curve (i.) with (i.) the actual statistics—all 13 terms of the 
“ Faktiske Fejllove” series, and with (ili.) the first 6 terms of the same series, we 
have the following results :— 

Values . | 
7 8 1) eae 9) | PIB es FS || 1g 
Go| TO 22) ON EO) | 2S Ba I eG Tey Il a 
(ii.) 3 7A SEENON EO NOL | FO) 2B BOI aia = Bip a 
iii.) DT 20 | Be ee GO) 48 eB ee Wes Pa a 

The generalised curve here gives slightly the better results in addition to its more 
easily realised form, and its fewer constants (iv.). 
