382 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
distances également infinies de la moyenne, et trouver toujours des probabilités qui y 
correspondent. Cette conception mathématique ne peut évidemment s’accorder avec 
ce qui est dans la nature. . . . Les limites extraordinaires au deli desquelles se 
trouvent les monstruosités, me semblent plus difficiles 4 fixer.” 
Indeed QUETELET’s attempt to fix these limits in the case of the height of human 
beings at 2°801 and -433 metres is purely empirical, and scientifically worthless. 
I prepose in this the first section of the practical part of this paper to consider how 
far the theory we have developed in the first part, enables us to find the range in 
various groups of physical and biological phenomena. 
Example I. The Range of the Barometer.—The following results for the curve of 
barometric heights are given on p. 352. 
Cn ale /aliso Pg = 1014 
fi SS GOS Py = 826°34. 
We have accordingly : 
py (Bog? — py) + 3p? = 400°581, 
that is, this expression is positive, and we have a limited range, 
We have further: 8, = °24401, 8, = 3°17391. 
Hence, determining the constants in the manner described in $14, we have: 
r = 30'13882 e = 150°7954 
b = 43°61016, 
M, = 95°3302 a, = 8°2688 
Ms = 22°8030 Oy = 35°3414. 
Next to find d, giving the distances of the centroid from the origin, or the distance 
on barometer between mean and maximum, we have by p. 370 
d = — ‘8983. 
Thus 
Range of barometer above mean = 9°1671 
x . below ,, = 84'4481. 
Now, in the scale upon which our curve is drawn in Plate 10, fig. 6, each centimetre 
equals =45 inch, and the mean barometer in Dr. VENN’s results equals about 297-931. 
Thus the maximum possible = 30/85 and the minimum possible = 26':49 ; the range 
of the barometer being about 4°36. Now, the highest barometer in Dr. VENn’s record 
= 30'°7, and the lowest 28”°7; it is clear, therefore, that we reach much nearer in 
