MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 383 
practice to the upper than to the lower limit of the barometric range.* The result 
here obtained for the barometric range is of course only tentative and approximate. 
Far larger statistics must be dealt with, and for a greater variety of places, we shall 
then be better able to judge how far the range, as ascertained from Dr. VENN’s 
statistics, is local, or if general, what modification or correction may be required. 
Calculating the value of y, we find for the curve of barometric heights : 
y = 21-642 (1 + x/8-2688)°™ (1 — «/35°3414)?™, 
This curve is traced on Plate 10, fig. 6. It will be seen to be extremely close to the 
observations. 
Although the expression 2, (3u." — m,) + 33° is not zero, it is interesting to see 
with what closeness the skew curve which is the limit to a point binomial can be 
fitted to the barometric observations. This is the curve of Type HI. Calculating 
its constants by aid of § 18, we find 
y — 92 (1 + LA LOG3) Gach etter 
while d, the distance between the maximum ordinate and the centroid-vertical, 
= ‘7864. This gives a maximum possible height of the barometer of 31”:22 instead 
of 307°85, there being of course no lower limit. The curve is shown in Plate 10, 
fic. 6, and will be seen to give a very close correspondence with the observations. 
The “skewness” of barometric results as given by the curve with limited range 
= °8983/3°184 = °2821, and as given by the curve of Type III. = ‘7864/3184 
= ‘2470,—no very great difference. 
The areal deviations of the two curves are almost exactly the same, being about 
7"1 sq. centims. or percentage error of 4:1. The normal curve is also drawn on 
the same plate. It diverges widely from the observations, the areal deviation 
= 26 sq. centims. or the percentage error 15°1,—about 3°7 times as great as in the 
case of either skew probability curve. 
Till a wider range of barometric observations have been analysed, it may be wiser 
not to draw too definite conclusions from the above results, contenting ourselves with 
the remark that the new skew curve gives far better results than the old normal 
curve of errors. 
* J am unaware if Dr. Venn’s results are reduced to sea-Jevel. The lowest recorded barometric 
height for the British Isles reduced to sea-level is 27'333 (at Ochertyre, Perthshire, January 26, 1884) 
and the highest (at Roche’s Point, Cork, February 20, 1882) is 3093. A statement that the barometer 
stood at 31''046 at Gordon Castle, in January, 1820, has hardly sufficient evidence. Supposing Dr. VeNn’s 
statistics to be unreduced Cambridge statistics, the expression theoretically found for the barometric 
range seems to be on the whole satisfactory. I have at present in hand other series of barometric 
heights. 
