96 PROF, K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Crab Measurements. No. 4. (Total Number of Crabs = 999.) 
Abscissse. 
Ordinates 
(1 unit = 1 crab). 
Abscissa. 
Ordinates 
(1 unit = 1 crab). 
1 
1 
11 
126 
2 
3 
12 
82 
.3 
5 
13 
72 
4 
11 
]4 
41 
.5 
40 
15 
28 
() 
5.5 
16 
8 
7 
98 
17 
7 
8 
121 
18 
0 
9 
152 
19 
0 
10 
147 
20 
2 
The first six moments were calculated exactly as in the previous case of § 9, by aid 
of Table I., except that a now equals 999, and we go a stage further to /r'g and p-g. 
h equals unity as before. We have 
p/= 9-684,684 
P3'= 101-3022 
P3'= 1,129-9971 
p/= 13,334-0710 
165,488-8438 
Pg' = 2,150,845-6867 
Pi = 0 
P2 = 7-5092 
P3 = 3-4751 
p^= 176-7280 
p-= 271-6007 
pg = 7,91.9-2781 
These results give for the position of the centroid d = p/ = 9-6847, and for the 
standard-deviation cr = y/p^ = 2-7403. This gives the modulus 3-874, and the central 
ordinate of the normal curve 145-44. The modulus, as calculated from the mean 
error, is 3-8634, so that the agreement is very close. The normal curve in fig. 3 is con¬ 
structed from the values d, = 9-6847, cr = 2-7403, and = 145-44 by aid of Table II. 
The following additional quantities were now calculated :— 
7^4 ~ Spa^ = 
= 
/^5 — = 
7^0 — 5p2Pi = 
^3 = 
7-5637 
-044,712 
— 22-6911 
10-6485 
— 31-9455 
1283-8486 
-606,45 
If we had a perfect probability-curve, pg, pg, — 3po”, and pg — 5pap^ ought to be 
zero. This, of course, we should not expect in any actual set of observations, but the 
comparative smallness of pg, pg, \g, e^, and shows a very fair approximation to 
the symmetry of the normal curve in these results. 
