268 On 'Best' Values of Constants in Frequency Distributions 
and putting m = m + Am, 
S {s - m)) 
Am = ^ — m (6). 
Starting with m equal to the mean of the observations I have found the 
improved values in the following two numerical examples. 
Illustration III. The first table given by L. Whitaker* contains the number 
of deaths per day of women over 85 years, published in the Times newspaper 
during the years 1910-1912. 
TABLE IV. 
Number 
of deaths 
per day 
Observed 
Poisson by first 
moment 
Poisson 
improved by 
minimum x' 
0 
364 
336-250 
331-133 
1 
376 
397-302 
396-334 
2 
218 
234-720 
237-186 
3 
89 
92-446 
94-630 
4 
33 
27-308 
28-316 
5 
13 
6-4532 
6-7782 
6 
2 
1-2708 
1-3521 
1 
1 
0-2508 
0-2715 
The m, x^ P and calculated from (5) were determined for the two distri- 
butions as given in Table V. 
TABLE V. 
TO 
P 
dm 
Poisson ... 
Poisson improved 
1-181569 
1-196903 
15-226 
14-943 
-0332 
-0361 
- 35-61 
- 0-75 
Illustration IV. As our second illustration we have taken a table of phagocytic 
frequencies published by Major McKendrickf. 
TABLE VI. 
No. 
of 
Deaths 
Observed 
Poisson by 
first moment 
Poisson 
improved by 
minimum x' 
0 
620 
605-924 
000-676 
1 
282 
303-568 
306-164 
2 
79 
76-044 
78-026 
3 
16 
12-699 
13-257 
4 
2 
1-5906 
1-6892 
5 
1 
•1738 
-1881 
* Biometrika, Vol. x. p. 67. 
•f Proceedings of the London Mathematical Society, Vol. xm. 1913, p. 401. 
