KiRSTiNE Smith 
267 
Gaussians found in this way were used for interpolation purposes and their constants 
are therefore given in the following table under (b) and (c). By (a) is indicated 
the Gaussian from which we started, namely that found by moments, Sheppard's 
correction being used. 
d{y^) d(v^) 
Assuming , and — to be linear functions of a and 7n, we determined 
am da 
from the cases (a), (b) and (c) values of o and m, given under (d), so as to make 
the differential coefficients zero. In the same way we found at last from the cases 
(a), (b) and (d) the constants of the Gaussian (e), the constants of which will be 
found in the following table. As will be seen we have succeeded in bringing the 
values of and ^ near to zero, certainly close enough for all practical 
purposes. 
TABLE II. 
m 
P 
dm 
da 
(a) 
83-06889 
3-431833 
10-205 
-895 
- -57 
+ 14-42 
(b) 
83-01498 
3-3.58380 
10-301 
-891 
- 10-50 
^ 9-97 
(c) 
82-98832 
.3-331365 
11 048 
•854 
~ 15-89 
- 20-76 
id) 
83-05329 
3-349421 
10-108 
-899 
- 4-59 
- 12-10 
(e) 
83-07774 
3-385991 
9-858 
•909 
+ -07 
+ -71 
TABLE III. 
Observed 
Gaussian 
curve by 
moments 
Gaussian 
improved by 
minimum 
75 and under 
9-5 
12-.3387 
11 -.3504 
76 
12-5 
12-6842 
12-0767 
77 
17 
22-0702 
21-3463 
78 
37 
35-2942 
34-6005 
79 
55 
51-8794 
51-4323 
80 
71-5 
70-0925 
70-1100 
81 
82 
87-0421 
87-6432 
82 
116 
99-3519 
100-4734 
83 
98 
104-2329 
105-6275 
84 
107 
100-5128 
101-8352 
85 
82 
89-0879 
90-0352 
86 
74 
72-5781 
72-9998 
87 
58 
54-3468 
54-2778 
88 
34-5 
37-4049 
37-0099 
89 
19 
23-6625 
23-1422 
90 
10 
13-7588 
13-2703 
91 
8 
7-3532 
6-9782 
92 and over 
9 
6-3093 
5-7910 
(4) Fit of a Poisson Limit to the Binomial. For a Poisson limit with the 
general term ^ we find 
° s ! 
d fv^l fn.^ m, — 
