Miscellanea 
427 
Health of Yeai-ling Male Babies. 
Frequency 
Pertnille 
Differences 
I. 
Very satisfactory 
54 
•038 
•038 
II. 
Satisfactory 
326 
•265 
•227 
III. 
Normal 
508 
■618 
•353 
IV. 
Indifferent 
129 
•708 
•090 
V. 
Unsatisfactory 
198 
•840 
•138 
VI. 
Dead 
221 
rooo 
•154 
Total 
1436 
The permilles are olitaiiied by a continuous process with the reciprocal of 1436 on the 
machine. The differences are obtained from the pennilles by subtraction and only differ in one 
case, that of the Normal Health, which if found directly from the frequency would be "354, 
and this is of no importance for our present purposes. Table I and the present Table provide 
at once : 
Abscissa 
Ordinate 
Difference of Ordinate 
Centroid 
+ 00 
0 
I. 
+ r7744 
•08265 
+ •08265 
+ 2-1750 
II. 
+ 0-6280 
•32754 
+ •24489 
+ 1-0788 
III. 
+ 0-3002 
•381.36 
+ ■05,382 
+ -1525 
IV. 
- 0^5476 
•34341 
-•0.3795 
- -4217 
V. 
-1-0194 
•23727 
-•10614 
- -7691 
VI. 
-•2,3727 
- 1-5407 
-00 0 
The whole work is very simple, as there is no trouble of interpolation at all. 
In actually computing the present table of ordinates to permilles a different process was 
needful for the first eleven rows from that for the remainder of the rows. From -110 to -880 it was 
found adequate to take the z's from Table III of the Tables for Statisticians which are given for 
a for every •Ol of value — and therefore for every ^005 of frequency — and interpolate by Everett's 
Central-Difference Formula to every •OOl of frequency. It was also sufficient to use only the 8^ 
terms. Such a method was not possible for the upper part of the table. Here up to ^02, the 
value of X was determined by inverse summation from the values in Table II of the Tables for 
Statisticians. Then z was actually computed from z = e ~ f i )r the columns under the rubrics 
v27r 
•000, ^005 and '010. From these columns the remaining colunui values were determined using 
Everett's Central-Difference Formula and including 8* terms whoie requisite. The three rows 
at the top of the table were found by determining x by inverse summation as before and 
calculating each individual value of z from its the first fifth of the table was thus far more 
laborious than the last four-fifths. The values of z were ultimately cut down to five figures. 
A superscript + or — is attached to every ^ alue of z ending in 5 for the aid of those who wish 
to use the table to four figures only, which is often adequate. 
We owe a careful revision of the table to Mr H. E. Soper, who used a much simplified 
process and modified the last figure in a number of cases. If m be the permille, i.e. |(l+a), 
X the abscissa and z the ordinate, he took the foi-mula 
fi, = ,,S„.-_+ 
which enabled him to start from the ^ of the nearest tabled m in Table II of the Tables for 
Statisticians. 
