Miscellanea 
537 
The following short table will be sufficient to indicate the nature of the cross-sections to any- 
one wishing to pursue the matter further. 
z-ordinates of y -arrays for given, special values of x/cr x . 
Array at xja x = 
~S 
o 
QQ 
<D 
« — i 
> 
O'O 
0'5 
1 '0 
-Z 5 1 
ss u 
% O 
o U 
o £> 
3:5 
0-223 
0-332 
0-388 
0-314 
0-165 
0-059 
0-015 
0-003 
3-0 
1-135 
1-688 
1-970 
1-589 
0-834 
0-297 
0-077 
0-015 
2\5 
4-536 
6 736 
7-811 
6 -223 
3-230 
1-145 
0-297 
0-059 
2-0 
14-881 
21-381 
24-195 
18-497 
9-269 
3-230 
0-834 
0-165 
1-5 
38-080 
55-053 
57-904 
39-890 
18-497 
6-223 
1-589 
0-314 
1-0 
85-096 
113-670 
100-499 
57-904 
24-195 
7-811 
1 -970 
0-388 
0:5 
155-888 
168-289 
113-670 
55-053 
21-381 
6-736 
1-688 
0-332 
6-0 
198-944 
155-888 
85-096 
38-080 
14-881 
4-536 
1-135 
0-223 
-0-5 
155-888 
97-562 
49-567 
22-036 
8-414 
2-644 
0-662 
0-130 
-1-0 
85-096 
49-567 
25-217 
11-369 
4-379 
1-381 
0-346 
0-068 
-IS 
38-080 
22-036 
11-369 
5-186 
2-010 
0-635 
0-159 
0-031 
-2-0 
14-881 
8-414 
4-379 
2-010 
0-781 
0-247 
0-062 
0-012 
-2-5 
4-536 
2-644 
1 -381 
0-635 
0-247 
0-078 
0-020 
0-004 
-3-0 
1-135 
0-662 
0-346 
0-159 
0-062 
0-020 
0-005 
o-ooi 
-3-5 
0-223 
0-130 
0-068 
0031 
0-012 
0-004 
o-ooi 
o-ooo 
Means 
o-ooo 
0-268 
0-494 
0-646 
0-723 
0-757 
0-766 
0-769 
III. 
Studies in the Meaning and Relationships of Birth and Death Rates. I. The Relation- 
ship between " corrected " Death-rates and Life Table Death-rates, by John 
Brownlee, M.D., D.Sc. Journal of Hygiene, Vol. xm. No. 2, pp. 178 — 190. 
There are three " death-rates " used by those who deal with the statistics of public health 
etc.; the "crude" death-rate found by dividing the total number of deaths in a district in 
one year by the total number of inhabitants ; the "corrected" death-rate found by applying the 
death-rates for age and sex to a standard population and calculating the rate from the figures 
so found ; and the " life table " death-rate which is the rate that would be found by working out 
a complete stationary population from the death-rates for each age and calculating the ratio of 
the total deaths among the assumed stationary population to the total stationary population. 
This result is simply the reciprocal of the "expectation of life" at birth. Dr Brownlee thinks 
that this last measure is the most satisfactory death-rate and his paper is an attempt to reach 
approximate values for it from the corrected death-i - ates. Although Dr Brownlee does not set 
them out in that way these approximations appear to be based on the use of an imaginary 
stationary population or populations and require, we think, to be tested more extensively than 
has yet been done before they are used for any practical conclusions. 
It appears to us that the use of the " expectation of life " at birth or of a single death-rate 
for a population as a whole cannot, however it is calculated, gauge completely the mortality 
of that population, and cannot therefore form an entirely satisfactory basis for comparative 
purposes : two populations may show the same death-rate or expectation of life and yet the 
mortality of one of them may, for instance, be heavy only in the first five years of life, while 
the other is light for the first five years but heavy at later ages. There must therefore be 
limitations in the use of any single figure, and if more than one figure is used we do not see why 
the death-rates at various ages should net- be employed as they stand. They are easier to 
interpret and no more difficult to deal with than the expectation of life at a series of ages, — an 
alternative measure implied by Dr Brownlee. 
In- the paper before us Dr Brownlee mentions that further work is to follow, and possibly it 
will show how he intends to overcome these difficulties. W. P. E. 
