422 
Miscellanea 
The value of ■)(^ for the Type II curve is only -016 while n' = 4. This value is so small as to 
be outside Elderton's table, so we put 
and from Sheppard's table find the first term to be -89894 while the second is -10052 so that 
P = -99946. The fit is practically perfect. This is not surprising since we have fitted a curve 
which is known to be the so-called "parallel" to the hypergeonietrical series to a hypergeometrical 
distribution. The value of x" for Professor Edgeworth's curve is 7-035 which with w' = 4 gives 
P = -071. The sum 8 (e^/U) is -000077 for the Type II curve and -061* for Professor Edgeworth's 
curve. He says (p. 470) that "the calculated frequencies correspond fairly well with the observed 
frequencies." The divergence between the total for the data (210) and for the calculated fre- 
quencies (220-1) is extraordinarily great and suggests that some errors may have crept into 
Professor Edgeworth's arithmetic. The values of S (e~/n) are -000077 for the Type II curve and 
-0335 for Professor Edgeworth's curve. 
ExAMPi.E in. Disfribution according to ages, of tlie Marriages of 
235,252 Spinsters. 
This example is described by Professor Edgeworth as one of "considerable abnormality," and 
he states (p. 462) "I should be considerably surprised if the Pearsonian types would stand the 
Pearsonian criterion in the case of Dr Isserlis' second example which consists of the distribution 
of 235,252 ages at marriage." 
The answer is that at any rate they stand the test nmch better than the curve fitted to this 
example by Professor Edgeworth. That the fit is a poor one is probably due not so much to 
the size of the total frequency (as Professor Edgeworth suggests) but to heterogeneity of the 
material t, due to misstatement of age. 
The observed frequencies are as follows : 
TABLE V. 
Age 
15— 
20— 
25— 
30- 
35— 
40— 
45— 
50— 
55— \ 60— 
65— 
ro- 
Total 
Frequency 
17.546 
118542 
70411 
20241 
5873 
1706 
636 
171 
64 28 
23 
ll 
235252 
Again quoting from the Phil. Mag. {loc. cit. p. 385): with arbitrary origin at 22-5 years and 
unit 5 years, the mean is at -5227798, the moments are /jj = -8294195, = 1-2482896, 
in = 5-901622] whence /Sj = 2-730913, jS^ = 8-578766 {. These values of /3i, 13^ indicate a curve 
of Type VI, but the criterion 
K = /3i O2 + 3)2/4 (4^2 - 3,iii) (2/32 " 33i - 6) = 1-151975 
is so nearly unity, that (having regard to the large values of /3i, /Sg) we may expect the transition 
curve of Type V to give nearly as good a fit. 
The curve of Type VI is 
y = (4-29787) 10" {x - 2-305660)6-599™ a;-"-*"™' 
with origin at 4-655444 years, mode at 22-625624 years, mean at 25-113899 years and x measured 
in 5 year units. 
* Not -07 (Prof. Edgeworth's value on p. 470). 
I On this point ef. W. Palin Elderton, Frequency Curves and Correlation, pp. ]42-3. 
{ The Phil. Mag. value, =8-77876 is wrong (though /j.^, /J^a, M4 are correct). Professor Edgeworth 
has used the wrong value, but the error is not enough seriously to influence his figures. 
