Miscellanea 
437 
VI. An attempt to ascertain the Prevalence of Syphilis in a large 
Urban Population. 
Notice of Fritz Lenz: Uber die Verbreitung der Lues, speziell in Berlin, und 
ihre Bedeutung als Faktor des Rassentodes. Archiv fur Rassen- und 
Oesellschafts-Biologie. May and June, 1910. Leipzig. B. G. Teubner. 
pp. 306 et seq. 
The underlying ideas of the memoir are to use (1) the relative statistics in two places, and 
(2) the death rates from certain causes in order to estimate the number of persons attacked by 
the diseases which end in death from those causes. These ideas are excellent, and ultimately 
many valuable results may be reached, but they are extremely difficult to apply without making- 
assumptions so wide that the conclusions become too rough to afford definite information. The 
particular case dealt with by Lenz is that of syphilis, which results in many cases in general 
paralysis of the insane, locomotor ataxia, etc., and the statistical problem involved in his work 
may be set out as follows : Given that syphilis is notified in Copenhagen, and that the deaths 
from general paralysis in Copenhagen and Berlin are known, find the proportion of males in 
Berlin who have at one time or another had syphilis. To solve such a problem one requires to 
know the age incidence of the deaths from paralysis, the age incidence of the syphilis notifications, 
the total populations in age groups (and the births) in both cities for several years, and some 
information as to the average after lifetime of syphilitics. Lenz neglects these preliminaries 
and boldly takes a short cut which assumes that if syphilis were notified in Berlin the noti- 
fications would bear the same proportion to the deaths from paralysis as the notifications in 
Copenhagen bear to the deaths from paralysis there. The syphilitic population is found by 
multiplying this number of notifications by the expectation of life at age 15. We have cut 
down Lenz's problem and have merely tried to indicate his method ; he adjusts some details 
on the way, but the errors in the method we have just indicated exist, we think, in his work, 
though at times they are obscured. The weakness is that the proportionate method will not 
hold because the populations vary and the age incidence in the two cities can hardly be the 
same, while the use of the expectation at age 15 is incorrect, because this would be the youngest 
age at attack, and if expectation is used at all it should be for the average age of attack. 
Besides this the expectation of life of a syphilitic is probably less than that of the population 
as a whole. 
These criticisms appear to us to dispose of his applications, but although the problem is an 
actuarial one of great difficulty it is certainly worth examination, and even though we do not 
agree with all his work we feel that much credit is due to Lenz for calling attention to the 
possibility of solving the problem of the extent of syphilis in this manner. 
W. P. E. 
VII. On the General Theory of the Influence of Selection on 
Correlation and Variation. 
By KARL PEARSON, F.R.S. 
(1) In 1901 a paper of mine was read before the Royal Society and shortly afterwards issued 
in the Philosophical Transactions* dealing with this matter. Very shortly afterwards I found 
out that the formulae therein developed did not depend for their accuracy on the frequencies 
being Gaussian in character. All the main conclusions were deducible without this limitation, 
* Vol. 200 A, pp. 1— GO. 
