192 
On Theories of Association 
The number unable to articulate is negligible ; all the deaf can make sounds and 
probably 90 °/ 0 could articulate with more or less success. Those who acquire 
deafness later in life retain their speech, but with impaired quality. The census 
returns club together the congenital and acquired forms. Where then is the 
" discrete " attribute ? As for the blind so for the instruction of the semi-deaf, 
special schools have been established by some educational authorities. There were 
19 scholars reported on in the Bristol Education Committee's Report for 1911 as 
attending the semi-deaf school at Broad Weir. From "very deaf" to "very slight 
deafness" we have every graduation of hearing from those that can only hear 
under 1 yard to those who can hear at 6 yards. There is every variation in 
speech from the " unintelligible," " now beginning to use a little," " voice very 
weak," up to "lisping nearly overcome " and "speech of good quality." Speech - 
reading forms an essential feature of the instruction, and the cases are those 
of transitional deaf-mutism. 
We entirely disagree with Mr Yule's statements that such attributes as blind 
and seeing, deaf and not deaf, mentally deranged and not deranged, " if not 
absolutely discrete, are very largely distinct from each other " (loc. cit. p. 638), and 
we wholly fail to follow his argument on this point. 
Mr Yule has apparently seized on recovery and death in cases of small-pox as 
discrete instances, but by Dr Macdonell and one of the present writers they were 
used to measure a continuous quantity — the severit}' of the attack. The data due 
to Dr Brownlee, and published by one of us in Biometrika, Vol. VII. p. 256, show 
that when the severity of the attack is classed by such categories as haemorrhagic, 
confluent, abundant, sparse, very sparse, that variate is essentially continuous, and 
that the mortality is largely confined to the two highest classes. Again when the 
immunity conferred by vaccination is reclassed under " unvaccinated," vaccinated 
over 45 years ago, 25 — 45 years back, 10 — 25 and 0 — 10, we at once recognise 
that vaccination regarded as conferring immunity is an essentially continuous 
variate. The same notion of continuity comes in, if we classify severity by the 
number of pustules on the face, comparison being made with a standard series of 
photographs of typical cases, or again show that area of vaccination scar affects 
the extent of the immunity. Mr Yule can hardly be ignorant of all this work, 
yet he lightly chooses the vaccination data as good illustrations of his method*. 
The classifications of intensity of attack by number of pustules and of vaccination 
by period since vaccination show in general frequency surfaces of a rough " cocked 
hat" type, and dispel at any rate the notion that immunity and severity can be 
treated as discrete variables. It is only the confirmed Mendelian who would 
classify any pigmentation character, whether of eye "or of coat or of flower, into 
two alternative groups. The intensity of pigment is undoubtedly a continuous 
* That he was, as long ago as 1899, acquainted with the varying intensity of vaccination is con- 
clusively proved by the following sentence from his memoir on ' Association ' (Phil. Trans. Vol. 194 A, 
p. 289) : " The association between non-vaccination and attack is very high indeed for young children 
— -8 to - 9 — but drops sharply to -5 (owing presumably to the loaning protection of the vaccination made 
in infancy) in the older age groups." The italics are ours. 
