Miscellanea 
173 
which he accepts, are based on adequate research and they arc in fact refuted liy Miss Lindsay's 
own material. For, if it can be shown that animal and vegetable calories have different results 
on the physical development of the children, it is clear that the first statement as to how many 
calories are needful for the proper maintenance of growth has no significance iintil a statement 
is made with regard to the source of the calories. Professor Paton cites no evidence for his 
statements; from what I have read on the subject of calories, I feel convinced that most 
of the data on the matter would not stand for five minutes any adequate statistical analysis. 
The Report, Professor Paton tells us, shows "very markedly the relationship between the 
physique and the food." Yet in a i)revious paragraph he says "that the physique is determined 
by the whole previous condition of life and by the influence of heredity, and that it is absurd to 
attempt to relate it solely to the diet." 
Now the only way to ascertain whether there was a marked relationship between the food 
and the physique of the children was to correlate the two for a constant age and investigate 
whether the correlations were such, having regard to their probable errors, that they could be 
considered significant. I did this with the result that the total calories in the food and the 
girls' weight for constant age was not definitely significant with regard to the probable error, 
while in the case of the boys the probable error was so large that it was impossible to say 
whether the relationship was really considerable or not. In fact no marked relationship could 
be deduced from Miss Lindsay's data, they were too inadequate. If Professor Paton's statement 
as to the influence of heredity is to be trusted, then even my cori-ection fi;)r age was inadequate, 
and the data ought to be corrected also for physique of parent ! If so, why was the parent not 
measured 1 
Professor Paton places before the readers of Biometrik-a two tables on which this "marked'' 
relationship is asserted by him to rest. One of the cases in his Table A, No. 32, is erroneously 
placed in this table ; the details show that the number of calories was 2949 and not 3822* ; 
it should be in Table B. These tables contain 16 l»i)ys' weights and 20 girls' weights. Professor 
Paton takes the British Association measurements, which are, of course, wholly inadequate as a 
test of Glasgow children, and making no real correction for age+ considers whether the children 
in the two tables were or were not above the quite arbitrary limit of 5 lbs. Iselow standard. He 
gi^'es us no measui'e at all of the significance of the result, whicli is based on the vagaries of 
sampling 16 boys of ages from 3 to 11, and 20 girls from 5 to 13 ; and he supposes in some way 
that this treatment can possibly refute the correlation coefficient, oTwC^ , of weight and food 
calories for constant age with its probable error ! I can, however, throw more light on the 
matter. Owing to the great courtesy of Dr Chalmers, Medical Officer of Health fiir Glasgow, 
I have been able to more than treble the number of weights of the hoyn and girls subjected 
to the dietaries. The results for total calories in food, Cp, now aret: 
Girls, 69 Boys, 55 
„r„.cp= + -21 ± -08, „r,„,.^= + -05 ± -09. 
Thus the relation for boys is now quite insignificant, and for girls may well be insignificant 
also. At any rate although both correlations are positive, there is no " marked " relationship 
between the physique and the dietary. Of course, it may be said that these weights {w) have been 
taken at some interval after the dietaries were recorded, but unless we assume the dietary to be 
a rough measure of the permanent feeding of the family, whose physique has been gradually 
built up for years before the dietaries were recorded, the observations must be discarded as of no 
value at all for testing physique, or as Professor Paton phrases it "development." 
* In the Appendix V of Rickety Families, it is given again ; this time as 2329 calories, 
t The deviation at each age would have to be measured in terms of the standard-deviation of weight 
at that age ; naturally the deviations are larger for older children. 
X I have to thank Miss B. M. Cave for the present series of correlations. 
