480 
A Second Study of the Human Viscera 
upon the weight of the whole body and that of the kidneys and liver. The 
required constants having been determined* we find: 
x 1 = -0369tf 2 + -3178^3 + -0192^ 4 + 2'6715 (1), 
where x 1 is the weight of the heart in ounces, x 2 the body-weight in pounds, x 3 the 
weight of the kidneys in ounces, x 4 the weight of the liver in ounces. 
The standard deviation of the prediction is 1235 ozs., giving a mean error of 
•96 oz. 
The value of such an equation depends upon the nature of the regression -f- 
which cannot be properly determined when the data are too few or too scattered 
to allow of grouping. A rough empirical test is to see how far the predicted value 
agrees with the known weight in a sample of the material. Blakeman applied this 
test in his series of brain weights. We took every third case in our selected series, 
determined the probable weight of the heart from the above equation and com- 
pared this with the recorded weight. The mean absolute error in the whole 26 
was "98 oz., which is in reasonable agreement with our expectation. We then 
asked ourselves whether the prediction could be improved. 
In the Tables II and III we have recorded, within brackets and inverted 
commas, some constants of " Body Length." Inquiry has elicited the fact that the 
" body length " was not true height at all but the length from the crown of the 
head to the end of the toes and had been recorded for the purposes of the under- 
taker. Since this measurement will be greatly affected by the degree to which 
the toes are flexed when rigor mortis sets in it does not necessarily bear a constant 
proportion to the stature, as was readily seen on examination of a short series of 
cases upon which both measurements had been made. Consequently the mean 
and standard deviation of this measurement are of no interest ; but, since we found 
it to be substantially correlated with other measurements, it seemed just possible 
that its inclusion in an equation would improve the prediction. We found : 
x x = -0S56x 2 + -3034^ + -0166a; 4 + -0418# 6 + '2518 (2), 
where x x = heart weight in ounces, x 2 = body-weight in pounds, x 3 = kidneys in 
ounces, oe 4 = liver in ounces, x 5 = " body length " in inches. 
Applying this equation to the 26 test cases as before, the mean error proved to 
be "97 oz., i.e. there was no sensible improvement in the fit. 
Lastly we considered the effect of only taking two variables, the body-weight 
and the weight of the kidneys. The equation was : 
x x = -0413# 2 + -3449^3 + 2-9187 (3), 
* In determining the various regression constants six places of decimals were retained in the 
coeflicients of total correlation, i.e. we did not use simply the values tabulated in this paper. The 
work was arranged on the plan introduced by Yule, but several of the constants were checked by 
re-calculation, using the minors of the fundamental determinant in the ordinary way. 
f An analysis of the data in Table VI of Greenwood's "First Study" shows that in the case of 
" healthy " organs the regression of heart weight upon kidney weight was effectively linear. For that 
'N 
case, N=413, r=-4004, , = -4174, and x j N /^r^ = i. 77 6. 
