M, A. Lewenz and K. Pearson 
379 
Now as Bi and are formulae destined to give Barnard Davis' capacity and 
not the true capacity they need not be considered here. What we have to compare 
are Fawcett's actually measured capacity, Dr Beddoe's ^3 and " P et L." 
Now looking up C. D. Fawcett's paper it will be found that the three skulls 
referred to have capacities of 1217, 1497 and 1222, which have a mean value of 
1312 and 7iot 1343 as Dr Beddoe calculates ! Further two out of the three skulls 
are $ and Dr Beddoe applies the formula to them to get his " P et L" prediction! 
Lastly Dr Beddoe entirely disregards Dr Lee's instruction to apply the formulae 
for the most closely allied race, if it be known*. As Dr Lee has provided a 
formula for Naqada crania, Dr Beddoe ought to have used this ; he would then 
have found for the predicted value of the three crania 1218, 1522 and 1197, giving 
a mean of 1312, differing by no single point and not by 19 as B^ does from the 
observed result. Let us however compare the results for the three crania as 
found by B^, not with the special Naqada formulae, but with Dr Lee's general 
formulae, paying, of course, the proper attention to sex. 
TABLE IIL 
P and -L Predicted 
Naqada Skull 
Capacity Measured 
Predicted 
Naqada 
General 
1308? 
1217 
1218 (- 1) 
1195 (-22) 
1154 (- 63) 
1497 
1522 (-25) 
1507 ( + 10) 
1602 ( + 105) 
5 21 ? 
1222 
1197 ( + 25) 
1175 (-47) 
1182 (- 40) 
Mean 
1312 
1312 (0) 
1292 (-21) 
1313 ( + 1) 
69 
Mean Error 
17 
26 
Now supposing we have followed Dr Beddoe coi'rectly his results were not only 
30 cubic centimetres wrong in taking the average of Miss Fawcett's three skulls, 
but 19 cubic centimetres wrong in using his own formula ! This brings his 
predicted mean into close accord with Miss Fawcett's observed mean result. But 
we see at once on examining the three individual predictions that his success is 
only achieved by the balancing of large individual errors. His mean error is four 
times as bad as the P and L Naqada prediction and nearly three times as bad as 
the P and L general formula prediction. Allowing for faults of arithmetic, results 
similar to these must have been actually before Dr Beddoe when he wrote : 
" Mes precedes nous conduisent a des resultats plus corrects qu'aucun des 
autres," etc. 
* The University College anthropometric workers have again and again insisted that regression 
formulae vary from race to race. See Phil. Trans. Vol. 196, A, pp. 243 et seq. ; Biometrika, Vol. 1. 
pp. 460-1 ; Vol. II. pp. 347 etseq. 
48—2 
