242 
DE. A. LEE AND PEOFESSOE K. PEAESOX OX 
Table XVI.—Naqa(4a Capacity calculated from Aino Formula (9). 
, Male. 
1 
Female. 
Actual capacity. 
Calculated. 
Diflerence. 
Actual capacity. 
Calculated. 
Dilference. 
1448 
1418 
- 30 
1266 
1271 
i 
+ 5 i 
1354 
1375 
+ 21 
1174 
1171 
- 3 : 
1354 
1379 
+ 25 
1148 
1146 
- 2 1 
1260 
1351 
+ 91 
1195 
1213 
+ 18 ! 
1481 
1502 
+ 21 
1160 
1228 
+ 68 ' 
1232 
1285 
"j- 0 3 
1120 
1223 
+ 103 
13.35 
1329 
- 6 
1248 
1209 
- 39 
1388 
1430 
+ 42 
1451 
1383 
- 68 
1326 
1288 
- 38 
1160 
1268 
+ 108 
1338 
1348 
+ 10 
1290 
1276 
- 14 
1305 
1413 
+ 108 
1106 
1124 
+ 18 
1224 
1366 
+ 142 
1214 
1159 
- 55 
1368 
1380 
+ 12 
1120 
1249 
+ 129 
1328 
1321 
- 7 
1190 
1280 
+ 90 
1475 
1435 
+ 40 
1304 
1276 
- 28 
1281 
1305 
+ 24 
1173 
1215 
+ 42 
1440 
1426 
- 14 
1152 
1137 
- 15 
1174 
1252 
+ 78 
1135 
1173 
+ 38 
1292 
1321 
+ 29 
1299 
1285 
- 14 
1253 
1374 
+ 121 
1158 
1152 
- 6 
INleaii error = 45 • 6 
Mean error 
= 43-15 
Now Tables XllT. and XIA^. show that the mean errors made for the 20 c? and 
20 ? German skulls, reconstructed hy the German formuhe (9) were respectively 
55'4 and 36'3 cul). centims. The same skulls reconstructed from the Aino formulm (9) 
give mean errors of 56'7 and 35‘0 cub. centims. ; while the Naqada skidls have mean 
errors of 45'6 and 43 T cub. centims. respectively. We may thus conclude that within 
the limits of error occurring in reconstructing capacity, foi'inula (9) as found for 
any race may lie safely used to calculate the capacity of an individual of a diHerent 
race. This is a very important result, and its basis will be further considered in the 
next section of this paper. We conclude that an average error of, say, 3 to 4 per 
cent, is all we shall make in ap])lying (9) to determine the skull capacity ot any 
individual not necessarily of the same race. 
(10.) Second Fundamental Frohlem. On the determination of the mean skull 
capacity of any local race of man from the reyression formulae of a second race. 
Professor Karl Pearson has shoAvn in a memoir, not yet published, that a general 
theorem hc)lds for the influence of selection on the regression formulm. A statement 
of this theorem is given by him in the ‘ Phil. Trans.,’ xk, vol. 192, p. 177. It may be 
summed up as follows : If selection has differentiated local races, then the regression 
formulae will in nenei'al chano-e from local race to local race, but that certain 
o o 
