M. A. Lewenz and K. Pearson 
389 
we consider preferable as it suffers from no such defect. Table XIII gives the 
results, compared with Dr Beddoe's compensation formula. We see at once that 
either of our formulae based on the obvious fact of non-linearity is far superior to 
TABLE XIII. 
U X S X Q 
B 
^3 
A 
Parabolic 
Formula 
Logarithmic 
Formula 
A 
Altbaierisch 
63118 
1503 
1530 
+ 
27 
1493 
-10 
1490 
-13 
English ... 
60878 
1477 
1439 
38 
1470 
- 7 
1459 
-18 
French 
59206 
1473 
1419 
54 
1428 
-45 
1424 
-49 
Aino 
63988 
1462 
1521 
+ 
59 
1491 
+ 29 
1500 
Etruscan 
62327 
1454 
1494 
+ 
40 
1490 
+ 36 
1480 
+ 26 
Malay 
59197 
1424 
1428 
+ 
4 
1425 
+ 1 
1424 
0 
Theban 
58223 
1388 
1376 
12 
1389 
+ 1 
1395 
+ 7 
Naqada ... 
57991 
1381 
1362 
19 
1379 
_ 2 
1387 
+ 6 
Copt 
57254 
1356 
1361 
+ 
5 
1344 
-12 
1353 
- 3 
Negro 
57373 
1348 
1344 
4 
1350 
+ 2 
1359 
+ 13 
Mean 
59955-5 
1427 
1427 
0 
1426 
- 1 
1427 
0 
Mean Error 
27-2 
14-5 
17-3 
Romans in Britain 
61609 
1385 
1490 
+ 
05 
1482 
+ 97 
1470 
+ 85 
Australians 
56722 
1277 
1347 
+ 
70 
1316 
+39 
1317 
+ 40 
New Hebridians 
57234 
1362 
1366 
+ 
4 
1343 
-19 
1352 
-10 
Kanakas 
63441 
1459 
1544 
+ 
85 
1493 
+ 34 
1494 
+ 35 
Marquesaus 
Dutch 
62145 
1491 
1507 
+ 
16 
1489 
- 2 
1478 
-13 
62327 
1502 
1515 
+ 
13 
1490 
-12 
1480 
-22 
Finns 
63447 
1497 
1559 
+ 
62 
1493 
- 4 
1494 
- 3 
Russians 
64614 
1529 
1570 
+ 
41 
1485 
-44 
1506 
-23 
Thais 
62827 
1483 
1539 
+ 
56 
1493 
+ 10 
1487 
+ 4 
Mean 
61596 
1443 
1493 
+ 
50 
1454 
+ 11 
1453 
+ 10 
Mean Error 
50 
29 
26 
Mean of 19 Races 
60733 
1434 
1458 
+ 
24 
1439 
+ 5 
1439 
+ 5 
Mean Error 
38 
21 
21 
his i?3, not only in the mean of each series, but in the mean error. In fact 
in only two cases out of the 19 races is he better than the parabolic and in only 
three cases better than the logarithmic formula. Thus in his Barnard Davis 
results he is nearly 100 per cent, worse than the logarithmic formula. Nor can 
he better himself by changing his multiplier because he has already got a zero 
deviation from the mean of his series in the Verstdndigimg measurements, i.e. the 
far better series. So soon as material is reduced on a uniform basis for inter-racial 
data, we believe it will be possible to adjust the constants of a non-linear inter- 
racial regression formula to read with a mean error of under 14 cms.'. We do not 
attempt this at present, because the bulk of sound material is insufficient. 
(11) We now turn to our last test, that on individual crania measured on the 
basis of the Frankfurt Concordat. We have taken 45 skulls by sampling at 
