32 DONALD C. BARTON 
running consistently large. The table gives merely a synopsis of the 
more important mean squares. 
The mean squares are given in 3 forms: the mean, the median, and 
the sum of the mean and median. The median which is used actually 
is the mean of the median 4 or 5 squared differences. The mean square 
differences are given in 4 sets: A, b, C, D. In set B, all 82 calculation 
stations were used. In set A, 4 slightly dubious stations on the right 
end of the observed profile were neglected. The central part of the 
observed profile was plainly irregular and reflecting the effects of 
shallow features not connected with the cap or salt. In C, therefore, 
the 15 central and the 4 northeast calculation stations at the right 
end were neglected. In D, the 15 central and the 4 calculation stations 
at the right end were weighted one; and the other 62 were weighted 
two. 
The results I-IV are really the condensed final results; and V— 
VIII are the condensed next-to-the-last results. 
A single line under I-VIII does not give a simultaneous series of 
mean squares respectively for (b—e) et cetera. But if, for example, 
the line I-A-mean is referred to, then 2.80 was the least mean square 
which could be obtained for (c—e) by varying the regional gradient — 
within certain plausible limits. But for the regional gradient under 
which ce had a mean square of 2.80, the mean square of cd is greater 
than 3.00, of cf is greater than 3.57 et cetera. By varying the regional 
gradient, the mean square of cd could be brought down to 3.00, but 
no regional gradient was found by which it was possible to bring it 
down to 2.80, and so on for the other forms, be, bf, and cf. 
The use of a small regional gradient toward the right gave dis- 
tinctly better results than the use of no regional gradient. 
Density assumption A gave the closest fit of calculated to ob- 
served gradient profile. The very slight change of the density assump- 
tions to those of B or C greatly increased the size of the mean square 
for all combinations of (6, c)—(d, e, f). Density assumption D gave 
some small mean squares for the median but a large discrepancy be- 
tween the median and the mean. The whole series of results under 
density assumption D showed the same discrepancy and also a com- 
bination of very small and very large differences between the ob- 
served and calculated profiles. 
The two forms, cd and ce, were consistently the best two in all 
the calculations. Either cd or ce was first in all calculations made, 
and in the final series I-IV, these two forms held first and second 
places. In some of the earlier calculations, one of them, more com- 
monly ce, was displaced from second to third place by be. The differ- 
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