ISOSTASY 567 
table corresponding to the assumption that the compensation 
is nine-tenths complete and the depth is 19.29 km. This gives a 
closer agreement in each case, as should be expected, since the 
assumption is nearer to that made by Hayford, but still the differ- 
ences from Hayford’s values are large—2’61 for Point Arena 
and 4”’97 for Uncompahgre. - 
If Mr. Lewis had followed out his own line of thought, when he 
reached this point he should have inquired what value of M, 
expressing in his notation the completeness of compensation, 
would make his values agree with Hayford’s values. If he had 
done so he would have found that a close agreement would occur 
for Point Arena with M assumed to be about .87 and thus the 
truth of his tacit assumption would apparently have been confirmed. 
Again, if he had tried Mt. Ouray he would have found that 
with M=.2 and /;,=19.29 km. the total computed deflection is 
—10%02, practically in agreement with the Hayford value. 
Note the contrast between the reduction to compensation only 
one-fifth complete necessary at this station to neutralize the 
effect of the assumed reduction in depth of compensation and the 
comparatively slight. reduction, to .87, necessary at Point Arena. 
But if Mr. Lewis had continued still farther and tried the same 
thing for Uncompahgre he would have found that for M=1.34 
and #;=19.29 km. the total computed deflection is +5747, 
practically in agreement with Hayford’s value. The value 1.34 
for M indicates 34 per cent of over-compensation. In other 
words, for Uncompahgre it takes an assumption of one-third over- 
compensation to neutralize the assumption of a reduction of depth 
of compensation, whereas Mr. Lewis’ whole argument is based 
upon the assumption that under-compensation is always necessary 
for such neutralization. 
The following table shows the results of the tests made in 
preparing this rejoinder using the five stationst which were available 
to Mr. Lewis. Each of the Lewis values which lies nearest to the 
Hayford value for that station is printed in italics. The values 
‘For all the 733 stations involved in the investigation the total topographic 
deflections are printed, but those for each separate ring are printed for these five 
stations only. Hence these are the only stations on which it was possible for Mr. 
Lewis, using publications only, to make the test indicated. 
