ISOSTASY 565 
than are those computed by Hayford. This is essentially Mr. Lewis’ 
reasoning. 
The tacit assumption is, however, not even approximately true, 
as shown in the following paragraphs, and hence all reasoning based 
on the assumption leads to erroneous conclusions. 
‘The reduction factor under discussion is the factor by which 
topographic deflections for a given ring must be multiplied to 
secure the resultant deflection due to both the topography and the 
assumed compensating deficiency or excess of mass below the 
surface of the earth. 
On pp. 26-33 of The Figure of the Earth and Isostasy five com- 
plete examples of the computations of the topographic deflections 
are printed. Note that this is one of the publications criticized 
by Mr. Lewis. His tacit assumption has been tested by using 
these examples, just as he himself should have tested it. 
In the following table the details of the test are shown for two 
stations. The value shown in the table for each ring is the resultant 
deflection due both to topography and to the assumed isostatic 
compensation. The values in the first column which is under 
the heading “‘ Point Arena”’ correspond, as indicated in the heading, 
to the assumption that isostatic compensation is but one-half 
complete and that it extends to the depth 19.29 km. Each value 
was obtained by multiplying the topographic deflection for the 
particular ring, as shown in the example on p. 32 of The Figure of 
the Earth and Isostasy, by the Lewis factor shown on p. 617 of his 
article. The next column shows the deflections for each ring 
corresponding to the assumption that the isostatic compensation 
is nine-tenths complete and the depth as before 19.29 km. The 
Lewis factors necessary for use in computing this column, as well 
as those mentioned elsewhere in this rejoinder, were computed 
from the formula given on p. 615 of the Lewis article. The third 
column shows the deflections corresponding to the assumption that 
the compensation is complete and the depth 113.7 km. 
According to Mr. Lewis’ reasoning the total for the first column 
under Point Arena, +5373, should differ but little from the total 
ior the third column, --15767. Whe actual difference, 38706, 1s 
very large. Similarly the corresponding difference for Uncom- 
