564 JOHN F. HAYFORD 
action suggested by him is possible. Now it happens that such 
counteraction is nearly impossible to any appreciable extent in the 
computations actually made. If Mr. Lewis had followed his own 
course of reasoning farther than he did, using the data printed in 
the publications criticized he would have convinced himself of this. 
He carries his reasoning farther on pp. 616-17 than elsewhere 
in his article. In the paragraph commencing near the top of 
p. 616 he shows that if with assumed complete compensation the 
assumed depth of compensation is made smaller, the reduction 
factors for each ring become smaller and that, on the other hand, 
if the isostatic compensation is assumed to be less than complete, 
the reduction factor for each ring becomes larger. It is also shown 
that when both these changes in assumption are made at the same 
time, the reduction factor becomes smaller for certain rings and 
larger for others. On p. 617 a concrete case of this kind is shown. 
The table there printed shows clearly that if in the place of assumed 
complete compensation extending to depth 113.7 km. one assumes 
a compensation but one-half complete and extending only to the 
small depth 19.29 km., the reduction factors for rings 29 to 13, 
corresponding to topography within 56 km. of the station, are all 
made smaller and those for the remaining more distant rings are 
all made larger. Thus far Mr. Lewis’ reasoning and results are 
all correct. For convenience, call such reduction factors as those 
shown in the middle column of the table on p. 617, Lewis factors, 
and call those such as are shown in the last column, Hayford 
factors. 
At this point Mr. Lewis’ logival process begins to go wrong. 
For at this point the tacit assumption is made, though not stated, 
that if the Lewis factors are smaller for some rings and larger 
for others than the Hayford factors the computed topographic 
deflections with the isostatic compensation considered will be 
about the same in the two cases. If so (that is, if the computed 
deflections are easily made about the same), then with effort 
corresponding to that already made by Hayford, other factors 
on Lewis’ basis, involving other assumptions as to depth and degree 
of compensation, can be found which will produce computed 
deflections more nearly in agreement with the observed deflections 
