576 JOHN F. HAYFORD 
reduced by such a change, 20 increased and two left as before. 
The test thus gives a neutral result. 
A similar test was made on the assumption that the compensa- 
tion is only one-half complete, as suggested by Mr. Lewis. Such 
a change would increase 29 of the 41 residuals. This is a strong 
indication that incompleteness of compensation does not exist 
to that extent. 
But Mr. Lewis might say in this connection, as he did in con- 
nection with the deflections of the vertical, that an error in assum- 
ing the compensation to be complete had been offset by an error 
in making the depth of compensation too great. On p. 105 of 
the new publication there is a table showing the effect upon the 
computed correction for compensation of changing the assumed 
depth of compensation from 113.7 km. to 85.3. The ten stations 
in this table are also in the table on p. 100. Hence it was possible 
by a comparison of the two tables to compute the value which must 
be assigned to Mr. Lewis’ quantity M, expressing the completeness 
of compensation, to make the assumed change in completeness at 
each station counteract the assumed change in depth. The com- 
parison was made and it was found that the ten necessary values of 
M vary for these ten stations from .56 to 1.78, with a mean of 
about unity. This showed, just as it has already been shown 
earlier in this rejoinder, in connection with deflections of the 
vertical, that there is no fixed relation between the effects due to 
changes of assumed depth of compensation and those due to changes 
of assumed completeness. 
Both these tests are incomplete because they utilize only a few 
of the 89 gravity stations and because they utilize only that por- 
tion of the compensation which is within 166.7 km. of the station. 
But the tests give sufficiently decisive results to show that further 
investigation along this line is reasonably certain to be fruitless. 
The most important confirmation by the gravity publication 
of conclusions previously drawn from deflections of the vertical, 
is that shown on pp. 117-21 of the gravity publication. From 
studies of deflections of the vertical 11 specified areas of excessive 
density (under-compensation) had been located in the United 
