564 
Journal of Agricultural Research 
Vol. XI, No. 11 
for constant days to silking—that is, with the differences due to season 
eliminated. * 1 
Damage does become somewhat less as the season advances, r— —0.36, 
but there is also a very slight tendency for the progenies with the longer 
season to have shorter prolongation, — 0.02. The partial correla¬ 
tion of prolongation and damage for constant days to silking is —0.76. 
Since the direct correlation is —0.71, the conclusion is that among prog¬ 
enies with the same days to silking the negative correlation between 
prolongation and damage is, if anything, higher than is indicated by the 
direct correlation. 
The effect of days to silking on the correlations between prolongation 
and the other measurements of in jury are all in the same direction—that is, 
any effect which days to silking may have had is to make the apparent 
relationship less close than the true one. The partial correlations for 
constant days to silking change the direct correlation between pro¬ 
longation and number of larvae from —0.60 to —0.73, that between 
prolongation and damage per larva from -0.75 to -0.76. 
In like manner the elimination of difference in “maturity” and 
“silking to harvest” fails to reduce the correlation between prolongation 
and the measures of injury. The partial correlation of prolongation and 
damage for constant maturity raises the direct correlation from —0.71 
to —0.79; when constant for “silking to harvest,” the direct correlation 
is unchanged. 
Another character that might be suspected of affecting the relation 
between prolongation and damage is husk leaves. The presence of 
husk leaves may make the ears either more or less attractive to moths 
when they are depositing their eggs and thus change the number of 
larvae gaining access to the ear. 
The partial correlation between prolongation and damage for con¬ 
stant husk leaves indicates that the net result is negligible, since it 
reduces the direct correlation of —0.71 to only —0.70. 
By applying the formula for partial correlations a second, third, and 
fourth time an expression may be obtained for the correlation between 
prolongation and damage with season, maturity, “ silking to harvest,” 
and husk leaves all constant. This was found to be — 0.83. The writers 
therefore conclude that if the relatively close interprogeny correlation 
between prolongation and damage is due to the association of pro¬ 
longation with other protective characters, these characters were not 
included in the notes. 
fI2 — (f 13^23) 
1 "The formula for partial correlations is ri2.3==~ T. 9 . -= 
* yi—ri$ 2 * * * * x 1—f23 8 
where r 12=correlation between variables 1 and 2, 
r 13= correlation between variables 1 and 3, 
f 23“correlation between variables 2 and 3, 
r i2.3=r 12 for constant 3. 
and 
