We have determined the variations in the emission measure of the solar
corona using EUV Imaging Telescope/Solar and Heliospheric Observatory
observations of iron lines in a quiet region of the Sun. The emission
measure is found to vary significantly in at least 85% of all the pix
els within 42 minutes. The variations are interpreted as heating event
s that bring chromospheric material above the one million degree thres
hold of the observed lines and that cool the coronal plasma below that
limit. A method to assess heating events has been developed. The ther
mal energy input by such microflares is calculated from the observed i
ncreases in emission measure and the derived temperature. Heating even
ts have been found in the range from 8 x 10(24) to 1.6 x 10(26) ergs.
The energy input by greater than or equal to 3 sigma events of the emi
ssion measure increase the amounts to about 16% of the average radiate
d power of the coronal plasma in the quiet corona. The frequency distr
ibution of microflares is an approximate power law of the form f(E) =
f(0)E(-delta), With a power-law index delta between 2.3 and 2.6. Since
the low-energy cutoff is due to sensitivity limitations and the power
-law index is steeper than 2, these observations demonstrate the possi
bility that microflares dominate the energy input into the quiet coron
a. The observed power law would have to continue to about 3 x 10(23) e
rgs in order to match the observed minimum heating requirement.