  The history of discovering of hot gas in galaxies is traced briefly, its main
properties are described and the desirability to make them more precise, in
particular to obtain additional data on the mass of such gas is pointed out.
For this purpose observations of the Sunyaev-Zel'dovich effect on hot gas of
coronas of elliptic galaxies are proposed. The absolute and relative
disturbances of the cosmic microwave radiation spectrum due to scattering of
relic photons by Maxwellian electrons are calculated according the formula of
the article. With the example of three elliptic galaxies it is shown that
observation of the SZ effect on such galaxies is quite possible. Kinematic SZ
effect arising due to peculiar movement and rotation of galaxies is available
for observation as well. Such observations combined with X-ray data would make
it possible to get more about properties of galactic gas, to obtain additional
information on rotation of galaxies, on possible accreting gas flows and on hot
galactic wind.
