  This article presents a power-spectrum analysis of 39,024 measurements of the
solar diameter made at the Mount Wilson Observatory from 1968.670 to 1997.965.
This power spectrum contains a number of very strong peaks. We find that eight
of these peaks agree closely with the frequencies of r-mode oscillations for a
region of the Sun where the sidereal rotation frequency is 12.08 year$^{-1}$.
We estimate that there is less than one chance in ten to the sixth power of
finding this pattern by chance.
