Observations from the first flight of the Medium Scale Anisotropy Measurement ( MSAM1-92 ) are analyzed to search for the Sunyaev-Zel ’ dovich ( SZ ) effect towards the Coma cluster . This balloon-borne instrument uses a 28 ^ { \prime } FWHM beam and a three position chopping pattern with a throw of \pm 40 ^ { \prime } . With spectral channels at 5.7 , 9.3 , 16.5 , and 22.6 { cm } ^ { -1 } , the observations simultaneously sample the frequency range where the SZ spectral distortion in the intensity transitions from a decrement to an increment and where the fractional intensity change is substantially larger than in the Rayleigh-Jeans region . We set limits on the Comptonization parameter integrated over our antenna pattern , \Delta y \leq 8.0 \times 10 ^ { -5 } ( 2 \sigma ) . For a spherically symmetric isothermal model , this implies a central Comptonization parameter , y _ { o } \leq 2.0 \times 10 ^ { -4 } , or a central electron density , n _ { o } \leq 5.8 \times 10 ^ { -3 } cm ^ { -3 } h _ { 50 } , a result consistent with central densities implied by X-ray brightness measurements and central Comptonization estimates from lower frequency observations of the SZ effect .