  Observations from the first flight of the Medium Scale Anisotropy Measurement (MSAM) are analyzed to place limits on Gaussian fluctuations in the Cosmic Microwave Background Radiation (CMBR). This instrument chops a 30\arcmin\ beam in a 3 position pattern with a throw of $\pm40\arcmin$; the resulting data is analyzed in statistically independent single and double difference datasets. We observe in four spectral channels at 5.6, 9.0, 16.5, and 22.5~\icm, allowing the separation of interstellar dust emission from CMBR fluctuations. The dust component is correlated with the \IRAS\ 100~\micron\ map. The CMBR component has two regions where the signature of an unresolved source is seen. Rejecting these two source regions, we obtain a detection of fluctuations which match CMBR in our spectral bands of $0.6 \times 10^{-5} < \Delta T/T < 2.2 \times 10^{-5}$ (90\% CL interval) for total rms Gaussian fluctuations with correlation angle 0\fdg5, using the single difference demodulation. For the double difference demodulation, the result is $1.1 \times 10^{-5} < \Delta T/T < 3.1 \times 10^{-5}$ (90\% CL interval) at a correlation angle of 0\fdg3. 
A Measurement of the Medium-Scale Anisotropy in the Cosmic Microwave   Background Radiation