A site testing telescope (STT) was placed for a period of 3 months outside the building, and for a period of 4 months inside the building of the Multiple Mirror Telescope (MMT) located on Mt. Hopkins, and measurements of the astronomical seeing were carried out with both the STT and MMT. A comparison of the simultaneous and interleaved measurements with the two telescopes reveals a tight correlation and a well-defined relationship between the seeing image sizes determined with each telescope. The STT predicts very well the size of a long-exposure image obtained with the MMT. There exists for the MMT an optical blur component of about 0.47 arcsec that is revealed in image size data obtained with only the MMT and that is also revealed and must be accounted for in comparisons between the STT and MMT. Also discovered is a downward component of seeing that is caused by a trailing downwind plume of cold turbulent air that is shed off the radiatively cooled exterior building surfaces. The interior dome component of seeing is remarkably small (upper limit about 0.2 arcsec). The median site seeing is determined to be 0.55 arcsec at an effective wavelength of 7165 A for the MMT observations, or about 0.59 arcsec at 5000 A. The 10 percentile value is about 0.28 arcsec (0.30 arcsec at 5000 A). The median seeing observed with the MMT from one and a half years of data is 0.72 arcsec (0.75 arcsec at 5000 A), and is degraded from the site value virtually entirely by the optical blur component.