FAR INFRARED DROPOUT GALAXIES IN THE HERSCHEL GOODS FIELDSTHE MOST MASSIVELY STAR-FORMING GALAXIES IN THE UNIVERSE ARE DUST ENSHROUDED AND RADIATE PRIMARILY IN THE FAR-INFRARED. AT HIGH REDSHIFTS THESE GALAXIES CANNOT BE EASILY FOUND WITH ULTRAVIOLET OR OPTICAL SEARCHES AND CONSTITUTE A MISSING PORTION OF THE UNIVERSAL STAR FORMATION HISTORY DETERMINED WITH CONVENTIONAL TECHNIQUES. CURRENT STUDIES SUGGEST THAT THESE OBSCURED GALAXIES CONTAIN A SUBSTANTIAL FRACTION (ABOUT 20%) OF THE STAR FORMATION OUT TO A REDSHIFT OF AT LEAST FIVE. THE GOALS OF THE PRESENT PROPOSAL ARE TO REFINE THESE MEASUREMENTS TO SEARCH FOR YET HIGHER REDSHIFT DUSTY GALAXIES TO STUDY THE MORPHOLOGIES AND OTHER PROPERTIES OF THESE GALAXIES AND TO DETERMINE HOW THE STAR FORMATION RATES IN THESE GALAXIES CORRELATE WITH THE X-RAY LUMINOSITIES. THE DEEPEST HERSCHEL IMAGING OBSERVATIONS ARE OF THE TWO GOODS FIELDS. HERE WE PROPOSE TO EXTEND THE WAVELENGTH RANGE OF THESE OBSERVATIONS TO 850 MICRON WHICH IS SENSITIVE TO VERY HIGH REDSHIFTS (Z OUT TO ABOUT 8) WHERE THE REST-FRAME WAVELENGTH OF THE OBSERVATIONS LIES CLOSE TO THE PEAK IN THE THERMAL DUST SPECTRUM. WE ARE MAKING THE 850 MICRON OBSERVATIONS WITH THE POWERFUL SCUBA-2 CAMERA ON THE JCMT TELESCOPE. COMBINED WITH THE SPITZER AND HERSCHEL DATA WE WILL BE ABLE TO MEASURE THE LONG WAVELENGTH SPECTRAL ENERGY DISTRIBUTIONS OF THE SCUBA-2 DETECTED GALAXIES AND SEARCH FOR THE HIGHEST REDSHIFT GALAXIES WHICH SHOULD BE FAINT IN THE SPITZER AND SHORTER WAVELENGTH HERSCHEL DATA (MID AND FAR-INFRARED DROPOUT GALAXIES). WE CAN OBTAIN THE MORPHOLOGIES FROM HST FOR THOSE GALAXIES THAT ARE VISIBLE AT OPTICAL OR NEAR-INFRARED WAVELENGTHS AND WE CAN MEASURE THE STAR FORMATION RATES FOR THOSE THAT ARE DETECTED WITH CHANDRA. SUBMILLIMETER DETECTED LUMINOUS DUSTY GALAXIES HAVE THE HIGHEST STAR FORMATION RATES IN THE UNIVERSE AND DETERMINING THEIR PROPERTIES AND REDSHIFT DISTRIBUTION IS KEY TO UNDERSTANDING THE FORMATION OF THE MOST MASSIVE GALAXIES IN THE UNIVERSE. THE PROPOSED WORK WILL ADD VALUE TO THE SPITZER HERSCHEL HST AND CHANDRA DATA SETS ON THE GOODS FIELDS THROUGH DEEP HOMOGENEOUS AND UNIFORM SAMPLES SELECTED AT 850 MICRON. TO FACILITATE THE USE OF THESE DATA BY OTHERS WE WILL PROVIDE REDUCED SCUBA-2 IMAGES CATALOGS AND DERIVED PROPERTIES SUCH AS FAR-INFRARED FLUXES AND COLORS ESTIMATED OR MEASURED REDSHIFTS AND STAR FORMATION RATES ON A DEDICATED WEBSITE.