IGF::CT::IGF CRITICAL FUNCTIONS - DECIPHERING CLUSTER OBSERVABLES: TRACING THE BARYONS IN CLUSTERS OF GALAXIES TO PROVIDE OBSERVATIONS OF MODERATE-REDSHIFT OPTICALLY-SELECTED CLUSTERS OF GALAXIES. THIS PROPOSAL REQUESTS FUNDING FOR TWO( 2) SUZAKU AO-5 OBSERVATIONS OF MODERATE-REDSHIFT OPTICALLY-SELECTED CLUSTERS OF GALAXIES. THESE OBSERVATIONS HAVE THREE (3) MAIN OBJECTIVES. THE FIRST IS TO QUANTIFY SYSTEMATIC DIFFERENCES BETWEEN THE PHYSICAL CHARACTERISTICS OF WELL MATCHED (IN REDSHIFT AND VELOCITY DISPERSION) X-RAY AND OPTICALLY SELECTED CLUSTER SAMPLES. WE WILL MEASURE THE X-RAY LUMINOSITIES AND TEMPERATURES OF THESE CLUSTERS, ALLOWING US TO COMPARE THE PROPERTIES OF THESE OBJECTS WITH STANDARD CLUSTER SCALING RELATIONS. WE ALSO EXPECT TO OBTAIN ROUGH MASSES AND ABUNDANCE MEASUREMENTS. OUR SECOND GOAL IS TO COMPARE X-RAY AND DYNAMICAL MASS ESTIMATES OF OUR TARGETS. DYNAMICAL MASSES WILL BE DERIVED FROM IN-HAND VELOCITY DISPERSION MEASUREMENTS. FINALLY, WE WILL ALSO USE THESE DATA TO CALIBRATE OPTICAL RICHNESS AS A MASS OBSERVABLE AND INVESTIGATE ITS SCATTER. THE TOTAL TIME FOR THE TWO OBSERVATIONS IS 134 KSEC. UNDERSTANDING RELATIONSHIPS BETWEEN BARYONS IN GALAXY CLUSTERS AND UNDERLYING DARK MATTER DISTRIBUTIONS IS CRUCIAL FOR USING CLUSTERS AS COSMOLOGICAL PROBES. RECENT WORK INDICATES MASSIVE LOW-LX CLUSTERS AT ALL REDSHIFTS, IN CONFLICT WITH SELF-SIMILARITY PREDICTIONS. THE ONLY WAY TO QUANTIFY THESE FINDINGS IS TO OBSERVE A SAMPLE CHOSEN INDEPENDENTLY OF X-RAY PROPERTIES. WE PROPOSE TO STUDY 13 CLUSTERS AT 0.15<Z<0.45, FOR WHICH ROBUST VELOCITY DISPERSIONS ARE MEASURED SUZAKU'S SUPERIOR THROUGHPUT IS REQUIRED TO COMPLETE THE LOW-DISPERSION, HIGH-Z SIDE OF THE DISTRIBUTION. WE PROPOSE XIS OBSERVATIONS OF THE REMAINING TWO (2) TARGETS, ALLOWING US TO RIGOROUSLY ASSESS BARYON CONTENT IN AN UNBIASED SAMPLE OF CLUSTERS. CLUSTERS OF GALAXIES ARE AN IMPORTANT SOURCE OF INFORMATION ABOUT THE UNDERLYING COSMOLOGY OF THE UNIVERSE. THE GOAL IS TO CHART THE EVOLUTION OF THE CLUSTER MASS FUNCTION, THEREBY PROVIDING VALUABLE INFORMATION ON THE PROGRESSION OF LARGE-SCALE STRUCTURE FORMATION.