B767-300 FLT CREW WHILE IN CRUISE HAS EICAS 'C HYD QUANTITY' INDICATION. FLT CREW HAS CONFERENCE WITH COMPANY AND ELECTS TO PROCEED TO DEST.

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ENRTE LEVEL CRUISE FL370; WE RECEIVED AN EICAS CAUTION MESSAGE 'C HYD QUANTITY' AND THE ASSOCIATED OVERHEAD 'QUANTITY' LIGHT. A REVIEW OF THE EICAS STATUS PAGE REVEALED A CTR HYD QUANTITY OF '.48RF.' FOLLOWING THE FLT MANUAL 'C HYD QUANTITY' IRREGULAR PROC; WE TURNED OFF THE CTR HYD SYS PUMPS AND THE QUANTITY STABILIZED IN THE MID .40'S. UTILIZING VHF AND LATER SATCOM; WE CONFERENCED WITH DISPATCH; MAINT AND B767 FLEET. THE PURSER WAS BROUGHT TO THE COCKPIT; BRIEFED; AND INFORMED THIS WAS TO BE A 'CABIN ADVISORY' AND THAT WE WOULD INFORM THE PAX VIA THE PA CLOSER TO LNDG. ATC WAS ADVISED OF OUR SITUATION AND WE DECLARED AN EMER FOR THE ARR TO AVOID DELAYS ON THE APCH. DURING THE ARR; WE TURNED ALL HYD PUMP SWITCHES BACK TO THE NORMAL ON/AUTO POS; EXTENDED THE LNDG GEAR AND LANDED FLAPS 20 DEGS (IN CONSIDERATION OF A GAR AND POTENTIAL INABILITY TO RETRACT FLAPS). ON THE ROLLOUT; WE DETERMINED WE HAD NORMAL FUNCTIONING OF BRAKES AND NOSEWHEEL STEERING AND TAXIED TO THE GATE UNEVENTFULLY. SUPPLEMENTAL INFO FROM ACN 686975: DURING THE REMAINING TIME; WE RECHKED THE MANUAL AND EXPECTED CHKLISTS: PARTIAL FLAPS WITH ALTERNATE EXTENSION AND ALTERNATE LNDG GEAR EXTENSION. ADDITIONAL MALFUNCTIONS MIGHT HAVE REQUIRED TOW OFF THE RWY. AT THE GATE WE LEARNED THAT WE DID IN FACT LOSE A LOT OF HYD FLUID; BUT WITH QUANTITY CLOSE TO 0; ALL SYS REMAINED OPERATIONAL.