A B737-200 IN CRUISE AT FL350 NOTED GRADUAL LOSS OF #1 ENG OIL; ON DSCNT AT 15000 FT; OIL QUANTITY WENT TO ZERO. EMER DECLARED AND ENG SHUTDOWN CAUSED BY A CRACKED OIL SCREEN HOUSING.

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AT FL350; IN CRUISE MODE; I NOTICED THAT OUR OIL QUANTITY HAD DROPPED FROM 4 GALLONS TO 1.25 GALLONS IN OUR #1 ENG. WATCHING THE GAUGE; IT STILL SHOWED DEPLETING QUANTITY. I CONTACTED ACR MAINT (MAINT CTL). THEY SAID IF I (AS CAPT) WAS COMFORTABLE; I COULD CONTINUE TO SYR. I ELECTED TO CONTINUE BECAUSE THERE WAS CONTRACT MAINT IN SYR AND THE SLOW DROP OF OIL QUANTITY. I WAS AT 15000 FT MSL DSNDING INTO SYR WHEN OIL WENT TO ZERO AND THE LOW OIL PRESSURE LIGHT CAME ON. IN ACCORDANCE WITH PROC; I SHUT DOWN THE #1 ENG. I DECLARED AN EMER; AND CONTINUED DSCNT TO A VISUAL L DOWNWIND AND LNDG. I DID NOT INFORM THE PAX; HOWEVER; THE FLT ATTENDANTS WERE INFORMED. UPON LNDG; AFTER CLRING THE RWY; I MADE A PA TO INFORM THE PAX THAT WE HAD DECLARED AN EMER DUE TO AN OIL LEAK IN OUR L ENG. I NEVER LET PAX KNOW I HAD SHUT DOWN THE ENG. THE LNDG WAS VERY SMOOTH; ROLLOUT WAS NORMAL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE AIRPLANE WAS A B737-200 AND THE LOSS OF OIL WAS CAUSED BY A CRACKED OIL SCREEN HOUSING. THE RPTR SAID THE FAA HAS MADE NO CONTACT WITH THE RPTR.