AN ACR LTT FLC; UNAWARE THAT THEY HAVE HAD AN ACFT EQUIP MALFUNCTION IN THEIR HDG SENSING; EXPERIENCES A HDG TRACK POS DEV. DEP CTLR GETS THEM ON A NEW HDG.

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DURING MY FIRST WK OF FLYING IN THE NE UNITED STATES AND THIRD DAY OF FLYING INTO LGA; WE WERE ASSIGNED THE WHITESTONE CLB AFTER DEPARTING RWY 13 (WHICH IS THE 175 DEG HDG UNTIL 2.5 DME AND THEN A L TURN TO 040 DEGS). AFTER LINING UP ON THE RWY AND CHKING INSTS AND NOTING THE ARPT SIGN SAYING CHK HDG OF 132.5 DEGS WE DEPARTED. AFTER FLYING WHAT WE THOUGHT WAS THE WHITESTONE CLB; WE WERE GIVEN A HDG AND DIRECT BDR WHEN ABLE. ABOUT 30 SECONDS LATER THE CTLR ASKED WHAT HDG WE WERE FLYING AND WE TOLD HIM LAST ASSIGNED HDG. AT THAT POINT HE SAID 'CHK YOUR INSTS' BECAUSE HE SHOWED US NEEDING TO TURN ABOUT 40 DEGS TO THE R AND SAID WHY OUR WHITESTONE CLB LOOKED SO DIFFERENT FROM NORMAL. WE ASKED TO BRIEFLY LEVEL OFF AND NOTED THE MAGNETIC COMPASS AND REALIZED WE WERE APPROX 45 DEGS OFF COURSE. AFTER RESETTING THE EHSI'S WE CONTINUED OUR CLB IN THE RIGHT DIRECTION. THEN THE CTLR ADVISED US TO CHANGE TO THE NEXT CTLR AFTER NOTING WE WERE ALMOST 8 MI OFF COURSE. I BELIEVE WHAT HAPPENED WAS A SIMULTANEOUS PRECESSION OF OUR INSTS ON ROTATION (EHSI'S); BECAUSE WE NEVER GOT A HDG FLAG OR ANY OTHER TYPE OF FLAG WHEN AIRBORNE. THE CONTRIBUTING FACTORS WERE DEFINITELY THE FACT THAT IT WAS BOTH CREW MEMBERS' FIRST WEEK IN THE NE AND THE LACK OF KNOWN VISUAL TOPOGRAPHICAL VISUAL POINTS. ALSO IT WAS THE FIRST TIME FOR BOTH OF US TO DO THE WHITESTONE CLB AND IN HINDSIGHT; I REMEMBER THINKING THAT THE INITIAL TURN AFTER TKOF WAS NOT AS DRAMATIC AS I SAW OTHER ACFT MAKING; BUT THOUGHT MAYBE THEY HAD RECEIVED VECTORS AFTER TKOF. THROUGHOUT THE DAY WE CONTINUED TO MONITOR THE EHSI'S AND MAGNETIC COMPASS MORE CLOSELY BUT DID NOT SEE A RECURRING PROB.