SMA PLT FAILS TO ASSURE CONTACT WITH TRACON AND FLIES THROUGH CLASS C AIRSPACE WITHOUT CLRNC. NOTIFIED OF ERROR WHEN HE CONTACTS CTR. CLASSIC EXAMPLE OF COM ERROR MISUNDERSTANDING.

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I HAD JUST DEPARTED FRG ON MY WAY HOME. I REQUESTED A L- HAND TURN OUT FROM THE RWY HDG (140 DEGS) TO MY COURSE OF 050 DEGS. FRG TWR SAID THEY COULD NOT PERMIT IT DUE TO HVY PATTERN TFC AND WAS INSTRUCTED TO USE 'STANDARD DEP.' I CONTINUED TO CLB ON THE RWY HDG OF 140 DEGS UNTIL I HAD PASSED 2500 FT MSL. ONCE CLR OF FRG CLASS D AIRSPACE; I TURNED TO MY DIRECT COURSE OF 050 DEGS AND CONTINUED TO CLB TO 3500 FT TO CROSS LONG ISLAND SOUND. AS SOON AS I HAD CLRED THE CLASS D AIRSPACE; I CALLED NEW YORK DEP ON THE PUBLISHED FREQ OF 125.7 AND INFORMED THE CTLR THAT I WAS 'WITH HIM.' HE SAID TO 'WAIT ONE' OR SOMETHING TO THAT EFFECT. I CONTINUED TO MONITOR THE FREQ AS I CLBED TO APPROX 3800 FT MSL. MY XPONDER WAS ON AND SET TO 1200. I LISTENED BUT THE CTLR WAS BUSY SO I WAITED. AS I CROSSED THE SHORELINE OF LONG ISLAND I CHANGED FREQ TO 'WHITE PLAIN' CTR ON 126.95 AND REQUESTED FLT FOLLOWING. A FEW MINS LATER THE CTLR INFORMED ME THAT I HAD FLOWN THROUGH LONG ISLAND CLASS C AIRSPACE WITHOUT TALKING WITH THEM. HE SAID I SHOULD HAVE BEEN BELOW 1500 FT OR ABOVE 4100 FT AS I PASSED THROUGH THEIR AIRSPACE. I MADE THE MISTAKE OF THINKING THAT BY CONTACTING NEW YORK DEP I HAD NO PROB FLYING THROUGH THE NW CORNER OF THE CLASS C AIRSPACE. THE NEW YORK CLASS B AIRSPACE IS JUST A SHORT DISTANCE FROM THE CLASS C AIRSPACE AND IS IN THE MODE C VEIL. I DID NOT REALIZE THAT I HAD FLOWN THROUGH THE CLASS C AIRSPACE.