MISSING ELT (EMER LOCATOR XPONDER) ANTENNA. FARS NOT COMPLIED WITH.

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PLEASURE FLT FROM 27C TO 50G; MI; FOR LUNCH. MY WIFE AND I WALKED BACK TO THE ARPT AFTER LUNCH AND MET AN FAA INSPECTOR ON THE ARPT INVESTIGATING AN ACCIDENT FROM 2 DAYS PRIOR. WE TALKED A FEW MINS AND HE ASKED 'IS THIS YOUR PERSONAL ACFT?' 'YES' I REPLIED. 'DID YOU KNOW YOUR ELT ANTENNA IS MISSING?' 'NO; I DIDN'T HAPPEN TO NOTICE IT;' I REPLIED. 'THEY CAN BREAK OFF ANY TIME;' HE SAID. MY WIFE ASKED ME 'WHAT ARE YOU GOING TO DO ABOUT IT?' I SAID 'I'LL BUY A NEW ONE.' WE DISCUSSED LCL ACCIDENTS; ETC; ANOTHER 10 MINS AND WERE READYING FOR DEP. INSPECTOR ASKED IF I HAD AN MEL. I REPLIED 'I DON'T THINK SO; NOT FOR THIS LITTLE AIRPLANE.' (CHEROKEE 180). HE ASKED 'WHAT ARE YOU GOING TO DO?' I REPLIED 'I'LL HAVE TO PLACARD IT INOP.' 'OH YEAH;' HE SAID. AT THIS POINT; I UNDERSTAND HIS RESPONSE TO BE IN AGREEMENT WITH MY PLANNED CORRECTIVE ACTION. (PLACARD THE PANEL 'ELT INOP.') AS WE FLEW HOME; I KEPT THINKING ABOUT HIS MEL QUESTION. AFTER RETURNING HOME; I CHKED THE REGS CONCERNING INOP EQUIP; MEL; AND ELT'S. THE PROPER CORRECTIVE ACTION PER 91.207 WAS TO REMOVE THE ELT; MAKE A MAINT RECORD ENTRY STATING DATE; MAKE; MODEL; SERIAL NUMBER AND REASON FOR REMOVAL; AND PLACARD THE PANEL 'ELT NOT INSTALLED.' BEING A LICENSED MECH; I COULD HAVE EASILY ACCOMPLISHED THIS IF I HAD BEEN AWARE OF THE NEED TO. I DON'T KNOW IF THE INSPECTOR REMEMBERED THIS PARTICULAR REG OR NOT. FROM NOW ON; I WILL ALWAYS KEEP A COPY OF THE FARS IN THE ACFT FOR REF. I NEED TO REVIEW THE FARS FREQUENTLY. I SHOULD HAVE DISCUSSED THE SIT AT GREAT LENGTH WITH THE INSPECTOR TO BE SURE WE HAD A CONSENSUS OF OPINION. I DON'T KNOW IF AN MEL HAD ANYTHING TO DO WITH MY 25 YR OLD; PART 91 AIRPLANE.