ACR LGT FORGOT TO CALL THE TWR FOR LNDG CLRNC FROM A LOW VIS IAP ILS APCH INTO EWR.

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FLT FROM IAH TO EWR. THE WX FORECAST FOR EWR PREDICTED EXTREMELY LOW VISIBILITY APPROX 4-6 HRS AFTER OUR SCHEDULED ARR. THE TEMP/DEW PT SPREAD WAS CLOSE SO WE UPDATED THE WX OFTEN. APCHING EWR WE WERE ASSIGNED TO HOLD AS THE VOLUME OF TFC EWR COULD ACCEPT WAS REDUCED DUE TO LOWERING VISIBILITY. WE HELD FOR 1 HR 30 MIN. WE FINALLY WERE CLRED FOR APCH AND THE NEW RVR CALLED TO US WAS BELOW MINS. WE THEN DIVERTED TO PHL. WE REFUELED AND WERE REDISPATCHED TO EWR WITH THE NEW RVR AT EWR GREATER THEN 4000 FT. BY THIS TIME THE COCKPIT CREW HAD BEEN UP OVER 20 HRS EVEN THOUGH THE DUTY DAY HAD BEEN MINIMAL. THINGS WERE COMPRESSED ON THIS SHORT FLT WITH RAPIDLY CHANGING VISIBILITY AT EWR; MANY CHKLISTS TO RUN ETC. THE FO WAS FLYING THIS LEG AND AS WE APCHED THE FAF I COULD TELL HE WAS GETTING BEHIND. WE WERE HANDED OFF TO TWR. I CHANGED FREQ BUT DID NOT CALL IMMEDIATELY DUE TO THE FO GETTING FURTHER BEHIND. AS WE WENT LOWER HIS PROBLEMS INCREASED SO I DECIDED TO TAKE CTL OF THE ACFT AND MAKE THE LNDG. NOBODY CALLED THE TWR FOR PERMISSION TO LAND. MY FAULT -- MY RESPONSIBILITY.