FAILED TO MAKE NOTE IN LOGBOOK OF MAINTENANCE RELEASE FOR FLT WITH INOPERATIVE AWI SYSTEM.

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DUE TO OUR GROSS WT 13595# AND HIGH TEMP; WE HAD TO USE A WET PWR SETTING OF 91%. NO DRY PWR SETTING WAS AVAILABLE. AS F/O; APPLIED TKOF PWR; TURNED ON THE AWI SWITCH AT 40% TORQUE WITH NO INDICATION OF A RISE IN TORQUE. AT 20 KTS WE ABORTED THE TKOF ROLL. THE AWI HAD WORKED PREVIOUSLY; SO I WAS NOT SURE IF IT WAS SOMETHING WE HAD OVERLOOKED OR IF THE AWI SWITCH HAD MADE GOOD CONTACT AND/OR IF THE SPD LEVERS HAD SENT THE SIGNAL TO THE SRL COMPUTER. THE SPD LEVERS WERE A LITTLE LOOSE. WITH THESE UNCERTAINTIES I CALLED FOR ANOTHER TKOF. ON THE SECOND TKOF ATTEMPT I MANUALLY HELD THE SPD LEVERS IN PLACE; BUT STILL NO INDICATION OF A TORQUE RISE IN EITHER ENG WHEN I TURNED ON THE AWI SWITCH. AGAIN WE ABORTED; THEN RETURNED TO THE GATE. WE OFF LOADED PAX AND I CALLED MAINT CONTROL. DURING THIS TIME THE PIH AGENTS GOT 3 PAX TO TAKE ANOTHER FLT. THIS PUT OUR WT DOWN TO 13000 LBS (INCLUDING 100 LBS FUEL BURN). AT THIS WT WE COULD MAKE A DRY TKOF USING 68%. MAINT TOLD ME THEY COULD NOT DO ANYTHING IN PHI; SO I TOLD THEM WE COULD MAKE A DRY TKOF AND THEN WRITE UP THE AIRPLANE AT BOI; OUR DEST. MAINT AND I AGREED TO THIS COURSE OF ACTION AND WE LEFT PIH WITH 3 LESS PAX USING 68% DRY. WHEN WE GOT TO BOI; I WROTE UP THE AIRPLANE. AFTER HAVING A COUPLE OF DAYS TO REFLECT AND SOME RECURRENT TRNING; I CLEARLY SEE WHERE THE MISTAKES WERE MADE. #1--ONE TKOF ABORT WOULD HAVE BEEN SUFFICIENT. #2--I MISUNDERSTOOD FAR 135.179; I SHOULD HAVE GOTTEN MAINT TO RSI THE AIRPLANE PER THE MEL OVER THE PHONE WHILE I MADE THE APPROPRIATE ENTRIES IN THE MAINT LOG. WX FOR MOST OF THE DAY HAD BEEN HOT--LOW HUNDREDS--AND THIS FLT WAS OUR LAST OF AN 8 LEG DAY. I FEEL THAT ALTHOUGH THERE WAS SOME CONFUSION AS TO INTERPRETATION OF LEGALITIES; AT NO TIME DURING THIS FLT WAS SAFETY COMPROMISED. IF THE FAA SHOULD DECIDE TO PRESS THIS CASE; IT WOULD DO SO OVER A MATTER OF COMPLIANCE RATHER THAN SAFETY. I HAVE RECOMMENDED TO TRNING DEPT THAT; ALTHOUGH I BELIEVE OURS TO BE ONE OF THE BEST TRNING FACS; WE SPEND MORE TIME DURING RECURRENT GND SCHOOLS IN THE FLT OPS MANUAL AND THE FAR'S.