A B737 FLT CREW FINDS OUT AFTER THE FACT THAT THEY HAD FLOWN WITH THE PORTABLE OXYGEN BOTTLE EMPTY.

Narrative

DURING PUSHBACK AND START OF THE #1 ENG; FLT ATTENDANT CALLED ON THE INTERPHONE INFORMING ME THAT AN ELDERLY FEMALE PAX WAS HYPERVENTILATING. FLT ATTENDANT SAID SHE WOULD KEEP ME UPDATED ON HER CONDITION. I DECIDED TO START THE #2 ENG AND CLR THE PUSHBACK CREW IN CASE WE NEEDED TO RETURN TO THE GATE FOR MEDICAL ASSISTANCE. AFTER ENG START AND COMPLETING THE AFTER START AND THE PRE-TKOF CHKLIST; WE GOT A CALL FROM THE CABIN. IT APPEARED THAT OUR PAX WAS BETTER AND ASSURED THE FLT ATTENDANTS SHE WOULD BE OK. I ASKED FLT ATTENDANT IF SHE WAS COMFORTABLE; IF OUR PAX WOULD BE ALL RIGHT FOR THE FLT. SHE RPTED THAT IT APPEARED THAT OUR PAX WAS EMOTIONALLY UPSET VERSUS A PHYSICAL PROB AND THAT OUR PAX'S FAMILY WAS ALSO CONFIDENT THAT OUR PAX WOULD BE OK TO CONTINUE. WITH THIS IN MIND; FLT ATTENDANT AND I WERE COMFORTABLE DEPARTING. ARRIVING AT OUR DEST; OUR ELDERLY PAX DEPLANED ON HER PWR. WE CONTINUED ON OUR NEXT LEG. AT THE GATE; FLT ATTENDANT ASKED ME IF WE COULD GET OUR PORTABLE OXYGEN BOTTLE REFILLED. SHE HAD FORGOTTEN TO TELL ME THAT THE PORTABLE OXYGEN BOTTLE HAD BEEN USED. I HAD A DISCUSSION WITH FLT ATTENDANT THAT WE HAD COMPLETED THIS LEG IN VIOLATION OF THE FAR'S BY NOT HAVING THE PORTABLE OXYGEN BOTTLE PUT ON DEFERRAL. THE NEXT COURSE OF ACTION WAS TO CALL DISPATCH AND MAINT TO MEL THE PORTABLE OXYGEN BOTTLE.