The Fragile Yellow Arc was one of two epochs in the lives of the residents of the planet Fragrance. It was the time from which a person fell in love until the time they died. It followed the Thin Purple Arc, the period of time roughly equivalent to human adolescence. When the two arcs were put together, they formed a metaphorical circle, around which each person got to travel once in their lifetimes.
The rules governing how one spent the Fragile Yellow Arc were rather strict. People of Fragrance only fell in love once in their lifetimes. Thus, if their partner died, their life had to be voluntarily ended, as well. Generally speaking, the object of one's affections returned those feelings; romantic rejection was extremely rare on Fragrance. However, if one was romantically rejected, one's life was forfeit, because love was regarded as a once-in-a-lifetime opportunity. Thus, when Rhythm fell in love with Barbara Wright at the beginning of his Fragile Yellow Arc, her refusal of him was effectively a death sentence. Though Barbara seemed prepared, in the end, to leave the TARDIS in order to remain with Rhythm and spare his life, the First Doctor dematerialised the TARDIS instead of opening the TARDIS doors. Barbara could only watch as he ended his own journey on the Fragile Yellow Arc by sailing his vessel alone on the Emerald Sea and apparently immolating himself. (AUDIO: The Fragile Yellow Arc of Fragrance)