The specific challenge of longitude calculation adds another layer of difficulty. Latitude — your north-south position — can be determined from a noon sun sight with relatively modest arithmetic. You measure the sun’s altitude above the horizon at its highest point, compare it to the sun’s calculated position in the almanac for that date, and the difference gives you your latitude. This calculation is robust against moderate errors and can be performed with a watch that is accurate to within a few minutes.
Longitude is harder. It depends on knowing the exact time — to within a few seconds — of a celestial observation, and comparing that time against Greenwich Mean Time. The difference between your local apparent time and GMT, multiplied by 15, gives your longitude in degrees. A one-second error in the time produces a quarter-mile error in longitude at the equator; a one-minute error produces a 15-mile error. For a sailor trying to hit an island chain that stretches only about 300 miles from end to end, in an east-west direction, a longitude error of more than 150 miles could mean missing Hawaii entirely.
Oldham’s watch had stopped during the capsize. She found it in the bilge, working, but with an unknown amount of elapsed time since it stopped. She needed to establish a known time reference before her longitude calculations would be reliable. About a week into the survival period, she established this reference — the specific method is described in the Explorer’s Web account as using the calculated position of a celestial body in conjunction with her watch time — and from that point forward her navigation was on firmer ground.