The last leg of Amelia Earhart's round the world flight is most often depicted as a straight line on a chart, as seen in the below illustration. This particular one was published by the TIGHAR outfit which believes that she ended up on Gardner Island (now called Nikumaroro), which is located south of Howland Island.
Her actual track, however (as discussed in the Loomis book), was slightly north of that straight line course. She flew first over Nukumanu, and then to Nauru, where she reported seeing the lights which were on to guide her. She also had been heard broadcasting on radio at both islands. Her course from Nauru toward Howland would have taken her over the Gilbert Islands (British owned) during night darkness. There were two very strong British run radio stations in the Gilberts, but they were not asked to assist in her flight.
A Line of Position (LOP) on the sun at sunrise, charted as a line perpendicular to her intended course, would have plotted out as 157 degrees/ 337 degrees - as seen on the maps. Amelia reported that she was on this LOP and flying north and south trying to locate Howland Island (or the Cutter Itasca near it). It is that LOP, which happens to fall through Gardner/Nikumaroro that bolsters support for those who believe she landed or ditched there.
Some researchers (like Loomis) feel that she may have been off course to the left far enough to not see smoke sent up by Itasca. And of course, radio direction finding was not working out. Amelia had previously ended up north of course during her Atlantic crossing and had to land at an alternate field. A navigator who had previously flown with her during flight tests of the Electra stated that she had a tendency to fly 3 degrees left of compass headings she was given.
Her stated intention to others prior to her last leg of flight was that if she failed to find Howland, she would fly back to the Gilberts and seek a suitable landing site. IF she was far enough left of course, and north of Howland, taking a heading to the west would have taken her instead to the Marshall Islands, which were Japanese controlled. Many Marshallese testified that she ditched her aircraft near Barre Island in the Mili atoll, and that she and Fred Noonan were picked up by the Japanese Navy.