by oneself （用作副词）(1) 独自一人(= alone),例如：She used to sit by herself and read.她从前常常独自坐着看书.(2) 独立地,单独地,自动地,如：He finished it by himself.他独立完成那件事.on one's own - 独立无助地
by oneself和on one's own都有独立做某事的意思
