Being very short of money and wanting to do something useful, I applied, （fearing as I did so, that without a degree and with no experience of teaching my chances of landing the job were slim. ）

句首划线部分而并列的现在分词短语作原因状语，I applied为主语和不及物动词作谓语，括号里的部分为fearing现在分词短语作applied的伴随状语。其中as I did so是fearing的时间状语，that从句为fearing的宾语从句，that为从属连词。without和with二个介词短语是that从句的原因状语，my chances of landing the job were slim为that从句的主系表结构。

译文：由于很缺钱同时又想干点有用的事，我就申请了。申请的同时我又担心我没有学位，也没有教学经验，我得到这份工作的机会是很渺茫的。

fearing现在分词短语作伴随状语的其它例句：

She went to her doctor, fearing (that) she might have cancer.