These are the principal timbers of the vessel, and upon their strength the safety of a ship chiefly depends. 

网友应该知道这个词组：depend upon （on）取决于；依赖于。

句子为了强调 upon 介词短语而提前，注意划线部分。正常语序是：

These are the principal timbers of the vessel, and the safety of a ship chiefly depends upon their strength. 

【翻译】这些是船的主要木材，船的安全主要取决于它们的强度。