through which to view the differing fortunes of both countries，这是定语从句的一种“缩略表达”。即：保留“介词 + which”，然后把主语（their similarities，在定语从句中用代词 they ）和相应的助动词、情态动词省略。补充完整应为：

through which they will view the differing fortunes of both countries.

这种定语从句的省略结构，在英语中十分普遍。又如：

Intellectuals have long dismissed TV, except as a lens through which to study the masses. 

知识分子长期以来就鄙夷电视，除非把它当作研究普通大众的渠道。

However, this interview provides a unique keyhole through which to view Bruce Lee's views on his life, art and career up to this time in his life.

然而这段采访却为我们提供了一个独特的视角，去窥探当时李小龙对于生活、艺术和事业的看法。

She had never had a real boyfriend before and so had no yardstick by which to compare Charles's behaviour 

她以前从没有过真正的男朋友，所以没有可参照的标准来对比查尔斯的行为。

《柯林斯高阶英汉双解学习词典》

But to do that, the system must have some criteria by which to make decisions. 

但是，要实现这一点，系统必须拥有据此做出决策的标准。