请求解释个英语语法问题

Question

Attached to the booking confirmation will be a note showing the balance due on your holiday and the date by which it is payable.

这是剑桥雅思阅读里的一句原话，请问在关系副词which前为什么要加by，还有一些句子是to which, with which等。都不太理解前面的那个介词，请求高人指点啊，万分感谢~
十分感谢朋友们的回答，谢谢你们。那向下面这句里的 "Half Of Which" 又是怎么理解呢？
When a sprinter runs, Yessis explains, her foot stays in contact with the ground for just under a tenth of a second, half of which is devoted to landing and the other half to pushing off.

Answer 1

要解答你的问题需要从两个方面着手，即，语法与词法。

1） 语法问题：
定语从句的引导词在定语从句里有三个功能：a/ 引出定语从句；b/ 在从句中代替先行词的词义；c/ 在从句中做一个语法功能。根据这三点，我们不妨将你的原句中定语从句单独拆分出来 “by which it is payable”，which 在从句中代替了先行词的词义，则 “by the date it is payable”。将句子弄顺后，“it is payable by the date”。能理解吗？
2） 词法问题：
by 介词的词义在这里是 “截止到 ...... 时候”，这样，你就明白了了吧。

关于其他几个介词 “to which” “with which” 等等，见例句 a/ We have sent you the agreement to which several other supporting document are attached.； b/ The government official distributed the tools with which local people are fighting the flooding.
使用合适的介词要看定语从句中动词或句意来确定，像第一句用了 “to” ，那是 attach 所需要的，第二句用了 “with” ，那是fight flooding with some tools 所需要的。

若再有不清楚，欢迎追问，以求理解。

追问

十分感谢您的回答，有点懂了，谢谢。那向下面这句里的 "Half Of Which" 又是怎么理解呢？

When a sprinter runs, Yessis explains, her foot stays in contact with the ground for just under a tenth of a second, half of which is devoted to landing and the other half to pushing off.

追答

不错，这里的现行词是 “a tenth of a second” ，half of which 在定语从句中做主语，引导词在定语从句里做 of 的介词宾语。即：half of a tenth of a second （which）。

Answer 2

楼下说的对，选其他人的答案吧。

Answer 3

句子大概意思：附在预订证明上的是一个注解，表明了你假期里的付款余额和付款截止日期。

by which it is payable 是一个定语从句，修饰先行词the date ,即说明什么样的日期，it代指balance due （付款余额），payable 意为“可付款的”，it is payable 这个句子的结构是完整的，如果去掉by ,the date which it is payable ,which 引导定语从句，一定会代替先行词在从句中充当某一成分，这里用which 代替the date 放在从句中哪个位置都不合适，如果加上by ,就不同了，by which 代替by the date 在从句中充当状语：it is payable by the date 。by 表示到某个日期为止，即到某个日期为止它是可付的，当然这个日期是写在注解note 里 .
其实介词by 也可以挪到从句里：the date which it is payable by .这样就清楚多了。

其实这种结构叫做：介词+关系代词引导的定语从句，关系代词在定语从句中做介词宾语时，从句常由介词+关系代词引导
当介词放在关系代词前面时，关系代词只能用which/whom即“介词+which/whom"且不能省略。但当介词位于末尾时可用that/which/who/whom.作介词的宾语，且可以省略。例如：
(1) The school (that/which) he once studied in is very famous."that/which"可以省略
= The school in which he once studied is very famous."which”不可省略
(2) Tomorrow I will bring here a magazine (that/which) you asked for.
= Tomorrow I will bring here a magazine for which you asked.
(3) We’ll go to hear the famous singer (whom/that/who) we have often talked about.
= We’ll go to hear the famous singer about whom we have often talked.
注意：
1. 含有介词的动词短语一般不拆开使用，如：look for, look after, take care of等
T This is the watch which/that I am looking for. (T=正确)
F This is the watch for which I am looking. (F=错误)

望采纳，谢谢！

Answer 4

by which 属于介词+关系代词引导的定语从句，表示：不迟于
关系代词which 前介词的选择首先考虑短语和词语搭配；然后考虑意思是否合适就可以了。

Answer 5

which 前的介词灵活的，要看具体环境哟

Answer 6

这些是介词啊，主要根据句意判定。