
English: 
Hi, guys， 
In this episode, let's talk about the Archimedes' principle to measuring the volume of the soil,
if give you a matchbox today,
want you to calculate the volume of this matchbox,
maybe you will think this's very easy, is the length x width x height
and then, to measure it's the length, width and height 
the volume = length x width x height
yes！ that's right !
but , if give you an object with an irregular shape today ,meanwhile want you to calculate it's volume,
for example, the watch , 
how's you will to calculate it ?
The first to propose a better solution to solve is Archimedes.
At that time, he wanted to measure the volume of the golden crown,
But anyway,
in fact,because the soil is an irregular shape item,
that we can use the same way to calculate.

Chinese: 
各位路人甲乙丙丁大家好
這一集我們來談使用阿基米德原理求定土壤的體積
今天如果給你一個火材盒
要你求火材盒的體積是多少
你會想說這很算簡單，就長X寬X高
就分別去量測長寬高的尺寸
乘起來就是它的體積
嗯！沒有錯
但是如果今天我給你一個不規則形狀的物品要你求它的體積
譬如說手錶
那你要怎麼樣去求呢？
最早提出一個比較好解決的方式的人叫阿基米德
他那時候想要量測的是王冠的體積
但不管怎麼說
因為今天土壤它其實也是一個不規則形狀的物品
所以我們一樣可以用同樣的方式去求
阿基米德怎麼做呢？
其實這個實驗非常簡單

English: 
just...originally to measure the volume of the golden crown was changed to measure the soil.
How will Archimedes do? 
In fact, this experiment is very simple.
He first prepared a container filled with water,
Then throw in the things you want to test and you're done.
you say" wow~ that's so easy,but you haven't told me how much it's volume is ?"
yes, this is what we want to talk about in this episode,
this the description how to derivation the volume of an object ,
first, let's first sees this experiment which will be at least two identities.
That is, before and after the experiment
Their weight and volume will not changed.
so, W1+W2=W3+W4 
then the volume conservation is V1+V2=V3+V4 
We should note here that it has three known conditions.
First, because the container is prepared by yourself.
So you should know how much water the container can hold,

Chinese: 
他先準備了一個容器裝滿了水
然後把你要測的東西丟進去就完成了
你說哇老師這麼簡單，你還沒跟我講他的體積是多少
對，這就是我們這一集要講的內容
就是講如何推導出你要求的物品體積
首先我們先來看一下這個實驗至少會有兩條恆等式
也就是實驗前和實驗後
他們的重量和體積都是不改變的
所以W1+W2=W3+W4
然後體積守恆，也就是V1+V2=V3+V4
這邊我們要注意它有三個已知條件
首先因為容器是你自己準備的
所以你應該要知道容器本身可以裝多少體積的水
再來第二個是你要測定物體的重量必需要是已知
通常這個不會太難，因為你可以透過秤重得到

Chinese: 
但是因為今天我們要測定的是乾土的體積
你在大自然中拿出來的土
通常裡面多多少少會有一些水在裡面
所以我們要先把它放進105度C的烤箱24小時
把土裡面的水蒸發掉
那剩下的就是乾土
然後我們再拿乾土去秤重
最後一個已知條件就是水的密度
這個我們可以查表得到
現在我們來看這兩條公式有哪些是已知數
首先裝滿水的容器你可以去秤重得到W1是多少
那裡面如果裝土粒的話
一樣可以秤重得到W3是多少
然後這個土粒的重量我們從烤箱拿出來以後
一樣去秤重得到W2
接下來因為容器是已知條件
在裝滿的情況下裡面不管裝的是水還是有物體摻在裡面
它的體積都一樣，所以V1=V3=V

English: 
The second ,it's weight already known before you want to measure the volume of an object ,
usually was no too hard,  because you can get it by the weighing.
But ,because today we are going to measure the volume of dry soil.
The soil is you took out in nature.
usually there will be some more or less water inside.
So we have to put it in the oven at 105℃ for 24 hours,
let the water in the soil evaporate,
That rest is dry soil.
then we take the dry soil to weigh,
The density of water is the last known condition,
and this we can check the table,
Now let's see what are the known numbers in these two identities,
First , you can take the containers filled with water to weigh, and then you can know is how much W1
then, if the containers filled with soil particles,
by the weighing ,the same you can know how much W3 is.
then after taken it out of the oven,
and by the weighing ,the same you can know how much W2 is.

English: 
Next, because the container is a known condition
in the case of it's filled,whether filled with water or has something mixed inside
It is the same volume, so V1=V3=V 
So now let's look at the weight identity
is there to get an unknown number W4 by using only an equation.
so by mathematical derivation, and then we can know how much W4 is 
meanwhile, we also know the water will be discharged after soil particles are put in,
then density = weight / volume
So through density formula ,and than we can know how much V4 is
so, V4 is also a derivation value.
than let's take a look at the volume identity,
it now to get an unknown number by becomes using only an equation 
the an unknown number V2 is the volume of dry soil and also we want to know how much it is 
So far this, Archimedes' principle reached its purpose

Chinese: 
所以現在我們來看重量守恆式
是不是就一條方程式求一個未知數W4
所以W4我們可以透過數學的推導得到它的值是多少
我們又知道土粒丟進去以後排出來的一定是水
然後密度=重量/體積
所以透過密度式我們可以得到V4的值是多少
所以V4也是一個推導出來的值
然後我們再看一下體積守恆式
現在是不是變成一條方程式求一個未知數
就是我們想要求的乾土體積V2
所以到此阿基米德原理就達到它的目的
這個實驗做完以後我們可以順便求兩個東西
第一個是我們可以拿乾土的重量去除上乾土的體積
這樣就得到土粒單位重，也就是寫做γ_s

Chinese: 
然後我們再把γ_s去除上水的密度γ_w
就得到了土壤的比重，可以寫作G_s
好，以上就是今天全部的內容，拜拜~~

English: 
After this experiment is done,we can finds two things in this way
first is we can take weight of dry soil divided by the volume of dry soil
This gives the unit weight of soil particles, it's written γ_s 
and then we take γ_s divided by density of water ( γ_w )
This gives the specific gravity of soil 
it's written G_s 
ok, the above is all the content today. Bye ~
