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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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And so we might need to work out various, more complicated, formulas here, where we multiply the pain times its duration and take into account its intensity, get the sheer quantity of pain that way.
我们需要编制出各种，更复杂的公式，以便增加痛苦的倍数，延续时间,还要考虑痛苦的强度，获得痛苦的纯量。
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No, instead we have to click other amount at bottom right there, when we have to input 4-0-0 in this screen 4-0-0 after consulting visually the little cheat sheet on the device itself it tells you in a very long chart how much one pass costs so we multiply and type in 4-0-0, we hit enter.
不，然而我们必须点击,右下边的这个，当我们需要在这个屏幕上,输入0,通过咨询那个设备上小说明,它在一个很长的图表上,告诉你，每一站需要多少钱，我们加起来,输入了4-0-0，点击输入。
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But remember that we need to multiply it by the volume here, the volume of some sphere we've defined.
但记住我们需要把它乘以体积，乘以一个我们定义的壳层的体积。
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Then it's very clear the way you patch it up is you multiply it by this constant and now we're all set.
很明显,弥补的方法就是,乘以这个常数就全部搞定了
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How do we do that correction? When I first tried this, I thought, fine I'll multiply by 365/60, but I forgot this is a leap year.
那么怎么换算呢,我第一次试的时候,我想,我乘以365/60,但是我忘了,今年是闰年
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And then for some reason, that nobody understands, 16/15 he decided to multiply again by 16/15, and that's how we get 32 for freezing of water and 96 in his words for the temperature in the mouth or underneath armpit of a living man in good health.
然后，因为同样的原因，没人搞得明白，他决定再乘以，现在水的冰点变成了32度,而96度，拿他的话来说,是健康状况良好的人,口腔或腋窝的温度。
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So, once we figure out what our probability of backscattering is, we'll just raise that to the 1/2, and we'll multiply that by 12 . 20 centimeters.
所以一旦我们,知道了散射概率，我们开根号。
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So if we actually go ahead and multiply it by the volume of our shell, then we end up just with probability, which is kind of a nicer term to be thinking about here.
乘以壳层的体积,我们就得到了概率，在这里从这个角度，理解问题更好一些,如果我们考虑的是。
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The beauty of that is now we have discovered a notion of what it means to multiply a vector by a number.
现在最美妙的就是我们就已经知道,数字乘以矢量的意义
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So if we take this term, which is a volume term, and multiply it by probability over volume, what we're going to end up with is an actual probability of finding our electron at that distance, r, from the nucleus.
如果我们取这项，也就是体积项然后，乘以概率除以体积，我们能得到的就是真正在距离,原子核ｒ处找到电子的概率。
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So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.
我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。
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a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.
在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。
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And when we describe this in terms of talking about chemistry terminology, we would call the first one the 1 s, and 1 is in parentheses because we're talking about the first electron there, and we would multiply it by the wave function for the second one, which is also 1 s, but now we are talking about that second electron.
当我们用化学术语来,描述它的时候，我们称第一个为“1s“,括号中的1是因为我们,在谈论第一个电子,而且我们会用它的波函数，乘以第二个,第二个也是“1s“,但是我们现在谈论的是,第二个电子。
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So, the number of nuclei, 119 if we were to sit and count these as well, is 119. So, we'll multiply that by just pi, r squared, to get that cross-section, and divide all of that by 1 . 39 meters squared.
如果你们数的话，原子核的数是，我们用它乘以πr的平方，得到横截面积，除以1。39平方米。
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