Mean Values.
Mean Values.
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平均值。
DOI：
10.1126/science.ns-21.541.333
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发表时间：
2010
期刊：
影响因子：
56.9
通讯作者：
E. Hayes
中科院分区：
文献类型：
--
作者：
E. Hayes
波特小姐对《太阳热和轨道偏心率》（《科学》杂志，6月2日）文章中的一点提出了善意的批评，这给了我们一个机会说一篇关于平均值的文章。由于n个量的平均值是它们总和的算术平均值，乍一看，这个词似乎是一个完全确定的词；但是，如果要求平均的量是某变量函数的连续值，那么显然，它们的大小不仅取决于函数的性质，而且取决于基本量的变化规律。因此，假设我们有等温线p v= Ct，并希望知道体积v= v~和体积v= Va′之间的平均压强。柯一些假设关于诉如果增量的变化应该是平等的,我们理解的“平均值”pre-ssure相对应的压力值的平均值的诉如果体积认为反过来依赖于其他变量以这样一种方式abscissa-increments不相等,平均值将平均pressure-ordinates对应的新系列的一系列值v下产生第二个假设。显然，这两种平均数通常是不相等的，但其中一种同另一种一样，都是“真正的平均数”。平均值的公式可以用一种比威廉姆森和托德亨特给出的通常的解析式更简单的方法推导出来。求y的均值，当y= f (x)且x是等分变量。如果将y= f (x)视为指向矩形b轴的曲线，则。如果(x) dx是面积A的表达式，面积A以x轴为界，两个坐标，以及曲线在边界坐标之间截取的部分。设A= A‘，其中A’是一个矩形，它的底等于A的底。A'是A中坐标的平均值
MISS PORTER" S kindly criticism (Science, June 2) of one point in the article," Sun-Heat and Orbital Eccentricity"(Science, Apr. 28), gives occasion to say a work in regard to mean values. Since the mean value of n quantities is the arithmetic mean of their sum, it would appear at first glance as if the term were a perfectly definite one; but if the quantitIes to be averaged are: successive values of a function of some variable, then clearly their magnitudes depend not only on the nature of the function, but also on the law of variation of the fundamental. Thus, suppose we have the isotherm, p v= Ct'and wish to know the average pressure between the volumes v= v~ and v= Va' It is necessary to ma. ke some assumption in regard to the variation of v. If its increments are supposed equal, we understand by the" mean value" of the pre-ssure the average of the pressures corresponding to the values of v. If the volume is assumed to depend in turn on some other variable in such a manner that the abscissa-increments are not equal, the mean value will now be the average of the new series of pressure-ordinates corresponding to the series of values of v arising under the second assumption. Evidently these two means will in general be unequal, but one is just as properly the'" real average" as the other. The formula for mean value may be derived by a method even simpler than the usual analytical one as given by Williamson and Todhunter. Let it be required to find th~ mean value of y where y= f (x) and x is an equicrescent variable. If y= f (x) be treated as a curve referred to rectangular b axes,. If (x) dx is the expression for the area, A, bounded by a the X-axis, two ordinates, and tbe portion of the curve intercepted between the bounding ordinates. Let A= A', where A'is a rectangle whose base equals the base of A. Then the altitude of. A'is the average of the ordinates in A. For let