FOR THE HUMAN MIND the absolute continuity of motion is inconceivable. —
对于人类思维而言，运动的绝对连续是无法想象的。 —

The laws of motion of any kind only become comprehensible to man when he examines units of this motion, arbitrarily selected. —
任何类型的运动定律只有在人类选择的运动单位上进行研究时才能理解。 —

But at the same time it is from this arbitrary division of continuous motion into discontinuous units that a great number of human errors proceeds.
但同时，正是从将连续的运动任意分割为不连续的单位中，产生了许多人类错误。

We all know the so-called sophism of the ancients, proving that Achilles would never overtake the tortoise, though Achilles walked ten times as fast as the tortoise. —
我们都知道古人所谓的悖论，证明阿基里斯永远无法追上乌龟，尽管阿基里斯的速度是乌龟的十倍。 —

As soon as Achilles passes over the space separating him from the tortoise, the tortoise advances one-tenth of that space: —
阿基里斯一旦越过与乌龟之间的距离，乌龟就前进了这个距离的十分之一： —

Achilles passes over that tenth, but the tortoise has advanced a hundredth, and so on to infinity. —
阿基里斯越过这十分之一，但乌龟已经前进了百分之一，依此类推，直到无限。 —

This problem seemed to the ancients insoluble. —
这个问题在古人看来是无解的。 —

The irrationality of the conclusion (that Achilles will never overtake the tortoise) arises from the arbitrary assumption of disconnected units of motion, when the motion both of Achilles and the tortoise was continuous.
结论（阿基里斯永远无法追上乌龟）的不合理性源于任意假设的不连续运动单位，而不是阿基里斯和乌龟的连续运动。

By taking smaller and smaller units of motion we merely approach the solution of the problem, but we never attain it. —
通过采用越来越小的运动单位，我们只是接近问题的解，但永远无法达到解决。 —

It is only by assuming an infinitely small magnitude, and a progression rising from it up to a tenth, and taking the sum of that geometrical progression, that we can arrive at the solution of the problem. —
只有通过假设一个无限小的数量，并从该数量上升到十分之一的等比级数求和，我们才能得到问题的解。 —

A new branch of mathematics, dealing with infinitely small quantities, gives now in other more complex problems of dynamics solutions of problems that seemed insoluble.
数学的一个新分支，处理无限小量，现在在动力学的其他更复杂问题中提供了看似无解的问题的解答。

This new branch of mathematics, unknown to the ancients, by assuming infinitely small quantities, that is, such as secure the chief condition of motion (absolute continuity), corrects the inevitable error which the human intellect cannot but make, when it considers disconnected units of motion instead of continuous motion.
这个新的数学分支，对于历史运动的规律研究中同样出现了同样的错误。

In the investigation of the laws of historical motion precisely the same mistake arises.
它假设无限小的数量，即确保运动的主要条件（绝对连续性），从而纠正了人类智力在考虑不连续的运动单位而非连续运动时不可避免的错误。

The progress of humanity, arising from an innumerable multitude of individual wills, is continuous in its motion.
人类的进步来自无数个人的意愿，其运动是连续不断的。

The discovery of the laws of this motion is the aim of history. —
发现这种运动的规律是历史的目标。 —

But in order to arrive at the laws of the continuous motion due to the sum of all these individual wills, the human mind assumes arbitrary, disconnected units. —
为了得出由所有这些个人意志之和产生的连续运动的规律，人类思维假定了任意的、不相连的单位。 —

The first proceeding of the historian is taking an arbitrary series of continuous events to examine it apart from others, while in reality there is not, and cannot be, a beginning to any event, but one event flows without any break in continuity from another. —
历史学家的第一步是选取一个任意连续事件序列，将其与其他事件分开研究，然而在现实中，任何事件都没有，并且也不能有一个起点，一个事件没有间断地从另一个事件流转而来。 —

The second proceeding is to examine the action of a single person, a sovereign, or a general, as though it were equivalent to the sum of many individual wills, though the sum of individual wills never finds expression in the action of a single historical personage.
第二步是研究一个单个人、一个君主或一个将军的行动，仿佛这个行动等同于许多个人的意愿之和，虽然个人意愿之和从来没有在一个历史人物的行动中找到表达。

Historical science as it advances is continually taking smaller and smaller units for analysis, and in this way strives to approximate the truth. —
历史科学在不断进步中，不断将分析单位缩小，以此方式努力接近真相。 —

But however small the units of which history takes cognisance, we feel that the assumption of a unit, disconnected from another, the assumption of a beginning of any phenomenon, and the assumption that the individual wills of all men find expression in the actions of a single historical personage are false in themselves.
但是，无论历史关注的单位多么小，我们都感到，假设一个与另一个无关的单位，假设任何现象的起点以及假设所有人的个人意愿在一个历史人物的行动中找到表达，这些假设本身是错误的。

Every conclusion of history can, without the slightest effort on the part of the critic, be dissipated like dust, leaving no trace, simply through criticism selecting, as the object of its analysis, a greater or smaller disconnected unit, which it has a perfect right to do, seeing that the unit of history is always selected arbitrarily.
历史的每个结论都可以毫不费力地通过批评的选择作为分析对象而被驱散，无论是一个较大还是较小的不相关的单位，这是完全可以做到的，因为历史的单位总是任意选择的。

Only by assuming an infinitely small unit for observation—a differential of history—that is, the homogeneous tendencies of men, and arriving at the integral calculus (that is, taking the sum of those infinitesimal quantities), can we hope to arrive at the laws of history.
只有通过假设一个无限小的观察单位——历史上的微分，即人类的同质性倾向，并通过积分运算（即取这些无限小量的总和），我们才能希望得出历史的规律。

The first fifteen years of the nineteenth century present the spectacle of an extraordinary movement of millions of men. —
十九世纪头十五年呈现出了一个惊人的百万人运动的景象。 —

Men leave their habitual pursuits; rush from one side of Europe to the other; —
男人们离开他们习以为常的事业，匆忙地从欧洲的一边到另一边； —

plunder, slaughter one another, triumph and despair; —
进行掠夺，互相屠杀，经历胜利与绝望。 —

and the whole current of life is transformed and presents a quickened activity, first moving at a growing speed, and then slowly slackening again. —
整个生活的潮流发生了转变，呈现出加速的活动，以不断增加的速度开始，然后又缓慢地减慢下来。 —

What was the cause of that activity, or from what laws did it arise? —
这种活动的原因是什么？或者说它出现了什么规律？ —

asks the human intellect.
人类智力提出这个问题。

The historians, in reply to that inquiry, lay before us the sayings and doings of some dozens of men in one of the buildings of the city of Paris, summing up those doings and sayings by one word—revolution. —
历史学家在回答这个问题时将我们放在巴黎市的一座建筑物中的几十个人的言行面前，通过一个词“革命”来总结这些言行。 —

Then they give us a detailed biography of Napoleon, and of certain persons favourably or hostilely disposed to him; —
然后他们给我们提供了拿破仑的详细传记，以及对他持有有利或敌对态度的某些人的传记； —

talk of the influence of some of these persons upon others; —
谈到其中一些人对其他人的影响； —

and then say that this it is to which that activity is due, and these are its laws.
然后说这就是这种活动的原因，这就是它的规律。

But the human intellect not only refuses to believe in that explanation, but flatly declares that the method of explanation is not a correct one, because in this explanation a smaller phenomenon is taken as the cause of a greater phenomenon. —
但人类智力不仅不相信这种解释，而且坚决宣布这种解释方法不正确，因为这种解释将一个较小的现象作为一个较大的现象的原因。 —

The sum of men’s individual wills produced both the revolution and Napoleon; —
众人的意志的总和产生了革命和拿破仑； —

and only the sum of those wills endured them and then destroyed them.
只有这些意志的总和才能忍受它们，然后摧毁它们。

“But whenever there have been wars, there have been great military leaders; —
“但每当有战争时，都会有伟大的军事领袖； —

whenever there have been revolutions in states, there have been great men,” says history. —
每当有国家革命时，都会有伟大的人”，历史如此说道。 —

“Whenever there have been great military leaders there have, indeed, been wars,” replies the human reason; —
“每当有伟大的军事领袖出现时，战争也随之而来，”人的理性回答道； —

“but that does not prove that the generals were the cause of the wars, and that the factors leading to warfare can be found in the personal activity of one man.”
“但这并不能证明是将军们引发了战争，战争的诱因并不能从一个人的个人活动中找到。”

Whenever, looking at my watch, I see the hand has reached the figure x, I hear the bells beginning to ring in the church close by. —
每当我看到手表上的指针指向x时，我就听到附近教堂的钟声开始响起。 —

But from the fact that the watch hand points to ten whenever the bells begin to ring, I have not the right to infer that the position of the hands of my watch is the cause of the vibration of the bells.
但是，仅凭手表的指针指向十点时钟声开始响起这一事实，并不能推断出手表指针的位置是钟声震动的原因。

Whenever I see a steam-engine move, I hear the whistle, I see the valve open and the wheels turn; —
每当我看到蒸汽机运转时，我就会听到汽笛声，看到阀门打开和车轮转动； —

but I have no right to conclude from that that the whistle and the turning of the wheels are the causes of the steam-engine’s moving.
但是，我无权从中得出结论，即汽笛声和车轮转动是蒸汽机运动的原因。

The peasants say that in the late spring a cold wind blows because the oak-buds are opening, and, as a fact, a cold wind does blow every spring when the oak is coming out. —
农民们说，晚春天会刮冷风，是因为橡树芽正在开放，而实际上，每年春天当橡树发芽时确实会刮冷风。 —

But though the cause of a cold wind’s blowing just when the oaks are coming out is unknown to me, I cannot agree with the peasants that the cause of the cold wind is the opening of the oak-buds, because the force of the wind is altogether outside the influence of the buds. —
但尽管我不知道橡树芽开始开放时刮冷风的原因，我不能同意农民们的观点，即刮冷风的原因是橡树芽的开放，因为刮风的力量完全不受芽花的影响。 —

I see in this simply such a coincidence of events as is common in every phenomenon of life, and I see that however long and minutely I might examine the watch hand, the valve, and the wheel of the steam-engine and the oak-bud, I shall not discover the cause of the bells ringing, of the steam-engine moving, and of the spring wind. —
我只是简单地认为这只是生活中常见的事件巧合，同时我也意识到，无论我多么仔细地观察手表的指针、阀门和车轮，还是橡树芽，我都找不到钟声响起、蒸汽机运转和春风吹拂的原因。 —

To do that I must completely change my point of observation and study the laws of the motion of steam, of the bells, and of the wind. —
要做到这一点，我必须完全改变我的观察角度，研究蒸汽、钟声和风的运动规律。 —

History must do the same. And efforts have already been made in this direction.
历史必须也要这样做。而且在这个方向上已经做出了努力。

For the investigation of the laws of history, we must completely change the subject of observations, must let kings and ministers and generals alone, and study the homogeneous, infinitesimal elements by which masses are led. —
对于历史规律的研究，我们必须完全改变观察的对象，必须将君王、大臣和将军置之不理，而研究引导群众的均质微小因素。 —

No one can say how far it has been given to man to advance in that direction in understanding of the laws of history. —
没有人能说清楚人类有多少能力去理解历史规律。 —

But it is obvious that only in that direction lies any possibility of discovering historical laws; —
但很明显，只有在这个方向上才有可能发现历史规律； —

and that the human intellect has hitherto not devoted to that method of research one millionth part of the energy that historians have put into the description of the doings of various kings, ministers, and generals, and the exposition of their own views on those doings.
迄今为止，人类智慧在这种研究方法上投入的精力还不及历史学家用于描述各种君王、大臣和将军活动，以及对这些活动的观点阐述的百万分之一。