On the basis of the physical interpretation of distance which has been indicated, we are also in a position to establish the distance between two points on a rigid body by means of measurements. For this purpose we require a " distance " (rod S) which is to be used once and for all, and which we employ as a standard measure. If, now, A and B are two points on a rigid body, we can construct the line joining them according to the rules of geometry ; then, starting from A, we can mark off the distance S time after time until we reach B. The number of these operations required is the numerical measure of the distance AB. This is the basis of all measurement of length. 1)
Every description of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coincides. This applies not only to scientific description, but also to everyday life. If I analyse the place specification " Times Square, New York," [A] I arrive at the following result. The earth is the rigid body to which the specification of place refers; " Times Square, New York," is a well-defined point, to which a name has been assigned, and with which the event coincides in space.2)
This primitive method of place specification deals only with places on the surface of rigid bodies, and is dependent on the existence of points on this surface which are distinguishable from each other. But we can free ourselves from both of these limitations without altering the nature of our specification of position. If, for instance, a cloud is hovering over Times Square, then we can determine its position relative to the surface of the earth by erecting a pole perpendicularly on the Square, so that it reaches the cloud. The length of the pole measured with the standard measuring-rod, combined with the specification of the position of the foot of the pole, supplies us with a complete place specification. On the basis of this illustration, we are able to see the manner in which a refinement of the conception of position has been developed.
(a) We imagine the rigid body, to which the place specification is referred, supplemented in such a manner that the object whose position we require is reached by. the completed rigid body.
(b) In locating the position of the object, we make use of a number (here the length of the pole measured with the measuring-rod) instead of designated points of reference.
(c) We speak of the height of the cloud even when the pole which reaches the cloud has not been erected. By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.
From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measures to make ourselves independent of the existence of marked positions (possessing names) on the rigid body of reference. In the physics of measurement this is attained by the application of the Cartesian system of co-ordinates.
This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body. Referred to a system of co-ordinates, the scene of any event will be determined (for the main part) by the specification of the lengths of the three perpendiculars or co-ordinates (x, y, z) which can be dropped from the scene of the event to those three plane surfaces. The lengths of these three perpendiculars can be determined by a series of manipulations with rigid measuring-rods performed according to the rules and methods laid down by Euclidean geometry.
In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available ; furthermore, the magnitudes of the co-ordinates are not actually determined by constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations. 3)
We thus obtain the following result: Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for "distances;" the "distance" being represented physically by means of the convention of two marks on a rigid body.
在对距离的物理解释的基础上，我们也可以通过测量来确定刚体上两点之间的距离。为此，我们需要一个“距离”（杆S），这是一次和所有使用，我们使用作为一个标准的措施。如果A和B是刚体上的两个点，我们可以根据几何学的规则构造连接它们的直线；然后，从A开始，我们可以一次又一次地划出距离S，直到到达B为止。这些操作的次数就是距离AB的数值测量。这是所有长度测量的基础。（一）
对事件场景或物体在空间中的位置的每一种描述都是基于刚体（参照体）上与该事件或物体重合的点的说明。这不仅适用于科学描述，也适用于日常生活。如果我分析“纽约时代广场”的场所规格，我会得到以下结果。地球是一个刚性的物体，地点的规格指的是；“纽约时代广场”是一个定义明确的点，它被指定了一个名字，它在空间上与之重合
这种原始的位置说明方法只处理刚体表面上的位置，并且依赖于该表面上存在的点，这些点是相互区分的。但我们可以在不改变我们对立场的规定的性质的情况下，从这两个限制中解放出来。例如，如果一团云在时代广场上空盘旋，那么我们可以通过在广场上竖立一根垂直的杆子来确定它相对于地球表面的位置，这样它就可以到达云了。用标准测量杆测量的杆长，结合杆脚位置的规范，为我们提供了一个完整的位置规范。在这一说明的基础上，我们可以看到位置概念的改进方式。
（a） 我们想象一个刚体，它引用了位置规范，以这样一种方式进行补充，使得我们所要求的位置的物体被达到。完整的刚体。
（b） 在定位物体的位置时，我们使用一个数字（这里是用测量杆测量的杆的长度），而不是指定的参考点。
（c） 我们谈论云的高度，即使到达云端的杆子还没有竖起。通过从地面不同位置对云层进行光学观测，并考虑到光的传播特性，我们确定了到达云层所需的磁极长度。
从这个考虑，我们看到，如果在描述位置时，可以通过数值方法使我们独立于参考刚体上标记位置（拥有名称）的存在，这将是有利的。在测量物理学中，这是通过应用笛卡尔坐标系来实现的。
它由三个相互垂直的平面组成，并与刚体刚性连接。参照坐标系，任何事件的现场（主要部分）将由三条垂线或坐标（x、y、z）的长度来确定（主要部分），这三条垂线或坐标（x、y、z）可从事件现场落在这三个平面上。这三条垂线的长度可以通过使用刚性测量杆的一系列操作来确定，这些操作按照欧几里德几何规定的规则和方法进行。
在实践中，构成坐标系的刚性表面通常是不可用的；而且，坐标的大小实际上不是由刚性杆结构决定的，而是通过间接的方法来确定的。如果物理学和天文学的结果要保持其清晰性，就必须始终根据上述考虑寻求位置规格的物理意义。（三）
因此，我们得到了以下结果：对空间事件的每一种描述都涉及到一个刚体的使用，而这类事件必须与之相关。由此产生的关系理所当然地认为，欧几里德几何定律对“距离”适用；“距离”通过刚体上两个标记的约定物理地表示。
Notes
1) Here we have assumed that there is nothing left over i.e. that the measurement gives a whole number. This difficulty is got over by the use of divided measuring-rods, the introduction of which does not demand any fundamentally new method.
[A] Einstein used "Potsdamer Platz, Berlin" in the original text. In the authorised translation this was supplemented with "Tranfalgar Square, London". We have changed this to "Times Square, New York", as this is the most well known/identifiable location to English speakers in the present day. [Note by the janitor.]
2) It is not necessary here to investigate further the significance of the expression "coincidence in space." This conception is sufficiently obvious to ensure that differences of opinion are scarcely likely to arise as to its applicability in practice.
3) A refinement and modification of these views does not become necessary until we come to deal with the general theory of relativity, treated in the second part of this book.