测绘工程专业英语课文全部翻译

Section 2 The Reliability of a Survey and Errors
测量误差的可靠性
Since every technique of measurement is subject to unavoidable error, surveyors must be aware of all sources and types of error and how they combine. If the accuracy of a measurement is defined as the nearness of that value to its true value (a quantity we can never know) then a surveyor must ensure that the techniques he chooses will produce a result that is sufficiently accurate. He must know, therefore, how accurate he needs to be, how to achieve this accuracy and how to check that the required accuracy has been achieved.
由于每个测量技术是不可避免的误差，测量员必须知道的所有误差的来源和类型，以及它们是如何结合。

如果测量的准确性，其真正的值（我们可以永远不知道的数量）的接近程度，该值被定义为，然后测量员必须确保他选择的技术将产生一个结果，是足够精确的。

因此，他必须知道他需要的精度如何，如何实现这一目标的准确性和如何检查所要求的精度已经达到。

Accuracy required
When surveying to produce a plan, the accuracy required is defined by the scale of the plot, since there should be no plottable error in the survey data. A good draughtsman can plot a length to within 0.25 mm and so, if a plan of an area is required at a scale of 1/1000, i.e., 1 mm on the plan represents 1 m on the ground, the smallest plottable distance is 0.25 m. Thus, for a survey at 1/1000 scale, all the measurements must be taken such that the relative positions of any point with respect to any other must be determined to 0.25 m or better.
当测量一个平面时,精度通常是根据展图比例决定的，因为在绘图中不能有测量误差。

一个好的绘图员可以在大约0.25毫米的范围内画图，假如一个地区的图纸比例尺要求是1/1000，即1毫米图上距离代表1米实地距离，那么最小的测距应该是0.25米。

因此，对于1/1000比例尺的测量，所有测量必须保证任意一点与其他任一点的相对位置不得大于0.25米。

The specifications of surveys for other purposes such as engineering works or property boundary definition might well be determined by engineering tolerances or legal standards.
基于测量规范可能被用于其他目的，如工程测量或财产边界的测量将由工程限差和合法的基准决定。

Achieving the specification
To ensure that the specification is achieved the equipment and methods must be chosen such that, not only will they collect the right sort of data, i.e., the correct combination of angles and distances, but that the data will be to the required accuracy. There are several types of error that occur and a knowledge of their importance and characteristics is essential in the understanding of the limitations of the techniques of measurement. The salient features will be stated now but further information is given in later chapters.
为了确保测量符合规范，仪器和数据应按照以下要求进行，并不是只是得到正确的数据，即更正角和边的关系，从而得到的数据满足精度的要求。

在测量中有几种类型的误差，掌握它们的重要性和特性对于理解测量技术的限差是必不可少的。

本章主要讲解这些误差的主要特征，后面的章节将提供进一步的阐述。

Mistakes 粗差
Blunders or mistakes are often inaccurately referred to as gross errors. Miscounting the number of tape lengths when measuring a long distance or transposing numbers when booking are two very simple, but all too common, examples of mistakes. These types of mistakes can occur at any stage of a survey, when observing, booking, computing or plotting, and they would obviously have a very damaging effect on the results if left uncorrected. However, by following strictly a well-planned observing procedure it is possible to reduce the number that occur and then independent checks at each stage should show up those that have been made. In practice, none should ever go undetected and uncorrected.
错误经常不准确的理解为粗差。

当测量很长一段距离时，读错尺的读数或记录两个简单的数时颠倒它们的
位置，这些都是很常见的错误例子。

这些类型的误差可以发生在测量任何阶段，当观测，记录，计算和绘图，如果不纠正这些错误，他们在结果上显然有一个非常有害的影响。

但是，通过严格周详的观测过程，可能杜绝这些错误的产生，然后在每个阶段应独立检测可以是这些错误显现出来。

在实践中，没有不可发现和不可纠正的粗差。

Systematic errors系统误差
Systematic errors arise from sources which act in a similar manner on observations. The method of measurement, the instruments used and the physical conditions at the time of measurement must all be considered in this respect. Expansion of steel tapes, frequency changes in electromagnetic distance measuring (EDM) instruments and collimation in a level are just a few examples of possible sources of systematic errors.
系统误差的来源于以相同的观测方式。

测量时要考虑这些方面，测量的方法、测量仪器和外界环境。

钢尺的膨胀，电磁测距仪的频率变化和水准仪的照准情况都是系统误差的可能来源。

These errors are of vital importance in activities which consist of adding together a succession of individual observations (see sections on leveling and traversing). If all the individual measurements contain the same type of systematic error, which by their nature always act in the same direction, then the total effect is the sum of them all.
这些误差在由一系列独立观测（参见水准测量和导线测量部分）累加在一起组成的测量值中极为重要，如果所有的独立测量包含相同类型的系统误差，且这些系统误差总是表现出相同的性质，那么总影响是所有这些的总和。

It must be ensured that measurements are as accurate as required by removing the effects of all factors that, if neglected, would result in a significant error. The errors caused by some factors can be eliminated with the correct observing procedure and others countered by applying corrections. Systematic errors are not revealed by taking the same measurement again with the same instruments. The only way to check adequately for systematic error is to remeasure the quantity by an entirely different method using different instruments.
通过消除所有因素的影响确保精度满足要求。

如何忽略这些因素将会导致重大的错误。

通过正确的观测程序以及纠正计算可以消除误差。

通过同样的仪器用同样的方法测量是检测不出系统误差的。

唯一能充分检测系统误差就是重测这些量通过使用完全不同的测量方法和测量仪器。

Random errors
Random errors are really all those discrepancies remaining once the blunders and systematic errors have been removed. Even if a quantity is measured many times with the same instrument in the same way, and if all sources of systematic error have been removed, it is still highly unlikely that all results will be identical. The differences, caused mainly by limitations of instruments and observers, are random errors.
随机误差事实上是除去粗差和系统误差后。

即使测定数量很多次以同样的方式与相同的仪器，和已被删除，如果所有系统误差的来源，它仍然是极不可能的，所有的结果将是相同的。

的差异，主要仪器和观察员的限制造成的，是随机的误差。

It is found in practice that these errors, although called random, have the following characteristics:
(1) small errors occur more frequently than large ones
(2) positive and negative errors are equally likely to occur
(3) very large errors seldom occur.
在实践中发现，这些误差，虽然称为随机的，具有以下特点：
（1）小误差发生的频率比大
（2）正面和负面的误差发生的可能性相同
（3）非常大的误差很少发生。

These characteristics are typical of errors which are normally distributed and it is assumed that we can use the mathematical theory based on the normal distribution to deal with the errors met with in surveying. 正态分布是这些误差典型的特点是，我们可以用基于正态分布的数学理论来处理这些测量中的误差。

Understanding the errors that limit the accuracy of the measurement techniques is but one step to ensuring specifications are achieved, as will be seen when the methods of survey are described:
了解限定测量方法精度的误差仅仅是确保满足测量规范的一步，按照如下的测量方法进行：
(a) The survey area is always totally covered with the simplest possible framework of high quality
measurements. If the rest of the survey work is carried out within this control the possible damaging accumulation of errors can be contained. This is often termed 'working from the whole to the part',（a）测区总是由高精度的测量框架所覆盖。

如果剩下的测量工作在这个控制网内进行的话，累积误差就可以得到有效地控制。

这通常被称为“从整体到的部分的工作，
(b) Observing procedures are designed so that (i) most mistakes that occur are discovered immediately and
(ii) possible sources of systematic errors eliminated.
（b）观测程序设计，（ⅰ）大多数误差及时被发现，（ii）系统误差得到有效地控制。

(c) Additional, or redundant, observations are taken so that all data can be checked for the mistakes,
systematic errors and random errors that do occur. For example, the three angles of a triangle would be observed although only two are required to define the shape. The third angle could be deduced but, when measured, acts as a check.
（c）多余的观测是用来检测粗差、系统误差、偶然误差的。

例如，一个三角形观测中，只要观测两个角就能决定其形状。

但第三角度的观测是用来检核的。

(d) Many quantities are observed several times. These repeated measurements and the observation of
redundant data serve both as checks and to improve on the precision of the final results.
（d）许多数据需要多次观测。

重复观测是用来检核并提高最终精度的。

Checking the survey
Even with all the checking procedures the surveyor employs, errors can still occur in the finished plan and for this reason final independent checks are required. For simple work this would involve inspecting the final plan in the field and comparing some measurements scaled off the plan with their equivalents on the ground.
虽然测量员按照检核步骤进行检核，但是误差仍然可以出现在最后的平面图中所以最后还需要进行独立检核。

对于这项简单的测量工作，需要到野外进行最后的平面图纸的检核和图纸距离放到实地进行比对。

Angle and Direction Measurement角度和方向测量
Horizontaland vertical angles are fundamental measurements in surveying.It is necessary to be familiar withthe meanings of certain basic terms before describing angle and direction measurement. The terms discussed here have reference to the actual figure of the earth.
水平角和竖直角是测量的基本测量工作,在描述角度和方向测量之前，有必要熟悉几个基本术语的含义,这里讨论的这些术语与地球的真实形状有关.
Basic Terms基本术语
A vertical line at any point on the earth’s surface is the line that follows the direction of gravity at that point. It is the direction that a string will assume if a weight is attached at that point and the string is suspended freely at the point. At a given point there is only one vertical line.A horizontal line at a point is any line that is perpendicular to the vertical line at the point. At any point there are an unlimited number of horizontal lines.A horizontal plane at a point is the plane that is perpendicular to the vertical line at the point.There is only one horizontal plane through a given point. A vertical plane at a point is any plane that contains the
vertical line at the point. There are an unlimited number of vertical planes at a given point.
地球表面任一点的垂线是指这点上沿着重力的方向的线,如果在这点上用线悬挂一个重物，当线自由静止时，这条线所呈现的方向即重力方向。

在给定的一个点上只有一条垂线。

一点上的水平线是垂直于过该点的垂线的直线。

过任一点的水平线有无数条。

过一点的水平面是垂直于过该点的垂线的平面,过给定的一个点只有一个水平面.过一点的竖直面是包含过该点的垂线的任一平面过给定的一点有无数个竖直面.
Horizontal Angle and Vertical Angle水平角和竖直角
A horizontal angle is the angle formed in a horizontal plane by two intersecting vertical planes, or a horizontal angle between two lines is the angle between the projections of the lines onto a horizontal plane. For example, observations to different elevation points
B and
C from A will give the horizontal angle ∠bac which is the angle between the projections of two lines (AB and AC) onto the horizontal plane. It follows that,although the points observed are at different elevations, it is always the horizontal angle and not the space angle that is measured .The horizontal angle is used primarily to obtain relative direction to a survey control point, or topographic detail points, or points to be set out. A vertical angle is an angle measured in a vertical plane which is referenced to a horizontal line by plus (up) or minus (down) angles, or to a vertical line from the zenith direction. Plus and minus vertical angles are sometimes referred to as elevation or depression angles respectively. A vertical angle thus lies between 0°and ±90°.Zenith is the term describing points on a celestial sphere that is a sphere of infinitely large radius with its center at the center of the earth. The zenith is an angle measured in a vertical plane downward from an upward directed vertical line through the instrument. It is thus between 0°and 180°.
水平角是指在一个水平面内由两相交的竖直面形成的角，或者说，两条线之间的水平角是这两条线在水平面上的投影线的夹角.例如，在A点观测不同高度的B和C点，其水平角∠bac是由AB和AC两条线在水平面上的投影构成的.由此得出结论结论，虽然被观测的点在不同的高度上，测出的总是水平角而不是空间角。

水平角主要用来由联测控制点获得相对方向，或者地形测量碎部点、或者放样点,竖直角是在一个竖直面内参考于水平线的正（仰）角或负（俯）角，或者相对于一个天顶方向的垂线的角.正负竖直角有时分别被称为仰角或俯角.
Obviously the zenith angle is equal to 90°minus the vertical angles. Vertical angles or zeniths are used in the correction of slope distance to the horizontal or in height determined. For the most part, the instrument used in the measurement of angles is called a transit or theodolite, although angles can be measured with clinometers, sextants (hydrographic surveys), or compasses. The theodolite contains a horizontal and vertical circles of either glass or silver. The horizontal and vertical circles of theodolite can be linked to circular protractors graduated from 0°to 360°in a clockwise manner set in horizontal and vertical plane. The horizontal circle is used when measuring or laying off horizontal angles and the vertical circle is used to measure or lay off vertical angles or zenith angles. Usually the units of angular measurement employed in practice are degrees, minutes, and seconds, the sexagesimal system.
竖直角位于0～90度之间.天顶方向是一个术语，用来描述在天球上的点，天球是一个半径无限大的球，其中心在地球中心。

天顶距是一个在竖直面内从一个过仪器的被定向为向上的竖直方向线向下测量的角。

它的范围是从0到180度。

显然，天顶距等于90度减去竖直角.竖直角或天顶距用于斜距化平距的改正或者高程的测量.在极大程度上，用来测角的工具被称为经纬仪，虽然角度可以用倾斜仪、六分仪、或罗盘仪来测，经纬仪有一个玻璃的或镀银的水平度盘和竖直度盘.经纬仪的水平度盘和竖直度盘与顺时针刻了0到360度刻划的圆分度器相连。

测或拨水平角时用水平度盘，测或拨竖直角或天顶距时用竖直度盘，通常角度测量法使用的单位是六十进制的度、分、秒。

Angle Measurement角度测量
A horizontal angle in surveying has a direction or sense; that is, it is measured or designed to the right or to the left, or it is considered clockwise or counterclockwise. In the above figure, the angle at A from
B to
C is
clockwise and the angle from C to B is counterclockwise. With the theodolite set up, centered, and leveled over at station A, then a simple horizontal angle measurement between surveying point B, A and C would be taken as follows:
在测的水平角有方向，就是说它是向左测还是向右测，或者是说，顺时针测还是逆时针测.如上图所示，在A点由B到C就是顺时针角，而从C到B就是逆时针角，经纬仪在A点安置、对中、整平后，在B、A和C测量点间的简单的水平角测量可以按下列步骤进行：
⑴Commencing on , say, “face left”, the target set at survey point B is carefully bisected and the reading on horizontal scale is 25°.
⑵The upper plate clamp is released and telescope is turned clockwise to survey point C. The reading on horizontal circle is 75°
⑶The horizontal angle is then the difference of the two directions, i.e. (75°-25°) =50°
⑴说示意，“盘左”，将B点的目标仔细分中，水平度盘读数为25度
⑵水平度盘制动螺旋松开，顺时针转动望远镜至C点，水平度盘读数75度
⑶水平角就是两个方向值的差值，即，(75°-25°) =50°
⑷Change face and observe point C on “face right”, and note the reading=255°
⑸Release upper plate and swing counterclockwise to point B and note the reading =205°
⑹The reading or the direction must be subtracted in the same order as 255°-205°=50°
⑺The mean of two values would be accepted if they are in acceptable agreement.
⑷换度盘方向至盘右并照准C点，记下读数为255度
⑸松开水平度盘，逆时针旋转至B点并记下读数为205度
⑹读数或者说是方向值按同样的法则相减，255°-205°=50°
⑺如果两个减出来的值的一致性是可接受的，取两个值的平均值。

Modern electronic digital theodolites contain circular encoders that sense the rotations of the spindles and the telescope, convert these rotations into horizontal and vertical (or zenith) angles electronically, and display the value of the angles on liquid crystal displays (LCDs) or light-emitting diode displays (LEDs). These readouts can be recorded in a conventional field book or can be stored in a data collector for future printout or computation. The instrument contains a pendulum compensator or some other provision for indexing the vertical circle readings to an absolute vertical direction.The circle can be set to zero readings by a simple press of a button or initialized to any value on the instrument.
Azimuth is the horizontal angle measured in a clockwise direction from the plane of the meridian, which is a line on the mean surface of the earth joining the north and south poles. Azimuth ranges in magnitude from 0°to 360°, values in excess of 360°, which are sometimes encountered in computations, are simply reduced by 360°before final listing. Bearing is the traditional way of stating the orientation of the line. It is actually the angle measured from the north or south.The bearing, which can be measured clockwise or counterclockwise from the north or south end of the meridian, is always accompanied by letters that locate the quadrant in which the line falls. For example, bearing N32W indicates a line trending 32°west of the north.It is equal to an azimuth of 328°.
Bearing S12W indicates a line trending 12°west of the south. It is equal to an azimuth of 192°. It is important to state that the bearing and azimuth are respect to true north.
现代的电子数字经纬仪包含编码度盘，能够感知轴和望远镜的旋转，并使之电子地转换为水平角度和竖直角度，并在液晶显示器或发光二极管显示器上显示出来，这些显示可以被一个传统的野外电子手簿或数据收集器记录，以便日后打印或计算。

这种仪器具有一个悬挂补偿器或其它装置，使竖盘指标读数指向一个绝对竖直方向，这个度盘可以通过简单的按一个键就将其置零，或初始化成任一值。

方位角是从子午面起算按顺时针旋转的角，子午线是在地球平均表面连接北极与南极的线。

方位角的取值范围从0度到360
度，超过360的值――有时会在计算时遇到，只需减去360度即可。

方向角是一种传统的描述直线方向的方法。

实际上，它是从南或北方向开始量测的角，方向角可以从子午线，北端或南端以顺时针或逆时针量测，总是伴以字母，用来标明直线所落在的象限。

方向角N32W代表一条直线从北方向转向西方向32度，它等于方位角328度，方向角S12W代表一条直线从南方向转向西方向12度，它等于方位角192度。

需要重点说明的是，方向角和方位角所用的是真北方向。

Unit 5 Traversing （导线测量）
The purpose of the surveying is to locate the positions of points on or near the surface of the earth.（测量的目的是确定地表或接近地表的点的点位。

）
To determine horizontal positions of arbitrary points on the earth’s surface and elevation of points above or below a reference surface are known as a control survey.（确定地表任一【arbitrary任意的】点的平面位置和确定点高于或低于一个参考面的高程的工作被称为控制测量）
The positions and elevations of the points make up a control network.（这些点的平面位置和高程组成了一个控制网）
There are different types of control networks depending on where and why they are established.（依照它们建立的地点和目的不同，有不同的控制网类型）
A control network may have very accurate positions but no elevations (called a Horizontal Control Network) or very accurate elevations but no positions (called a Vertical Control Network).（一个控制网可能有精确的平面位置而没有高程（称为平面控制网），或者有精确的高程而没有平面位置（称为高程控制网））
Some points in a control network have both accurate positions and elevations.（有些控制网的点既有精确的平面位置也有精确的高程）
Control networks range from small, simple and inexpensive to large and complex and very expensive to establish.（控制网的范围从小的、简单的、便宜的网到大的、复杂的、昂贵的网）
A control network may cover a small area by using a “local”coordinate system that allows you to position the features in relation to the control network but doesn’t tell you where the features are on the surface of the earth, or cover a large area by consisting of a few well-placed and precise-established control points, which is sometimes called the primary control.（一个控制网可以是覆盖小范围，使用区域坐标系统，允许你相对于控制网确定地貌特征【feature】，但却不告诉你它们在地表的什么地方；或者覆盖一个广大区域，由少数被适当安置并精确测设的控制点组成，有时被称为基础控制）
The horizontal positions of points in a network can be obtained in a number of different ways.（控制网的点的平面位置可以由许多不同方法来获得）
The generally used methods are triangulation, trilateration, traversing, intersection, resection and GPS.（一般使用的方法有，三角测量、三边测量、导线测量、交会测量、后方交会测量、和GPS测量）
The main topic of this text refers to the traversing.（这篇课文主要讲的是导线测量）
Triangulation（三角测量）
The method of surveying called triangulation is based on the trigonometric proposition that if one side and three angles of a triangle are known, the remaining sides can be computed by the law of sines.（这种测量方法称为三角测量，基于三角法则，如果三角形的一条边和三个角已知，剩下的边可以用正弦定理计算出）Furthermore, if the direction of one side is known, the direction of the remaining sides can be determined.（而且，如果一条边的方向已知，余下的边的方向也可以确定）
And then coordinates of unknown points can be computed by application of trigonometry.（那么未知点的坐标就可以使用三角法计算出来）
Trilateration（三边测量）
Since the advent of long-range EDM instrument, a method of surveying called trilateration was adopted to combine with triangulation.（自从远距EDM出现以来，一种叫做三边测量的方法用来和三角测量联合使用。

）The trilateration is based on the trigonometric proposition that if the three sides of a triangle are known, the three angles can be computed by the law of cosines.（三边测量基于三角法则——如果三角形的三条边已知，那么三个角可以由余弦定理计算出）
Trilateration possesses some advantages over triangulation because the measurement of the distances with EDM instrument is so quick, precise and economical while the measurement of the angles needed for triangulation may be more difficult and expensive.（三边测量具有一些相对于三角测量的优势，EDM测距快速、准确、经济，而三角测量所需的角度测量则相对困难和昂贵）
For some precise projects, the combination of triangulation and trilateration which is called triangulateration is applied.（在一些精密工程当中，三角测量和三边测量联合使用，被称为边角测量）
Traversing（导线测量）
A survey traverse is a sequence of lengths and directions of lines between points on the earth, obtained by or from field angle and distance measurements and used in determining positions of the point.（导线是一系列地球上点之间的有长度和方向的直线，由野外角度和距离测量获得，用来确定点位）
The angles are measured using transits, theodolites, or total stations, whereas the distances can be measured using steel tapes or EDM instruments.（角度可以使用经纬仪或全站仪来测，而距离可以使用卷尺或EDM来测）
A survey traverse may determine the relative positions of the points that if connects in series, and if tied to control stations based on some coordinate system, the positions may be referred to that system.（导线可以用来确定互相连接点的相对位置，如果想控制某些坐标系中的站点，其位置应参考该坐标系）
From these computed relative positions, additional data can be measured for layout of new features, such as buildings and roads.（从这些计算出的相对位置，另外的数据可以量出来，用以放样新的地物，如：建筑物和道路。

）
Since the advent of EDM equipment, traversing has emerged as the most popular method to establish control networks such as basic area control, mapping, control of hydrographic surveys and construction projects.（自从EDM的出现，导线测量作为最常用的建立控制网的方法显现出来，例如基础区域控制、图根控制、水道测量控制和建筑工程控制）
In engineering surveying, it is ideal way to surveys and dimensional control of route-type projects such as highway, railroad, and pipeline construction. （在工程测量当中，导线测量是线型工程测量和立体控制的理想方法，线型工程例如公路、铁路、和管线建筑）
In general, a traverse is always classified as either an open traverse or a closed traverse.（总体上，导线总是分为支导线和闭路导线【按说open traverse是支导线，closed traverse是闭合导线，而connecting traverse 是附合导线】）
An open traverse originates either at a point of known horizontal position with respect to a horizontal datum or at an assumed horizontal position, and terminates at a station whose relative position is not previously known.（支导线起始于一个水平位置已知（相对于一个水平基准）或水平位置假定的点，终止于相对位置事先未知的站点。

）
The open traverse provides no check against mistakes and large errors for its termination at an unknown horizontal position and lack of geometric closure.（由于其终点位置未知并且缺乏图形闭合，支导线不能提供对错误和较大误差的检核）
This lack of geometric closure means that there is no geometric verification possible with respect to the actual positioning of the traverse stations.（这种图形闭合的缺少意味着没有几何上的检核可能性，对于实
际的导线点的确定。

）
Thus, the measuring technique must be refined to provide for field verification.（因而，这种测量技术应当提供野外的检核使之精确。

）【字面的意思是该技术应当被精确化提供给野外确认】
At a minimum, distances are measured twice and angles are doubled.（至少，距离测两遍，角度测两个测回。

）
Open traverses are often used for preliminary survey for a road or railroad.（支导线经常用于道路或铁路的初测）
A closed traverse can be described in any one of the following two ways:（闭路导线可以由下面两种方式的任一种描述：）
⑴A closed loop traverse, as the name implies, forms a continuous loop, enclosing an area.
（闭合环路导线，正如名字所示，呈一个连续的环，围绕一个区域）
This type of closed traverse starts at assumed horizontal position or at a known horizontal position with respect to a horizontal datum and ends at the same point.（这种闭路导线起始于一个平面位置假设或相对于一个水平基准已知的点，并终止于该点）
⑵A connecting traverse starts and ends at separate points, whose relative positions have been determined by a survey of equal or higher order accuracy.（附合导线起始和终止于不同的点，它们由等于或高于规定精度的测量测设）
A known horizontal position is defined by its geographic latitude and longitude, or by its X and Y coordinates on a grid system.（一个已知的水平位置是由它的大地经纬度或格网系的X Y坐标表示）Closed traverses, whether they return to the starting point or not, provide checks on the measured angles and distances.（闭合导线，无论它们是否回到起始点，都能提供角度和距离检核。

）
In both cases, the angles can be closed geometrically, and the position closure can be determined mathematically.（在两种情况中，角度可以在几何上闭合，位置闭合可以数学的确定【计算出来】）Therefore they are more desirable and used extensively in control, construction, property, and topographic surveys. （因此它们更理想【desirable理想的】，在控制测量、建筑测量、房地产测量和地形测量使用更广泛）
As we mentioned above, a closed traverse provides checks on the measured angles and distances.（正如我们上面所提到的，闭合导线可以提供角度和距离的检核）
For example, the geometric sum of the interior angles in an n-side closed figure should be (n-2)×180°, but due to systematic and random errors of the measurements, when all the interior angles of a closed traverse are summed, they may or may not total the number of degrees required for geometric closure.（例如，在一个n边闭合图形当中，内角和应该是：(n-2)×180°，但是由于【due to】测量中系统误差和偶然误差的存在，当闭合导线所有的内角加起来后，其角度和【total】可能等于或不等于其几何理论闭合差值）
The difference between the geometric sum and actual field sum of the interior angles is called angular closure.（内角和的理论值和实际值的差值被称为角度闭合差）
The total error of angular closure should be distributed evenly to each angle (if all angles were measured with the same precision) before mathematical analysis of the traverse.（在导线进行数学分析之前，角度闭合差应该平均分配到每个角上（如果所有的角都是相同观测精度））
The important point before doing this is that the overall angular closure can’t be beyond the survey specifications.（重要的一点是，在这样做之前，所有的闭合差都不得超过测量规范）
Closed traverses provide also checks on the measured distances, and the position closure can be determined mathematically, which means that an indication of the consistency of measuring distances as well as angles should be given to a traverse that closes on itself.（闭合导线同时提供测量过的距离的检核，。