THE ADJUSTMENT OF TRIGONOMETRICAL LEVELS AND THE EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

This paper is written primarily with the object of ascertaining how other Colonies and Dominions deal. with the adjustment of their trigonometricallevels; further, since the greater part of Nigeria is now covered by a framework of levels of primary accuracy it is of interest to examine the results. Moreover, the evaluation of the coefficient of refraction, and from it the temperature lapse-rate, is of some importance in view of the recent publication of the War Office Aneroid Tables. These tables are based on a standard lapse-rate of temperature.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In a previous article on this subject (Empire Survey Review, January 1937) the writer sought to show that for trigonometrical observations of vertical angles made near noon in the Tropics the coefficient of refraction depends chiefly on height above ground level in the case of stations sited within a few hundred feet above the general level of the ground surface. Indeed, the computed values of the coefficient K show a definite and appreciable increase with “h”, the height of the observing station above ground level; it is usually assumed that K decreases with increase in height above the Mean-Sea-Level surface. From analysis of the results obtained by varying h but holding the heights above Mean Sea Level fixed the writer came to the conclusion that the variations in K could only be due to abnormal values of dt/dh and d²t/dh², “t” denoting the air temperature. Now it is generally recognized by meteorologists that abnormal lapse-rates of temperature do frequently occur in the lower air layers in the Tropics; but up to the present time no temperature soundings in Nigeria are available. Recently, however, the writer came across the results of the aerological soundings made by an expedition in East Africa during the year 1908. The results of many of the soundings were of no use for the purpose of this paper; many of the observations were not taken at or near noon, and in others counterlapses of temperature in the lower layers indicated that conditions were not normal. A set of observations taken at Mombasa between 10 and 11 a.m. were eventually chosen as offering an example of what might reasonably occur in the lower layers of the atmosphere.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

TRIGONOMETRIC HEIGHTS AND REFRACTION

Abstract

In the past there has been considerable discussion on the above subject in this Review. There is a bibliography at the end of this article in which the full titles of previous articles are given. For brevity, reference to them in the following text is made by number only. Recently, Gulatee summarized present knowledge and asked how other Survey Departments dealt with this matter. Consequently, it was considered that it would be helpful to set out in detail the procedure adopted by the Directorate of Colonial Surveys for obtaining trigonometric heights, with particular reference to primary and seoondary chains and nets.     

CORRECTION OF PLANE-TABLE HEIGHTS FOR CURVATURE OF THE EARTH AND ATMOSPHERIC REFRACTION

Abstract

Most text-books on surveying limit their discussion of the correction of vertical angles for curvature of the earth and atmospheric refraction to the correction of angles taken with a theodolite during triangulation and omit any reference to those taken with a clinometer. This is rather illogical, as in well-observed triangulation, with all vertical angles measured in both directions, no correction for these effects is necessary, whilst in plane-tabling on small scales where sketching at considerable distances is frequently employed the application of corrections for these effects is essential.     

THE VARIATION OF THE ATMOSPHERIC COEFFICIENT OF REFRACTION WITH THE NATURE OF THE SOURCE OF LIGHT

Abstract

In working out vertical heights on the Akuse-Kete Krachi chain of triangulation in the Gold Coast a fairly considerable difference was found between values of the coefficient of refraction obtained from observations taken during the day and those taken at night, the mean values being 0.069 for daylight observations to heliographs and 0.087 for night observations to lamps. This difference no doubt is due mainly to the condition of the atmosphere during the day differing from its condition during the night rather than to any effect due to different sources of light. A new chain has recently been observed in Western Ashanti, and the index of refraction for the daylight observations again gave a lower value than that obtained from the night observations, the figures being 0.073 and 0.099 respectively. For the night work three different sources of light were used, hurricane lamps for short lines, Tilley vapour-pressure lamps for lines of intermediate length, and McCaw acetylene signalling lamps by Watts for long lines. It occurred, therefore, to the writer to examine the results to see if the mean values of the index of refraction showed any variations for the different light sources, since it seemed reasonable to suppose that the constitution of the light emitted from each source would be different and hence that the coefficient of refraction might vary.     

三角高程测量中天顶和斜距的计算

本文通过分析大气密度与大气垂直折光系数的关系 ,推导出消除了大气垂直折光影响的天顶距和斜距计算公式 ,既拓宽了天顶距的适用范围 ,又提高了三角高程测量成果精度。     

ELIMINATION OF ERRORS OF LATITUDE AND REFRACTION IN THE PAIRING OF AZIMUTH OBSERVATIONS

Abstract

In a previous Article (Empire Survey Review, ii, II) I described a simple graphical method for the elimination of latitude error in observations for azimuth. It was pointed out that the ideal method of adjustment of azimuths would be a simultaneous elimination of both latitude and refraction errors and, with that in view, a purely theoretical method of such an adjustment was demonstrated in the last paragraph of the article. It has now occurred to me that a fairly simple mathematical solution is possible.     

A TEST FOR THE RELIABILITY OF TRIGONOMETRICAL OBSERVATIONS

Abstract

I should like to reply to the Editor's comments on the above article, published in the E.S.R., v, 34, 226 (October 1939).     

A TEST FOR THE RELIABILITY OF FIRST-ORDER TRIGONOMETRICAL OBSERVATIONS

Abstract

Generally speaking there is a tendency for observations to be judeged by the magnitudes of the triangular errors, although the misclosures of the side equations are equally important. This note explains how to formulate a compehensive criterion covering the two types of misclosure and given in terms of the mean traingular ? _m for which definite limits are usually laid down.     

A NOTE ON THE TRIGONOMETRICAL SURVEY OF SOUTHERN RHODESIA

Abstract

After the completion of Simms's Geodetic Chain in 1901 and the publication of the results in 1905—Volume iii of the Geodetic Survey of South Africa—nothing further of a geodetic nature was done until 1928 when a short chain was run westwards from Simms's chain, at about latitude 17° 10′, to fix the Copper Queen mining area. The Eastern Circuit was commenced shortly after this; it runs from Salisbury eastwards to the Portuguese Boundary, southwards through Umtali to about latitude 20° and then westwards, joining Simms's chain again to the east of Bulawayo. Another chain running north from Simms's work has been commenced near Bulawayo. The several series are exhibited on the outline map attached.     

中性大气折射的映射函数

在球对称大气模型下，我们导出了与余误差函数形式相联系的中性大气折射改正的母函数，并进一步讨论了它的几种数学展开形式。由此方法建立的映射函数可以对各类大气模型直接进行参数拟合。     

LOCAL ATTRACTIONS AND THEIR INFLUENCE ON THE DETERMINATION OF HEIGHTS ABOVE MEAN SEA LEVEL

Abstract

The Mythical Spheroid.—The preceding article dealt with the fact that the spheroid of reference is a myth and that, even if it were not, we could not get hold of it at any given place. In order to apply corrections to observed quantities or, more generally, to operate upon them mathematically, we must make some assumption such as that of the spheroidal level surface. Probably a lot of harm has been done by attaching the notion of too concrete a thing to the spheroid. Disputes and misconceptions have arisen. People talk of“putting the spheroid down at a point” and imagine that the obedient thing is still at their feet when they get to another point, perhaps distant, in their system of triangulation or what not. Actually the spheroid may be disobedient not only as regards the direction of the vertical but also because it is above their heads or below their feet. What happens is that at each point afresh the computer treats the observations as if they were made there on the surface of a spheroid. In the same way, but travelling still farther along the road of hypothesis, he may treat observations for astronomical positions as if the compensation for visible elevations were uniformly distributed as a deficiency of density down to a depth of 122·2 kilometres. That was the depth which happened to give the smallest sum of squares of residuals in a certain restricted area, but nobody imagines that it corresponds with a physical reality, especially the ·2! It was a convenient mathematical instrument which, once the theory was to be given a trial, had to be fashioned out of some assumption or another. All this has little to do with geodetic levelling but is meant to try to banish the spheroid out of the reader's mind or at least to the back of his mind. In what follows we shall be compelled to make a certain amount of use of the family of spheroids but always with the above strictures in view.     

LOCAL ATTRACTIONS AND THEIR INFLUENCE ON THE DETERMINATION OF HEIGHTS ABOVE MEAN SEA LEVEL

Abstract

Preliminary Note.—The substance of this article was written in 1921 at the request of Lieut-Col. Wolff, who was then in charge of the Levelling Division of the Ordnance Survey and with whom the author collaborated in writing “The Second Geodetic Levelling of England and Wales, 1912–21” under the direction of Sir Charles Close. It was not intended for publication and was not again considered until 1928, when a discussion by correspondence was started by the Surveyor-General of Ceylon on the subject of hill circuits in levelling. In this discussion the survey authorities in Great Britain, Canada, India, and South Africa took part, but the main theme was the accumulation of error due to the large number of sightings necessary in hilly country and the question whether a common formula for such country and for flat country was justifiable. In his contribution Dr. van der Sterr made a brief allusion to the subject of the present paper and Dr. de Graaff Hunter went into details. His contribution and the following remarks therefore have some arguments in common.     

一种符合视觉规律的,基于地图数据的虚拟地景仿真

本文分析和解决了两个关键性问题，使计算机所生成的虚拟地景符合人的“越近看得越清”视觉规律，并通过实例对该方法的实现过程给予了详细的描述。     

DISTANCES AND REFRACTION ON OR NEAR THE APPARENT HORIZON

Abstract

An observer looking seawards views the horizon along a curvilinear path which is tangent to the surface of the sea. The distance to the tangent point depends on the height of his eye. The angle of depression of the ray at the observer's standpoint is known as “the dip of the visible sea horizon”.     

EXAMPLES OF CURVATURE AND REFRACTION CORRECTIONS TO VERTICAL ANGLES

Abstract

The correction to observed vertical angles for curvature and refraction can be found by adding a log factor to the log distance, which gives the log of the correction in seconds. This factor is 8·144 for metres and 7·628 for feet. The examples will make this clear. For machine computation, the correction in seconds can be obtained by multiplying the length in metres by 0.0139 or the length in feet by 0·00425. Alternatively, this can be done on the slide. rule by dividing the distance in metres by 72 or in feet by 235. The mean coefficient of refraction is taken as 0·07.