The effect of vertical refraction on geodetic leveling has been widely studied as one of the most important error sources in leveling. The refraction error will be accumulated systematically in proportion to the slope of survey route, vertical temperature gradient and the square of sight distance. Therefore, refraction may significantly increase systematic errors if the terrain profile around the circuit is asymmetric. The systematic misclosure due to refraction effect may exceed the random observation errors and consequently misclosures with a constant sign (negative or positive) may take place in all the cases of repetition surveys along the same leveling routes. In Japan, since the end of the 19th century several repetition surveys of the first order leveling have been made by the Geographical Survey Institute. In this paper, eighteen circuits in the north-eastern district of Honshu island are examined where two circuits of No. 6 and No. 10 have always negative misclosures of which the probabilities due to random errors are 0.007 and 0.047 respectively. The computation of a misclosure due to free-air gravity anomalies and the simulation of accumulation of refraction errors using a simple model are examined in No. 6 and No. 10 circuits. Details of simulation are as follows: (1) the distance of every section between bench marks is 2 km, (2) the slope of section between bench marks is uniform, (3) the observed elevation difference at any setup is within 2 meters, (4) the temperature difference At between 0.5 m and 2.5 m above level ground is 1.0°C and is in proportion to the solar radiation per unit surface area on a slope, (5) the direction of the sun is always south and (6) the altitude of the sun is fixed as 10°, 30° and 55° in respective models. Both circuits show similar topo-graphic asymmetry having mountainous area along the western route and rather plane area in the eastern route so that negative misclosures in clockwise measurement were anticipated before simulation computation. However, it is resulted that in No. 6 circuit positive misclosures are obtained while negative misclosures are obtained in No. 10 in every pair of parameters in the simulation. On the other hand, a large negative misclosure is obtained from the effect of free-air gravity anomalies in No. 6 circuit. Concludingly, it may be explained that observed negative misclosures in No. 6 were originated mainly from the gravity anomaly while those of No. 10 were originated from the refraction

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The root mean square error expressed by the formula
m=±√1/4n[dd/R]
has been generally used to estimate the accuracy of precise leveling. This formula is based on the assumption that forward and reverse levelings of a section should be independent each other and they should be of the same accuracy, and that a sum of differences between the two levelings along a route should be zero.
However, there are many cases in which survey results do not satisfy this assumption. The sum of the differences often deviates appreciably from zero.
In this paper, other methods of estimating the leveling accuracy are examined in which correlations between readings are taken into consideration. The methods are applied to the leveling results in the Tokai area . The results show that the correlation coefficient between forward and reverse measurements is practically zero whereas that between right and left graduation readings is about +0.4 and the total error of the precise leveling is estimated as about ±0.5 mm/km.

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The string gravity meter has so far been used as a gravity sensor of the "Tokyo Surface Ship Gravity meter". This paper summarizes the results of laboratory experiment on the stability of the sensor, and it is expected that the sensor can be used for the measurement of the earthtide if the problem of temperature regulation and external vibration is solved.

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A program to calculate terrain correction terms of gravity by using a meshed mean height data file is developed. A region around measurement station is divided into the following sub-regions and is applied by different calculation methods: (1) "nearest" subregion (within a mesh which includes the station) : topography is approximated by four pentahedrons in which the station is situated on one of corners; (2) "near" sub-region (within four meshes surrounding the station) : topography is approximated by 12 subrectangular prisms; (3) "intermediate" sub-region (within about 4km from the station): topography is approximated by sets of a rectangular prism given by the original file; (4) "far" sub-region (up to the limit region to calculate the terrain correction term): topography is approximated by sets of a bar into which mass of each rectangular prism is assumed to be concentrated. For (1) to (3), analytical solutions for a pentahedron and a rectangular prism are applied, respectively. For (4), an approximate formula, "line -mass method", is applied. An accuracy of the calculation is examined by using a topography modeled by a hemisphere of a radius 3000 m. For 500 and 250 m meshed mean height data, the error is evaluated to be within 10 and 2%, respectively. Some examples of terrain correction terms in central part of the Japanese Islands are illustrated.

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This article is a supplementary report following the previous one on the sensitivity characteristics of LaCoste & Romberg gravimeters (model G) and deals with a measuring accuracy of gravity measurements performed throughout the whole period of international gravimetric connections which were carried out at selected cities mainly along the Circum-Pacific zone from 1979 to 1982. An optimal offset angle of the LaCoste & Romberg gravimeter (model G) was experimentally examined on the basis of theoretical considerations. It was ascertained that the optimal angle is variable not only with gravity value at each measuring station but also with zero-drift accompanied to the readout amplifier. The result of the examination revealed that the setting error of the gravimeter at each gravity measurement was small; namely, its amount due to the bubble drift was just cancelled by zero-drift of the readout amplifier. It was confirmed that the gravity measurements were performed with high accuracy; in other words, the measuring error caused by the setting errors of all gravimeters employed for the present investigations was less than 0.01 mgals usually and 0.02 mgals at maximum throughout the whole period of the investigations.

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Almost all kinds of observations refering to any geodetic network can be strictly adjusted on the reference ellipsoid by the PAG-U Program. First program was made in 1966 [1]. Computations of crustal strains were added in 1971 [3]. Strains are computed on the local plane-coordinates transformed through a simple formula (1) for individual triangle. If the crust is distorted according to a linear transformation with the lapse of time, relations (2) exist between old and new coordinates of three stations in a triangle, and we can find six strain-constants xo, yo, a, b, c and d for every triangle. In those constants xo and yo refer to parallel movement of the crust alone. All kinds of horizontal crustal strains such as rotation, dilatation, maximum shear, major and minor principal axes of a strain ellipse are computed by using those constants through formulas from (3) to (8) in the previous paper [3]. PAG-U Program has been frequently used to find geodetically crustal deformations in GSI and PASCO. Recently standard deviations have been added to strains in the PAG-U Program in order to estimate rigorously reliabilities of strains. Fig. 1 is flow-chart of revised part in the program. Main part of correction in the program is to insert the computation of (3) in which Ce is a variance-covariance matrix of all strains in a triangle, C is a variance-covariance matrix of unknown column vector X found in old and new geodetic net-adjustments, and T is a coefficient matrix of old and new δλi cos pi and δpi (i=1, 2, 3) in the formulas of all strains. Of course δλi and δpi are small increments to be added to assumed longitude and latitude of st. Pi through net-adjustment. Unknown in longitude is merely not 62 but δλ cos p in PAG-U, because δλ cos p is more convenient than 52 for free-net adjustment. Of course standard deviation of every strain is root of corresponding diagonal element in Ca. The actual computation of T in (3) is not so simple as to be expected from its simplicity, because strains are not directly expressed as functions of longitude and latitude but indirectly as functions of a, b, c and d. There are quaternary propagations in errors between strains and ellipsoidal coordinates. They are propagation relations such as first between strains and (a, b, c, d), second between (a, b, c, d) and plane coordinates of three stations, thirdly between plane coordinates and azimuths (A) and distances (S) of three geodetic lines from local origin to each station, and fourthly between (A, S) and ellipsoidal coordinates. In spite of complexity in propagation of errors, T is accurately found by computing numerically twelve coefficients consisting of old and new (δλicos p i, δpi, i=1, 2, 3) at each steps of the quaternary propagations of errors. An example of actual result of crustal strains with their standard deviations is shown in the Table I.

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Density of sedimentary layers can sometimes be approximated by a function increasing exponentially with depth. An interpretation technique is developed for the gravity anomaly generated by a two-dimensional vertical fault cutting such sedimentary layers. The densitydepth relationship is estimated from an example of measured gravity data.

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