gravimeter observations comparing pendulum stations at cambridge

GRAVIMETER OBSERVATIONS COMPARING PENDULUM STATIONS AT CAMBRIDGE, YORK,

NEWCASTLE-UPON-TYNE, EDINBURGH AND ABERDEEN

W. BuLlerwell*

(Communicated by B. C. Browne)

(Received 1951 October 30)

Summary An extensive network of gravimeter stations has been observed by the

Geological Survey of Great Britain using a Frost gravimeter. In the course of this survey gravimeter observations were made at recent pendulum stations in York, Newcastle-upon-Tyne, Edinburgh and Aberdeen. At these stations the gravimeter determinations gave values for differences in gravity from Pendulum House, Cambridge, which were consistent with the pendulum observations of Browne, Cook, McCarthy and Parasnis (1950). If the value of gravity at Pendulum House, Cambridge, is assumed to be 981 -26500 cm/sa the values at the other stations are found by combining the pendulum and gravimeter observations as :-

York, Minster Crypt 981 '41474 Cm/S*& 0'0001 I Newcastle, King's College Edinburgh, Royal Observatory Aberdeen, Marischal College

98150608 cm/s8f 0-00012 981 *58014 cm/s'+ 0~00013 981 '69597 cm/se+ 0-00014

From the observations at these pendulum stations an accurate calibration factor was obtained for the Frost gravimeter and th is was found to differ sisnificantly from the calibration factor determined from Observations in the tower of Westminster Cathedral. Further measurements at Westminster Cathedral showed that the vertical variation in gravity is not linear but is distorted near the base of the tower, probably due to local terrain effects.

I. Introduction.-During the past decade extensive gravimeter surveys have made a great deal of detailed information available for considerable areas in England. The main body of this information has arisen from individual surveys by the Anglo-American Oil Company t (White, Ig4g), the Anglo-Iranian Oil Companyt (Falcon and Tarrant, Ig51), the Department of Geodesy and Geo- physics, Cambridge University t (Cook, 1950 a), and by the Geological Survey.t Several different instruments have been used during the surveys, so that before individual areas can be linked and consistent values of gravity derived it is necessary to adopt values for the calibration factor and accuracy of each instrument. Deter- mination of the calibration factors in turn involves the observation of changes in the instrumental readings between points for which the differences in gravity are known, and this is usually achieved by making gravimeter observations either at pendulum stations or at various heights in a tall building.

Dr A. H. Cook has carried out a preliminary adjustment of the results of gravimeter surveys over Southern England and has discussed the calibrations of the

* Communicated by permission of the Director, Geological Survey and Museum, London. t These organizations are referred to in the text by the abbreviations A.A.O.C., A.I.O.C..

Cambridge, and G.S.M., respectively.

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304 W. Bulhwell instruments concerned (Cook, 1950 a). Two of these instruments had been calibrated from readings taken at different heights in the tower of Westminster Cathedral, and though Dr Cook was able to make comparisons between pendulum and gravimeter observations at a number of pendulum stations, he found that these were insufficient to determine any errors in the gravimeter calibrations because the uncertainties of the pendulum observations (1.8 milligal) were too great and the differences of gravity over which the comparisons could be made were too small. Thus at that time the Westminster Cathedral calibrations were the most satisfactory available, though it was possible that they might be subject to small errors arising (I) from the relatively small change in gravity, about 17.5 milligals, from floor to upper platform, 185 ft., of the tower, or ( 2 ) from possible departures from the normal Free Air Vertical Gradient (Hammer, 1938) assumed in calculating the gravity changes with height.

During 1949 members of the Department of Geodesy and Geophysics, Cambridge University, made new pendulum observations from which the differences of gravity between Pendulum House at Cambridge and stations at York, Newcastle-upon-Tyne, Edinburgh and Aberdeen were found (Browne and others, 1950). These stations are situated at roughly equal intervals along the direction in which, due to the effect of latitude, the change in gravity is most rapid. For the new observations the standard deviation of each difference from Cambridge was 0.18 milligal. They therefore provide a suitable and accurate base line for the control of present and future gravimeter surveys and for the calibration of gravimeters.

Consequently the Geological Survey decided to extend its gravimeter network during the field season of 1950 to include observations at Pendulum House, Cambridge, and at each of the new pendulum stations listed above. The objectives were as follows:-

(I) to confirm the consistency of measurement of the new pendulum stations, (2) to reassess the calibration factor of the G.S.M. Frost gravimeter, (3) to observe connections between previous gravimeter surveys and the new

(4) to establish new gravimeter stations closely linked to the pendulum

The whole of this work was satisfactorily completed and a detailed account of the investigation follows.

2. The G.S. M. gravimeter and initial calibration.-All the field connections described in this section were made by means of a Frost gravimeter, Type G. S.C., No. C 2-49, brought into use by the Geological Survey in 1948. This meter is similar to that used by A.I.O.C., and has been found consistently reliable during its period of service. From examination of closure errors and repeated observations the standard deviation of a single observation has been found as 0.05 milligal.

The initial calibration of this instrument was carried out by measurements at different heights in the tower of Westminster Cathedral on 1948 November 26. In this tower seven stages above the ground floor can be reached by lift, but the Ist, 4th, 5th and 6th stages have a flooring of wooden boards which provides a less firm support for the gravimeter than the stone floors at the other stages. At the time of the experiment it was not possible to take observations on the 3rd stage and

pendulum stations,

stations to be used as bases in future work.

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Gravimeter observations at pendulum stations 305 the measurements were therefore confined to positions on the ground floor and and and 7th stages. Heights between the various meter positions were obtained directly by two independent sets of measurements which agreed to 0.1 ft. and these heights were translated into gravity differences assuming the normal Free Air Gradient, 0.09406 milligal per foot. During the gravimeter observations twelve measurements were made of the change in reading between the ground floor and the 7th stage, and seven measurements between the and and 7th stages. Though the meter repetition was excellent the results of the calibration were not considered wholly satisfactory, in that significantly different calibration factors were obtained from measurements relating to different height intervals, as shown below :-

Height Interval Calibration Factor 0.09435 & O . O Q O ~ I milligal/dial division o.og511 k 0~00016 milligal/dial division

and stage to 7th stage Ground floor to 7th stage

It was unfortunately not possible to make additional observations at the other stages in the Cathedral tower for some considerable time after the initial calibration, since extensive alterations to the lift shaft were in progress. Investigations were, however, conducted to examine whether the behaviour of the instrument under rapidly changing conditions might have given rise to an apparent change in calibration between the two height ranges. The effects of variation in external temperature, magnetic field and pressure were examined. It was found that the behaviour of the instrument was not affected by variation of the external temperature and of the magnetic field, but Observations made in the pressure chamber of the Aerodynamics Division at the National Physical Laboratory revealed a small but systematic pressure effect of about 0.1 milligal per inch of mercury. This pressure effect was quite inadequate to account for the observed changes in calibration factor derived from the Westminster Cathedral measurements. I t has, however, been applied to the calibration factors quoted above, and to all the field measurements given later in this paper; and recording of the barometric reading on a sensitive aneroid has been incorporated in the routine of observation at each field station.

The discrepancies in the calibration factors for different height ranges therefore remained imperfectly explained, but since it was likely that the effect of local disturbing masses in the tower would be greatest near to the ground level the calibration factor obtained between the and and 7th stages (0.09435 milligal/dial) was provisionally accepted.

In 1949 May observations were made round a closed circuit from the site of the absolute determination at the National Physical Laboratory (Clark, 1939) and included Observations at Pendulum House, Cambridge. No closure error was observed on this circuit and opportunity was therefore taken to calculate the calibration factor necessary to produce agreement with the adjusted value of 72.69~0.1zrnilligal for the Cambridge-N.P.L. link given by Dr A. H. Cook (Cook, 1g5oa). This gave a calibration factor of 0.09437 & o.ooo16milligal per dial division, and therefore appeared to confirm the value previously accepted from the measurements at Westminster Cathedral.

Nevertheless, when early in 1950 a gravimeter link was observed between Pendulum House, Cambridge and the new pendulum site in the crypt of York Minster, the gravity difference obtained by use of the factor o.og437 milligal per dial division was inconsistent with the value given by the pendulum, and it was

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306 W. B u h e l l

IWPS

MARTON

lOe3,b

-

therefore considered necessary to extend the observations to the other new pendulum stations.

3. The Geological Survey’s network of gravimeter stations.-A diagram of the network of observations which forms the main subject of the present communi- cation is given in Fig. I. It shows the main gravimeter stations and the observed

\ I \*>.05

8- I 4IYORK

y B U g I N 4 I

\pa lUI.’3(l

- -

ABINGTON EDINBURGH

. ~ W A O L t N C O ? F RJ. -21- - - 1 r -L -N

ABINGTON EDINBURGH

IWDUERPOOL

Calibration factor: 0.09437 mgal/dial.

differences of gravity, calculated by use of the calibration factor 0.09437 milligat per dial division. Almost all connections were observed by the method known as “Forward Looping” (Nettleton, 1940, p. 38) as the mean of two individual connections, the few exceptions being those shown by dotted lines, which were based on a single observation of drift.

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Gravimeter observations at pendulum stations 307 In addition to the links shown in Fig. I, Uttoxeter, Hatton, Swadlincote,

Four Oaks and Atherstone are connected through a complicated linkage of the Midlands Network in which 49 primary base stations are inter-connected by 112 observed gravity links. Bath and Radstock are also connected through the Somerset Network shown in Fig. ZA, and an independent network, shown in Fig. ZB, connects the gravimeter station at Perth to a gravimeter station close to and linked with the pendulum station at Aberdeen.

‘“‘““7 a% 1” Rh’ W D

I 8 I I I , *ZZ.J* I I I I

BRlSrnL

I‘OMPXIN MARTIN

FIG. aA.

Calibration factor: 0.09437 mgalldial.

FIG. 2B. Calibration factor: 0.09437 mgalldicrl.

The gravimeter stations at Cambridge, Teddington, York, Newcastle, Edinburgh and Aberdeen were sited just outside the buildings housing the pendulum stations, and except at Cambridge, where the gravimeter station was within a few feet of the pendulum station and at the same height on a concrete foundation, additional short connections were observed from the gravimeter stations to the exact positions previously occupied by the pendulums. It was noted that at York and Aberdeen, where the horizontal distance between the gravimeter and pendulum stations was small, the observed gravity changes differed

G 22

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W. Bullerwell

signdicantly from the changes which would have been predicted from the changes in height assuming the normal Free Air Gradient.

4. Adjustment of the observations.-Differences of gravity relative to Cambridge for the main stations named in Fig. I were found by adjusting the observations by the method of least squares. From the double observations on the main links between adjacent stations (a distance of about 20 miles) the observed deviation was never greater than 0.04milligal and normally less than 0-ozmilligal. In the adjustment, weights were assigned to each link roughly inversely as the squares of the standard deviations, rounded off to simple integers from I to 10. The single links (shown dotted on Fig. I) were given weight 0.5.

The adjustment was carried out using a normal electrical desk calculating machine and it was found desirable to subdivide the adjustment into smaller stages. A preliminary value was obtained for the gravity difference between Bath and Radstock from adjustment of the Somerset Network (Fig. ZA) and this adjusted value was incorporated into the main network (Fig. I). Similarly, all stations in the Midlands Network were adjusted for differences relative to Atherstone, and the adjusted values for the relevant stations shown in Fig. I incorporated into the main network, and given weights corresponding to the uncertainties calculated in the preliminary adjustment. The network connecting Perth and Aberdeen was adjusted separately to obtain the gravity difference between these stations, which was then combined with the adjusted value between Perth and Cambridge to provide the value for Aberdeen relative to Cambridge.

The adjustment of the observations involved some heavy computation and various methods were examined. Solution of the normal equations by systematic elimination (Jeffreys, 1939) proved to be too complicated to handle for the intri- cate networks. In applying the relaxation process (Southwell, 1940) it was found that many of the equations were ill-conditioned, so that the convergence was slow, and that it was laborious to find the uncertainties of the adjusted values by this method, though the normal equations themselves were set up most quickly by a tabulation process similar to the initial stage in applying the relaxation method.

Methods of solution dependent on the practical use of matrix theory as developed by Dr L. Fox (1950) were found most satisfactory and the complete adjustment was eventually carried out by these methods. The normal equations were developed in terms of departures from a trial solution and their solution and the individual uncertainties determined simultaneously by inversion of the matrix formed from these equations. Where the uncertainties for only a few stations were required (as for the stations linked into the Midlands network) it was found quicker to obtain the gravity differences by solving the normal equations directly from the lower triangular matrix and to determine the uncertainties of the values for the selected stations by a process of back-substitution. The main advantages of the matrix methods were found to lie in the completely automatic nature of the procedure and in the ease with which stage-by-stage checks on accuracy could be applied, so that if the computation is interrupted it can readily be resumed.

5. The adjusted gravimeter measurements.-From the adjustment of the gravimeter observations, calculated by assuming the calibration factor o.og437 milligal per dial division, the differences in gravity from that at Pendulum House, Cambridge for the principal gravimeter stations were those shown in Table I.

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Gravimeter observations at pendulum stations 309 The additional observations connecting the gravimeter and pendulum stations

and the adjusted value for the gravity difference between the gravimeter stations at Perth and Aberdeen are as shown in Table 11.

Combining these results, the differences of gravity between Pendulum House, Cambridge and the other pendulum stations which have been calculated from the gravimeter measurements are those shown in Table 111.

TABLE I Adjzrsted Gravity Dtferences from Pendulum House, Cambridge

Difference of gravity Station from Cambridge

(dligal) York Gravimeter + 150'60f 0.13 Newcastle (North Road) +243*63 k 0.14 Edinburgh Gravimeter f318 .34k 0.17 Perth Gravimeter +370'54f 0.21

TABLE 11 Measurentents of Gravity between Principal Stations

Observation Gravity difference (milligal)

York Gravimeter to York Pendulum Newcastle (North Road) to Newcastle Pendulum Newcastle Gravimeter to Newcastle Pendulum Edinburgh Gravimeter to Edinburgh Pendulum

Perth Gravimeter to Aberdeen Gravimeter

+0'02+ 0'02

- o - ~ k 0.01 -0.69k 0.01

- I '145 0.01

f62-84f 0.03 Aberdeen Gravimeter to Aberdeen Pendulum f0.43 f 0'01

(Adjusted value)

TABLE I 1 1 Differences in Gravity from Pendulum House, Cambridge, based on measurements with

Frost Meter c2-49 using Calibration Factor 0.09437 m'lligalper dial division Gravity difference

(millisall Pendulum station from Cambridge

York + 150*62$_ 0.14 Newcastle t242'50k 0.15 Edinburgh -t317'20f 0.17 Aberdeen +433-81$_ 0'21

6. Comparison of pendulum and gravimeter measurements.-It is now possible to combine the gravimeter measurements with the pendulum measurements (Browne and others, 1950) to obtain the best values of gravity, relative to Cam- bridge, at the pendulum stations. Further, since the pendulums have no calibration error, the calibration factor of the gravimeter may be included as one of the unknowns, and the correction to the calibration factor previously assumed may be determined following the method given by Dr A. H. Cook (1950 b). Writing gc, g,, g,, g, andg, for the values of gravity at the pendulum stations at Cambridge, York, Newcastle, Edinburgh and Aberdeen, respectively, writing K for the correction to the calibration factor of the gravimeter, and giving the observations weights (W) inversely proportional to the squares of their standard deviations (u), then the observation equations are those shown in Table IV.

c 22*

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310 W. BuUenaell TABLE IV

obsmtion Equations Trial

W value 0 - T T

6 149.85 o 6 241.22 o 6 315-08 o 6 430.90 0

9 149.85 0.77 8 241.22 1-28 6 315.08 2-12 4 430.90 2.91

Measurement Observed

d u e 0

149.85 241-22

315'08 430'90 150.62 242.50

433.81 317'20

U

0.18 0.18 0.18 0.18 0.14 0.15 0.17 0'21

CdC. value

C 149.74 241.08 315.14 430'97 150.69 242.61 317'14 433'70

0-c +o*r I

- 0.06 -0.07 - 0.07

+0*06 + O . I I

Sume :

+0'14

-0.11

wx (0-ag 0.0726 0.1176 0*0216 o-oagq O.OA+41 0.0968 0.0216 0.0484 0.4521

X'

0.37 0.61

0.15 0.25 0'54

0.27 2.42

0'11

0.12

The trial value of K is zero ; the units are milligals. K and the corrections, %, to the trial valuesg,, -gc are :-

The normal equations for

15x5. - 135558K = 6-93

12Xe - 1903.2 K = 12-72 IOX, - I735'2@= 11.64

I@: 1 - 1940 K = 10.24

- 1355.58~~ - 1940Xn - Ig03*2Xe - 1735.24~~ + 203108696K = 12611.33 The solution of these equations is :- x,=o.~~mgal , x,=o.~qmgal, x, = + 0.06 mgal, x, = + 0.07 mgal,

K = 0.63 per cent. There are three degrees of freedom, so that the standard deviation of an observation of unit weight is

{ i ~ w x ( 0 - ~ ) 2 ) 1 / 2 = 0.39 mgal. Using Jeffreys' (1939) procedure, the standard deviations of the unknowns have been found as:- u(y) = 0-11 mgal, u(n) = 0.1'2 mgal, u(e) = 0.13 mgal, u(a) =0.14 mgal,

a(K) = 0.04 per cent. x2 in the final column of Table IV is C(O-C)2/u2, where u is the value for the observation in the same row of the table. x2 for the adjustment is 2.4 on three degrees of freedom, and the probability of a larger value occurring by chance is about 50 per cent.

The combined results of the pendulum and gravimeter observations therefore lead to the following values for the differences of gravity between the various pendulum stations and Pendulum House, Cambridge :

York Newcastle Edinburgh Aberdeen

The method of weighting appears to be satisfactory.

I- 14974 mgal f 0.11 + 241.08 mgal f 0-12 + 95-14 mgal f 0.13 + 430-97 mgal f 0-14

The correction to the assumed calibration of the G.S.M. Frost gravimeter is - 0.63 per cent f 0.04.

The residuals between the combined adjusted values given above and the individual pendulum and gravimeter observations, the latter based on the corrected calibration factor, can be seen from the column (0-C) of Table IV. These all lie within the standard deviations of the individual observations, which are therefore entirely consistent when the deduced correction to the gravimeter

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Gravimeter observations at pendulum stations 311 calibration has been applied. It is clear therefore that these pendulum stations provide an excellent base line for future gravimetric surveys.

7. Further investigations at Westminster Cathedral.-From the comparisons at the pendulum stations the calibration factor of the G. S.M. Frost gravimeter appears to be unusually well determined. The deduced correction to the earlier accepted calibration factor was, however, unexpectedly large and significantly exceeded the standard deviation of the initial calibration at Westminster Cathedral which, as already pointed out, appeared consistent with observations between Cambridge and the N.P.L. It was therefore considered advisable to check whether the calibration factor had altered appreciably since the initial calibration by repeating the Westminster Cathedral measurements. A further series of measurements was therefore undertaken in Westminster Cathedral tower on 1951 May 10, when two gravimeters were employed-the Frost meter No. 4g.and a Worden meter No. 66. The Worden gravimeter had only recently been brought into use by G.S.M., but before making the observations at Westminster Cathedral it had been tested in the field and observations compared with those obtained using the Frost meter at twelve stations over a range of 112 milligals. Whilst these observations were not considered sufficient to provide an accurate relative calibration of the two instruments it was found that observations made directly with the Worden meter, that is assuming a calibration factor of unity, differed by less than 0.3 per cent from the comparison measurements made with the Frost meter and calculated employing the calibration factor consistent with the pendulum measurements.

In the initial stage of the 1951 May observations at Westminster Cathedral, the Frost meter was used to repeat the observations previously made in 1948 November between stations on the 2nd and 7th stages of the tower and a point in the entrance hall immediately south of the main entrance door. Great care was taken to reproduce as nearly as possible the conditions of the original observations. Instrument positions were reoccupied at the exact height and to within two or three inches in horizontal position. The coarse range setting of the instrument had previously been adjusted to ensure that the observations covered the same instrumental range. Five readings were made in the entrance hall and four readings each at the 2nd and 7th stages. The calibration factors deduced from these observations differed from those determined in 1948 November as follows :-

Change in Calibration Factor - 0.14 per cent & 0.26 per cent - 0.30 per cent & 0.28 per cent

Measured Gravity D@erence Entrance hall to 7th stage 2nd stage to 7th stage

The observations are therefore inadequate to determine precisely any change in instrument calibration, but do not account for the correction factor of - 0.63 per cent f 0.04 per cent obtained from the comparisons with the pendulums. Further, the new measurements confirmed the previous observations of a si@- cant difference in the calibration factors deduced, assuming the normal Free Air Vertical Gradient, from instrument observations taken separately between the 2nd stage and 7th stage, and the entrance hall and 7th stage. This might partly have been due to the fact that the station in the entrance hall was not vertically below the other two stations, and it was decided to examine the vertical gradient in the tower more fully.

A series of measurements was therefore taken to include observations at each stage from the ground floor (lift hall) to the 7th stage, at points vertically above

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W. Bullemell

each other on the north side of the lift platform at each stage. Two separate readings were taken with both the Frost meter and the Worden meter at every level. The Worden meter appeared to be more affected by vibration than the Frost and its repetition was not quite so good. For the purpose of investigating the vertical gradient of gravity it was decided to calculate gravity differences from the 7th stage assuming a calibration factor of unity for the Worden meter and a calibration factor of 0.09378 mgal/dial (in agreement with the pendulum comparisons) for the Frost meter. Heights between the actual meter positions were obtained from two independent sets of measurements for the stations in the entrance hall, ground floor lift hall, 2nd stage and 7th stage: Differences of level between the lift platforms at these stages were also measured and the values agreed closely with those given by A. H. Cook (1950 a). For the heights to the remaining stages the values given by Cook were accepted and the meter positions at these stages were at platform level.

The results of these measurements are given in Table V. TABLE V

Observations at Westminstm Cathedral Gravity

n o d

Height difference Worden Meter No. 66 Frost Meter No. 49 from =s-g

Residual Meter

Pi t ion r h s t a g e Gravity standard Residual Standard (feet) gradient difference deviation gw-gn difference deviation gf-gn g, (mgal) 'W (msal) (msal) gr ( m d ) (msal)

7th Stage 6th 5 6 4th 3rd and 1st Lift Hall Entrance Hall

0

- 25.8 - 52.0 - 79'9 -111.6 - 145.3 -161.9 - 185.9 - 187.5

0

+ 2.43 + 4-89 + 7'52 + 10.50 + 13.67 + 17-49 + 17-64 + 15-23

... 0 -06 0.03

0.07 0.07 0.07

0'02

0'02 0'02

... +0'04 -k 0.04

-0'01 +O.&

-0.08 -0.16 -0.34 -0.33

... + 2.45 + 4.87 + 7.51 + 10.48 +I337 +15.01

+ 17.33 + 17.14

... 0'01 0.03

0.04 0'02

0'01

0'02 0'01 0'01

... + 0'02 -0-02

- 0'0 I - 0'02 -0'10

-0'22

-0.35 -0.31

The additional observations taken with the Frost meter at the entrance hall, lift hall, 2nd and 7th stages have been included in Table V.

Table V is summarized in Fig. 3 as a graph showing the residuals of the gravimeter observations from the free air values calculated against height in the tower. This shows clearly the deviation from linearity in the vertical variation of gravity. The observations taken with the two instruments satisfactorily confirm each other in the general form of the curvature. If the calibration factor for the Frost meter obtained from the comparison against the pendulum is accepted, it is possible to estimate the departure from the normal Free Air Gradient in absolute terms. The results then indicate that the theoretical Free Air Gradient holds good from the 3rd stage upwards but that below this stage there is a significant departure, gravity differences from the 7th stage being too small. This appears to suggest that at the lower levels values of gravity have been locally reduced. Such an effect could arise from the disturbing effects of the main mass of the Cathedral and excavations below ground level. At present insufficient information is available regarding the local disposition of mass to allow quantitative estimation of the probable Id anomaly.

Since for observations involving the lower floors the actual gravity values are less than the theoretical, calibration assuming the Free Air Gradient value yields a

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Gravimeter observations at pendulum stations 313 calibration factor which is too high. The 1951 May observations in the tower suggest that the measurements relating to the 2nd and 7th stages of the tower will lead to a calibration factor in error by 0.73 per cent f 0.07 per cent, which is in fair agreement with the discrepancy between the initial calibration and that found by comparison with the pendulums.

\ \

I\ I

I I I I

\ I I I \

9

P /9

p

lo0

I

I

-5WSTACf

- 4T-M STAG1

- 3R'JSTACI

- IWSTAGE

I VSTACf

(O~SERVED- THEORETICAL) GRAVITY DIFFERENCES FROM 7VSTAGE

FIG. 3.--CaIibration of G.S.M. gravimeters, Westminster Cathedral, rg51 May 10.

T o complete the observations at ' Westminster Cathedral, VerticdTForce Magnetometer measurements were made to test whether changes in magnetic field were sufficiently large to require compensation. Observed changes in vertical magnetic field were as follows :-

Tower Stage Vertical Magnetic Field 7th o (assumed)

2nd - 0.023 gauss Ground floor + 0.045 gauss

4th - 0'001 gauss

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3=4 W. Bullerevell These changes are insufficient to produce any errors in the gravity measurements made with either of the G.S.M. gravimeters.

8. The daj%rence ingravity between N.P.L. and Cambridge.--It was stated in a previous section that the initial calibration of the Frost gravimeter was checked by a comparison of Observations between Cambridge and the National Physical Laboratory with the adjusted value for this difference based on previous observations. It follows that when the calibration factor of the Frost gravimeter is modified to provide agreement with the pendulum determinations at York, Newcastle, Edinburgh and Aberdeen, the derived value for the National Physical Laboratory is no longer consistent with the previous determination. There appears therefore to be need for some new independent determination in Southern England. The relative pendulum measurements at present being carried out by the Department of Geodesy and Geophysics, Cambridge University, to compare Pendulum House, Cambridge with the National Physical Laboratory and Southampton are therefore of considerable importance and the results are awaited with interest.

Summary and conclm*ms.-A series of gravimeter observations between the recent pendulum stations at York, Newcastle, Edinburgh and Aberdeen suggests that the pendulum measurements are highly reliable and provide a valuable basis for the adjustment of gravimetric networks and calibration of gravimeters.

Measurements between the pendulum stations gave an accurate calibration factor for the Geological Survey’s Frost gravimeter which differed significantly from that obtained from measurements taken in Westminster Cathedral tower. A further investigation of the variation of gravity with height in Westminster Cathedral indicated that calibrations based on the assumption of the normal Free Air Vertical Gradient may be in error and are probably too high.

A revision of the gravity connections between Cambridge, the National Physical Laboratory and stations in Southern England could best be based on additional relative pendulum observations. m

Acknowledgments.-Facilities for making the observations and the maintenance of equipment at the pendulum stations were freely extended, and sincere thanks are expressed to the Very Rev. E. Milner White, the Dean of York ; Professor W. E. Curtis of the Physics Department, King’s College, Newcastle ; Professor W. M. H. Greaves, Astronomer Royal for Scotland; Professor T. C. Phemister of the Geology Department and Professor R. V. Jones of the Natural Philosophy Department, Marischal College, Aberdeen ; and to the Administrator of West- minster Cathedral.

I wish to thank Mr B. C. Browne and Dr A. H. Cook of the Department of Geodesy and Geophysics, Cambridge University, for details of pendulum and gravimeter stations, and geophysicists of the AngleIranian Oil Company for much helpful information regarding instruments and gravimeter stations.

I should like also to thank my colleague Mr P. M. Howell, who made some of the gravimetric observations and assisted in the computations.

Geological Survey and Museum, London :

1951 W Y .

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Gravimeter observations at pendulum stations 315 References

Browne, B. C., Cook, A. H., McCarthy, E. J. and Parasnis, D. S. (1950), " Gravity rneasure- ments at York, Newcastle-upon-Tyne, Edinburgh and Aberdeen ", M. N., Geophys. Suppl. , 6, 91-1 08.

Clark, J. S. (1939)) " An absolute determination of the acceleration due to gravity ", Phil. Trans. Roy. SOC. A, 238, 65.

Cook, A. H. (1950 a), " Values of gravity, at stations in Southern Britain ", M.N., Geophys. Suppl., 6, 9-27.

Cook, A. H. (1950 b), " Pendulum observations at Dublin, Sligo, Galway and Cork ' I ,

Geophys. Mem. of the Dublin Institute for Advanced Studies, No. 2, Part 3. Falcon, N. L. and Tarrant, L. H. (195 I), " The gravitational and magnetic exploration of parts of the Mesozoic covered areas of South-Central England ", Q. J.G.S., 106, 141, 1950.

Fox, L. (1950)~ " Practical methods for the solution of linear equations and the inversion of matrices )', J. R. Statistical SOC., Series B, 12, 120.

Hammer, S. (1938)~ '' Investigation of the vertical gradient of gravity ", Trans. A w . Geophys. Union, 19th Annual Meeting, p. 72.

Jeffrey, H. (1939)~ The T h o r y of Probability (Oxford). Nettleton, L. L. (1940)~ Geophysical Prospecting for Oil (New York). Southwell, R. V. (1940), Relaxatim Methods in Engineering Science (Oxford). White, P. H. N. (1949)~ " Gravity data obtained in Great Britain by the Anglo-American

Oil Company Limited ", Q.J.G.S., 104, 339, 1948.

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gravimeter observations comparing pendulum stations at cambridge

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