CHAPTER VIII.

ASTRONOMY AND GEODESY IN AUSTRALIA : Part 7.

By Pietro Baracchi, F.R.A.S.,

Government Astronomer of Victoria.

“The Commonwealth of Australia; Federal Handbook, prepared in connection with the eighty-fourth meeting of the
British Association for the Advancement of Science,
held in Australia, August, 1914.”
pg.326-390. (1914)

By British Association for the Advancement of Science.
Federal Council in Australia, Australia.
Commonwealth Bureau of Census and Statistics, George Handley Knibbs

(2) GEODESY.

(a) Trigonometrical Surveys of High Precision.

Though many careful surveys have been effected in Australia, chiefly with a view to laud settlement, trigonometrical surveys of high precision are, so far, confined to the three Eastern States. Of these only a brief description will now be given.

Queensland.

The trigonometrical survey in this State extends approximately from 26° 30′ to 29° 30′ south latitude, and from 151° 15′ to 153° 15′ east longitude. It comprises 74 triangles and a base line of about 7 miles in length situated at Jondaryan. Its terminals are Mount Irving and Mount Maria, which are respectively 216 and 162 feet above the general level of the intervening ground.

The measurement of this base was made in 1884 by means of two steel tapes 100 feet long, about half-an-inch broad, and 0.01 inch thick.

These were compared with a standard bar of steel octagonal in section 1½ inches in diameter and 10 feet long, which was kept floating when in use in a trough of mercury, with thermometers plunged in it for obtaining the temperature of the bar. This bar was compared in 1883 with the New South Wales Standard Bar 0.I.4, which gave its standardised length at 62° F. as 9.9998581 feet, which value was adopted throughout the operations of the trigonometrical survey.

In the base measurements the two tapes were placed “in wooden troughs and shaded by a board, a tension of 20 lbs. was applied by means of a spring balance, and five thermometers, whose index errors had been determined by comparison with a standard thermometer, were used along each 100 feet of tape. The troughs were supported upon pegs driven in the ground and set on even grade by means of a levelling instrument. Marks were made in copper discs inserted in the pegs at each hundred feet, the distance between the tape ends and the marks being measured by micrometer microscopes.

Ten sections, the six central ones averaging nearly 1 mile and the other two at each end being nearly half-a-mile mile long.

The terminal points of these sections were marked by stones sunk into the ground and set in concrete. Each stone had a metal plug, upon which a small mark was made denoting the terminal point of the section.”

Three measurements were made with each tape, giving six independent values.

The two sets of three values made with each tape gave two mean results, which showed a difference of 0.117″ inches.

Ten-inch theodolites (Everest pattern), by Troughton and Simms, provided with micrometer microscopes reading to one second of arc, were generally employed on the survey, and a 12-in. altazimuth was used at a few stations.

The angular measurements were obtained from two to eight readings made on each of eleven positions of the circle. The closing errors were within 1″ for 29 triangles, from 1″ to 2″ for 29 other triangles, from 2″ to 3″ for 11 triangles, and upwards of 3′ for the remaining 5 triangles. The greatest closing error was 3.90″, and the average 0.95″.

“The astronomical datum is the position of the station at Jimbour as determined by Captain Morris, R.E., and Lieut. Darwin, R.E., in 1882,” while they occupied this station for the observation of the transit of Venus. [pg.376]

The longitude was determined by direct exchange of time signals with the Sydney Observatory by telegraph. In deducing from this datum the latitudes and longitudes of the trigonometrical stations, the elements used by Colonel James in the Ordnance Survey of Great Britain, in 1858, were adopted.

The azimuth datum was determined by astronomical observations made with a 20-in. transit instrument at Bloodwood, this being the apex of one of the triangles standing on the base line.

Astronomical observations for latitude and longitude were also made at several stations.

A comparison of the astronomical with the geodetic values for the four stations of Bloodwood, Brisbane, Haystack, and Mount Domville gives the following differences respectively. (40)

Latitude (geodetic − astronomical) −02″; +1.17″; +5.37″; −1.17″.

Longitude (geodetic − astronomical) +6.57″; −0.05″.

A minor triangulation of the City of Brisbane was carried out in 1890.

The principal triangulation was discontinued in 1891.

Victoria.

The preliminary work of clearing mountain tops for a trigonometrical survey of the State of Victoria was commenced in 1853 under Captain Andrew Clark, R.E., after his appointment as Surveyor-General of Victoria, as already mentioned ; but the primary triangulation was not actually commenced till seven years after.

In 1860 a base line was laid down on the Werribee Plains about 4.942 miles in length, which was subsequently extended by triangulation to a further length of 5.651 miles, making a total distance between the terminal points 10.593 miles.

“Each end of the measured base was defined by a solid mass of masonry built 5 feet into the ground, capped by a heavy stone with gun-metal plug and platinum centre, on which the terminal dot was marked. A heavy protection stone was placed over the cap stone, and this was surmounted by a timber pyramid, with pinnacle accurately centred over the platinum point.” (41)

The measurement of this base was made by three iron bars 10 feet long and 1 inch square, with the ends turned round for about 4 inches in length, one end of each bar being finished quite flat and polished, and the other end being a segment of a sphere of 5-ft. radius, also polished. They were encased in wooden troughs 6 inches square, with hinged tops cut in three sections for the convenient examination of the three thermometers resting on each bar, the steel ends only being freely exposed 2½ inches out of the case.

The lengths of these bars were compared with due care “with a 10-ft. ordnance standard lent by the New South Wales Government” (40) and verified later by a similar standard obtained by the Government of Victoria from the Ordnance Survey Department of England.

In the actual measurement the bars were supported on pine trestles fitted with brass sockets on their top frames to receive a brass tripod. These frames carried a brass “camel,” provided with the requisite fittings for bringing the ends of the bars accurately into juxtaposition. The three bars were placed in series with distances of about ¼ inch between the spherical [pg.377] end of one and the flat end of another, and the distance between the two was obtained by passing between them a graduated wedge of hard bell-metal 7 inches long and 2 inches broad, with faces inclined at angle of one-half a degree.

The difference of level between the terminal of the base being only 14 feet, and the intervening ground being fairly flat, the bars were adjusted by levelling into a horizontal position throughout the measurement.

A part of the southern portion of this base was re-measured to the extent of 2.11 miles, and the difference between the two results was found to be 0.308 inches, which was sufficiently small “ to justify the assumption that by the original measurement the Werribee base was probably as accurate as any measured up to that time.” (40)

The lengths of this base are as follow :—

(41) Measured base 26091.82 feet Extension by triangulation to Green Hill terminal 29839.83 Total length 55931.65

The instruments used for angular observations were an 18-in. altazimuth, by Troughton and Simms, and a 13-in. theodolite, by Ertel, both being provided with micrometer microscopes by which the circles were read to 1″ ; two 12-in. theodolites read by micrometer microscopes to 4″ and 10″ respectively ; a 10-in. altazimuth and other theodolites of smaller size.

The triangulation was expanded in a decade throughout the extent of the Colony south of the 36th parallel of south latitude.

In this survey 209 stations of the first order, 267 of the second order, and a larger number of subsidiary points were connected and marked.

An average number of 170 observations were made at each of the primary stations to determine their positions. The triangulated area is about 70,000 square miles.

It was intended to measure a very suitable base of verification to the westward of Mount Gambler and Mount Schanck, in South Australia, these being the extreme western points connected with Victorian triangulation, but the work was not carried out.

A portion of the boundary line between the States of New South Wales and Victoria is a straight line running from a point near the source of the Murray River to Cape Howe on the east coast. The terminals of this line were agreed upon in 1870, and in order to determine their geographical co-ordinates with all possible accuracy, they were connected with the primary triangulation which was, for this purpose, extended to “The Pilot” and Mount Kosciusko, in New South Wales, these being the extreme eastern points of the survey.

The true azimuth of the line having been deduced by calculation from the co-ordinates of the terminal points, the line was ranged on the ground to the computed bearing and marked in 1872, starting from one marked terminal, and reaching the coast to within 17 inches of the other marked terminal.

The line was run by Messrs. A. C. Allen and A. Black, and the result is a fitting tribute to their skill, energy, and endurance in the accomplishment of an exceedingly difficult undertaking with such a remarkable success. [pg.378]

Colonel Clarke’s elements of the figure of the earth were used in working out the results of the Victorian survey.

New South Wales.

The territory of this State extends from the Murray River to the 29th parallel of south latitude, and from the eastern coast westward to the 141st meridian of east longitude.

About one-fourth of its whole area has been covered with a trigonometrical survey of high precision, which was initiated in 1867, carried on for a few years, suspended for some time, resumed in 1891, continued since over an extent of 43 million acres, and still progressing.

The base line of this survey, 5½ miles in length, is situated at Lake George, and a verification base of about 7 miles was laid down and measured at Richmond.

The survey comprises 119 stations of the first order, 583 of the second order, and 1,380 of the third order, all of which have been very substantially and permanently marked and connected, and whose geodetic co-ordinates are accurately known.

Some 490 additional stations have been piled and prepared for observation, of which 15 are to be ranked as first order, 75 second order, and 400 third order stations.

The stations of the first order constitute the primary skeleton of the survey, being a net of fundamental triangles whose sides range usually from 35 to 40 miles in length.

Astronomical observations for azimuth, latitude and longitude were made at many of these primary stations.

The second order stations are distributed at distances varying from 15 to 20 miles, this being the average length of the sides of the secondary triangles. These stations were connected by actual observations made upon them with smaller instruments than those used at primary stations, but with sufficient precision to meet all the practical requirements of a triangulation for the purpose of accurate mapping. No astronomical observations were made at these stations.

The sides of triangles connecting stations of the third order are from 7 to 10 miles. The positions of these stations were fixed by intersections based on observations made from surrounding stations of higher order, and their accuracy is sufficient for connecting all chain surveys on a uniform system.

The original base on Lake George was laid down and its measurement commenced in 1868, under the superintendence of Mr. G.R. Smalley, but it was abandoned before completion owing to an abnormal rise of the water of the lake, which covered parts of the line to a depth of 2 feet.

A new site for the base was selected in 1870 by Mr. P.F. Adams, the Surveyor-General at the time, under whose direction the measurement of its length was made twice by Mr. A.C. Betts.

The adopted standard of length was that of “Standard Bar 0.I.4.” referred to at p.175 of Colonel Clarke’s work on the comparison of standards published in 1866. (41)

This bar is of cast iron, 10 feet in length, the length being defined by microscopical dots marked near its ends. It is encased, and fitted with [pg.379] adequate support to prevent flexure, and provided with thermometers and micrometer microscopes for the observation of its marks. It was obtained many years before from the Board of Ordnance in England.

The actual measurement of the base was made with three 10-ft. bars of pine wood, encased and evenly supported, in wooden troughs 6 inches by 6 inches, and a little less than 10 feet in length, so as to allow a short portion of the ends of the bars to project outside. The ends were fitted with small brass plugs, upon each of which a terminal microscopic dot was marked, the distance between the terminal dots being the actual length of the bar. These lengths were standardised each morning and evening during the progress of the work by comparison with the Standard Bar 0.I.4.

Each trough was supported on two “camels” provided with vertical, lateral, and longitudinal motion by means of which the three bars could be accurately placed in series along the line with the terminal dots of adjacent bars arranged in close pairs, always at the same distance, leaving a small constant amount of free space between the bars. This adjustment was made by means of a double microscope attached to the leading end of each trough. The microscope consisted of a single tube with two objectives at one end, rigidly mounted side by side, and two parallel webs, fixed on a diaphragm, at the upper end of the tube in the common focal plane of the objectives. By adequate means of adjustment the pair of dots could be brought in the fields of view and adjusted so as to bring each image into accurate bisection with each respective wire. The adjustment for parallelism of the optical axes and the distance between the webs having been previously ascertained, it was assumed that a constant distance between the adjacent bars was maintained throughout the measurement.

“The difference between the length of this base as found from the measurement and re-measurement was 0.542 inches in the total length of 5½- miles.”

The verification base at Richmond was measured in 1879-80 by Mr. Conder twice.

The first measurement was made with the same three pine bars with which the Lake George base was measured, and in the second three 10-ft. rods of steel 3/8 of an inch in diameter were used. These rods were wrapped in blankets, and encased in wooden troughs with glass windows for inspection of the attached thermometers. The arrangement of terminal dots, the auxiliary apparatus for support, adjustment, and observations, and the methods employed in carrying out the work were in every respect similar for both sets of bars, and throughout the base operations at Lake George in 1870 and at Richmond in 1879-80. The length of both sets of bars was again standardised by daily comparison morning and evening with the same standard as adopted in 1870, namely, the Ordnance Bar 0.I.4

The results of the two measurements were as follow :—

“The combined error of measurement of the two bases and of the intervening triangulation produced an apparent discrepancy of only If inches in the length of the Lake George base. The bases were assumed to be correct, [pg.380] and an adjustment of the triangles was made in order to eliminate this small apparent difference.” (40)

The instruments employed in astronomical observations and angular measurements were as follow :—

Two altazimuth instruments by Troughton and Simms, with object glasses of 3-in. aperture, provided with filar micrometer and delicate levels for latitude determinations by the Talcott method ; circles read by four micrometer microscopes to 1″.

All observations, astronomical and geodetical, were made with these instruments at the primary stations.

Theodolite by Troughton and Simms, object glass 2½−in. aperture and 26 inches focal length, horizontal circle 10 inches in diameter read by two micrometer microscopes to 1″, and two parts of a vertical circle 10 inches in diameter reading by vernier to 5″.

Observations at second order stations, and all vertical angles for the determination of relative heights, were made with this instrument.

Recently a 10-in. Repsold theodolite, of the same pattern as that used in the trigonometrical survey of South Africa, was procured, and is intended to be employed in the future in place of the heavier 18-in. altazimuth.

The observed directions from a primary station to another station of the first and second order depended on twenty pointings made in reversed positions of the instrument.

The number of pointings was reduced to ten for second order stations, and to five for stations of the third order.

The great accuracy of these observations is shown by the following statement of the closing error of triangles.

In 171 triangles in which all angles have been observed with the large altazimuth the closing error is 0.70″.

In 235 triangles, with two angles only observed with the larger, and one angle observed with the smaller instrument the average closing error is 1.15″.

In 245 triangles, in which only one angle was observed with the 18″ alt-azimuth, and the other two with the 10″ theodolite, the closing error is 1.29″.

In 173 triangles, with all the angles observed with the smaller instrument the closing error is 1.30″.

The probable value of the average closing error of the triangles, computed according to General Ferrero’s formula, for the primary triangulation of New South Wales is 0.54″, which is less than the error similarly computed for the great trigonometrical surveys of Great Britain, India, and most of the other countries, and the closing error for triangles observed with the smaller instruments is, on the same criterion, reduced to 1.00″.

Astronomical observations for latitudes were made at 74 stations with the 18″ altazimuth by the Talcott method.

Azimuth was determined at 66 stations by meridian observations of circumpolar stars, made with the same instrument.

The longitude of 10 primary stations, and of 29 other important places in the State, were determined by the direct exchange of clock signals with the Sydney Observatory.

For the calculation of geodetic latitudes and longitudes, the co-ordinates of the Sydney Observatory adopted as the datum were : — Latitude 33° 51′ 41.1″ ; longitude 141° 12′ 23.1″. [pg.381]

The elements of the figure of the earth adopted in the calculations of the survey are those of a spheroid with—Major axis a = 20923134 feet ; polar c = 20853429 feet.

Minor triangulations have been made around such important centres of the State as Sydney, Albury, and Newcastle, which were afterwards connected with the primary system.

Since the expansion of the geodetic survey of this State from the Lake George base in 1876, the principal observers in charge of the work were Messrs. W. J. Condor and J. Brooks. It was the former who set the high standard of accuracy which was worthily maintained by the latter.

Mr. T. F. Furber has been Director of the Survey for many years, and to him is due much of the credit of having planned means and methods by which this important undertaking has been brought to its present state of general efficiency and exemplary precision.

Mr. Furber, in his valuable paper (40) from which the information required or the above account was mainly drawn, mentions the names of P. F. Adams, late Surveyor-General, “to whom the very existence of the survey is in a large measure due,” and the late H. C. Russell, who, during the whole progress of the survey, aided in many ways where his scientific attainments were of the greatest service.

In May, 1912, a Conference was held in Melbourne at which the Director of Commonwealth Lands and Surveys, the Surveyor-General, and the Government Astronomer of New Zealand, and the Surveyors-General of the Australian States met to discuss, among other things, the question of a Geodetic Survey of Australia.

The following resolutions bearing on this matter were passed by the Conference :—

(41) “That, in the opinion of this Conference, it is desirable that a Geodetic Survey of Australia should be undertaken.

“ That, in order to give effect to the foregoing resolution, this Conference respectfully recommends that such survey be undertaken by the Commonwealth Government, and submits in support thereof the following reasons :—

“ (a) That the time has arrived when the Commonwealth should take its place in the scientific investigations of the world, not the least important of which are the determination of the figure of the earth, its density, and other cognate matters.

“ (b) That work of this character, involving the highest form of survey should be effected under the supreme authority of Australia, as it is essential that it should be carried out with the greatest degree of accuracy on a uniform basis and a definite plan the individual parts being co-ordinated and eventually forming one homogeneous whole.

“ (c) That the system which has hitherto prevailed by which the individual States carried out this work with instruments of varying character has resulted in divergent standards of accuracy, rendering the work to a great extent unsatisfactory, and, though much of it is of high grade, portions of it are impossible of reconciliation and co-ordination with a continental scheme. [pg.382]

“ {d) That the desirableness of this work being undertaken by the Commonwealth Government is evidenced by the fact that the Geodetic Survey of the United States is carried out under the direct control of the Federal Government, and that the South African Geodetic Survey is also under one central control.

“ (e) That such survey is absolutely necessary for the production of accurate maps, will be of high value in connexion with cadastral and geological surveys, and form a basis for topographical work for defence and other purposes. It will, moreover, provide a standard of accuracy for surveys of every description throughout the Commonwealth.

“ (f) That it will afford an invaluable base to which settlement surveys already effected can be connected, providing data for reestablishing boundaries, which, with increasing density of settlement, becomes a matter of great importance. Further, as regards the sparsely occupied areas of Australia, such a survey, if carried out in advance of settlement, will be of the greatest utility and assistance in effecting the settlement surveys which can at any future time be reproduced with a minimum error and at a relatively low cost, preventing litigation consequent upon other methods.”

It is earnestly to be hoped that the Commonwealth Government will sanction the recommendations of this Conference, and that the proposed undertaking may be carried out, so as to enable Australia to furnish in due course a contribution which should prove itself to be one of the greatest value and importance for the advancement of modern geodesy.

(b) Pendulum Observations.

Determinations of the gravitational value of “g” have been made in Australia at various times by different observers, since the early years of the nineteenth century, generally, by differential methods based on the swings of pendulums of the “invariable” type, and, in one case, by the actual measurement of a “second’s pendulum” of the reversible or Bessell’s type.

The earliest gravimetric observations made in Australia seem to be those of the French Expedition under Freycinet, who swung three pendulums at Sydney in 1819, and the latest are those of Dr. Wright, of Canada, which he made at Melbourne in April of this year (1913) on his return from Scott’s Antarctic Expedition.

During this period of 95 years, the value of “g” has been determined at all the capitals of Australasia one or more times independently, forming a series of 24 results, 9 of which are for Sydney, 7 for Melbourne, 1 for Brisbane, 1 for Perth, 1 for Hobart, 4 for New Zealand, and 1 for Campbell Island.

The whole of this work has been discussed by the International Geodetic Association, and a summary of it, with brief descriptions of the observations made, apparatus employed, and estimated probable error of each result, is published in the Reports of the 13th, 14th, 15th, and 16th Conferenz der internalionalen Erdmessung, from which the appended table is taken.

The table shows, by the satisfactory agreement of the values obtained by several observers at different times, that the gravitational constant “g” has been well ascertained for the Australian stations. [pg.383]

DETERMINATION IN AUSTRALIA OF THE VALUE OF “g” REDUCED TO THE POTSDAM SYSTEM.

[pg.384] The values in the table are from Bericht über die relativen Messungen der Schwerkraft mit Pendelapparaten in der Zeit von 1808 bis 1909 E. Borrasa Verhandlungen 16ten allgemeinen Conferenz der internationalen Erdmessung.

In the table “g” is the observed value reduced to the Potsdam system.

Writing φ the latitude, H the height in metres, θ the density of the local earth formation, g′−g the topographical reduction, then

g_o = g + 3086×10^-7 H the value reduced to sea-level.

g_o′ = g_o + [3θ / 4 × 5.52] (g−g_o) + g′−g the value corrected for the protuberant earth,

γ_o = 978.030 [1 + 0.005302 sin² &minus 0.00007 sin² 2φ] the value computed from Helmert’s formula.

g_o′ − γ_o = the gravitational anomaly.

I am indebted to the Government Astronomers and Surveyors-General of the Australian States for supplying me with accounts of the work of their respective departments ; to Professor Ernest Scott and Mr. H. Wright for interesting historical notes on the astronomical work of early navigators ; to Messrs. J. Tebbutt, C. J. Merfield, W. Gale, and H. Wright for information in regard to amateur astronomy ; to Dr. J. M. Baldwin for arranging the results of pendulum observations ; to Mr. J. A. Maroney for preparing the list of papers in Appendix B, and for giving valuable assistance in looking up authorities ; and to some others who have helped me in various ways. To all of these I tender my sincere thanks.

The length of the original article far exceeded the limits of space prescribed by the Editor, and owing to my inability to deal with the difficulty. Dr. E. F. J. Love undertook the heavy and troublesome task of reducing to its present size, for which I am very greatly obliged to him.

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