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Volume 39, 1906
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Art. II.—Transpacific Longitudes.

[Read before the Wellington Philosophical Society, 5th April, 1906.]

On the 31st December, 1900, articles of contract were made by Her Majesty's Government, Canada, New South Wales, Victoria, New Zealand, and Queensland on the one part, and the Telegraph Construction and Maintenance Company on the other, for the construction and laying of the Pacific cable. The contract called for the completion of the whole cable on or before the 31st December, 1902. The cable was finished two months earlier, and, after undergoing the required test of a month, entered upon its commercial career on the 8th December, 1902. Thus was the project that had been advocated with persistence from some quarters for a quarter of a century an accomplished fact; the missing link of about eight thousand miles across the Pacific between Canada and Australia, in the world's metallic girdle, was now supplied.

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Before laying a cable a survey is always made along the proposed route in order to select the most favourable ground, just as the railway engineer runs lines of levels before the final location of the railway. The cable engineer determines his levels by means of the sounding-line (piano wire), and at the same time obtains samples of the ocean-bed. It may be stated here that the direct route of the Pacific cable between the stations was departed from in order to avoid hills, craters, and hard or undesirable ground for the cable to rest upon.

From the survey the number of miles (nautical) required for the different flections was as follows: From Vancouver Island to Fanning Island, 3,654; from Fanning to Suva, Fiji, 2,181; from Suva to Norfolk Island, 1,019; from Norfolk to Southport, Queensland, 906; Norfolk to Doubtless Bay, New Zealand, 513.

The first section of the cable is about a thousand miles longer than any that had been laid before. This necessitated a considerable increase in copper for the conductor and in guttapercha for the dielectric. The working-speed of a submarine-telegraph cable depends on, and is inversely proportional to, the product of the total resistance of the conductor multiplied by the total electro-static capacity of the core, so that, other things being equal, the speed varies inversely as the square of the length of the cable. In the long section there were used 600 lb. of copper and 340 lb. of guttapercha per nautical mile; on the Suva-Fanning section 220 lb. of copper and 180 lb. of guttapercha; and on the remaining three sections the copper and dielectric were in equal proportions of 130 lb. each.

In the neighbourhood of Fiji, at a depth of 2,500 fathoms a temperature of 34.1μ Fahr. was noted, being the lowest temperature taken during the survey. There is very little difference in the temperature of the ocean at great depths, say below 3,000 fathoms, over a great extent of the earth's surface, the temperature being only a few degrees above the freezing-point, or 32μ Fahr.

The greatest depth, 3,070 fathoms (about three miles and a half), was found on the Fanning-Fiji section, where the bottom specimens consisted principally of radiolarian ooze. This ooze is found at the greatest depths, and was obtained by the “Challenger's” deepest sounding in 4,475 fathoms. The United States steamer “Nero” sounded in 5,269 fathoms (six miles), this being the deepest sounding recorded in the ocean, and the-material brought from the bottom was radiolarian ooze.

Of the 597 samples of sea-bottom obtained on the Pacific-cable survey, 497 were such that they could be divided into distinct types of deposits. It was found that 294 samples referred to globigerina ooze, sixty-five to red clay, forty-three to radio-

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larian ooze, forty-five to coral mud or sand, twenty-seven to pteropod ooze, twelve to blue or green muds, and eleven to organic mud or clay.*

The pressure at a depth of 3,000 fathoms, in which a considerable portion of the Pacific cable is laid, is about 4 tons to the square inch. When the cable is being laid at such depths, it will be approximately twenty miles astern of the ship before it touches bottom.

Deep-sea cables last longer in the tropics than in the northern oceans. The reason is to be found in the fact that in the tropics marine life, from which globigerina ooze is derived, is more abundant than in the more northerly or southerly waters. It is the sun and the warmed surface-water that call into life these countless globigerina, which live for a short space, then die and fall to the bottom like dust, making such a good bed for the cable to rest in. In the arctic currents where the surface is cold the water does not teem with life in the same way as it does in the tropics, and consequently there is less deposit on the bottom of the ocean.

A submarine cable consists first of a core, which comprises the conductor, made of a strand of copper wires, or of a central heavy wire surrounded by copper strips as in the Pacific cable, and the insulating covering, generally made of guttapercha, occasionally of indiarubber, to prevent the escape of electricity. As far as cabling is concerned, this is really all that is necessary—an insulated conductor. This, however, would not, in the first place, be sufficiently heavy to lie in the ocean, and, secondly, would be too easily injured and destroyed by the many vicissitudes to which it would be subjected. For this reason a protection in the form of a sheathing of iron or steel wires surrounds the core, the nature, size, and weight of the sheathing being dependent upon the depth of the water and kind of ground over which it has to be laid. The deep-sea section, being the best-protected from all disturbing influences outside of displacement of the earth's crust by earthquakes or volcanic action, is naturally the one of the smallest dimensions; and for the shore end, which is exposed to the action of the waves; to driftwood, to the grinding of ice in the more northerly latitudes, and to the danger of anchorage, especially of fishing-boats, the sheathing must be very heavy. So that, while the deep-sea cable is somewhat leas than 1 in. in diameter, that for the shore end is nearly 2 ½ in. in diameter. The action of the waves is limited to a depth of only about 13 fathoms, so that their influence on the cable, manifested by wear and chafing, is confined to the shore end.

[Footnote] * Report of Sir John Murray.

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The Pacific cable is equipped with the most modern apparatus at the various stations, and the cable is worked duplex—that is, messages are sent and received on the same cable at the same time.

Canada had carried longitude work from Greenwich across the Atlantic and thence to Vancouver. The completion of the British Pacific cable offered an opportunity for continuing the work across the Pacific in the interests of navigation and geography, besides tying for the first time longitudes brought eastward from Greenwich with those brought westward, making the first longitude girdle round the world.

In October, 1902, the Hon. Clifford Sifton, then Minister of the Interior, authorised the carrying-out of the transpacific longitudes, and the Governors of the South Seas, Australia, and New Zealand were respectively officially notified thereof. In preparing the programme for carrying out the work the climatic conditions of the various stations to be occupied were studied so that the most favourable times and seasons might be chosen. It was found that Suva, Fiji, was the governing factor, as it was by far the rainiest place of the series. The work was placed in my charge, and Mr. F. W. O. Werry, B.A., was associated with me as the other observer.

The instrumental outfit of the two observers was practically the same. Each observer was provided with a Cooke and Son astronomic portable transit, each of 3 in. clear aperture, the one of 34 in. the other of 36 in. focal length. Each transit was provided with reversing-apparatus. The transits of stars were observed over eleven threads in groups of three, five, and three respectively. The eye-piece attachment carried a micrometer (one revolution about a minute of arc with thread parallel to the transit threads) for latitude work; and the whole attachment was necessarily movable through 90μ, so that the movable or micrometer thread becomes horizontal. The recording of transits was made, by means of a key, on a Fauth barrel chronograph. Each observer was provided with two sidereal box chronometers, one being a spare instrument in case of accident. There were, besides, dry cells, switchboards, and minor accessories to complete the outfit. I carried, too, a half-seconds pendulum apparatus and a Tesdorpf magnetic instrument, the latter similar to the ones furnished Drygalski, of the “Gauss,” on his Antarctic expedition.

At each station—that is, at Fanning, Suva, Norfolk, South-port, and Doubtless Bay—a brick or cement pier was built, and an observing-hut covering the same. At Vancouver, which is used as a longitude reference point for the whole of British Columbia, we have a permanent transit-house.

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Bamfield, on the west shore of Vancouver Island, is the eastern end of the Pacific cable, and was not occupied as an astronomic station, but simply as an exchange station—that is, for the comparison of the Fanning and Vancouver chronometers, to be described more fully later.

Longitude work consists in simply determining the accurate sidereal time for each of two places, the longitude of one of them being known, at an absolute instant, and then comparing such times: the difference between them will be the difference in longitude. The operation may be briefly stated: Each observer determines the error of his sidereal chronometer at a particular instant; then by means of the telegraph line or cable the two chronometers are compared, to be explained later; this comparison may be likened to an instantaneous photograph of both chronometers. Applying the respective chronometer corrections for the instant of comparison to the times thus shown by the two chronometers, we obtain the absolute local sidereal time for each place for the same instant; and, as before, the difference between these times is the difference of longitude.

Now, suppose we have a transit instrument with a single vertical thread, and that thread situate in the axis of collimation; furthermore, the axis of the telescope horizontal, no inequality nor ellipticity of pivots, and the pointing of the telescope truly in the meridian; then, if we record the transit of a star across the thread, and the time noted is free from personal equation, we obtain immediately the clock-corrections by comparing the observed time with the right ascension of the star for that time and day. The many conditions imposed in the last sentence show the many sources of error, the effect of which must be evaluated ere we obtain the desired quantity—the clock-correction; in other words, the true local sidereal time at a given instant.

We must therefore devise means for determining the instrumental errors, some of which are practically constant—inequality and ellipticity of pivots; while the others—level, azimuth, and collimation—are more or less variable from day to day. Careful readings, at the beginning and end of a season, of the former will evaluate them. For the latter we will speak of the level-corrections first. This quantity is determined directly by means of the striding-level placed upon the axis of the instrument. Readings should be taken as frequently as the intervals between stars admit. With sensitive levels, reading about a second of arc for divisions, great care must be exercised in allowing the level to come to rest. My own practice is not to take a reading until fully a minute has elapsed after placing the level, and as a light is necessary for reading at night, the reading should be taken quickly, for even a short exposure of the level to light

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will cause a change in the reading. I consider a six-minute interval between stars the minimum during which a deliberate reading (including reversal of level) for inclinations of the axis can be made. How to treat the various level-readings for one position of the instrument will depend upon circumstances. The readings may show a decided and unquestionable gradual change of level; in such a case the readings may be plotted and the level-reading for each star interpolated therefrom. If, on the other hand, the level - readings are confined within the errors of reading and small fluctuations, we may then take the mean of the various readings as the reading for that position of the instrument. The angular value of the level - reading expresses the angle between the vertical plane (in the case under consideration the meridian) and that described by the transit; the two great circles intersect each other in the horizon, where the level-correction is nil. The level factor, usually designated by B, is expressed by cos (φ—δ) sec δ. This factor computed for each star, multiplied by the inclination of the axis, expressed in time, gives then the level-correction to be applied to the respective transits. Errors of level are measured directly, while those of azimuth and collimation with portable astronomic instruments are not directly measured, as is the case with the large transits in observatories. This leaves then the determination of three unknowns—the azimuth, collimation, and clock corrections; the minimum number of stars to determine which is three. With only three stars, however, there would he no measure of the accuracy of the observations, for one, and only one, value for each of the unknowns would satisfy the three observation equations; there would be no probable error. If the instrument is not in the meridian it is evident that the times of transit of stars north of the zenith will suffer a correction of opposite sign from those to the south. If the telescope is pointing west of north, north stars transit too late, and south stars too soon; and vice versa if pointing east of north. As polar stars move slowly they are well adapted for obtaining the azimuth-correction, and hence one polar star is included in each time set for each position of the instrument, and the general azimuth-factor is sin (φ—δ) sec μ.

With the collimation-error, however, the correction for north and south stars is of the same sign for one position of the instrument; but when the instrument is reversed, then the error is of opposite sign, and the transits of stars are similarly affected. The effect of the collimation - error becomes therefore more apparent and is more accurately deduced when some stars are observed in one position of the transit, and others with the telescope or axis reversed.

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The effect of the collimation-error on the times of transit varies directly as the secant of the declination of the star, hence the collimation factor is sec μ.

In order, therefore, to obtain a satisfactory time-determination—which is really the quantity sought—we observe more than the absolutely necessary three stars, and find the most probable value by the method of least squares.

In the programme of the transpacific longitudes it was arranged that (barring cloudy nights) on each night there should be two independent time - determinations; each determination to be derived from fourteen stars, divided into two groups of seven each, of which one was a polar. Furthermore, one group was observed clamp east, and the other clamp west. The six other stars of each group were “time” stars, and selected near the zenith and south (in the Northern Hemisphere) thereof. Instead of three we now have fourteen observation equations from which to deduce the three unknowns, already mentioned, by the usual method of forming the three normal equations. It is desirable to reduce the effect of azimuth and collimation on the derived clock-correction; we attain this by making the algebraic sum of the azimuth-factor as small as possible, and similarly with the algebraic sum of the collimation-factors.

In deducing the time - correction it evidently must signify the correction at some particular epoch, for every clock and chronometer has a rate. The epoch chosen is generally the mean of the various transits constituting a set, and the transit of each star is corrected for rate, as if all stars had been observed at that mean time. If, after having obtained the azimuth and collimation errors, we apply them with their respective factors to each transit and compare this corrected transit with the apparent right ascension corrected for aberration, we obtain the clock-correction of that transit or star, and the difference between this and the clock-correction of the normal equation gives us a residual. Each star thus furnishes a residual, and from them is found the probable error of a single observation as well as of the deduced clock-correction from all the stars. The average probable error of the latter is about 0.01 s. for good work.

A word about rate. Rate is one of the most difficult problems with which we have to deal in field longitude work. It is not the magnitude of the rate, although a small rate is very desirable, but the constancy: this is the crux. A chronometer may have an apparently constant daily rate, yet the hourly rate for the twenty-four hours may and does vary. Again, the rate is not the same when the current is on as when it is off; the former obtaining when observing and the latter the rest of

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the day. The rate deduced from two independent time-determinations of the same night, when the temperature is practically constant during the time of observation and the clock is in circuit with the battery (one cell) only during that time, is seldom, if ever, the same as that obtained from day-to-day observations.

In our programme we have two independent time-determinations for each night. Each set of transits is reduced to the epoch of the mean of the times of transit of the stars comprising that set. The rate which is applied for each transit to the mean epoch, and for which some magnitude must be assumed, is practically a vanishing quantity in the resulting clock-correction. The ideal time of exchange would be at that epoch when the effect of rate is eliminated. But, for various reasons, this is found to be impracticable. In the programme, then, of two independent time-determinations, for obvious reasons the exchange was arranged to take place about midway between the two epochs.

An interpolation between the two epochs gives the clock-correction at the instant required—that of the signals. This assumes that the rate is constant during the interval and is represented by a straight line. If extrapolation is necessary, as sometimes occurs, the rate-value has less weight. It is highly desirable that the temperature of the chronometer be kept as uniform as possible, and, if necessary, special provision made to attain this end.

We are supposed now to have made a complete time-determination, and are ready for exchange of signals—that is, of a comparison between the two clocks of the two stations.

As some of the exchanges were over land lines, I shall explain this method of exchange first, taking the case of Vancouver and Bamfield. Each of these stations was supplied with a switchboard. The portable switchboard has been in use many years and has given every satisfaction. On it are mounted a talking relay, a signal relay, and a pony or clock relay; the last is never on any circuit but that of the chronometer with one dry cell. Besides, there is an ordinary talking-key and a signal-key, the latter breaking circuit when depressed while the ordinary telegraph-key makes circuit. Along one edge of the board there is a row of binding-posts for connecting with the clock, chronograph, main line, and batteries, of which there are three dry cells for the chronograph, and, as stated, one for the chronometer. And, lastly, there is a three-point switch, by means of which the main line can be thrown on or off the points of the clock relay, and plugs to cut in or off any relay. While observing, the chronograph-circuit passes over the points of the clock

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relay, and, as the clock or chronometer breaks circuit every two seconds (omitting the 58th second so as to identify the minute), the points of the clock relay separate every two seconds, and hence record the clock-beats on the chronograph. In the chronograph-circuit is the break-circuit observing-key too, by means of which the transit of each star over the eleven threads is recorded.

It is customary when beginning the exchange to put the telegraph-line for a minute at each station over the points of the clock relay, whereby the circuit of the main line is broken by each chronometer every two seconds—that is, we let the clocks (chronometers) record simultaneously over the line, each chronograph thus obtaining the record of both clocks. From this record we immediately see the relative position of the respective minutes—in fact, of the seconds too—enabling one readily to identify corresponding arbitrary signals, by means of which the more accurate chronometer-comparison is made. Theoretically, the comparison by the chronometers recording directly over the line, as above, is as good as by arbitrary signals. The trouble lies in scaling or measuring the former. As, for an interval of a minute, the relative position of the two-second breaks of the two chronometers is the same, after having measured one such interval on the chronograph sheet the mind is involuntarily biassed; we know that all the others should be the same, and, consequently, we cannot measure, say, thirty, our minimum number, with that freedom of mind which would be the case if we did not know what measure to expect: hence the device of the arbitrary signals. In this case each chronometer records only on its own chronograph. One observer now sends by means of the signal (break-circuit) key twenty arbitrary signals; the chronograph - circuit, which always passes over the points of the clock relay, is now made to pass too over the points of the signal relay, which is on the main-line circuit. Hence a signal sent will be recorded on each chronograph, and each chronograph has its own chronometer-record for interpreting any signal, just as it interprets the transits while observing.

As the word implies, these arbitrary signals are intentionally made irregular, and will average about two seconds apart. The other observer now sends, similarly, forty signals, and again the former twenty more, so that the mean of the times of sending of the two observers about coincides, thereby eliminating differential rate of the two chronometers. It is customary when sending signals to give a rattle with the key at the beginning and end of each set. If there is no trouble on the line the whole exchange is over in five minutes. A few minutes are required for conversation about the condition of the sky. If the prospects

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are hopeless for the night for one, the other desists from further observations. The accuracy with which these comparisons are made is far beyond the accuracy that is possible in a time-determination: while the probable error of the latter is, say, 0.01 s., that of the former is generally less than 0.002 s.

The exchange on the cable is similar to that just described of arbitrary signals. The chronograph here is replaced by the paper fillet of the cable service. It is scarcely necessary to observe that nowadays signals (messages) on the cable are not read by means of deflections of a small mirror, interpreted on an opal glass scale by means of a reflected beam of light, but are read from the fillet of paper on which a siphon records in ink the deflections. As the current is very weak the siphon is not in direct contact with the paper, but, by an ingenious vibrating device, it deposits a tiny drop of ink at very brief intervals. A cable message looks like a profile of the Rocky Mountains, the ups and downs having an interpretation like the dots and dashes in the Morse system of telegraphy. From experience it is found impracticable to have the clock recording directly on the cable for interpreting signals sent or received. However, it is necessary to have a time-measuring scale on the fillet. We accomplish this by attaching another siphon to the frame of the cable instrument. This one is quite independent of the cable. It is actuated by a long vertical rod attached to the horizontal arm of an ordinary sounder, and connected to the siphon by a silk fibre. This latter siphon drags an ink-line on the fillet. The sounder is put in circuit with the clock, and hence every time the clock or chronometer breaks circuit the sounder makes a sharp break in the line on the fillet, and a time-scale is obtained close to and parallel to the zero-line of the cable-siphon. By projecting vertically these recorded clock-breaks on to the cable-siphon record, we can interpret in time the arrival or departure of a signal. We must know, however, the relative position of the two siphons. The signals are sent with one of the two cable-keys (on cables there are always two keys, one for sending positive and the other for sending negative currents). To the lever of the cable is adjusted another lever which is in the clock-circuit. It is so adjusted that the moment the cable-key makes contact—that is, sends a current into the cables—at the same moment the clock-circuit is broken, thereby both siphons record the event simultaneously, and the parallax between the two siphons is obtained. As a check on the value thus obtained for the parallax, a slight tap is given to the frame carrying both siphons, thereby disturbing both, and the parallax obtained. By the above arrangement, when sending signals we have two records on the fillet, one by the clock-siphon, the other by the

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cable-siphon. In receiving signals there is, of course, only the record of the cable-siphon, the other siphon recording only the chronometer-beats, which, on the fillet, measure about 1 in. for the two seconds. The speed of the fillet may be varied to any degree. It will be seen that a comparison of clocks by this means is simply a matter of careful linear measurement. Were the records at the two stations instantaneous, then the two records would be identical; but such is not the case. Each signal arrives late at the distant station, and therefore the two records will differ by twice the time of transmission, assuming that the time of transmission is the same in each direction, an assumption which we cannot avoid. On the long section of the cable between Bamfield and Fanning, about four thousand two hundred statute miles, the time of transmission was a third of a second, equivalent to about twelve thousand statute miles per second.

In the first longitude-work by cable before the introduction of the recording-siphon, instead of arbitrary signals, the clock-beats were sent by hand at intervals generally of ten seconds, and the time of arrival of the signal, as indicated by the reflecting-galvanometer, was noted by the “eye and ear” method. The uncertainties and “personal equation” in this method of exchange and comparison of clocks are apparent.

We have now explained briefly how the clock-correction is obtained for a given instant, and how the comparison of the two clocks is made. The application of the clock-corrections respectively to the times of exchange gives apparently the local sidereal time for each place at the same instant. Each value is, however, affected by a small correction—the personal equation of each observer. As the quantity sought is the difference between the local sidereal times, the absolute personal equation of each observer is unimportant; it is the difference between the two personal equations that affects the difference of longitude. On land lines, where the ready means of transportation is good, it has been customary (up to the present, when, by the introduction of the registering-micrometer, the personal equation is eliminated) for the observers to exchange stations, the mean result of the two differences of longitude being free from personal equation: this is on the assumption that the personal equation of the observers remains constant during the longitude campaign. On this assumption, if there is a series of stations odd in number, and the observers occupy alternate stations, it will be seen that the odd-numbered stations will be free from personal equation, and the even-numbered ones affected by it. Now, between British Columbia and Australia, and also between British Columbia and New Zealand, the number of stations is odd—i.e., there are three intermediate stations, Fanning, Suva, and

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Norfolk; hence Southport (Queensland), Doubtless Bay (New Zealand) and Suva (Fiji) are free from personal equation.

Personal - equation observations were, however, made at Ottawa by the two observers using the same clock and determining its correction at the same time on the same stars with the two transit instruments, and the resulting difference of personal equation, 0.124 s., applied to Fanning and Norfolk.

Southport was connected with the observatories at Sydney and at Brisbane, and similarly Doubtless Bay with the observatory at Wellington. Personal-equation observations were made between the respective observers.

It was on the 29th September, 1903, that the first satisfactory clock exchange was had with Sydney, and so this night may be considered as the one when for the first time longitude from the west clasped hands with longitude from the east, and the first astronomic girdle of the world was completed. The immediate reasons for the first telegraphic connection in longitude between Australia and the prime meridian, Greenwich, were (1) with a view of confirming the position of the eastern boundary of the Colony (now State) of South Australia, 141° E.; (2) for obtaining the longitude of stations to be occupied for observing the transit of Venus in 1882. To attain this end connection was made astronomically between Sydney, Melbourne, Adelaide, Port Darwin, and Singapore. A connection was made, too, between Sydney and Wellington. All Australian and New Zealand longitudes at present rest on the position of Singapore as accepted in 1883, which then, quoting from the Government report for 1886 of South Australia, “had twice been telegraphically determined—first in 1871 by Dr. Oudeman, of Batavia, and Mr. Pogson, of Madras, and more recently by Commander Green, United States Hydrographic Department.” The determinations of the latter were accepted. It may be remarked that at this time the Thomson (Lord Kelvin) recording-siphon had not yet been introduced, and that the clock exchanges between Port Darwin and Singapore over the cable were made by use of the deflecting mirror or reflecting galvanometer, already spoken of, a method involving more or less uncertainty in noting by “eye and ear” the movement of the mirror and the instant of time of its occurrence.

Singapore was dependent in position upon Madras, the initial meridian for the great trigonometrical survey of India.

For over a century observations have been taken from time to time to determine the longitude of Madras. The early ones, before the advent of cables and telegraphs, were dependent mostly on lunar observations, some on Jupiter's satellites. In 1891 the Survey of India had not adopted the then best value, so that at the International Geographic Congress held at Berne

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in that year the question arose, why the known error in longitude of 2′ 30″ was not corrected on the Indian maps and charts. This gave rise to a discussion in India, and the whole longitude work was reviewed, with the result that a determination de novo was decided upon, carrying the work directly from Greenwich via Potsdam, Teheran, Bushire, and Karachi, where connection was made with the three arcs of the great trigonometrical survey between Karachi and Madras. This work was carried out by Captain (now Major) S. G. Burrard, R.E., and Lieutenant Lenox Conyngham, R.E., in 1894-6. The resulting longitude of Madras was 5 h. 20 m. 59.137 s. ± 0.022 s.

In 1903 a redetermination of Greenwich-Potsdam was carried out by Professor Dr. Albrecht and Mr. Wanach. Stations were exchanged and observations made with a Repsold registering-micrometer. The exchange of stations was made to test the elimination of personal equation by means of the registering-micrometer, and the result was highly satisfactory, the weighted mean of the one result agreeing with the weighted mean of the other to the third place of decimal of a second of time. It may be stated here that the introduction of the registering-micrometer in longitude-work marks a distinct epoch in that class of work, not only in assuring greater accuracy in the results, but also in very materially reducing the cost of longitude-work of the first order by saving of time and money in doing away with the necessity of exchange of stations. Since the completion of the transpacific longitude-work, the two Cooke transits used in that campaign have been provided with the registering-micrometer made by Saegmueller, of Washington, and the longitude work of 1905 was carried out with that attachment.

From the 1903 determination by Albrecht we have for the longitude of Potsdam 0 h. 52 m. 16.051 s. ± 0.003 s. This value is 0.098 s. greater than that of Burrard obtained in the series of 1894-6 referred to above.

In the reduction (1885) of the Australian longitudes, the longitude of Madras was accepted as 5 h. 20 m. 59.42 s., and the derived value of Sydney was 10 h. 4 m. 49.54 s.

In making the comparison between the longitude of Sydney as brought from Greenwich eastward with that brought westward, the best and most recent available data are utilised for the longitude of Madras.

Taking, then, Albrecht's value for the arc Greenwich-Potsdam, and the values of Burrard for the arcs Potsdam-Madras, we obtain for the longitude of Madras 5 h. 20 m. 59.235 s. ± 0.021 s.

As there have been no new determinations of the various arcs from Madras to Sydney, the values given in the report of May, 1885, by Ellery, Todd, and Russell, on Australian longitude, are used. Adding the latter to the above-accepted value,

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we obtain for Sydney 10 h. 4m. 49.355 s. ± 0.088 s. The Canadian value is 10 h. 4 m. 49.287 s. ± 0.058 s. Difference, 0.068 a. = 1.02″ = 84 ft. for the latitude of Sydney—that is, the first girdle of the world closed within 84 ft.

New Zealand.

The longitude of Wellington is discussed in the report of 8th August, 1884, of the Surveyor-General of New Zealand, and in Appendix No. 1 of that report Mr. C. W. Adams fully describes and tabulates the result of the determination for the difference of longitude between Sydney (Australia), and Wellington. The time-determinations of this series are of a high order, and deserve every confidence. At the time (1883) the siphon recorder had not been introduced on the cable, so that the clock-beats were sent by hand and the deflections of the reflecting-galvanometer were noted by eye. As Mr. Adams says in the above appendix, “I received them at Wellington by reflecting-galvanometer, but, instead of noting each signal by ‘eye and ear,’ I simply tapped the key and recorded each signal on my chronograph”—that is, as soon as the motion of the light-spot had impressed itself on the brain, the key was tapped to record the event. Although many trials were made for “the loss of time in receiving signals,” and the results are inconsistent amongst themselves, yet the lack of self-recording cable-apparatus is the weak point in the 1883 determination for difference of longitude. The range for difference of longitude for the 1883 determinations is satisfactory, but of course may involve constant errors without affecting the range. As we shall presently see, the inter-agreement between the difference of longitude between Sydney and Wellington obtained in 1883, and that in 1903, when the siphon recorder was used, is remarkably close.

As Mr. T. King, observer at Wellington, has so fully given the evolution of “the longitude of the Colonial Observatory, Wellington,” in the “Transactions of the New Zealand Institute,” vol. xxxv, 1902, pp. 436-47, it is not necessary here to cover the same ground.

As has already been explained, the determination of the longitude of Southport (Australia) and Doubtless Bay (New Zealand) is free from personal equation, and, so far as the Canadian work is concerned, these two places are necessarily better determined than places dependent upon them. In other words, Doubtless Bay is better determined in longitude in the Canadian arcs than is Wellington; for Wellington to be as well determined as Doubtless Bay would mean perfect observations and perfect exchange of time-signals between the two places, which is of course impossible, no matter how good the work.

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Upon my arrival in Wellington in November, 1903, I was very cordially received by Sir James Hector and Mr. T. King. Sir James, by the way, we Canadians claim as a kinsman, for we have not forgotten the very valuable work he did nearly half a century ago in the Rocky Mountains in connection with the Palliser expedition. The Hon. Mr. Richard J. Seddon, Premier, who had been officially notified of my coming, offered every facility for the successful issue of the work, and Sir Joseph Ward, Postmaster-General, kindly placed the telegraph-lines at my disposal. Mr. King and I discussed the work in hand—the connection of Doubtless Bay and Wellington. The star programme, the routine of observing and exchange of time-signals were followed as already explained. Mr. King in his time work always observes by “eye and ear,” and this method he followed too in the longitude work, including the personal-equation observations, while I, as usual, recorded my observations on the chronograph.

The main consideration was the installation of electric apparatus to enable the exchange of time-signals between the two stations. After explaining to Mr. J. K. Logan, Superintendent of Government Telegraphs, what was required, the electrician, Mr. Buckley, and Mr. Chisholm installed the necessary batteries and relays at the observatory, a description of which, furnished me by Mr. Logan, follows later. A brief résumé of the apparatus at the Wellington Observatory may be given.

The observatory was established in 1869, and is used for time service only. It is situate on the summit of the hill within the old cemetery, and overlooks the city, harbour, and surrounding country. The building has two rooms—a clock-room and a transit-room.

Clocks.—In the former are three mean-time clocks, and one sidereal—Dent No. 39720—having electrical attachment making contact or circuit every second except the 60th in order to identify the minute. The clocks are all mounted on brick and cement bases, and are fastened to substantial braced frames.

Transit.—The transit is by Troughton and Simms, and is mounted on a rather high stone pillar. It has an aperture of 2 ¾ in., and a focal length of 32 in. The reticule has seven threads at equal equatorial intervals of about 17 seconds of time. There is a sensitive striding-level, and one oil-lamp for illuminating the field. The single small setting-circle reads to minutes, and the reversing of the telescope is done directly by hand.

Meridian Mark.—The meridian mark, placed thirty-five years ago, which also serves for testing collimation in the daytime, is a 3 in. iron bar set in cement, and shows well above the skyline of the Tinakori Range to the north.

Chronograph.—The chronograph is of the Morse pattern and

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records on a tape. It is provided with two styles, side by side. The one records, embossing by make-circuit, the second-beats of the sidereal clock, while the other similarly records the signals by the transit-key, also the clock or arbitrary signals received (from Doubtless Bay) when making a comparison of the clocks for the determination of the difference of longitude. The transit and arbitrary signals on the tape are readily interpolated and expressed in time from the embossed dots or records indicating the seconds of the local sidereal clock.

Electric Apparatus.—Mr. J. K. Logan, Superintendent of Government Telegraphs, has furnished the following description and diagram of the arrangement especially installed at the Wellington Observatory for the differential longitude work with Doubtless Bay, as this was the first time that an automatic exchange of clock-signals had been made with the observatory. (The Wellington clock made contact (circuit) every second, while the chronometer at Doubtless Bay was arranged to “break” circuit.)

Two British Post Office polarised relays, the coils of each of which were joined in parallel, giving a resistance of 150 ohms. for each relay, were connected in multiple through three Leclanché cells to the terminals of the clock. 120 Leclanché cells, with the copper earthed, were joined to one of the local terminals of one of these relays, and, by adjustment, the tongue of this relay was made to bear against the stop connected to that terminal. The terminal connected with the tongue was then joined to the copper terminal of a Siemens relay of 500 ohms resistance. The line was connected to the Z (zinc) terminal of the Siemens relay through a switch arranged to disconnect it from the time-recording instruments and connect it to the speaking (Morse) instruments when required. The local terminals of the second British Post Office polar relay were connected through eight Leclanché cells to the terminals of the magnet-coils of the back style of the chronograph. The local terminals of the Siemens relay were conducted through eight Leclanché cells to the terminals of the magnet-coils of the front style of the chronograph. At every make of the clock the tongue of the Post Office relay that was connected to the back style of coils made contact and caused the style to emboss, thus registering every clock-beat. The other Post Office relay at every beat of the clock broke contact at its tongue; the line-current was thus broken and a signal recorded at Doubtless Bay. As this line-current passed through the Siemens relay at the observatory, and while passing held the tongue of that relay open against the bias given to it, at every break of the current the tongue, by reason of that bias, moved across and closed the local circuit, thereby recording marks on the front style. When signals were to be received

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from Doubtless Bay, the observatory battery of 120 cells was cut off, battery being applied to the sending end. At every break of the current at Doubtless Bay the Siemens relay tongue moved to close the circuit and the breaks were recorded by the front style, marks being made at the same time by the observatory clock with the other style. Arbitraries were received from Doubtless Bay in the same way. When arbitraries were being sent from the observatory it was arranged, by means of a two-way switch, to cut off the clock from one Post Office relay—i.e., the one the tongue of which was in the main-line circuit. This relay was then worked by the closing of a key, the line current being broken at the tongue of the relay in the same way as when the clock was operating the relay. This break was recorded at Doubtless Bay and also on the front style at Wellington, by the movement of the tongue of the Siemens relay, at the same time the clock was recording on the back style. It is desired to indicate that for received signals the tongue of the Siemens relay had to move to close the circuit, and the front style then to move to mark the tape. The signals of the observatory clock had to cause the Post Office relay tongue to move to close the circuit, and the back style then to move to mark the tape. The record of the outgoing signals either from the clock or by arbitraries was got after the clock or the key had caused the Post Office polar relay tongue to break the circuit, which in turn caused the Siemens relay tongue to move to close the circuit of the front style, and which style had then to move to impress the tape. The line was 704 miles long, Wellington to Doubtless Bay, and was of 11 ½ copper throughout, 200 lb. to the mile.”

No repeaters were used.

As it was impracticable for the observers to exchange stations it was decided to observe for personal equation at Wellington, and this was done.

I took train to New Plymouth, thence by steamer to One-hunga, and Auckland, and thence by the “Clansman”—the connecting-link between the world and Ultima Thule—to Doubtless Bay. Here, close to the cable-station, the pier and observatory were built. The foundation—a cubic yard—of the brick pier (22 in. by 27 in.) was in compact sand, and hence very satisfactory. The telegraph-line was led directly into the observatory and there connected with the switchboard. It may be remarked that another pier was built in another building where gravity observations were made with the Mendenhall half-seconds pendulum; magnetic observations were also taken.

A triangulation has been carried over the North Island by the Survey Department of New Zealand, and by instructions

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of the Surveyor-General, Mr. J. W. A. Marchant, the District Surveyor, Mr. V. J. Blake, made a connection of the triangulation from Station 20 on the west side of the entrance to Mangonui Harbour to the observatory, and by that means obtained the position of the observatory in terms of the New Zealand initial station and meridian. At Doubtless Bay the superintendent of the cable-station, Mr. C. L. Hertslet, rendered invaluable services both in the cable and land-line exchange of signals. His thorough knowledge of the circuits quickly overcame any difficulties or mishaps that arose.

Six independent determinations of difference of longitude between Doubtless Bay and Norfolk were obtained, and the same number between Doubtless Bay and Wellington.

We will now deduce the longitude of Doubtless Bay, giving the various transpacific arcs determined in 1903.

Longitude.
Stations. Difference of Longitude Probable Error. Time. Probable Error. Arc. Probable Error.
H. M. S. S. H. M. S. S. " " "
Vancouver 8 12 28.368 W. ±0.050 123 7 5.520 ±0.75
Vancouver-Fanning 2 25 5.406 ±0.021
Fanning 10 37 33.774 W. ±0.054 159 23 26.610 ±0.81
Fanning-Suva 1 28 43 837 ±0.008
Suva 11 53 42.389 E. ±0.055 178 25 35.835 ±0.82
Suva-Norfolk 0 42 1.243 ±0.011
Norfolk 11 11 41.146 ±0.055 167 55 17.190 ±0.82
Norfolk-Doubtless Bay 0 22 15.000 ±0.021
Doubtless Bay 11 33 56.146 ±0.060 173 29 2.190 ±0.90
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The geographic position of Station 20 was furnished by Mr. Marchant, Surveyor-General.

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We have then—
Longitude, Station 20 173 31 37.1
Station 20 to Station A (by Mr. Blake) 0 2 24.1
Station A 173 29 13.0
Station A to observatory (by Mr. Blake) 0 0 3.66
Observatory 173 29 9.34

or, 11h. 33 m. 56.623 s. The Canadian value is 11 h. 33 m. 56.146 s. Difference, 0.477 s., or 7.15”, or 595 ft. for the latitude of Doubtless Bay.

It may be remarked that the position of Station 20 is dependent upon the initial station, Mount Cook, at Wellington, through a chain of triangles about seven hundred miles long. From the roughness of the country it was expedient to carry on a network of triangulation for land survey and settlement purposes, and the refinements of a primary triangulation were not aimed at. In the closing for Wellington it will be found that the difference is 0.038 s., or 0.57”, and of the same sign as the above, making thereby the difference between the telegraphic determination, Wellington-Doubtless Bay, and the one obtained by triangulation 0.439 s., equivalent to 549 ft. at the latitude of the latter.

In the following table is given the deduction of each difference of longitude, Doubtless Bay-Wellington. Column 1 gives the date; column 2 the direction in which the arbitrary signals were sent; columns 3 and 4 the respective sidereal times at the two stations of the mean of the times of the signals sent; column 5 is the comparison of the scalings of the same signal—that is, each signal is measured on the two chronographs and expressed in time to the hundredth of a second of the respective clock; there would be at least thirty such signals, and each signal would show the “difference” between the two clocks at that instant, plus or minus the “transmission-time,” according to the direction sent, westward or eastward; the “difference” given in column 5 is the mean of the thirty individual differences. If the two clocks had no rate, or the same rate, then the difference between the comparison of signals sent in the two directions would give twice the transmission-time; when, however, the clocks had different rates, we must introduce the correction

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“relative rate” of column 6 to one of the comparisons (the later one is taken to correspond to the sign of the rate) in order to make it comparable with the other. Column 7 has been explained. The difficulties encountered with rate have already been adverted to. They become very apparent when deducing the transmission-time, especially when that quantity is very small, as in the present instance. When we are dealing with transmission-time of a third of a second, as is the case between Fanning and Bamfield, one or two hundredths of a second variation affects but little the various transmission-times; but it is very different when the transmission-time falls near the limit of certainty of the rate. The relative rate of the 18th December was deduced as the others from the best available data, and the result shows a negative value of a hundredth of a second for transmission-time. This, however, does not affect the difference of longitude. Columns 8 and 9 give the deduced clock or chronometer corrections respectively at the two stations for the same instant, the mean of the times of the two exchanges. With the three data then—the difference between the two clocks at an absolute instant, and the respective clock - corrections for that instant—we obtain column 10, the difference of longitude, each with its respective probable error deduced from the probable error of the respective clock-corrections.

We have then the following values:— H. m. s s.
Dec. 6—Difference of longitude 0 5 9.231 0.027
" 7 " 0 5 9.200 0.018
" 11 " 0 5 9.225 0.032
" 12 " 0 5 9.156 0.021
" 17 " 0 5 9.210 0.032
" 18 " 0 5 9.199 0.020
Weighted mean 0 5 9.198 0.007
Personal equation 0 0 0.257 0.045
Difference of longitude 0 5 8.941 0.045
Doubtless Bay longitude 11 33 56.146 0.060
Wellington longitude 11 39 5.087 0.075
Sidereal Time Chronometer Correction
Date. Direction. Wellington. Doubtless Bay. Difference. Relative Rate. Transmission Time. Wellington. Doubtless Bay. Difference of Longitude.
1903. H. m. H. m. H. m. s. S. S. S. M. s. M. s.
Dec. 6 Wellington to Doubtless Bay 3 20.67 3 15.96 0 4 42.655 +0.347 0.019
Doubtless Bay to Wellington 2 44.47 2 39.74 0 4 43.039
Mean 3 2.57 2 57.85 0 4 42.847 -5.189 -0 31.573 5 9.231
" 7 Wellington to Doubtless Bay 3 27.24 3 22.77 +0 4 28.059 +0.096 0.018
Doubtless Bay to Wellington 3 16.17 3 11.70 0 4 28.191
Mean 3 21.70 3 17.23 0 4 28.125 -3.180 -0 44.255 5 9.200
" 11 Wellington to Doubtless Bay 3 31.66 3 28.2 0 3 38.167 +0.076 0.026
Doubtless Bay to Wellington 3 23.39 3 19.76 0 3 38.296
Mean 3 27.53 3 23.89 0 3 38.232 +1.119 -1 29.874 5 9.225
" 12 Wellington to Doubtless Bay 3 41.72 3 38.32 0 3 24.142
Doubtless Bay Wellington 4 1.58 3 58.18 0 3 24.018 +0.171 0.024
Mean 3 51.65 3 48.25 0 3 24.080 +3.530 -1 41.546 5 9.156
" 17 Wellington to Doubtless Bay 4 5.70 4 3.27 0 2 25.720
Doubtless Bay to Wellington 4 26.16 4 23.73 0 2 25.659 +0.144 0.041
Mean 4 15.93 4 13.50 0 2 25.690 +3.702 -2 39.818 5 9.210
" 18 Wellington to Doubtless Bay 3 52.85 3 50.61 0 2 14.365 +0.083 -0.010
Doubtless Bay to Wellington 3 42.20 3 39.95 0 2 14.428
Mean 3 47.53 3 45.28 0 2 14.397 +4.582 -2 50.220 5 9.199
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Based on the present value of Sydney, 10 h. 4 m. 49.54 s., and the 1883 value, Sydney-Wellington, 1 h. 34 m. 15.77 s., gives the longitude of Wellington (N.Z.I. report, 1902, p. 442) 11 h. 39 m. 5.31 s. This requires the correction of -0.185 s., the same as applied to Sydney for the adopted value of Madras, dependent upon the work of Professor Albrecht and Major Burrard. We have then for the value of Wellington via Madras-Sydney, 11 h. 39 m. 5.125 s.

The Canadian value is 11 h. 39 in. 5.087 s. Difference, 0.038 s., or 0.57″, or 43 ft.

We have at Wellington, then, another closing of the girdle of the world, as we had the first at Sydney.

The weakest link, yet good, in the longitude of Wellington is the personal equation of the two observers; all the other links are very strong. The observations therefor were made with the same (Wellington) instrument, as it was impracticable to build another pier and mount my Cooke transit there

A final word in closing. Gratifying as the above closing-error is, it is questionable whether one would be justified at the present time, with our improved methods, in making a circuit of the globe in longitude, with the number of stations necessary therefor, in expecting à priori a closing-error of less than one-tenth of a second.

The task that Canada set out to perform, to bind Australia, New Zealand, and the Pacific islands to Canada by the “all-red line,” thereby completing the first astronomic girdle of the world, has been successfully accomplished.