The method adopted for comparing chronometers by means of these instruments was as follows:—Everything being ready for the exchange of signals, the observer at one station seated himself, where he could see the face of the chronometer, with his hand on the cable key. At ten seconds before the beginning of a minute as shown by the second hand, he pressed his key several times in quick succession, thus sending a series of impulses through the line, which appeared at the other end as a rapid movement of the light to and fro. This was a warning signal, and the observer at the second station with his eye on the light, tapped his chronograph key in the same way making a series of marks, which indicated the beginning of the comparison. The first observer exactly at the sixtieth second by his chronometer pressed his key quickly and firmly and repeated this operation at every fifth second for one minute. The second observer tapped his key promptly as soon as he saw the light move, thus registering the time on his chronograph. The minute at which the first signal was sent, was then telegraphed, and repeated back, to insure against error, and the operation was repeated until sixty-five signals had been sent from one station and received at the other. Then the second observer sent the same number of signals to the first in precisely the same manner, thus giving sixty-five comparisons of the chronometers in each direction. The results derived from this method are affected by errors from two causes. One is the personal error of the observers in sending and receiving signals and the other the time consumed by the electric impulse in traveling over the line and through the instruments. If the same strength of battery is used at each station, and the resistance of the instruments is the same, the errors arising from this latter source will be eliminated by the double exchange. The observer sending the signals kept his eye on the chronometer and counted the second beats by both eye and ear, moving the hand which he had on the key slightly in unison with the beats, and could thus be sure of pressing the key at the proper time within a very small fraction of a second. At the other end of the line, considerable time is lost after the actual movement of the light before the observer can press his chronograph key, and the principal error affecting the result is the difference of this time in the two observers, which was found to be very small.
As I have said, the cable was first used in the measurement between Kingston and Aspinwall, Lieut. Commander Green occupying the former station, and Mr. Rock the latter. After the successful completion of this link, measurements were made from Santiago de Cuba to Kingston, and to Havana. It was the intention to measure from this last point to Key West, but about this time yellow fever broke out there and the expedition was ordered by the Secretary of the Navy to return. The Fortune arrived at Washington in April, 1875, and the time until November was spent in working up the winter's observations. Speaking in a general way this work is as follows:—From observations extending over many years, the exact positions in the heavens of a large number of fixed stars have been found, so that their times of passing any meridian can be computed with great accuracy. The transit instrument is furnished with an eye-piece containing a number of parallel lines usually made of spider silk. These are placed in the focus of the instrument, and it is set in position, so that the middle line of the group is in the plane of the meridian. The observer provides himself with a list of desirable stars, and setting his instrument on those he may choose, records the time at which they pass each of the spider lines, by tapping his chronograph key. If there were no instrumental errors to be discovered and allowed for, if the star's place were known absolutely, and the observer had no personal equation, then it would be only necessary in order to find the error of the clock, to observe one star upon the middle line of the reticle. The difference of the clock time of transit and the real time as already known, would be the clock error and no further trouble would be required. But as none of these conditions are fulfilled, it is necessary to multiply observations in order to eliminate accidental errors, and to obtain instrumental corrections which may be applied so as to get the most probable result. Accidental errors of eyesight and perception are nearly eliminated by taking the star's transit over several lines instead of one and using the mean. Some of the instrumental errors are from the following causes. If the pivots which support the telescope are unequal in size the axis of the tube will be thrown to one side or the other of the meridian, and the star will be observed either before or after it crosses. The weight of all transit instruments causes a flexure of the horizontal axis and this effect is at its maximum in those of the prismatic pattern. The spider lines must be adjusted so that the middle one is exactly in the axis of the tube, or as this can seldom be done the resulting error, called the collimation, must be found. The horizontal axis of the instrument must be as nearly level as possible, and the error in this respect must be found by frequent applications of a delicate spirit level. Finally the instrument must be directed as nearly as possible to the north and south points of the horizon, and a correction must be made for any error in this respect. The result of each of these errors is to cause the star's transit to be recorded too early or too late, and to get the true result they must all be found and applied with their proper signs. The inequality of pivots and the flexure correction are found by delicate measurement and observations, when the instrument is first used, and are recorded as constants to be applied in all subsequent work. The level tubes are graduated and the value of their divisions obtained in angular measure. The collimation error is found by observing stars near the zenith in one position of the instrument and then reversing and observing others, or by taking the transit of a slow moving star over a portion of the spider lines then reversing and observing the same intervals in the opposite order. The error of azimuth, or deviation from the north and south line, is found by comparing the observations of stars whose zenith distances differ considerably. These corrections all being found and applied to the observation of each star, the result is the correct time of transit as shown by the chronometer, and the difference between that time and the true time, is the error of the chronometer. A mean of the observations of several stars on the same night, gives a very accurate value for this clock error, and by comparing the results of several nights' work, the rate is found. By applying the rate to the clock error it is reduced to any required epoch, as for instance, the mean time of the exchange of time signals, and the difference of longitude is easily found. As may be imagined the computation and application of all these errors, exercising the greatest care to insure accuracy is a long and tedious process. The operations described give a very close result, but in order to arrive at the greatest accuracy obtainable the computations are made again by the method of least squares.
In the Autumn of 1875, the expedition again took the field, this time in the side wheel steamer Gettysburg, which was much better adapted to the work than the Fortune. The first link measured was between Key West and Havana. Key West had already been telegraphically determined by the Coast Survey, and now afforded a base for the system of measurements completed and for those to follow. The next measurement was between Kingston and St. Thomas. Then from the latter place to Antigua and to Port Spain, Trinidad. From Port Spain, measurements were made to Barbadoes and Martinique. The position at St. Thomas was then re-occupied, and measurements made thence to San Juan, Porto Rico, and to Santa Cruz. This ended the work in the West Indies, differences of longitude having been measured between nearly all the important points connected by telegraph. The Latitude of all the stations, was also determined by the zenith telescope method, and the position of the stations was referred either to the observation spot previously used, when that could be identified, or to some prominent landmark.
Between St. Thomas and Santa Cruz, the measurement was made twice, the observers exchanging stations at the completion of the first series of observations. This was to eliminate the effect of their personal errors, and to obtain a value of these, which might be applied to the other measurements. It has long been known that different people perceive the same phenomenon at different times, varying with different individuals, but reasonably constant with the same individual. In the particular case of observing the transit of a star, most people will record it on a chronograph from one to three tenths of a second after it happens. In the method of observing by eye and ear the error is generally much greater. The whole question of personal equation, however, is a mixed one and I will not attempt to discuss it, but will only give some of the results obtained in this particular work. In longitude measurements the error from this cause is half the difference of the personal equation of the two observers. If this difference remained constant, then it would be easy to find it once for all, and apply it to all measurements made by the same observers. In the West India work, it was assumed that it did remain constant, and half the difference between the two measurements made from St. Thomas to Santa Cruz, was applied to all the other links. The correction was quite small, being only 0s.025. In subsequent work by the same and other observers it was deemed wiser not to apply any corrections at all, rather than one that was probably not exact, and might be much in error. To show the fluctuations to which this elusive quantity is subject, I will cite the results of some observations made to determine it, by observers engaged in this same work at a subsequent period. In April and May, 1883, at Galveston, Texas, two observers D. and N. having just completed a telegraphic measurement between that place and Vera Cruz, Mexico, made some observations for the determination of their relative personal equation, by observing transits of alternate stars under the same conditions as near as possible. Both used the same instruments, transit, chronometer and chronograph. On April 30, two sets of observations were made, showing the difference of the equations to be 0s.26. On May 1, one set gave 0s.32, and another 0s.29. On May 2, only one set was made giving 0s.36, a variation of 0s.07 in two days. In June 1884, one year later, another series of observations of the same character was made at the Naval Observatory in Washington, and on the same nights the personal equation machine invented by Prof. Eastman, was used as a comparison. This is an instrument in which an artificial star is made to record its own transit over the wires of a reticle, while the observer records the same with a chronograph key. The difference is manifestly the personal error of the observer. This gives the absolute equation of the observers, and their difference is the relative equation, and should accord with that found by the method of alternate stars. Some of the results were as follows:—On June 4, the difference by machine of their personal errors was 0s.16 and by star observations 0s.24, on the 15th of June the machine gave 0s.10 and the stars 0s.24, on the 16th, machine 0s.14, stars, 0s.13, a very close agreement, on the 17th, machine gave 0s.07 and stars 0s.18. The observer N. combined with another, C., who had not had as much experience in observing, gave still more discordant results. On June 20, the machine gave as their relative equation, 0s.08, while star observations gave 0s.27, on June 23, machine 0s.13, stars 0s.51, and on June 28, machine, 0s.20, stars 0s.35. In the case of the first two observers a mean of the determinations amounting to about 0s.20 might have been applied to the measurements made by them, but as these were made under all conditions of climate, in latitudes varying from 30° N. to 36° S. and in different states of health and bodily comfort, it was concluded not to introduce any correction at all rather than one that might be considerably in error. In all of the work it has been the custom as far as possible to place the observers alternately east and west of each other, so that the result of personal error in one measurement is neutralized to a greater or less extent in the next. Of course the method of exchanging stations and making two measurements of each meridian distance would afford the best solution of this problem, but except in certain favorable conditions, this is precluded by considerations of time and expense. In the measurement between Galveston and Vera Cruz mentioned above, it had been the intention to exchange stations, but by the time the first measurement was finished the season was rather far advanced, there was danger of yellow fever in Vera Cruz and an observer going there at that time, if he escaped disease would have had the certainty of being quarantined from entering the United States for three weeks or a month after leaving Mexico.
Upon the completion of the West Indian work, and the publication in 1877, of the results, it was determined by the Bureau of Navigation to send an Expedition for the same purpose to the east coast of South America. Cables were in use extending from Para in northern Brazil to Buenos Ayres in the Argentine Republic. A cable had at one time connected this system with the West Indies, through British Guiana and Trinidad, but one of the links was broken and there was no prospect of its repair, otherwise the Station established at Trinidad in 1874 might have been taken as the starting point. There was direct communication however between England and Brazil, by the way of Portugal, and the Madeira and Cape de Verde Islands. Lisbon seemed to afford the most convenient place to start from, but its longitude had never been determined by telegraph and it was decided to request the French Bureau of Longitudes to coöperate by making this measurement from Paris. This request was readily granted, but for some reason the agreement was not kept. For the use of the Expedition the old fashioned sailing ship Guard was furnished and Lieut. Com. Green was given command. Mr. Rock being otherwise employed his place was taken by Lieut. Com.(now Commander) C. H. Davis, U. S. N. The instruments having been placed in good order, and new supplies furnished where necessary, the expedition sailed from New York for Lisbon in the latter part of October, 1877. The Guard was a slow sailer, the weather was rough and the wind generally ahead, consequently a month was consumed in making the passage. It was the intention to make the first measurement between Lisbon and Funchal, Madeira. Lieut. Com. Davis with party and instruments occupied the latter station, proceeding by mail steamer at the first opportunity. The cable from England does not land directly at Lisbon, but at a small town called Carcavellos on the coast about twelve miles from the city. As it was not practicable to connect the land line from Lisbon direct to the cable, it was necessary in making the exchange of signals to adopt another method, or rather combination of methods. An officer of the ship was sent to Carcavellos, furnished with a chronometer and chronograph. When the time came for exchanging signals, he first compared his chronometer with that at Lisbon, by the automatic method, in use on land lines, then with the Funchal chronometer over the cable using the mirror galvanometer. Finally a second automatic comparison was made with Lisbon. From the data furnished by these comparisons it was an easy matter to compute the difference between the chronometers at Lisbon and Funchal. The Lisbon party had been received with great courtesy by the director of the Royal Observatory, Capt. Oom of the Portuguese Navy, and had been given the use of a small detached observatory near the main building. The party at Funchal selected a site on the ramparts of an old fort, which afforded a clear view and was near the landing place of the cable. Here occurred an accident to the transit instrument, which fortunately was easily remedied. Near the beginning of the observations on the first night the wind, which was blowing almost a gale, lifted a part of the roof off the observatory, and dropped one section of it inside. The transit was knocked off the pier, and was at first thought to be much injured. Fortunately the precaution had been taken to bring along a couple of spare instruments, borrowed from the Transit of Venus Commission for use in case of such an accident. The Funchal party was provided with one of these, which was set up for use by the next night, and the injured one was sent to Lisbon for repairs. The injury proved to be less than supposed and the repairing was an easy matter. Upon the completion of this measurement the Lisbon party proceeded to St. Vincent one of the Cape de Verde Islands. This is a barren and desolate spot of volcanic formation, but being on the route of steamers from Europe to Africa and South America is of much importance as a coaling station. Measurements were made from this point to Funchal and to Pernambuco in Brazil, and the Guard then sailed for Rio Janeiro. Upon arriving at that point after a long passage, it was found that the cable between Rio and Pernambuco was broken, and there being no immediate prospect of its being repaired, the Pernambuco party was ordered by mail steamer to Rio, and thence to Montevideo. A measurement was made between Rio and Montevideo and then between the latter place and Buenos Ayres, Lieut. Com. Green occupying the Montevideo station for that purpose. The position of the observatory at Buenos Ayres was referred to that occupied by Dr. B. A. Gould, Director of the Argentine National Observatory, in a similar measurement a short time before between that place and Cordova.
Both parties now returned to Rio, only to find that the cable was still broken. In order to be ready for work as soon as it should be repaired, Lieut. Com. Green proceeded to Bahia with the ship and established a station there, Lieut. Com. Davis with his party remaining in Rio. After waiting a month, and there still seeming to be no prospect of the repair of the cable, the expedition finally sailed for home, arriving at Norfolk, Va., after a pleasant and uneventful voyage of forty-five days. Repairs to the cable were not completed until several months afterward. In May of the next year, the party was again sent out, to complete the measurement on the Brazilian Coast, and also to measure from Greenwich to Lisbon, the French Bureau of Longitudes having failed to carry out its promise to measure from Paris. There being no ship available for the purpose the traveling was done by mail steamer. Upon arrival in England, an interview was had with the Astronomer Royal, who readily agreed to assist in the work. Lieut. Com. Green accordingly established his observatory at the landing place of the cable at Porthcurnow in Cornwall, and Lieut. Com. Davis proceeded to Lisbon and occupied the station used there the year before. Owing to the foggy and rainy weather prevalent in England at that season, it was found impossible to make any astronomical observations at the Porthcurnow observatory. The work was therefore done in this way:—Observations were made at Greenwich and at Lisbon, and Porthcurnow and Carcavellos were used as transmitting stations. The chronometer at Porthcurnow was compared automatically with the clock at Greenwich, and by cable with the chronometer at Carcavellos. The latter was compared automatically with that at Lisbon, before and after the cable exchange. At this time there were made at Carcavellos, some experiments with a view to making the receipt of the time signals over the cable automatic, thus doing away with the personal equation of the receiver. The instrument in use for the regular business of the cable was what is known as the siphon recorder, also the invention of Sir Wm. Thompson. In this a small coil of fine wire is suspended by a fibre of silk, between the poles of a powerful permanent magnet. The currents from the cable pass through this coil and the action is to deflect it to the right or left, just as the mirror is deflected in the instrument already described. Attached to this coil is a siphon made of a capillary glass tube. One end of the siphon dips into a reservoir of aniline ink, and the other hangs immediately over the centre of a fillet of paper, which is unwound by clock-work. If the siphon touched the paper, the feeble currents sent through the cable would be powerless to move it, on account of the friction, and in order to produce a mark some means must be found of forcing the ink through the capillary tube. This is accomplished by electrifying the ink positively and the paper negatively, by means of a small inductive machine, driven by an electric motor. The effort of the two electricities to unite, forces the ink through the tube and it appears on the paper as a succession of small dots. When the paper is in motion and the coil at rest, a straight line is formed along the middle of the fillet by these dots, but as soon as a current is sent through the coil the siphon moves to the right or left making an offset to this line. These offsets on one side or the other are used as the dots and dashes of the Morse alphabet. A time signal sent over the cable while this instrument was in circuit, appeared as a single offset on the paper, and it was only necessary to graduate the paper into seconds spaces by the local chronometer, in order to have the automatic record required. The ordinary chronometer circuit could not be put through the coil directly, as it would then charge the cable and interfere with the signals, and besides, the current, unless by the introduction of a high resistance it was reduced in strength, would infallibly give such a violent motion to the coil as to break the siphon, if it did no other damage. The result was obtained in this way; an ordinary telegraph relay was put in the chronometer circuit and the armature of course moved with the beats. To this armature was fastened one end of a fine thread. The other end was attached to a slender piece of elastic brass which was fixed at one end to the framework supporting the paper, in such a way that the other end touched the metallic vessel holding the ink, except when the thread was drawn tight enough to pull it away. This the armature of the relay did while the circuit through the chronometer was complete, but as soon as it was broken at the beginning of a second, the tension of the thread was relaxed and the brass sprung back against the ink well, allowing the positive and negative electricities to unite independently of the siphon. The ink then ceased to flow, until the spring was drawn away, thus leaving a small blank space in the line of dots and forming a very good chronographic record. This was liable to a small error due to the length of time that elapsed between the release of the spring by the armature and its impact on the ink well. Had there been time for more extensive experiment this difficulty might have been overcome. Or if the same method had been adopted at both stations, the result would have been affected by only the difference between the times of movement of the brass spring which would have been minute. Lack of time for experiment, and the fact that the observers were averse to introducing untested methods into a chain of measurements most of the links of which were already completed, prevented any use being made of this achievement. The measurement between Greenwich and Lisbon being satisfactorily completed, Lieut. Com. Green by order of the Navy Department returned to the United States, and the links between Rio and Pernambuco and between the latter place and Para, were measured by Lieut. Com. Davis and the writer, completing the work of the expedition, after which the party returned to Washington.
The computation of this work, showed the somewhat surprising fact that the heretofore accepted position in longitude of Lisbon, differed from the true one by about two miles. The longitude of Rio Janeiro had always been more or less in doubt, various determinations had differed by as much as nine miles, but the position finally decided upon by the best authorities agreed very closely with that obtained by telegraph.
The next expedition was sent out by the Bureau of Navigation to China, Japan and the East Indies, Lieut. Com. Green being still in charge. The officers composing the party sailed from San Francisco by mail steamer in April, 1881, for Yokohama, where they joined the U. S. Steamer Palos. From Hong Kong north to Vladivostok in Eastern Siberia the cables were owned by a Danish company. From Hong Kong to the south and west they were the property of English companies. Beginning at Vladivostok observations were made at all stations on the Asiatic coast except Penang, as far as Madras, India. It was intended to try and make some use of the automatic method of receiving time signals, on this work, but on arriving in Japan it was found that the recording instrument used by the Danish company was entirely different from that used by the English lines. It consisted of a series of electro-magnets acting on a single armature, which carried a siphon made of silver. The signals consisted of long and short movements, to one side of the middle line, instead of equal deflections on both sides as in the Thompson recorder. An attempt was made to convert this instrument into a relay, by causing the siphon to make and break a circuit, but it was not successful. The movements of the siphon were not regular enough, and the contact was not firm. Consequently the mirror method of exchanging signals was still adhered to.
The longitude of the position occupied in Vladivostok, had been determined telegraphically from Pulkova, by the Russians, using the land lines across Siberia. The English had also determined the position at Madras, using the cables through the Mediterranean and Red Seas. The work of the United States Expedition joined these two positions, completing a chain of measurements extending over many thousand miles, made by observers of different nationalities in various climates. It was to be expected that considerable discrepancy would be found in the final result, but taking the longitude of Vladivostok as brought from Madras, and comparing it with that determined by the Russians, the difference was only 0s.39. Taking everything into consideration, this result was gratifyingly close. Upon the conclusion of this series of determinations, the connection of Lieut. Commander Green with the work was severed, he receiving his promotion to the rank of Commander.
The next work was under the charge of Lieut. Com. Davis, and consisted in the determination in 1883-84, of positions in Mexico, Central America and the west coast of South America. Cables had just been completed, extending from Galveston, Texas, to Vera Cruz, thence across Mexico to the Pacific and down that coast to Lima, Peru, where connection was made with another system extending to Valparaiso. Galveston was a point determined by the Coast Survey, and the measurement thence to Vera Cruz was the first one made. It was completed in May '83, and in the Autumn of the same year the party proceeded to the South American coast, and stations were established and observations made at various points from Valparaiso to Panama, and at one point, La Libertad, in Central America. It was at first the intention to extend the series across the Isthmus of Tehuantepec and connect with Vera Cruz, but lack of time prevented this, and as the station at Panama determined nearly ten years before, afforded a convenient starting point, the idea was abandoned. From Valparaiso, a measurement was made with the coöperation of Dr. Gould to his observatory at Cordova, using the line across the Andes, and exchanging signals automatically. These measurements constituted the final links in a long chain, extending from the prime meridian Greenwich across the Atlantic to the United States, thence via the West Indies to Panama, down the west coast of South America to Valparaiso, across the Andes to Cordova and Buenos Ayres, up the east coast to Pernambuco, across the Atlantic to Lisbon, and thence to Greenwich, altogether a distance of eighteen to twenty thousand miles. The two longitudes of Cordova, as brought from Greenwich by the two routes, differed from each other by only 0s.048, a result which speaks well for the accuracy of the methods employed. When preparations were being made for this expedition, it was determined to accomplish if possible something in the way of getting rid of the personal equation in exchanging signals. An idea which had been suggested by work done by Major Campbell, R. E. in the measurement between Bombay and Aden, seemed to promise well. It was to be used with the siphon or other form of recorder. The ordinary double current cable key with two levers, was arranged with an additional lever in such a manner that while in ordinary use in the telegraph office, it could also be put in circuit with the chronometer and chronograph in the observatory, and a signal sent through the cable would have its time of sending registered on the chronograph. Ordinarily in speaking over a cable line, connection is made in such a way that the current sent does not pass through the recorder at the sending station, as a violent movement of the siphon would result. By means of a shunt, however, it is possible to control this movement somewhat. Suppose now, that the connections at each station are made in such a way, by means of this key and the shunt, that a signal sent from one, is registered on both recorders and on the sender's chronograph. The observers leaving their assistants to take care of the chronographs, go to the respective telegraph offices, and all being ready, the observer A taps his key. This sends an impulse through the cable, which appears on A's recorder, as a violent jump or kick of the siphon. On B's recorder it is registered as a deflection like the ordinary dot or dash, at the same instant is recorded on A's chronograph the time of sending. As soon as B sees the signal on his recorder, he taps his key also registering the signals on both recorders and on his chronograph. A, seeing B's signal again taps his key, and so on, as long as desired. The result is that each observer has a record on his siphon fillet of all signals sent and received, while the times of those he sent are recorded on his chronograph. By the use of the diagonal scale and the Rule of Three, he can without difficulty find the times of the signals received. The siphon recorders are well made, and the paper moves with great regularity. This system was used in the measurement between Galveston and Vera Cruz with great success. It was intended to employ the same method throughout the measurement on the west coast of America, but on arriving at Lima, it was found that the company owning the lines south of that point still used the mirror galvanometer, and it was of course necessary to return to the old method. The improved key was used however, which eliminated the error in sending signals.