Vol. II. No. 1.
THE NATIONAL GEOGRAPHIC MAGAZINE.
PUBLISHED BY THE
NATIONAL GEOGRAPHIC SOCIETY.
WASHINGTON, D. C.
Price 50 Cents.
CONTENTS.
On the Telegraphic Determinations of Longitude by the Bureau of
Navigation: Lieut. J. A. Norris, U. S. N.
Reports of the Vice-Presidents:
Geography of the Land: Herbert G. Ogden
Geography of the Air: A. W. Greely, Chief Signal Officer, U. S. A.
Annual Report of the Treasurer
Report of Auditing Committee
Annual Report of the Secretary
National Geographic Society:
Abstract of Minutes
Officers for 1890
Members of the Society
Published April, 1890.
PRESS OF TUTTLE, MOREHOUSE & TAYLOR, NEW HAVEN, CONN.
THE NATIONAL GEOGRAPHIC MAGAZINE.
Vol. II. 1890. No. 1.
ON THE TELEGRAPHIC DETERMINATIONS OF LONGITUDE BY THE BUREAU OF
NAVIGATION.
BY LIEUT. J. A. NORRIS, U. S. N.
The following definitions are given by Chauvenet in his Spherical and
Practical Astronomy.
"The longitude of a point on the earth's surface is the angle at the
Pole included between the meridian of that point and some assumed first
meridian. The difference of longitude between any two points is the
angle included between their meridians." To describe the practical
methods of obtaining this difference or angle, by means of the electric
telegraph both overland and submarine, and especially those employed by
the expeditions sent out by the Navy department, is the object of this
paper.
* * * * *
Before the invention of the telegraph various methods more or less
accurate in their results were employed, and are still in use where the
telegraph is not available. The one most used and giving the best
results was that in which a number of chronometers were transported
back and forth between two places the difference of whose longitudes
was required. "For," as the author quoted above says, "the
determination of an absolute longitude from the first meridian or of a
difference of longitude in general, resolves itself into the
determination of the difference of the time reckoned at the two
meridians at the same absolute instant." If a chronometer be regulated
to the time at any place _A_, and then transported to a second place
_B_, and the local time at _B_, be determined at any instant, and at
that instant the time at _A_, as shown by the chronometer is noted, the
difference of the times is at once known, and that is the difference of
longitude required. The principal objection to this plan is that the
best chronometers vary. If the variations were constant and regular,
and the chronometer always gained or lost a fixed amount for the same
interval of time, this objection would disappear. But the variation is
not constant, the rate of gain or loss, even in the best instruments,
changes from time to time from various causes. Some of these causes may
be discovered and allowed for in a measure, others are accidental and
unknown. Of the former class are variations due to changes of
temperature. At the Naval Observatory, chronometers are rated at
different temperatures, and the changes due thereto are noted, and
serve to a great extent as a guide in their use. But the transportation
of a chronometer, even when done with great care is liable to cause
sudden changes in its indications, and of course in carrying it long
distances, numerous shocks of greater or less violence are unavoidable.
Still, chronometric measurements, when well carried out with a number
of chronometers and skilled observers have been very successful. Among
notable expeditions of this sort was that undertaken in 1843, by Struve
between Pulkova and Altona, in which eighty-one chronometers were
employed and nine voyages made from Pulkova to Altona and eight the
other way. The results from thirteen of the chronometers were rejected
as being discordant, and the deduced longitude was made to depend on
the remaining 68. The result thus obtained differs from the latest
determination by 0^{s}.2.
The U. S. Coast Survey instituted chronometric expeditions between
Cambridge, Mass., and Liverpool, England, in the years 1849, '50, '51
and '55. The probable error of the results of six voyages, three in
each direction, in 1855 was 0^{s}.19, fifty chronometers being carried.
Among other methods of determining differences of time may be mentioned
the observation of certain celestial phenomena, which are visible at
the same absolute instant by observers in various parts of the globe,
such as the instant of the beginning or end of an eclipse of the moon,
the eclipses of Jupiter's satellites by the shadow of the planet, the
bursting of a meteor, and the appearance or disappearance of a shooting
star. The difficulty of identifying these last mentioned objects and
the impossibility of foretelling their occurrence prevents the extended
use of this method.
Terrestrial signals may be used and among these can be included those
sent by the electric telegraph. But when two stations are near together
a signal may be made at either or at an intermediate station, which can
be observed at both, the time may be noted at each of the stations and
the difference found directly. These signals may be made by flashes of
gunpowder, or the appearance and disappearance of a strong light, or a
pre-concerted movement of any object easily seen. The heliotrope
reflecting the image of the sun from one station to the other with an
arrangement for suddenly eclipsing it, is a useful and efficient
apparatus.
Various truly astronomical methods have been employed with good
results, of these may be mentioned moon-culminations, azimuths of the
moon, lunar distances, etc.
Coming now to the use of the electric telegraph for this purpose the
following is a rough outline of the methods employed. Suppose two
stations A and B connected by wire, and provided with clocks,
chronographs and transit instruments. A list of suitable fixed stars is
compiled and each observer furnished with a copy. The observer at A the
eastern station, selects a star from his list and sets his transit
instrument upon it. He is furnished with a key by which he can send
telegraphic signals over the line and also mark the time on his own
chronograph. The instant he observes the star crossing the spider line
which represents the meridian, he taps his key, thus registering the
time on his own chronograph and on that at station B and this operation
he repeats with as many stars as necessary. B has his instrument set
for the first star, and when it crosses his meridian, he taps his key
marking the time on his own chronograph and also on A's. Then,
disregarding instrumental and personal errors and the rate of the
clock, A has a record of the times at which the star passed both
meridians. The difference of these times is the difference of longitude
sought, except for an error due to the time occupied in the
transmission of the signal over the wire between the stations. B also
has a record of the same difference of time with the same error
affecting it in the opposite way. A mean of these two differences, will
be the true difference with the error of transmission eliminated. This
method has the advantage of not depending upon the computed position of
the star. The instrumental errors may be allowed for, as well as the
rate of the clocks, and the personal error may be eliminated by the
exchange of stations.
There are disadvantages inseparable from this method, however,
especially when the meridian distance is great. A star observed at the
first station, may be obscured by clouds at the time of its meridian
passage at the second. And the weather generally, at the two stations
may be cloudy, so that while stars can be observed at intervals, yet it
may be impossible to note the meridian passage of the same star at both
places on the same night. Then the telegraph lines are usually the
property of some commercial company and while their use for a short
time might be freely granted, yet a protracted occupation of them as
necessary when the meridians are distant from each other, would prove a
serious hindrance to their regular business.
The method at this time most generally employed, is to observe at each
station a number of stars entirely independently of the other. From
these stars are deduced the clock errors and rates upon the respective
local times. Then at some prearranged period, communication is opened
between the stations, and a comparison of the clocks made which shows
their exact difference at a given instant. By applying the error to the
time as shown by the clock at this instant, the exact local time at
each station is the result, and applying the difference between the
clocks as shown by the comparison, the required difference of longitude
is readily obtained.
These methods originated, as did the electric telegraph, in the United
States, and soon after Morse's invention came into practical use, they
were extensively employed by the Coast Survey, in accurately
determining points in every part of the country that could be reached,
no pains being spared to make the determinations as accurate as
possible. Upon the completion of the first successful Atlantic cable in
1866, an expedition was organized and placed in charge of Dr. B. A.
Gould, for the purpose of measuring the meridian distance between
Greenwich and the Naval Observatory at Washington. This was
successfully carried out in spite of numerous difficulties, and the
result proved that the determinations already made upon which the most
reliance was placed were decidedly in error. The result from the
chronometric expedition in 1855 previously referred to differing over a
second of time.
In constructing charts for use at sea, the accurate determination of
latitude and longitude is of the utmost importance. The navigator
starting on a voyage must know the exact position of his destination as
well as the location of dangers to be avoided. He must know the error
and rate of his chronometer when he sets out, but as the rate is not
constant he should have some means of re-rating it at any place where
he may stop. If the longitude of this place is well determined, the
operation of obtaining the error and rate is an easy one, and may save
his vessel from loss.
Surveys, of coasts or countries must have well established starting
points, and while the latitude of a place is comparatively easy to
determine, the longitude, except when the telegraphic method is used,
is attended with more or less uncertainty.
In 1873, Commodore R. H. Wyman, U. S. N. Hydrographer to the Bureau of
Navigation, organized by permission of the Navy Department, an
expedition for the telegraphic determination of longitude in the West
Indies and Central America. The submarine cables of the West India and
Panama Telegraph Co. had just been completed, extending from Key West
through Havana and Santiago de Cuba, south to Jamaica and Aspinwall,
and east through the Virgin and Windward Islands to the northeast coast
of South America, thus affording admirable facilities for the accurate
determination of many points. It had long been known that the
longitudes of various points in the West Indies and in Central and
South America, did not harmonize, there having been no systematic
attempt to determine them with relation to each other or to a common
base. Longitudes in the western part of the Caribbean Sea depended upon
the position of the Morro lighthouse at Havana, which had been
determined by occultations. Further to the eastward, positions depended
upon that of Fort Christian at St. Thomas. This in its turn depended
upon the observatory of Major Lang in the Island of Santa Cruz about
forty miles distant. This position depended upon numerous observations
of moon culminations and occultations. Martinique and Guadeloupe in the
Windward Islands had been surveyed by French officers who based their
positions upon longitudes derived from moon culminations. The absolute
determination of these starting points would of course fix all points
derived from them.
The U. S. Steamer Fortune was designated by the Navy Department for the
conveyance of the expedition, and Lieut. Commander (now Commander), F.
M. Green, U. S. N. was placed in charge. This officer had given great
attention to the subject, was a practiced observer, and exceptionally
well qualified for the position. The services of Mr. Miles Rock, a
skillful astronomer and computer who is now chief of the boundary
survey of Guatemala, were obtained as principal astronomical assistant.
The breaking out in the autumn of 1873, of the trouble with Spain and
Cuba, over the Virginius affair, delayed the expedition until the next
year, but in November 1874, a start was made from Washington, and after
a short stay in Kingston, Jamaica, Aspinwall was reached early in
December. Mr. Rock with one set of instruments proceeded immediately to
Panama, while Lieut. Commander Green remained in Aspinwall with the
other. The outfit for each party consisted of:--first, a portable
observatory. This was made of wood in sections, framework of ash,
covered with tongued and grooved pine boards. The sections were
connected when set up by iron knees and bolts. When packed it was not
difficult to transport, and it could be put up, or taken down in an
hour. When set up it was about eight feet square, with doors in all
sides, and a shed roof. The roof was made in three sections, the middle
one being hinged so that it could be raised for observing. These
observatories proved to be very strong and serviceable. They remained
in use for a number of years with occasional slight repairs, were
transported many thousand miles and set up in a great number of places
in Europe, Asia, North and South America. They were designed by Mr. J.
A. Rogers, and constructed at the Washington Navy Yard. Upon arriving
at a point where observations were to be made, after obtaining the
necessary permits from the local authorities, a suitable location for
the observatory was the first consideration. The essential requirements
were, a clear view of the heavens in the meridian, firm ground, a spot
secluded enough not to attract attention from inquisitive idlers, and
proximity to the telegraph office, or end of the telegraph line. Such a
spot being found and permission being obtained from the owner for its
use, an approximate meridian line was laid out by compass, and the
house set up with reference to it. Experience soon showed the
advisability of making certain additions to the observatory not
contemplated by the designer, but which added much to convenience and
comfort. A foundation was made, of timbers about six inches square,
mortised together at the ends which could be placed in position and
leveled before the observatory was set up, rendering this operation
much easier and giving greater stability. A floor was laid upon joists
supported by this foundation. Shelves were put up at various points,
affording resting places for tools and small instruments, while a table
in one corner, supported the chronometer, and offered a convenient
place for an assistant to record observations, etc.
The principal instrument used was the transit. Those furnished for the
use of the expedition were designed by Mr. J. A. Rogers, and
constructed under his supervision in the repair shop of the
Hydrographic office. The object glasses, made by the Clarks at
Cambridge, were of 2½ inches clear aperture with a focal length of
thirty inches. The instruments were of the prismatic or "broken" form
in which the eye-piece is at one end of the axis, and the light is
reflected from the object glass to the eye by a prism placed at the
junction of the telescope tube with the axis. The observer does not
have to change the position of his eye, no matter what the zenith
distance of the star may be. This renders observation much less
fatiguing and conduces to accuracy. The eye-piece was furnished with
the usual spider line reticle and also with a filar micrometer for the
measurement of zenith distances for latitude. A vertical finding circle
was on the eye-piece end of the axis, and the instrument was provided
also with a horizontal circle, fourteen inches in diameter, graduated
to ten seconds. Other necessary parts were the striding and zenith
telescope levels, and the illuminating lamps. The ends of the axis were
supported by Ys at the ends of a transverse arm which in its centre was
screwed to the top of a vertical axis supported in a socket surmounting
the tripod. This vertical axis was slightly conical in shape and
accurately fitted into its socket. A screw was so placed underneath,
that the axis, and with it the instrument, could be raised slightly,
when it was easily revolved horizontally into any desired position, a
reverse movement of the screw then lowered the axis into its seat, when
the instrument was held firmly by the friction. For supporting the
instrument there was used at first, a portable pier made in the shape
of the frustrum of a cone, of strong oak staves, firmly bound with iron
hoops, and when set up, filled with sand or earth. Subsequently a brick
pier was found to be more stable and the wooden ones were discarded.
Of equal importance with the transit was the Chronometer. The
expedition was supplied with four of these made by Negus of New York.
They were regulated to sidereal time, and provided with a break circuit
arrangement. This consists of a toothed wheel acting on a jewel pallet
attached to a light steel spring. In this spring is a platinum point,
which touches another platinum point, except when the spring is acted
upon by the toothed wheel. These points are connected respectively with
terminals on the outside of the chronometer, and are insulated from
each other except at their point of contact. The electric circuit is
complete through the chronometer except when the teeth of the wheel
acting on the jewel pallet separate the points. The circuit is opened
for about one-fortieth of a second and closed during the rest of the
time. One tooth in the wheel is omitted and the circuit remains
unbroken at that point which is the beginning of each minute. Each
chronometer is provided with a condenser to take up the extra current,
and avoid burning the contact points. These chronometers were most
excellent instruments, the rate was generally small and very regular,
and did not seem to be influenced in any way by the passage of the
current. They are still in use, and are as efficient as ever.
The expedition was at first provided with a substitute for the
chronograph in the shape of the old fashioned Morse telegraph register.
In this a steel point or stylet was pressed by the action of an
electro-magnet against a long fillet of paper, unwound by clock-work at
a rate more or less regular. This magnet was in circuit with the
chronometer and with a break circuit key in the observer's hand. As
long as the electric circuit was closed the stylet made a continuous
indented straight line on the paper; but as soon as it was broken,
either by the chronometer or the observer's key, the stylet flew back
and left the paper unmarked until the circuit was again closed. The
effect of the action of the chronometer was to graduate the fillet of
paper into a series of straight indentations, from one to two inches in
length, separated by unmarked spaces from 1/16 to 1/8 inch in length.
When the key was pressed an independent clear space was left on the
paper, and by the relation in distance between the beginning of this
space and the beginning of the second spaces immediately preceding and
following, the time of pressing the key was determined. The omission of
the break at the sixtieth second, made the mark of double length, and
hence the beginning of the minute was easily recognized. These
instruments served their purpose very well, but had several
disadvantages. The rate of movement of the paper was not regular; when
the clock-work was first wound up the motion was rapid and the second
spaces long, and as the spring ran down the marks became shorter and
shorter. Another drawback was the great length of the fillet; with
spaces only an inch in length, it required five feet of paper to record
a minute in time, and after a night's observation, there would be
several hundred feet to examine, measure and record, occupying the
greater part of the following day. By stopping the instrument between
the observations something was gained in this respect, but this tended
somewhat to confusion and error in keeping the record. They were only
used for one season's work, and in their stead were procured two
cylinder chronographs, made by Bond of Boston. These were fine
instruments, but somewhat too delicate to stand the necessary
transportation. In these instruments as in most other chronographs, a
cylinder about six inches in diameter is made to revolve by clock-work
once in a minute. An electro-magnet mounted on a carriage actuated by
the same clock-work moves alongside the cylinder, in a direction
parallel with its axis, at the rate of about an eighth of an inch in a
minute. The armature of the magnet carries attached to it a pen, the
point of which rests upon a sheet of the paper wrapped around the
cylinder. While the circuit through the coils of the magnet is
complete, the pen makes a continuous spiral line upon the paper, but
when the circuit is broken by the chronometer, or key, it flies to one
side making an offset, and immediately returns to its position, as soon
as the circuit is again closed. The result is to graduate the whole
surface of the paper into second spaces, from which the observations
can be read off with the greatest ease.
For supplying the electric current, there was used at first, a
modification of the Smee battery, but this proving very uncertain in
strength, a gravity battery was substituted, and afterwards a number of
LeClanché cells were procured.
Upon the first expedition, no telegraph instruments were carried, but
the use of such as were needed was easily obtained from the telegraph
companies. The line between Aspinwall and Panama was in good condition
and no trouble was experienced in exchanging the time signals by which
was effected the comparison of the chronometers. Wires were stretched
from the observatories in each place to the respective telegraph
offices, and for the exchange of signals were connected directly to the
ends of the line.
Everything being ready, the routine of the work was as follows:--The
transit being carefully leveled was placed in the meridian by
observation of zenith and circumpolar stars. From six to ten time
stars, and two or three circumpolars were then observed, the instrument
was reversed in the Ys and nearly the same number of stars observed in
the new position. At some time agreed upon, generally when the regular
work of the telegraph line was over for the day, the wires were
connected up and one of the operators came to the observatory to assist
in holding communication. By a simple arrangement of relays, in the
line and chronograph circuits the chronometer at one station was made
to register its second beats on the chronograph at the other, which was
all the time being graduated into second spaces by its own chronometer.
This was done for about five minutes and the times of beginning and
ending noted. Then the connections were reversed and both chronometers
allowed to beat for five minutes on the chronograph at the first
station.
This method of exchanging signals was only practicable on land lines or
very short cables. The ordinary relay used on a land line requires a
strong current to work it, and would not be affected in the least by
the delicate impulse sent over a long cable, consequently when the
expedition came to compare chronometers over the 600 miles of cable
between Aspinwall and Kingston, it was necessary to use another method.
At that time the instrument in general use on submarine cable lines was
what is known as Thompson's mirror galvanometer. It consists of a coil
of very fine insulated wire wound with great care on a spool or bobbin
of vulcanite, about three inches in diameter and 1½ inches thick. In a
hole in the centre of the spool is made to slide a small tube, so that
the end of the tube will be in the centre of the coil. In the end of
the tube is mounted a small mirror, swung in a vertical position on a
single upright fibre of silk. Horizontally across the back of this
mirror is secured a small permanent magnet, in length about the
diameter of the mirror or about one-eighth to one-quarter of an inch.
The mirror and magnet together weigh only one or two grains. When an
electric current is sent through this coil it deflects the magnet and
with it the mirror to the right or left. The apparatus is exceedingly
sensitive so that it is influenced by very feeble currents.
Communication has been maintained with an instrument of this kind over
the Atlantic cables, by the current proceeding from a battery composed
of a single copper percussion cap with a small scrap of zinc and a drop
of acidulated water. The use of the mirror is to make visible the
movements of the magnet. The coil is mounted upon a standard so as to
be about eight inches above the table. At the distance of eighteen
inches or two feet is placed a lamp. This is surrounded by a screen
which cuts off all the light, except that which passes through a tube
directed towards the mirror. Lenses in the tube focus the light on the
mirror and thence it is reflected to a vertical white surface, a sheet
of paper for instance, at a suitable distance and appears as a small
and brilliant spot. A movement of the magnet causes a horizontal
deflection of this spot to the right or left depending upon the
direction of the current passing through the coil. As these movements
can be produced at will by means of the key at the sending station, it
is only necessary to apply to them the dots and dashes of the Morse
alphabet, to have a very ready and perfect means of communication. To
the uninitiated spectator the facility with which the practiced
operator translates these apparently meaningless movements is
remarkable. If the cable is long and not in good condition the signals
are sometimes almost imperceptible, while any slight jar of the table
or apparatus will produce a large and irregular effect. Earth currents
also will cause vibrations hard to distinguish from the signals, and
if, as sometimes happens, the battery is connected in the wrong way,
the signals will be reversed. In spite of these drawbacks the skillful
operator reads off the message and rarely makes an error. This
instrument is still in use on some of the cable lines, but on most of
them it has been replaced by a recording instrument, also the invention
of Sir Wm. Thompson, which is almost as sensitive, and of which I will
speak later on. The key used in connection with these instruments, both
the mirror and recorder, is arranged with two levers, so connected that
pressing one of them causes a current to be sent over the line in one
direction, while the other sends it in the opposite.
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 0^{s}.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 0^{s}.26. On May 1, one set gave 0^{s}.32, and another 0^{s}.29.
On May 2, only one set was made giving 0^{s}.36, a variation of
0^{s}.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 0^{s}.16 and by star observations 0^{s}.24, on the
15th of June the machine gave 0^{s}.10 and the stars 0^{s}.24, on the
16th, machine 0^{s}.14, stars, 0^{s}.13, a very close agreement, on the
17th, machine gave 0^{s}.07 and stars 0^{s}.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, 0^{s}.08, while star observations gave
0^{s}.27, on June 23, machine 0^{s}.13, stars 0^{s}.51, and on June 28,
machine, 0^{s}.20, stars 0^{s}.35. In the case of the first two
observers a mean of the determinations amounting to about 0^{s}.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.