



Produced by Ron Swanson





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