INSTRUMENTS OF PRECISION.
THE MERIDIAN CIRCLE.—The accurate registration of the positions of the
heavenly bodies is one of the most important functions of an
astronomical observatory. When the apparent places of an object at a
sufficient number of different times have been duly recorded, it becomes
possible to investigate the laws upon which its changes of position
depend, and to predict its positions at subsequent times for the benefit
of navigators and others to whom such predictions are of practical
utility. For this purpose various instruments have been devised, but in
all cases where it can be employed, the _transit circle_, or _meridian
circle_, as it is indifferently called, is generally conceded to give
the most trustworthy results.
With this instrument the observations are made when the celestial body
under observation is crossing the meridian of the place where the
instrument is set up, that is, when it “transits,” or “souths.” At this
time the accuracy of the observations is least impaired by the
ever-varying effects of atmospheric refraction.
The meridian circle consists of a refracting telescope—seldom exceeding
6 inches in aperture—which is fixed to a hollow axis at right angles to
itself, and this axis is supported horizontally in an east and west
direction, so that the telescope is only free to move in the plane of
the meridian. A large graduated circle—or frequently two such
circles—attached perpendicularly to the hollow axis, and read by
microscopes fixed to the walls or iron pillars which support the axis,
completes the essential parts of the instrument.
As the field of view of the telescope covers a considerable area, it
becomes necessary to provide some means of marking the exact point
within it which represents the meridional axis of the instrument. This
is accomplished by placing at the common focus of the object-glass and
the positive eye-piece a system of “cross wires,” consisting of
tightly-stretched spider threads, two of which are fixed horizontally
and nearly in contact, and five or seven vertically at equal distances
apart. What the observer has actually to do is to incline the telescope
at such an angle that the star is seen to traverse the space between the
two horizontal threads, and then to record the exact times, by means of
a chronograph and sidereal clock, at which the star appears to cross
each of the equidistant vertical threads. By thus making five or seven
observations and taking the average, greater accuracy is attained.
The time observations, as we have already seen, determine the right
ascension of the star under observation, while the declination is
indicated by the readings of the graduated circle, if the latter is so
placed as to read 90° when the telescope is directed to the Pole.
The ideal meridian circle is thus simplicity itself, but the mechanical
difficulties encountered in making such an instrument are insuperable.
Perfect right angles and perfect circles exist only in our minds, so
that after all the undoubted skill and care bestowed on its
construction, the actual meridian circle is only an approximation to the
ideal. Still, when the instrument is provided with levels and other
means for estimating its deviation from the meridian plane in which it
ought to move, the actual observations are capable of correction by
mathematical processes, so that the final statements of positions
sensibly represent those which would follow from the use of a perfect
instrument.
The greatest possible care is taken to secure rigidity in all parts of
the meridian circle. The hollow horizontal axis is supported on bearings
which rest either on heavy piers of iron or walls of masonry, and the
axis and telescope tube are firmly joined together at their
intersection. The bearings for the axis are turned with extreme
precision, and, to reduce the friction upon them, the pressure of the
instrument is counterpoised by an arrangement of balancing weights.
Adjustments are provided for every needful purpose. The cross wires are
fitted in a small frame which can by suitable fittings be given a small
movement in the field of view until the right place for them is found,
while the horizontality of the axis and its correct direction can be
secured by other adjusting screws.
Since most of the observations have to be made at night, the field of
view will generally be dark, and the exceedingly delicate spider lines
will be invisible unless some means of illuminating them be provided.
Usually a very tiny mirror is fixed diagonally at the intersection of
the axis and the telescope, where it is held in position by a stiff
wire. A light shining through the hollow axis is thus reflected into the
field of view, and the threads are rendered visible. The intensity of
this illumination of the field can be regulated in accordance with the
brightness of the star under observation.
The instrument having been erected, one of the first tests applied to it
is to see that it is correctly _collimated_, or, in other words, that
the optical axis of the telescope is perpendicular to the axis of
movement. For this purpose the telescope is directed to some distant
object, such as a building, and some mark which falls on the
intersection of the central spider threads is noted. The axis is then
reversed end for end by a mechanical arrangement, and the telescope
again pointed at the same object. If the mark again falls on the
intersection of the cross wires, the collimation is correct; if not, the
wires are moved with the frame containing them until the error is
corrected.
To test the horizontality of the axis, a spirit-level long enough to
stretch across the bearings, and called the “striding level,” is
provided.
Various methods are employed for adjusting the instrument so that the
telescope moves as truly as possible in the plane of the meridian.
Collimation and level being correct, the telescope will move in a
vertical plane, whatever may be the error in the direction of the
horizontal axis, and therefore any star passing through the zenith will
cross the centre of the instrument at the same moment that it crosses
the meridian. A star away from the zenith, however, will not be seen on
the cross wires when it crosses the meridian, unless the axis be truly
east and west. Hence, by taking the difference of time between the
observed transits of a star near the zenith and one a long way from the
zenith, and turning the whole instrument in azimuth until this
difference is equal to the difference of right ascensions of the two
stars, the instrument is readily placed in the meridian.
Another useful method of adjustment is to observe the upper and lower
transits of a circumpolar star. If the instrument moves truly in the
meridian, the interval between the two transits will evidently be twelve
sidereal hours.
Next, the declination circle has to be adjusted so that it reads 90°
when the telescope is directed to the celestial pole, or zero when an
equatorial star is under observation. An obvious way of doing this is to
take the readings when Polaris, or other circumpolar star, is at upper
and lower transits; the celestial pole lying midway between these
positions, the average of the two readings, when corrected for
refraction, should be 90°, and the circle would be shifted round in its
fittings until this was the case.
Such, in mere outline, are the processes by which the meridian circle is
set up. In actual practice, the greatest possible refinement is brought
to bear on the adjustments, and every precaution taken to estimate the
various errors so that due allowance may be made for them in the
reduction of the observations. It has even been shown that the heat of
the observer’s body, by affecting the lower side of the telescope tube
more than the upper, introduces sensible errors in the measures of
declination. Hence it is important to use metals of high conductivity in
the construction of meridian instruments, so that errors due to the
varying temperatures of different parts may be reduced to a minimum.
As an illustration of a modern meridian circle, we select that of the
Lick Observatory. (Fig. 53.) This instrument has an aperture of six
inches, and embodies all the improvements which have been introduced by
the Berlin firm of Repsöld & Co.
The observatory containing a meridian circle is usually a very simple
structure, as it is only necessary to provide an opening to the sky
along a north and south line. This is sufficiently provided for by a
series of narrow shutters in a building of ordinary construction.
To prevent confusion it may be pointed out that the term “transit
instrument” is frequently restricted to a meridian instrument which is
not supplied with large circles for the accurate measurement of
declinations, although it may have a small circle to assist in directing
the telescope. The use of such an instrument is evidently limited to the
determination of time and right ascension.
[Illustration:
FIG. 53.—_The Meridian Circle of the Paris Observatory._
]
THE ALTAZIMUTH.—Although the meridian circle furnishes us with the most
accurate method of determining celestial positions, its use is somewhat
restricted by the fact that it can only be employed for the observation
of objects on the meridian. It sometimes happens, however, that bodies
cannot conveniently be so observed, and other methods become necessary.
This is especially the case with the moon during the first and fourth
quarters, when it crosses the meridian in daylight, and it is then that
an instrument called the _altazimuth_ is of special value. This is
something like a transit circle in which the base supporting the piers
is made to turn on a vertical axis, so that the telescope can be
directed to any part of the heavens whatsoever. A fixed horizontal
graduated circle, read by verniers or microscopes attached to the
revolving part, gives the azimuth of the telescope when an observation
is made, and the altitude is furnished by the vertical circles. The
azimuth circle is adjusted to read zero when the telescope is pointed
due north, and the altitude circle to zero when the telescope is
horizontal. To secure the first adjustment, after correcting level and
collimation, a star may be observed before it crosses the meridian, and
again when it has exactly the same altitude after passing to the west;
midway between the two positions would be due south, and the circle
should read 180°. In adjusting the vertical circle, the telescope is
made to point downwards to a trough of mercury, and it is known that the
telescope is truly vertical when the reflected image of the cross wires
is coincident with the wires themselves; the circle should then read
90°.
From a knowledge of the sidereal time at which a celestial body has an
observed altitude and azimuth, the more useful co-ordinates of right
ascension and declination can be calculated by spherical trigonometry.
One of the largest instruments of this class has recently been erected
at Greenwich Observatory. The aperture of the telescope is 6 inches, and
the rigidity of the various parts may be gathered from the fact that the
instrument weighs something like six tons.
A _theodolite_ is a small portable form of altazimuth specially adapted
for the needs of surveyors, but occasionally employed in astronomical
work.
THE WIRE MICROMETER.—Notwithstanding that an equatorial telescope is
usually furnished with circles for estimating the positions of objects
observed, or to serve as a guide in directing the telescope to objects
of known position, it is not entitled to be called an instrument of
precision in the sense we are now considering. The provision for driving
by clock-work and other causes are antagonistic to constancy of
adjustment, and hence determinations of positions by the circles alone
might be many seconds in error. Most large telescopes, however, are
provided with some form of micrometer which not only serves for the
measurement of planets, lunar craters, and the like, but may also be
used to measure the angular separation of adjacent stars. In this way,
by making a “triangulation” of stars visible in the field of view, and
including at least two which have had their precise positions determined
by the meridian circle, the positions of objects can be measured with
great accuracy.
This method is especially valuable in the case of comets, which may
cross the meridian in daylight, and are often too dim to be seen with
the altazimuth.
Several forms of micrometers are in use, but the so-called _wire_ or
_filar micrometer_ is most commonly seen in our observatories. The
essential parts are very similar to those of the reading microscope (p.
172). Two parallel spider threads are so arranged on sliding frames that
they may be brought into coincidence, or separated, by means of very
finely-cut screws. Perpendicular to these are two fixed threads almost
close together. The system of “wires” is viewed by a positive eye-piece,
and the whole is attached to a draw tube so that it may be placed in
position at the eye end of the telescope. In order that the wires and
telescopic images may be sharply defined at the same time, the plane of
the wires must be at the principal focus of the object-glass. The screws
are provided with large heads which are graduated so as to show the
hundredth of a revolution, and counting wheels register the numbers of
complete turns.
Matters are so arranged that when both counting wheels indicate zero,
the spider threads are coincident. Then, supposing one of the screws be
turned through a revolution, the threads will be separated by a definite
amount; an equal and opposite movement of the other screw will double
the separation, and in all cases the distance between the threads will
be registered in turns, and fractions of turns of the screws.
The next proceeding is to ascertain what is called the “value,” in
angular measure, of the micrometer screw. This value will evidently
depend upon the pitch of the screw and the focal length of the telescope
to which the micrometer is applied, so that measurements merely stated
in terms of revolutions of the screw would serve no useful purpose. It
can easily be calculated that the images of two stars which are 28′ 39″
apart will be separated by an inch at the focus of a telescope of 10
feet focal length; then, if the screws have 100 threads to the inch, the
angular separation of the wires corresponding to a single revolution
will be one-hundredth part of 28′ 39″, that is, 17″·15, and the latter
would be the value of that particular micrometer when used with the
telescope in question. If the focal length of the telescopic
object-glass were 20 feet, the linear separation of the images of two
such stars as we have considered would be 2 inches, and the value would
therefore be halved, so that measures of twice the accuracy would be
possible. Since the stellar images and the cross wires are equally
magnified by the eye-piece, the value of the screw is in no way affected
by using eye-pieces of different powers.
In practice it is necessary to determine the value of the micrometer
screw by actual measurement. For this purpose, the wires are separated
by a known number of revolutions, say twenty, and the micrometer is
adjusted so that a star of known declination travels exactly between the
two fixed wires when the telescope remains at rest. With the telescope
still fixed, the number of seconds required by the image of the star to
traverse the distance between the separated wires is noted, and knowing
the angle through which the star must have moved in that interval, the
angular value of one turn of the screw is at once deduced. For work of
extreme precision each individual turn of the screw must be separately
evaluated, and allowances must also be made for changes of temperature.
When measuring the apparent diameter of a planet, the two threads are
separated until the image just lies between them, and the sum of the
readings of the two screws multiplied by the angular value of one turn
gives the diameter in seconds of arc. The distance having been formed by
other observations, the diameter of the planet in miles can be
determined in the manner to which reference has already been made (p.
142).
[Illustration:
FIG. 54.—_The Micrometer applied to a Binary Star: a b, Fixed Threads;
c d, e f, Movable Threads; s s, Components of Binary Star._
]
One of the most important applications of the micrometer is in the
measurement of double and binary stars. In this case the fixed threads
are made to enclose the two stars, and the movable threads are made to
bisect the star-images. (Fig. 54.)
THE POSITION CIRCLE.—It is frequently necessary to be able to specify a
direction, as in the case of a planet’s equator, or the line joining the
components of a double star. Such directions are expressed by “position
angle,” which may be defined as the angle from the north point, reckoned
from 0° to 360° through east, south, and west. For these observations, a
_position circle_ is usually attached to the micrometer. This is a
circle graduated from 0° to 360°, which can remain fixed in position as
regards the telescope, while the part containing the wires and
micrometer screws can be rotated by means of a rack and pinion. A
vernier attached to the movable frame indicates the required angles.
To adjust the position circle the vernier is set to zero, and the
telescope directed to a star; the circle and micrometer are then
together turned round until the diurnal movement of the star, which is
east and west, makes its image to traverse the space between the fixed
wires. The movable threads will then lie in a north and south direction.
The circle remains in this position during subsequent observations,
while the micrometer is rotated until the movable threads are in the
required direction, the position angle then being read off on the
circle.
THE HELIOMETER.—Another means of measuring small angles for astronomical
purposes is afforded by the instrument called the _heliometer_, which,
as the name will at once suggest, was invented for measurements of the
sun. This instrument is a telescope mounted equatorially, but differs
from the ordinary telescope, inasmuch as the object-glass is cut across
the centre, and means are provided for separating the two halves by
moving one or both parts in the direction of the line of bisection, and
also for measuring the amount of displacement. The cell containing this
somewhat peculiar object-glass can be rotated so that the line of
division of the lens may be placed in the same direction as the line
representing the distance to be measured.
The action of the instrument depends upon the fact that any small part
of a lens is competent to form a complete image of a celestial body, so
that when an object-glass is bisected, and the two halves separated
laterally, two distinct images will be produced, each differing only
from the image formed by the complete lens in being less bright.
To measure the distance from a star to a planet, let us say, as in
observations of the parallax of Mars, the lenses are separated to such
an extent that the image of the star formed by one half, coincides with
that of the planet formed by the other half, and the amount of
separation noted. As a check, the measurement is repeated with the
lenses separated in the opposite direction. The angular value
corresponding to a known separation of the semi-lenses being determined,
just as in the case of the micrometer screw, the angle between star and
planet at once follows. Angles ranging from a few minutes to about two
degrees can be measured in this way with great accuracy.
In the hands of Dr. Gill, of the Cape Observatory, the heliometer has
yielded very valuable results in connection with the distances of the
sun and stars.
OTHER INSTRUMENTS.—There are other instruments which may fairly be
classed as instruments of precision, but space permits little more than
a mention of their names.
The _zenith telescope_ is a telescope specially designed for the
measurement of the angular distances of stars from the zenith, for
precise determinations of latitude by Talcott’s method.
The _prime vertical instrument_ is nothing more than a transit
instrument, so arranged that the observing telescope swings in a
vertical plane which is perpendicular to the plane of the meridian. From
the observed times at which a star passes the prime vertical on the
eastern and western sides, the latitude of the place of observation can
be ascertained with great accuracy.
It is perhaps at sea that the labours of astronomers are of most direct
value in everyday affairs, and it is precisely here that the instruments
of high precision cannot be employed, in consequence of the absence of
firm supports. Nevertheless, there is one instrument—_the sextant_—which
yields results that satisfy all requirements when carefully constructed
and placed in good hands. A graduated arc extending over about 60° (from
which the name is derived) is supported by a light framework, and
pivoted truly on the centre of the arc is the radius bar, or index arm,
which carries a vernier for reading off the angles to be measured. A
plane mirror is fixed to the index arm, over the centre of movement, and
another, of which only half is silvered, is fixed to the frame near its
outer edge. A small telescope parallel to the surface of the frame is
directed towards the fixed mirror, so that the continuation of its axis
is in line with the boundary between the silvered and clear part of the
glass. Thus, while one object may be seen by direct observation through
the clear glass, another, in quite a different direction, may be seen
after reflection from the surfaces of the two mirrors.
The sextant is chiefly used for measuring the altitude of the sun, about
noon for the determination of latitude, and in the morning or evening
for the correction of chronometers. In such observations, the sextant is
held in the right hand, with its plane vertical, and the sea horizon is
sighted directly with the telescope; the index arm is then moved until
the reflected image of the sun is brought into coincidence with the
horizon. The reading is then taken, and if the adjustment is such that
zero is indicated when the reflected and direct images of the same
object are observed, it will give the altitude. The actual angle
recorded by the sextant is only half that between the objects observed,
but by numbering half degrees as whole ones, the true angles are read
off directly. For observations of the sun the instrument is provided
with coloured glasses of different shades, attached so that they can
readily be interposed to reduce the intensity of the light.