Der Meridiankreis und der Vertikalkreis.  Pages 43 - 46, Lehrbuch der 
Astronomie, by Elis and Bengt Stroemgren.  Berlin: Julius Springer, 1933.  
Translated by Dr. Wulff Heintz, Swarthmore College.  Taped by Chris Ray, 
transcribed by Peter Abrahams.


   Every transit instrument has to be equipped with a small vertical circle 
by which the telescope can be pointed in the right direction (north-south) 
in advance of the observation, so that a given star comes into the field of 
view.
   When this vertical divided circle has such dimension that it permits the 
reading of angles with the same precision with which the telescope can be 
positioned, then the usefulness of the instrument is considerably enhanced.  
It is then called a meridian circle or transit circle.  The others are 
called 'transit instruments used in time service'.
   This transit circle can be used simultaneously with the time of 
culmination of the star, to determine its meridian altitude.
   The arrangement of the older type of this instrument is visible in 
figure 26, where c-c marks the divided circle, which follows the instrument 
as it is moved through the meridian, north & south.  'M' means four reading 
devices.
   The alidade is here, four cornered frame, attached to the pier or 
pillar, at which at the top there is a level 'v' in order to control 
possible small displacements of its position, as has been previously 
explained with the universal instrument (small transit instrument).
   When the star approaches the center wire of the reticle, then the 
telescope is positioned such that a star comes at the same time to the 
horizontal wire or (in case the horizontal wire is double), in between the 
two wires.  Afterwards, the circle can be read.
   (During the motion through the field of view, only equatorial stars will 
exactly run parallel to the horizontal wire, otherwise the stars describe 
parallel circles.  Every straight line in the field of view is a great 
circle in the sky, determined by the plane, so this straight line in the 
center of the objective.)  
   In order to determine from this the meridian altitude, a zero point, the 
zenith point of the circle, is needed.  The method described for the 
universal instrument (which is reversing the telescope) cannot be used 
here, because there is no vertical rotation axis, and it would take too 
long, it is too heavy.  (p44)  In a large instrument, a reversal at the 
bearings is too cumbersome an operation to be used advantageously with this 
instrument.  There are two other methods.
   First, a collimator is a small telescope equipped with a cross wire or 
reticle, which is on a pier north or south of the main telescope and at the 
same height, usually in the same room.  It is positioned at the same height 
and with the objective turned towards the main telescope.  When such a 
collimator is equipped with a cylindrical tube, with two bearings on a 
frame with three positioning screws, it can be positioned horizontally by a 
lever.  If the optical axis is aslant in the tube, then this can be 
investigated by a rotation of the telescope in its bearings, and if 
necessary by shifting the crosswire.  When daylight or artificial light 
enters the collimator through the eyepiece, the rays originating at the 
cross wire become parallel after passing through the objective.  When the 
main telescope is then pointed at the collimator, one can see this 
crosswire as well as a distant object.  If now the horizontal wires in both 
telescopes are made to coincide, the optical axis of the transit instrument 
is horizontal, as well as that of the collimator.  The circle reading in 
this event gives us one of its horizontal points.  
  It is easier to determine the nadir point of the circle, opposite the 
zenith.  A vessel with mercury is placed under the telescope, and the 
objective is turned downwards, facing this horizontal mirror.  If now from 
the top, by a special eyepiece, light illuminates inside the telescope, 
then the rays emerging from the crosswire exit the objective parallel, and 
after, being reflected from the mercury, return in the same way.  At the 
eyepiece the wires as well as their mirror image is seen.  If these two 
images of the horizontal wires are made to coincide, then the optical axis 
is in a vertical plane, at right angles to the meridian, and also to the 
plane of the circle.  
The nadir point, thus determined, lies 90 degrees off the two horizontal 
points and 180 degrees off the zenith.  
   Apart from the meridian circle, meridian heights are also determined by 
way of the so-called vertical circle.  This has a vertical reading circle, 
like the meridian circle, to read altitude differences, but is arranged for 
rotation around a vertical column or pier, into any arbitrary azimuth, or 
can it easily be reverted for the purpose of transit observations.  In the 
vertical circle, one does not demand the high stability of the azimuth as 
required for transit observations, and the possibility of reverting the 
instrument gives advantages in altitude determination.  In any observation, 
the vertical circle can be reversed, and thus the zenith point determined.  
That the rotation axis about which the telescope is moved is vertical can 
be controlled by a level in the plane of the vertical circle; or by this 
level, any changes in inclination can be determined and later corrected.
   In measures of height or altitude, the flexure of the telescope has to 
be taken into account.  By the effect of gravity, both the objective end 
and the eyepiece end are slightly lowered, unless the telescope is exactly 
pointed towards the zenith or nadir.  If this lowering of both sides is 
equal, then the direction of the optical axis is unchanged from the forces 
of gravity.  Generally, there are small differences in the two halves of 
the tube.  These effects of gravity are variable with the zenith distance.  
From experience, the order of magnitude is about one arc second.  This 
flexure has the effect, that the angular rotation of the optical axis and 
of the circle are not exactly the same.  The flexure is highest in the 
horizontal position of the telescope, and in zenith and nadir is zero.  It 
goes with the sine of the zenith distance.  The component of gravity at 
right angles to the axis of the telescope is proportional to the sine of 
'z'.  It is therefore to be assumed that the flexure is proportional to the 
same.  The size of the flexure in the horizontal position can be determined 
by collimators.  Two collimator telescopes, as previously described, one to 
the north and one to the south, are exactly pointed towards each other, so 
that through one telescope, the two crosswires are seen coinciding.  The 
optical axes of the collimators are then parallel.  Now measured with the 
instrument to be investigated (the vertical circle), by successive 
settings, on the two collimators, the angle between their optical axes.  
(p46)  If it is found to be exactly 180 degrees, then the horizontal 
flexure is zero.  Any difference from 180 degrees is double the horizontal 
flexure.  The flexure at other zenith distances results from the horizontal 
flexure, assuming that the sine law is valid, and thus all observations can 
be corrected from the effects of flexure.  Mounting a small mirror in front 
of the objective of the instrument, then a reflected image of the 
horizontal wire appears next to the direct image, see page 44.  The 
distance between the direct and the reflected images of the wire is twice 
the angle between the optical axis and the normal direction (right angle 
direction) to the mirror.  By suitable arranging of the mirror, it can be 
positioned so that gravity only effects parallel shifts of the mirror.  
Then, when the telescope is rotated, potential changes of the angle between 
the optical axis and the normal to the mirror are caused solely by the 
telescope flexure.  Measuring the distance between the direct and reflected 
image at the wire, in various positions of the telescope, gives the 
corresponding flexure terms.  These measures have confirmed that the 'sine 
z' law is valid.



(From another text, seemingly the observing record of Wulff Heintz)

   Operation of the circle.   Declinations.
   In measuring zenith distances, only one setting on the wire could be 
made with a slow motion, followed by reading the circle in both pairs of 
wires of all four microscopes.
   The nadir point (using mercury vessel) was determined at the beginning 
and end of the observing time, and also at 2.5 - 3 hour intervals, and then 
linearly interpolated.  Each nadir reading consisted of two separate wire 
settings, followed by reading the circles.  The mean absolute difference of 
the pairs of measures was 0.3 arc seconds.
   The basement underneath the transit circle has ventilation shafts and 
after the mercury vessel was secured against drafts by stuffing some paper 
in the shaft, even in windy weather, it was sufficient to close the windows 
upstairs in the observing room to get an adequately sharp reflected image.
   The diurnal rate of the nadir point is considerable, especially in the 
position of the reading circle on the west side, where, during summer 
evenings with sharp decline in temperature, rates up to 1 second per hour & 
a total of 6 seconds per night were observed.
   The thermometer in a metal cabinet outside the building was read every 
hour, on the average, but at shorter intervals during the rapid temperature 
decline in the early evening.  The barometer and hygrometer were read at 
about three hour intervals.  This serves to determine the refraction.  The 
station barometer is a mercury barometer, and there is a psychrometer for 
measuring absolute humidity (motor driven 'sling' psychrometer).  The 
refraction was calculated according to the tables, including a correction 
for water vapor pressure and a correction for the temperature indicated by 
the outside thermometer.  The inside thermometer showed that the inside 
temperature was rather constant, relative to the outside.  The measurements 
were then corrected for latitude variations, tilt of the wire, division 
errors of the circle, and the curvature of the parallel (the star is not 
running parallel to the wire unless the star is on the equator).  The 
motion of the pole was derived from preliminary coordinates of the pole as 
supplied by an IAU Commission.  The tilt of the wire was repeatedly 
determined per year and was constant.  The division circles have not 
changed compared with the earlier investigations, therefore the average of 
the earlier investigations was adopted.  The curvature of the parallel was 
almost negligible since most observations were made within a few seconds of 
the transit of the meridian.  The attempt to determine the flexure of the 
telescope was by reflected observations in a mercury horizon, not 
underneath but south of the telescope, but the horizon was not steady 
enough.  The previous observer at the instrument measured with a collimator 
and found no flexure.  I have to agree that further examination of the 
instrument systems did not show any error that looked like it was related 
to the sine of the zenith distance.  (This Repsold instrument was built 
with two tubes, one tube inside the other).  This is different from the 
vertical circle, which showed considerable flexure.  Investigating the 
declination circle by means of fundamental stars, the original declinations 
were only used to gain a qualitative image of run of the errors.  To derive 
an independent system of declinations, only the differences of altitudes of 
the same stars in upper and lower transit and the positions of planets 
relative to the equator were used.  Two orientations of the circle, west or 
east, showed in all zenith distances a constant, about 0.4 arc seconds, 
which is explained by a random difference in the divisions.  Then we can 
combine the two, circle east and circle west, into one system.  (When you 
reverse the axis, you get a systematic difference, and since it is constant 
& affects only the zero point, I can take the average of the zero point & 
it will not make an error.)
   Comparing measurements of the same stars in different seasons shows an 
annual variation of about 0.12 arc seconds, which may be ascribed to 
seasonal variation in the atmospheric layers in the vicinity of the 
building (heat radiation, not parallel to the ground, but elevated), or to 
changes in the instrument.  Apart from a small difference in the early 
evening, other systematic errors in the declination did not occur later in 
the night.  There is also the suspicion of the twilight effect; where the 
eye perceives the positions of stars differently in the twilight than 
against the dark sky.  Twilight effect could not be found in my 
observations.
   Towards the two horizons, there were systematic differences in the 
zenith distances that were small, up to 1/2 arc second; and the second, 
towards the south, is shown by the planet positions.  There was an 
hypothesis by an earlier observer that this could be an anomaly of 
refraction at the upper edge of the building.  However, the edge of the 
building is at a distinctly different zenith distance than where I found 
the discontinuity or jump in the zenith distances. 
   The outcome was, it was a combination of periodic division circle error 
of the mount (0.15 arc seconds), together with the difference between 
northern refraction, closer to another building & warmer, compared with the 
south.  Combining these two terms, I got a very good representation 
(Periodic error is from the ruling machine; there are random errors and 
periodic errors.)
   The problem is, to separate the effects of: periodic division error; 
flexure; refraction anomalies due to the shape of the building; or an 
abnormal refraction constant.
   The right ascensions.
   Beginning in 1956, all transits were recorded over four revolutions 
which gave 20 contacts of the chronograph.  The mean of the contacts is 3.5 
arc minutes east of the optical axis -- that can be determined by 
collimation.  The chronograph paper ran two centimeters per second, the 
inclination of the axis was read in 2.5 to 3 hour intervals by the level, 
always with the telescope in a horizontal position.  Then follows the 
determination of how much one division of the level is, in arc seconds.  To 
determine the unevenness of the pivots which rest in the bearings, Labitska 
[spelling?] (the previous observer), had a lever which touches the pivots 
from above, and you can read on a scale how much it is tilted.  (A 
traveling lever which connected with the axis of the telescope, and any 
out-of-round would cause the lever to rise or fall a measurable amount.)  A 
bending could not be found.  (Additional measurement procedures 
introduced.)  After the measurement readings had been separated from the 
motion of the marker around the center of the pivot, there were still 
unclear remainders, much larger than in the measurements made previously by 
the lever.  The correction for unroundness of the pivot was therefore 
considered to be more reliable and applied to the observations.  
   The reduction of the observations followed, an iterative method using a 
desk calculator; and with the equations, including the clock correction, 
the azimuth, and the collimation, (the normal intervening fourth unknown -- 
the tilt of the axis -- had been removed by the level readings, using a 
level hung off the axis from the pivots; this is why we had to determine 
the arcsecond value of one division on the level.)  Then comes the 
reduction methods.  During the first iteration, the pivot readings were 
applied, and the clock rates were improved during the night (as recorded on 
the chronograph, interpolated over a number of weeks).  There remain 
differences between circle east and circle west, which were found to be 
almost symmetrical to zenith, and that indicated the remaining error of the 
pivot corrections.  Then followed systematic differences with respect to 
declination.  Then, the observations were divided into groups of hours in 
several zenith distance zones, in order to get from the run of the right 
ascension and the closing error.  In summing up these differences all 
around the sky (involving several seasons), you get the systematic 
differences of the fundamental catalog of right ascension, versus the clock 
error.  The variation of the resulting closing error with zenith distance, 
clearly indicated systematic diurnal change of azimuth.  And with the 
already mentioned systematic change of the inclination, this leads to the 
conclusion that with dropping temperature during the night, either the 
western drum of the telescope (where it rests on the pivot), or else the 
pivot itself, is deformed so that the western bearing moves down and north.  
Since the aberration of the azimuth in strong cooling (spring and summer 
evenings) was particularly pronounced; I preferred to put it proportional 
to temperature instead of time.  It was then found that there was a 
substantial azimuth change of 11 milliseconds of time per degree centigrade 
temperature decline.  After all these corrections had been made, another 
iteration became necessary, in order to get to the final positions of the 
stars.  There was not a significant closing error in the pendulum clock.  
The results were 'binned' & thus we obtained the 'alpha alpha' correction 
that has been confirmed at other instruments, that was 13 milliseconds of 
time, which agrees with my earlier result from the southern sky.
   The observing program must include stars in the north and the south, in 
upper & lower transit, including all sides of the sky in the early and the 
late night time.  This is necessary to separate the effects of refraction, 
azimuth change due to the movement of the telescope axis (assuming that the 
inclination of the axis had been accurately determined by the level, 
otherwise there would have been too many unknowns).  For each star, you 
must make the described procedure, record it, and then make a setting on 
the center wire & immediately read the microscope; and go on to the next 
star.  This is interrupted at a few hours interval by nadir readings -- 
lifting the lid from the mercury vessel, pointing the telescope at the 
nadir; and also interrupted by reading the meteorological instruments to 
determine atmospheric conditions inside & outside the building -- mercury 
barometer, outside & inside thermometers, and psychrometer.  The pendulum 
clock was in a temperature controlled closed room with walls one half meter 
thick in another part of the building, and showed no diurnal variation.  It 
was electrically connected to the chronograph, and gave the time on the 
chronograph paper.
   Visual observations consisted of placing the star on the left side of 
the field (right side in the southern hemisphere).  The star was followed, 
and 20 contacts made over four revolutions.  The exact center was 
calculated (3.5 arc minutes east of the optical axis); as a correction to 
the collimation -- as if the telescope were pointing 3.5 arcmin east, 
equivalent to 15 seconds of time.  All contacts were made before the 
transit.  Other observers follow the star for a few revolutions east, then 
make a central setting in declination in the middle, and then follow the 
star to the west.  But this costs too much time.  
   The curvature of the parallel is the factor caused by the distance of 
the star from the equator producing a curved path across the sky.  However, 
if you are within a few arcminutes of the meridian, it is a very small 
effect.  I read the zenith distance at a point very close to the optical 
axis, make a setting within a few seconds of time, and have recorded the 
right ascension beforehand.  This procedure includes the correction for the 
curvature of the parallel, which is significant only for stars close to the 
pole.
   Reference star positions were determined over many years and compiled 
into the Fundamental Catalog.  This purports to give the position and 
proper motion for a limited number of stars.  I used at that time the FK-3 
Catalog, and my work was used along with others, to prepare the FK-4 
Catalog.  The FK-5 Catalog is now in use.




Home page: http://www.europa.com/~telscope/binotele.htm