Mitscherlich type goniometer
horizontal circle reflecting goniometer
two-circle contact goniometer
Already in 1669 Niels Stensen proved the constancy of interplanar
angles in quartz crystals. Still it took more than a century
before it was recognized that this property holds for all crystal
species and not just for quartz crystals. It was Jean Baptiste
Louis de Romé de l’Isle (1736-1790) who generalized
this fundamental law of crystallography that is presently known
as "Steno's law".
Actually this property was incidentally discovered by de l'Isle's
assistant, Arnould Carrangeot, in the course of making terra
cotta models of the crystals in de l'Isle's collection. For
this purpose in 1780 he developed a simple instrument to measure
the angles between crystal faces. The instrument that became
known under the names of "application goniometer"
or "contact goniometer"
was nothing more than two limbs connected by a joint. The limbs
could be applied to two adjacent crystal faces and eventually
the angle between the limbs could be measured. The accuracy
of the contact goniometer was about 15' at best.
In 1809 Wollaston developed an optical goniometer where the
reflection of light was used to exactly position a set of crystal
planes belonging to one crystallographic zone. For this purpose
the crystal was mounted on a rotatable horizontal axis. This
axis was connected to a graduated circle. The crystal was positioned
such that a zone axis (and as such the edge between two adjacent
crystal faces belonging to that zone) was parallel to the rotation
axis of the graduated circle. Upon rotation of the circle, the
crystal faces to be measured reflected the light from a source
located at long distance, at specific angular positions. As
such the angle between the normals to the respective crystal
faces could be measured. With this instrument, known as the
"Wollaston goniometer" or "Wollaston reflecting
goniometer", accuracies down to 5' could be obtained.
Later, a mirror was added to improve the positioning of the reflections from the crystal faces. This could also be accomplished by means of a low powered observation telescope and measurements down to accuracy of 1' could be made.
In 1843 Mitscherlich introduced a high precision goniometer with a vertical circle and a telescope that was firmly attached to the base of the instrument; a variety of Mitscherlich-type goniometers of increasing complexity were produced over the years.
In the Virtual Museum Wollaston- and Mitscherlich-type goniometers are classified under the grouping "vertical
In 1839 Babinet introduced a new type of goniometer equipped with two telescopes, one serving as a collimator for the light source and the other containing the reference. The Babinet goniometer could therefore be used in any orientation.
The instrument became known
as the "horizontal
circle goniometer". Horizontal circle instruments typically
attained an accuracy of 30". This kind of instruments was
put on the market by firms like Fuess (Berlin) and Troughton
and Simms (London).
An advantage of the horizontal circle was an improved attachment of the crystal. In vertical circle instruments heavy crystals could easily move from their position and spoil the measurement.
The main drawback of single circle instruments was that they
could only measure the faces of one zone at a time. To measure
the faces of another zone, the crystal had to be detached, remounted
and measured again and this process had to be repeated several
times in order to obtain a complete measurement of the whole
The English crystallographer W.H. Miller was the first, in 1874,
to use a goniometer with two circles and thus overcoming the
problem of remounting the crystal over and over again. The original
posthumous publication of 1882 apparently attracted little attention
and his method was rediscovered independently by Fedorov (1889),
Goldschmidt (1893) and Czapski (1893). The principle of these
instruments was that the crystal was mounted on an axis that
was at his turn mounted on another axis perpendicular to the
first one. As such the position of several crystal faces could
be measured one after the other and the angular positions (phi
and rho) plotted on a Wulff net. These instruments were called
"theodolite goniometers", "Goldschmidt goniometers".
To overcome certain indexing problems three circle instruments
were developed at the end of the 19th century. Because they
were very expensive and complicated to adjust, they only found
very limited use.
In 1896, Goldschmidt also invented a two-circle
contact goniometer. This instrument was suited to measure
larger crystals than with the equivalent optical goniometer.
After 1900 the development of the goniometer slowed down, mainly
because x-ray-diffraction made his entrée in crystallography.
In the first half of the 20th century some major improvements
to goniometers were still made by Terpstra in the Netherlands
and Codd and Moore in England. Today goniometers are definitively
moved to the gallery of historical instruments as witnesses
of the historical development of mineralogy and crystallography.
Therefore the Virtual Museum also holds some of these 20th century
instruments in its collection.
- Burchard, U. (1998) History and Development of the
Crystallographic Goniometer, The Mineralogical Record,
- Leiss, C. (1899) Die optischen Instrumente der Firma
R. Fuess, Leipzig
- Medenbach, O., Mirwald, P.W. and Kubath, P. (1995)
Rho und Phi, Omega und Delta – Die Winkelmessung in
der Mineralogie, Mineralien Welt, 6 (5), 16-25.
- Stoe & Cie. (1929) Mineralogische Instrumente, Heidelberg
- Terpstra, P. and Codd, L.W. (1961) Crystallometry,
- Tutton, A.E.H. (1911) Crystallography and Practical
Crystal Measurement, London