common window: in the first cell, at the edge of the dial, is found the
dominical letter; in the second, the cycle of the sun; in the third, the
character; in the fourth, the sign; and, in the fifth, the house of the
planet dominating the year. The second dial shows the epacts, with the
golden number. The third, and last of all, shows the Roman cycle.
Finally, as indicated by the epact and the dominical letter in an
immovable table added outside, are the feastdays and other movable
events of the year; that is, Easter, the four seasons, the Rogation
Days, etc.
VII
But lest the various movements of the indices and the various beginnings
of the divisions tend to cause some fatigue, the precaution has been
taken, that all the indices by common law are moved from the top towards
the right of the observer, and from thence all the arithmetic divisions
of the circles take their beginning. And lest the multitude of different
figures should deceive the eye, the larger divisions of the circles have
been marked by Roman numbers, that is, by capital letters of the
alphabet; others, in other places, by differently colored numbers. Thus,
the movements of the indices, the distribution of the circles and the
multitude of numbers not only do not disturb the eyes and the mind, but
rather marvelously delight them.
VIII
After having completed briefly the description of the dial and the
indices and their motions, I have not without reason delayed in
satisfying the desires of many who wish to learn at least the method by
which, from this mechanism, may be calculated the true times of new and
full moons, and their ecliptics. In order to make these matters clearer,
it is necessary that they be explained here at greater length.
With the indices, then, adjusted astronomically-geographically to the
longitude of any given region, and to the mean time whether past,
present or future, and assuming the clock to be in normal operation (as
at present it has been for a whole year and more), then the moon will be
in conjunction with the sun in the heavens. When the equations on the
mechanism are examined, the sun and moon shall be found to be in the
same degree of longitude, and in the same part of a degree. There will
also be an ecliptic new moon that is in conjunction with a solar
eclipse, or rather with a terrestrial eclipse. This will occur if, at
that time, both apexes of the first index, located below the center of
the clock, are hidden by the two segments of the circle extending from
the center of the mechanism through the lowest index.
And the eclipse will be greater and greater and, consequently, visible
in more regions of the earth, the more deeply the two pointers,
indicating the distance of the sun from its apogee, are hidden in the
center of the segments.
But whether the eclipse takes place in the head or in the tail of the
dragon, or whether it is north or south, is indicated by the small disk
of the sun attached to one of the two pointers hidden by the segments of
the circle. If, at that time, the little disk shall be found in the head
of the dragon inscribed on the plane of the dial, then the sun has been
snatched from the earth and ingloriously entombed, as it were, in the
huge jaw of the dragon. Then, ... the heavens themselves will lend aid
to the woeful pomp of the senseless funeral in full darkness by suddenly
lighting the unhappy lamps of the fixed stars. However, if the little
disk occupies the tail of the dragon on the mechanism, then the sun in
the heavens also, as if freed from the toils of the immense dragon's
tail, will emerge without difficulty.
The center of the eclipse will traverse the hemisphere of the earth
north of the solar path, always nearer to the pole of the ecliptic, in
proportion to the inclination of the disk to the north. On the other
hand, if the little disk inclines to the left semicircle, then the
people south of the solar path will enjoy the spectacle of the total
central eclipse.
But if the little disk remains neutral (inclining neither way) and
remains halfway between the two sections of the circle, then the
greatest solar eclipse will take place at the equator and those who live
near the poles of the ecliptic will not enjoy a trace of that eclipse.
This is because the half of the equatorial diameter enormously
outmeasures even the greatest apparent semidiameters of the sun and of
the moon, even taking as a norm the smallest horizontal parallax of the
moon.
What has been said about the true new moon is to be understood also,
proportionately, about the true full moon. For when, with respect to the
equations of the centers, the moon shall be distant on the mechanism by
a full semicircle from the sun (also in the heavens it will be truly in
opposition to the sun) there will be a true full moon. Likewise, the
moon in the heavens will be in eclipse if, at the time of opposition,
the pointers of the little index (which we mentioned before) situated
below the center of the clock are so far away from the belly of the
dragon that they are forced to lie under the two smaller segments of the
circle which, in all full moons, are always to be moved from the index
of the synodic moon to the region of that little index. As a matter of
fact, the closer the little pointers approach to the middle of the
segments, the more obscured it will be.
You will know, furthermore, that the eclipse of the moon occurs in the
head of the dragon if the disk of the little moon, attached to the other
point of the little index, is raised to the head of the dragon;
conversely, when the little disk of the moon inclines to the tail, the
eclipse is taking place in the tail of the dragon.
And, accordingly, when you observe the little moon of the index inclined
to one or other section of the circle, so also in the heavens, the
eclipse of the moon is only partial and the northern or the southern
part of the moon is illuminated.
The current time will indicate whether the lunar eclipse is visible or
not. As the new moon ecliptic falls during the day, the eclipse will not
be visible, since the earth denies a sight of the moon which is below
the horizon. But, conversely, if there are no clouds, the eclipse will
be visible anywhere, if the luminous bodies are ecliptically in
opposition at night.
Since lunar eclipses appear to all people as being of the same magnitude
and duration, and begin and dissipate at the same absolute moment of
time, I decided to reveal another facet of this spectacle on the right
side of the center of the clock (see chapter III above). There, at the
time of the true ecliptic full moon, as the pointer of the third little
index shows, you can ascertain the hours, etc., of duration, and the
inches of greatest obscuration. The little moon attached to the index is
a model of the actual eclipsed moon.
IX
Thus, with the aid of this machine, solar and lunar eclipses of the past
can be recalled and future ones can be foreseen. Indeed, if the index of
prime minutes is speeded up by hand, whose wheel imparts motion to the
other indices and shields, then, the dials and openings will foretell
the year, month, day, hour, etc., of any future eclipse. I foresaw that
the times would thus be evolved too slowly, and that the clock wheels
would be considerably worn by repeated experiments (if, for instance, by
the rotation of the index of prime minutes, to whose period only a
single hour corresponds, the future new and full moon ecliptics were
being investigated). Therefore, I took care that the wheel which
immediately communicates motion to the index of the synodic moon should
be so fitted internally to the mechanism that by the reversal of any
external index, the wheel would be removed from its proper position;
whenever desired, it could be quickly and most accurately restored to
its proper place.
In this way, since the close meshing of the wheels is released, you can
extend the experiment for many years, even for many centuries. You have
only to guide with your hand the index of the synodic moon on the
circles, always intently observing whether, in the passage which this
index makes over the little index, both pointers of the little index are
hidden by the segments of the circle. Having observed this, look at the
index moved by hand, for if this has carried the solar disk halfway
between the two larger segments of the circle to the region of the
hidden little index, then you will know that eclipse will be a solar
eclipse. On the other hand, you will know that it will be a lunar
eclipse, if the index (moved by hand) has carried the moon, situated
between the two smaller segments of the circle, to the same region
(i.e., the hidden part of the circle). The solar disk and the lunar disk
alternately will reveal to you the circumstances of both eclipses. The
current year will be given by the Julian period, reducible to any
desired epoch, and, contained in the solar cycle, the golden number and
the Roman cycle. The month of the year and also the day of the month
will be indicated by the pointer of the little index, first on the right
side of the clock. And what I have said of future eclipses should be
equally understood of past eclipses, so long as the index, which can be
moved either way at will, is moved in reverse.
Finally, though 55 wheels were employed to carry so many dials, all are
driven by one source of power not exceeding the third part of a Germanic
hundred-weight which, suspended at the geometric height of five feet
(about the ordinary stature of a man), keeps the whole machine in
operation for a hundred days and more.
Although the machine repeats hours and quarter hours at will and,
consequently, the number of wheels and the rest of the apparatus
necessary for these functions is thereby increased, it has not grown to
an unwieldy size, however much one might erroneously imagine it to be.
It does not exceed the bulk of ordinary clocks hanging from a wall;
indeed, it scarcely equals these.
The entire machine, ready for operation, does not weigh more than 156
ounces, although it is made of steel or brass throughout and further
weighted with two bells and a rather large brass dial-plate.
Of course, there are many more things to be said, especially about the
mechanical structure of the wheels, but fearing to tire my kind reader
unduly by exceeding the bounds of a summary, I am forced to put an end,
though unwillingly, to this sufficiently shortened explanation of the
work. I have hope of giving satisfaction to many more when I shall have
communicated to the learned world another and completely new automatic
work, grander than this present one. It is already theoretically
completed in all its calculations, but still to be worked out
mechanically from the very beginning, if but God, thrice Best and
Greatest, bless the undertaking and mercifully grant life and health--to
whom be in, and from, and through all things, all honor and glory in
eternity and beyond.
BIBLIOGRAPHY
The following works have been used in compiling the material for this
paper. They are frequently referred to in the text in shortened form.
AMBROSI, FRANCESCO. _Scrittori ed artisti Trentini._ Trent:
Giovanni Zippel, 1883.
BONOMI, L. _Naturalisti, medici e tecnici Trentini._ Trent:
privately printed, 1930.
BORGHESI, FRANCESCO. _Novissima ac Perpetua Astronomica
Ephemeris Authomatica Theorico-Practica._ Trent: Giovanni
Battista Monauni, 1763(?).
---- _Novissimum Theorico-Practicum Astronomicum Authoma Juxta
Pariter Novissimum Mundi Systema._ Trent: Giovanni Battista
Monauni, 1764.
ENGELMANN, MAX. Philipp Matthaeus Hahn. Berlin: Verlag Fischer,
1923.
ESPOSTI, ALFREDO DEGLI. La sala 'Innocente Binda' al Museo
della Scienza e della Tecnica di Milano. _La Clessidra_ (July
1960), anno 16, no. 7, pp. 18-21.
FRANCH, LEONE. _La Valle di Non._ Trent, 1953.
LLOYD, H. ALAN. _Some outstanding clocks over seven hundred
years, 1250-1950._ London: Leonard Hill, 1958.
MOSNA, EZIO. _Trento._ Trent, 1914.
PERINI, AGOSTINO (compilatore). _Statistica del Trentino,
Biblioteca Communale del Trentino._ Vol. 2, p. 57 (cons. 6,
carta 9).
PIAMONTE, GUISEPPE. _La nauna descritta al viaggiattore._
Milan, 1829.
PIPPA, LUIGI. Antonio Bartolomeo Bertolla. _La Clessidra_
(January 1961), anno 17, no. 1, pp. 22-25.
SAN CAJETANO, DAVID A. _Praktische Anleitung fuer Kuenstler, alle
astronomische Perioden durch brauchbare bisher noch nie
gesehene ganz neue Raederwerke mit Leichtigkeit vom Himmel
unabweichlich genau auszufuehren, sammt Erweiterung der Theorie
des neuen Raedergebaeudes._ Vienna: privately printed, 1793.
TOVAZZI, GIANGRISOSTOMO. _Biblioteca Tirolese._ Vol. 2, art.
329, MS. 168, pp. 406-407. Trent, 1780.
VISCHER, GEORGE F. _Beschreibung mechanischer Kunstwerke,
welche unter der Direktion und Anweisung M. Philipp Matth.
Hahn, Pfarrers in Kornwestheim..._. Stuttgart: Mezler, 1774.
VON BERTELE, HANS. The development of equation clocks. _La
Suisse Horologere_ (1959-1961), parts 1 through 5.
WENHAM, EDWARD. Tall case clocks. _The Antiquarian Magazine_
(May 1927), vol. 8, no. 4, p. 33. [The Borghesi clock is
illustrated only from a photograph of the Anderson Art
Galleries in New York, and mislabeled "Astronomical Clock made
in Jena, 1656, in elaborate mahogany case."]
* * * * *
U.S. GOVERNMENT PRINTING OFFICE: 1964
For sale by the Superintendent of Documents, U.S. Government Printing
Office Washington, D.C. 20402--Price 70 cents
Index
Aristarchus of Samos, 54
Bertolla, Alessandro, 65
Bertolla, Bartolomeo Antonio, 31, 34, 36, 47, 51, 52, 57, 62, 63
Borghesi, Father Francesco, 31, 70, 71
Brahe, Tycho, 54
Butzjaeger, Johann Georg, 36, 37
Charles VI, Emperor of Austria, 32
Cles, Baron of, 57, 59
Copernicus, 54
Di Noris, Cristoforo Sizzo, 59
Evelyn, John, 32
Francis I, Emperor of the Holy Roman Empire, 42, 44, 52, 58
Hahn, Father Philipp Matthaeus, 33
Klein, Father ----, 33
Lippi, Fra Lippo, 42
Longomontanus, Christian Severin, 54
Maria Theresa, Empress of Austria, 31, 41, 42, 44, 57, 58
Meton, 48
Monauni, Giovanni Battista, 40, 52
Philolaus, 54
Ptolemy, 54
Pythagoras, 54
Quare, Daniel, 32
Riciolus, 54
San Cajetano, Brother David a, 33
San Daniele, Father Aurelianus a, 33
Sully, Henry, 32
Tompion, Thomas, 32
Tovazzi, Giangrisostomo, 57, 58
Williamson, Dowe, 32
Williamson, Joseph, 32
Winters, Father S. X., S.J., 42
Winz, Johann Christian, 36, 37
Wisshofer, Peter, 36, 37
* * * * *
Transcriber's note:
Footnotes have been moved to the end of the main section of the paper,
and illustrations have been moved to eliminate breaks in paragraphs. Two
'side bar' sections set off from the main text in the original are
indicated by lines of asterisks before and after the side bar. Minor
punctuation errors have been corrected without note. The following
typographical errors have been corrected:
p. 37 ... his curiosity increased ... [Had 'curiousity'.]
p. 41 Bertolla apparently wavered in ... [Had 'waivered'.]
p. 43 ... contained within asterisks, carries ... [Had 'carrie'.]
p. 45 ... Assidvo proni donant di cvncta labori. [Had 'ronip'.]
p. 45 ... assiduous laborer.) The same ... [Had 'saem'.]
p. 48 ... 12 signs of the anomaly, within ... [Had 'anamoly'.]
p. 51 ... the larger size of uppercase letters ... [Had 'letter'.]
p. 54 ... rightly conceive my new system of the ... [Had 'sytem'.]
p. 55 ... leading point of the system ... [Had 'they'.]
p. 55 ... Cancer; Austral [the southern] ... [Closing bracket added.]
p. 55 ... of the earth are always held in one ... [Had 'alway'.]
p. 56 ... all things in their circles so that ... [Had 'than'.]
p. 56 ... satellites, etc., eccentrically ... [Had 'excentrically'.]
Footnote 4: _Philipp Matthaeus Hahn_ [Had 'Matthaus'.]