The Borghesi Astronomical Clock in the Museum of History and Technology
[Pg 44] In the upper spandrels of the dial are two more cherubs bearing ribands with inscriptions. In the lower left corner is a magnificent engraving of Atlas upholding the globe of the world, inscribed with the zodiac, over his head. The lower right corner features the figures of two noblemen apparently examining and discussing an orb upon a table, the significance of which is not clear.
Beginning with the uppermost part of the frontispiece, there are nine inscriptions in Latin on the dial plate. The topmost is Franciscvs I sit plan. Dominator aeternvs. The phrase has reference to Francis I, who was Emperor of the Holy Roman Empire, from 1745-1765, and husband of Empress Maria Theresa of Austria. The phrase may be translated as "May Francis I be the eternal ruler by favor of the planets" or more simply "Long Live Francis I, Emperor." Although the dial plate of the Borghesi clock is inscribed with his name, the records indicate that the clock was presented to Maria Theresa. Francis I may have already died before the presentation was made.
From the left to right over the tableau of the Holy Trinity is the phrase "Lavs sacrosanctae Triadi Vni Deo, et Deiparae" (Praise [be] to the most Holy Trinity, to the one God, and to the Mother of God).
Within the upper left and right spandrels is inscribed:
Isthaec, Signum grande apparvit in Coelo * sancta Dei genitrix amicta sole * Illibato pede Lvnae et serpentis nigra premens Cornva * bis senis pvlcherrime Coronata syderibvs * Tempe indesinenter clavsa, scatvrigo signata * Cedrvs in Libano, Cypresvs in Monte Sion * Mater pvrae Dilectionis sanctaeqve spei * Chara patris aeterni proles, Verbi Mater, sponsaqve procedentis *, gratiae et gloriae circvmdata varietate.
This inscription is a eulogy to the Virgin Mary assembled from the texts of Holy Scripture. In addition, each lemma, contained within asterisks, out the chronogram 1764, the year the clock was completed. Each lemma is translated and identified from the Douay-Rheims version of the Bible:
This woman: a great sign appeared in Heaven (Apocalypse 12:1) * The Holy Mother of God clothed with the sun (Apocalypse 12:1) * And with unharmed foot crushing the black horns of the moon (Apocalypse 12:1) and the serpent (Genesis 3:15) * Most beautifully crowned with twice-six (Apocalypse 12:1) * A garden [Tempe] enclosed, sealed with a fountain [spring of water] (Song of Songs 4:12) * Like a cedar in Lebanon, and a cypress tree on Mount Zion; (Ecclesiasticus 24:17) * Mother of pure love and of holy hope: Beloved daughter of the Eternal Father, Mother of the Word, Spouse of the Holy Spirit: (Ecclesiasticus 24:24) * Surrounded with a diversity of grace and glory (Psalms 44:10).
At the lower left corner below the figure of Atlas upholding the world is the phrase, Assidvo donant di cvncta labori. (The favorable gods willingly grant all things to the assiduous laborer.) The phrase is quoted by Father Borghesi in the text of his second volume. The last inscription appears at the lower right corner under the figures of the two noblemen, Diligit avdaces trepidos fortvna repellet. (Fortune favors the daring and rejects the timid.) The last two inscriptions are in dactylic hexameter. They appear to be original compositions inasmuch as no classical prototypes have been identified.
[Pg 47] In addition to the inscriptions previously noted on the outer dial plate, there are three major inscriptions in the central dial. The outermost states Circulus horarius Soli, Lunae, Fixis, Nodis, Aestuique marino communis (the hour circle, common to the sun, the moon, the fixed stars, the nodes and to the sea tide). This inscription is divided into four parts by the insertion of four divisions for the day into canonical hours: [Horae] Nocturnae (night hours); Matutinae (morning hours); Diurnae (daytime hours) and Vespertinae (evening hours).
The next section of the central dial is inscribed Intumescite—Detumescite (rise and fall of the tides) repeated at intervals of approximately every six hours. Within the next section is the following inscription, inscribed continuously around the ring:
Lege fluunt, refluunt, dormitant hac maris undae: Ad Phoebi et Phoebes concordia iussa moventur Aequora; discordi iussu suspensa quiescunt.
Translated, this is:
By this law the sea waves ebb and flow and lie dormant: When Phoebus and Diana agree in their commands, the waters are moved; when they disagree, the waters lie silent.
Within the central boss of the dial plate, the name of the maker is inscribed:
Bvrghesio Doctore, et Bertolla Limatore Annaniensibvs*
Translated, this is:
[By] Doctor Borghesi and Bertolla, mechanician citizens of Anáuni.
There are 12 windows in the frontispiece, through each of which appears an indication relating to time. Beginning at the top of the frontispiece of the dial, the first opening occurs on the breast of the imperial eagle. This indicates the dominating planet, represented by its symbol, and its house.
The opening in the eagle's left claw, labeled "Lit. Dom." is the dominical letter. The first seven days in the month of January are each assigned one of the letters a through g in order of appearance. The letter which coincides with the first Sunday within this period is called the dominical letter, and it serves for the following year. In leap year, two letters are required, one to February 29th and the letter next proceeding for the remainder of the year. This letter is used in connection with establishing the date of Easter Sunday. The date of Easter regulates the dates of the other movable feasts.
The eagle's right claw is labeled "Cyc. EpEC" and represents the epact, or the age of the moon on January 1st. It serves to find the moon's age by indicating the number of days to be added to each lunar year in order to complete a solar year. Twelve lunar months are nearly 11 days short of the solar year, so that the new moons in one year fall 11 days earlier than they did the preceding year. However, 30 days are deducted as an intercalary month since the moon has made a revolution in that time, and the remainder, 3, would be the epact.
Below the imperial eagle two winged cherubs support a riband with three indictions of the Julian period. This period of 7980 years is the product derived from multiplying together the sums of 28, which represents the cycle of the sun; 19, representing the cycle of the moon; and 15, which represents the Roman indiction. The Julian period is reckoned to have begun from 4713 B.C. so that the period will be completed in A.D. 3267. The first of the three openings is marked "Ind. Rom." or "Roman indiction," which was an edict by the Emperor Constantine in A.D. 312, providing for the assessment of a property tax at the beginning of each 15-year cycle. It continues to be used in ecclesiastical contracts. The second opening, which occurs immediately below the eagle, is marked "Cyc. Sol." (cycle of the sun). This cycle takes a period of 28 years, after which the days of the week once again fall upon the same days of the month as they did during the first year of the former cycle. There is no relationship with the course of the sun itself, but was invented for the purpose of determining the dominical letter which designates the days of the month on which the Sundays occur during each year of the cycle. Since cycles of the sun date from 9 years before the Christian era, it is necessary to add the digit 9 to the digits of the current year and then divide the result by 28. The quotient is the number of cycles which has passed, and the remainder will be the year of the cycle answering to the current year. The third opening on the riband is labeled "Num. Aur." (golden number).[Pg 48] Meton, an astronomer of Athens, discovered in 432 B.C. that after a period of 19 years the new and the full moons returned on the same days of the month as they had before, and this is called the cycle of the moon. The Greeks were so impressed with this calculation that they had it inscribed in letters of gold upon stone, hence the golden number. The First Council of Nicaea in A.D. 325 determined that Meton's cycle was to be used to regulate the movable feasts of the Church.
Immediately above the chapter rings is an opening through which the orb of the sun is visible.
In a separate chapter in his second volume, entitled "Descriptio Authomatis Summa totius Operis Mechanici" (Description of the Automaton—Summary of the Complete Mechanism), Father Borghesi provided a description of the functions of the various indicators, prefixing it with the short poem shown in figure 18. He then continues:
In the middle of the frontispiece, as at the center of the universe, the terraqueous globe of the week revolves, with a daily motion turning from right to left, bringing with it from the round window the coming day and at the circumference the circle of hours common to the sun, to the moon, to the fixed stars, to the head and tail of the dragon, and to the raging sea.
The second circle revolves the synodic-periodic measure of the raging sea, the days of the median lunar-synodic age, the signs and individual degrees of the signs of the distance of the moon from the middle of the sun within the time of 29 terrestrial revolutions, hours 18.104.22.168. This circle revolves likewise from right to left around the center of the earth. In this second circle, another little orb revolves, bringing with it the epicycle of the moon, in which the little circle of the moon (whose illuminated middle always faces towards the sun), running from left to right through the signs of the anomaly; within 13 revolutions of the earth, hours 18.39.16. It descends from apogee to perigee and in just as many others it returns from perigee to apogee, to be carried down thus to true, back and front from the longitude and distance from the sun and from the middle of the earth.
The third circle (on which I have tried to indicate astronomically-geometrically in their places, the degrees of lunar latitude both in the south and in the north, and some fixed stars, those, namely, which can be separated by us from the moon which goes between) from left to right turns around the center of the earth, stretching out the head and tail of the dragon, on the inside above the second circle for noting and measuring the sun (but I should rather say the earth), and the eclipses of the moon, within 346 revolutions of the earth, hours 14.52.23.
The fourth circle, in which the heaven of the fixed stars, reduced to the correct ascent of our times, the signs of the zodiac and the individual degrees of the signs, the months of the year and the single days of the month can be seen, likewise makes its journey around the earth from left to right in 365 terrestrial revolutions, hours 5.48.56.; that is, within a median astronomical year. Above this annual orb, the sun, in its small epicycle, gliding through the 12 signs of the , within the space of 182 terrestrial revolutions, hours 15.6.58., from left to right, falls from apogee to perigee; and, within the same time, rises from perigee to apogee, and brings with it, the index, namely its central radius, inhering to the axis of the equatorial orb and cutting the four greatest circles from the center.
When the sun has been moved around, Iris shows from six windows the era, that is, the current year. Two winged youths take their place next to Iris, carrying the Julian period: namely, the Roman indiction, the cycle of the sun and the golden number, on a leaf of paper held between them. The imperial eagle stands out on top (as if added to the frontispiece) carrying on its breast the dominating planet and in its talons the ecclesiastical calends (that is, the dominical letter and the epact).
Two attachments, in the form of small superimposed dials are situated at the base of the dial plate, at either side and immediately below the fourth chapter ring. In his second volume, Father Borghesi stated that they "are not moved from inside the clock, but the one at the right [inscribed concitat and retardat] serves for loosening [accelerating] and tightening [retarding] time; that is, the reins of the perpendicular."
In other words, the purpose of this attachment is for adjusting the pendulum to make the clock operate fast or slow. The second attachment, which appears at the left, and which is inscribed "Claudit" (close) and "Aperit" (open) serves the purpose of "... preparing the mechanism in a moment, as swiftly as you wish, for sustaining the astronomical experiments of which you will hear later; when these things have been done, it restores the mechanism to its natural motion at the same speed."
This adjustment relates to the final section of Father Borghesi's second book, entitled "Chronologo-Astronomicus Usus Authomatis" (Chronological-Astronomical Use of the Automaton), which is translated from the Latin in its entirety:[Pg 49]
With one glance at this automaton, you can quickly answer these questions: What hour the sun shows, the moon, any fixed star, the head and tail of the dragon. Is the sea swelling with periodic heat [at high tide?] or is it deflated [low tide], or quiescent? How many days is it from mean new moon or full moon? By how many signs and degrees is the moon distant from the sun, and from its nodes? What sign of the zodiac does the sun occupy, the moon, the head and tail of the dragon? Is the sun or the moon, in apogee or perigee, ascending or descending? What is the apparent speed of the sun and of the moon? What is the apparent magnitude of the solar and lunar diameter, and of the horizontal parallax of the umbra and penumbra of the earth? What is the latitude of the moon? Is it north or south? Does the moon hide [occult eclipse] any of the fixed stars from the earth dwellers, and which of these does it obscure? Is there a true new or full moon? Is the sun in eclipse anywhere on earth? What is the magnitude, and the duration of this eclipse, with respect to the whole earth? Can it be seen in the north or in the south? Is the moon in eclipse? Total or partial? Of what magnitude, etc.? What limb of the moon is obscured? How many years have passed from a given epoch? Is this year a leap year, or a common year—first, second, or third after leap year? What is the current month of the year, and what day of the month and of the week? Which of the planets is dominant? What days of the year do the various feasts fall on, and the movable feasts during the ecclesiastical year? And many other similar questions, which I pass over here for the sake of brevity.
Besides, this device can be so arranged for any time whatsoever, past or future, and for the longitude of any region, and can be so manipulated by hand, that within the space of a very short time there can be provided in their proper order, the various orbits of the luminous bodies, their alternating eclipses, as many as have taken place through the course of many years, or even from the beginning of the world; or those that will be seen as long as the world itself shall last, with all their attendant circumstances (year, month, day, duration, magnitude, etc.). All these can be seen with great satisfaction of curiosity and of learning, and hence with great pleasure to the soul. In the meanwhile, the little bells continually play, at their proper, respective times. So that, all exaggeration aside, a thousand years pass, in the sight of this clock, as one day!
I am aware of your complaints, O star-loving reader—that my description is too meager and too succinct. Lay the blame for this on those cares, hateful both to me and to you, more pressing, which forbid me and deprive you of a methodical explanation of the work.
Father Borghesi specified that the entire mechanism was equal in weight to a seventh part of a Centenarii Germanici, a Germanic hundredweight. This is probably the Austrian centner which is equivalent to 123.4615 pounds. Therefore, the clock mechanism weighs approximately 17.6 pounds.
The clock operated for a hundred days and more at a single winding, according to Father Borghesi, and by means of a pendulum with a leaden bob weighing 60 Viennese pounds, attached at a height of 5 feet. Father Borghesi stated the weight of the pendulum to be 60 librarum Viennensium, but the Viennese libra does not appear among the weights of the Austrian Empire. However, using the average libra, an ancient Roman unit of weight equal to 0.7221 pound, it may be assumed that the driving weight should be approximately 45 pounds.
Father Borghesi, however, does not venture to provide any description whatsoever of the movement of his second clock in his book. He gave the following reasons:
But beyond this, I entirely omit [a description of] the further apparatus of the very many wheels, etc., inside the clock which carry on its functions, lest I become too verbose for some persons. To explain more thoroughly the internal labyrinth of the entire mechanism, from which the movement of the circles or heavens, etc., are derived, would seem to entangle in too many complicated perplexities.... Therefore, that I might not delay longer, and perhaps to no purpose, I have thought it better to leave the whole work to the proportionate calculus of the arithmeticians and the technical skill of mechanics. If they have any desire to construct a similar mechanism, they will follow the aforesaid motions of the heavens, etc., not only by one means alone but by many, more swiftly through thoughtful study than by any amount of instruction.
For whoever is well versed in the theory of calculus and sets to work at any given project, will discover any desired motion by a thousand and more ways, by one or another gearing of wheels; which an industrious mechanic will carry out in actuality and without too much difficulty. Nor is there any reason for anyone to be discouraged, so long as he is not disgusted by the amount of labor for there is nothing truer than the old saying "The favorable gods grant everything to the assiduous laborer."
Nay, further, even this little work itself can be improved on and surpassed by new inventions. Otherwise that other old adage, almost as old as the world, would prove false, "What you have found already done, you can easily repeat, nor is it difficult to add to what has already been invented." Relying on this principle, I have already conceived some new things to be added to the present little work.
There is a discrepancy between Father Borghesi's written description in his second book of the number of bells and those which currently exist in the clock. At the present time, there are two sets of bells attached to the upper part of the movement. While Father Borghesi indicated that there were two sets of bells in the clock, he described the first set by stating that:
... there are three bells inside the clock: The largest, when struck by a little hammer at each mean new moon, signifies the new moon. The smallest indicates in the same way the full moon at the time of the mean full moon, by automatic sound. When on the equatorial earth, the sun appears anywhere in eclipse, two bells (the largest and the medium) sounding together automatically, announce that eclipse at the time of the mean new moon. (I think it is evident that eclipses of the sun occur at new moons and eclipses of the moon at full moon.)
When the moon is eclipsed, the smallest and the medium bells, simultaneously and automatically, announce the event to the ear at the time of the mean full moon. Besides, at the proper time and automatically, the largest of these bells announces the current solar hour and the smallest bell strikes the quarter hours.
In the clock today, the first set consists of a smaller bell fixed within a larger one. It is presumably these bells that indicate the eclipses and also strike the hours and quarter hours. A pull cord attached to the striking mechanism repeats the current hour and quarter hours at will. The second set consists of nine meshed bells struck with individual hammers operated by means of a pinned cylinder as in a music box. On the hour, the chimes play one of two melodies, which may be changed at will. While not identified, these appear to be Tyrolean folk melodies. The largest of this set of bells is dissimilar to the other chimes, and may be the third bell described by Father Borghesi to signify the new moon.
One of the most curious aspects of the second clock produced by Father Borghesi and Bertolla, as well as of the second published volume, is the presence of chronograms which occur repeatedly on the clock dial and throughout the Novissimum Theorico-Practicum Astronomicum Authoma from the title page to the end of the book. Interestingly enough, Father Borghesi did not utilize this device even once in his first little book.
Webster defines a chronogram as an inscription, sentence, or phrase in which certain letters express a date or epoch. The method used by Father Borghesi for forming chronograms was a simple one. He used combinations of uppercase and lowercase letters in two sizes in the inscriptions on the clock dial and in his writings. At first this curious combination in the inscriptions on the dial plate was a source of considerable speculation. The extremely fine quality of the engraving and artistry was such that these combinations could only be deliberate in nature and not the accidental whims or accidents of the engraver. Accordingly, they must be chronographic in intention. Such proved to be the case.
Borghesi used the larger size of uppercase to form the chronogram, and each chronogram was complete within a phrase or line. He accomplished this by using for this purpose those letters of the alphabet which form the Roman numerals. The uppercase letters found within words are copied off in the order in which they appear in the inscription or phrase. These are then converted into their numerical equivalents, and totaled. Taking the[Pg 52] uppermost inscription on the clock dial as the first example:
FranCIsCVs I sIt pLan. DoMInator aeternVs
The letters which are intended to form the chronogram are:
C I C V I I L D M I V
100 1 100 5 1 1 50 500 1000 1 5
These figures added together total 1764.
The second inscription on the clock dial which forms a chronogram is
LaVs saCrosanCtae TrIaDI VnI Deo, et DeIparae
L V C C I D I V I D D I
50 5 100 100 1 500 1 5 1 500 500 1 = 1764.
The third inscription required a little more planning, because of its greater length. Accordingly, Father Borghesi divided it into nine parts, each of which is separated from the other by means of asterisks. Each of the nine parts of the inscription formed a chronogram which, in every instance, totals to the date 1764, the year in which the second clock was completed. The same procedure was followed with the inscriptions in the lower left and the lower right corners of the dial as well as with the maker's inscription within the central disk. This inscription is
BVrghesIo DoCtore, et BertoLLa LIMatore AnnanIensIbVs
V I D C L L L I M I I V
5 1 500 100 50 50 50 1 1000 1 1 5 = 1764.
The inscriptions within the chapter ring are not utilized for chronograms, however. It is apparent that Father Borghesi was required to make a most careful selection of the texts for his inscriptions in order that none of the phrases included any additional letters which formed Roman numerals than would total to the date he desired to indicate, namely, 1764. Where it was necessary, he employed an asterisk to separate parts of texts so that each would produce the same total. Any letter that did not form a Roman numeral, even if capitalized or used in a larger size, did not interfere with the formation of the chronograms.
In spite of his ingenuity in designing a text which would include only such of the letters representing the Roman numerals which would provide the chronograms for 1764, Father Borghesi experienced some difficulties, particularly in place names. He accordingly changed them in order to avoid the inclusion of letters that would have disturbed his totals. Examples are MEGGL instead of MECHL, which had an extra C, and RVNNO instead of RVMO, which had an extra M.
When the clock had been completed and proved to work successfully, Borghesi once more reduced a description of the clock and its function to published form in a second little volume published by Monauni. This second work was also in Latin, the title of which is translated as The Most Recent Theoretical-Practical Astronomical Clock According to the Equally Most Recent System of the World. As with his first book, Father Borghesi devoted a number of pages to a preface addressed to the reader, which is translated from the Latin:
This mechanical instrument was far from being ready for public notice. A great deal of time and work remained to produce a machine of this new system from the very foundations; then, by a most accurate calculation to bring the motions of many wheels up-to-date with the most recent astronomical observations; and, finally, to fashion it with the craftsman's file, often enough with a weary hand. All this work I had performed eagerly, so that, while in my room, I might contemplate leisurely, both day and night, the true face of the heavens and the seas unobscured by clouds, even though I had no astronomical equipment. But, then I remembered that, in my book on the first clock, I had promised a description of a new (at least, as far as is known to me) clock. Moreover, friends with astronomical interest, who took part in the oft-repeated astronomical experiments concerning this clock, persuaded me that the intellectual world would enjoy having a greater knowledge and a description of this work. However, it was not only the promises nor the desires of many which moved me to write this work, but I also thought it was necessary to set forth, before the description of the clock, an exposition of the astronomical system according to which this clock was constructed, so that the complete work would be evident to all. I was concerned about making this timepiece more acceptable and more understandable to those people who are far distant and unable to see it, so that this present exposition would obtain credulity among all. I could find no better method than to set forth for the reader the theory of the universe which I figured out after many sleepless nights.
In testing this theory day after day, it not only appeared to be complete, and true, but each day it appeared more conformable to reality; it captured my mind in such a way that I finally adhered to it. I desired, while I lived, to erect this work as a monument to the theory. To do this, I digressed a bit from the true-to-life pattern to the mechanical order so that I could transfer all the movements of the heavens, etc. (which I enjoyed thinking about more), to the plane surface of the clock's face. In this way, the ecliptical spectacles of the stars, etc., would appear at their proper times clearly before the eyes of the viewer. I could also avoid many difficulties which otherwise, perhaps, even the hands of the most skillful craftsmen could never solve.
You ought to know, therefore, that as a result of my nightly meditations, I have rejected, after much consideration, all the explanations of the universe thus far published. All other theories of the make-up of the universe, however admirable, and however many there are, turn the sun and earth around in an ecliptic in an annual movement. Thus, Philolaus was the first to move the earth from the center of the universe and move it through the void; afterwards, Aristarchus of Samos and then Copernicus moved the earth with the moon. The Egyptians, as well as Pythagoras, Ptolemy, Tycho, Riciolus, Longomontanus, etc., thought that the sun moved through the degrees of the ecliptic each year. But I attributed this movement to neither earth nor sun for the movement of both is only apparent. I did not vainly surmise the annual equilibrium in all astronomical observations to be from the daily movement of the same axis moved at the poles of the heavens. Nor, in like manner, is there a better way to satisfy physical experiments. To you, then, most cultured reader: If you, perhaps, can make any use or draw pleasure from this most faithful description of my new theory and the mechanical instrument, refer it first to God on High from whom is everything that is best, and then to those avidly awaiting this little work. Lastly, if you find any statement less fitting; in your humanity, do not disdain to excuse it.
In Father Borghesi's second volume, there is a separate chapter entitled "An Exposition of the Latest Theory of the Universe." This follows the introduction to the reader, and in it Father Borghesi proposed:
That you might rightly conceive my new of the world and mechanically, as it were, construct it, imagine for yourself, beneath that most happy seat of the Blessed and above all other heavens, a kind of spherical convexity, everywhere equidistant from the center of the earth, and endowed with absolutely no motion.
On the inside, at two points diametrically opposite each other, this convexity has two most sturdy poles (to speak mechanically), projecting towards the center (which you call the poles of the heavens), and the largest immobile semicircle, in some manner is drawn from the center of one pole to the center of the other. This semicircle in the middle, namely at a point equidistant from each pole, is thought to be secured by some sign, for example, by that "o," for arranging more perceptibly the seat of the sun (as will be shown later). This much must be conceived first.[Pg 55]
You must understand that imposed on these poles is the first mobile [Primum Mobile], everywhere convex, and divided, into 12 equal parts [Dodecatemoria], by the 6 greatest circles, intersecting each other at the centers of the poles. Then it is divided by another equally great circle, everywhere equidistant from the poles, into two hemispheres. One hemisphere of 12 parts, proceeding in order from west [setting] to east [rising] should be assigned the respective signs of the zodiac; that is, one to Aries, the next to Taurus, and so on, etc. The circle which cuts those 12 parts transversely in the middle, you call the ecliptic. Then, these capital spaces of the Primum Mobile are subdivided by degrees, minutes, etc., both in longitude and in latitude, so that this heaven represents a kind of great spherical net, extended to capture the longitude and latitude of the stars, and Mobile on the aforementioned poles. Note, however (and this is almost the leading point of system), in that circle of longitude which divides the sign of Gemini from Cancer and Arcitenens [Sagittarius] from Capricorn, you must conceive two points, directly opposite each other and removed about twenty-three and a half degrees from the poles: Boreal [the northern] between Gemini and Cancer; Austral [the between Sagittarius and Capricorn. These two points by some power (imagine it is magnetic power), equal between them, hold the terraqueous orb suspended in the middle, by acting on the axis of the same orb (imagine it is iron) in such a way that the earth is continually drawn to those two points as to two opposite centers. It is never nearer to one, for as it is about to move towards one, the opposite power is constantly drawing it back. Thus, both those points and the axis of the earth are held in one common line, wherever those points happen to be carried by the rotation of this heaven.
Again, it is necessary for you to conceive in this heaven, first, two great circles, bisecting each other at right angles in the centers of these two magnets. One of these circles, passing through the first point of Aries and Libra in the ecliptic, is called equinoctial colure: the other circle, passing consequently between the first point of Cancer and Capricorn, is called solstitial colure. Beneath these are likewise imagined many other great circles, in the centers of the magnets dividing crosswise in the shape of an "X." But if, receding from these magnets, you describe circles (parallel to each other and ever greater and greater, up to the greatest circle which you will perceive is called the equator), equidistant from each magnet and obliquely splitting the ecliptic in the equinoctial colure, you can then behold a great, new, woven net in this heaven of the Primum Mobile. This net most beautifully expands to extract the straight ascent and descent of the stars, etc., from the vast ocean of the heavens, catching the straight ascent in the greatest circles and, in other unequal circles, parallel to each other and obliquely cutting across, most safely catching the descent.
[Pg 56] Immediately below the Primum Mobile place the heaven of the fixed stars (and, that the idea might be clearer), revolving separately on the same poles on which the Primum Mobile revolves. Through this heaven, the filaments of the little nets, etc., seem to the eyes of you on earth as if they shine. In this heaven, you should conceive in their fixed places, the fixed stars, a proportionate, inviolable distance from each other, and, indeed, if you will, the heavenly images, etc., depicted, and all carried along at the same time with their heaven by one motion.
Conceive a straight line running from the center of the earth to that sign "o" noted in the semicircle of the supreme immobile heaven. On this line, greatly below the heaven of the fixed stars, place the center of the solar epicycle, holding an area in common with the ecliptic and subject to absolutely no motions, but at such a distance from the center of the earth that the semidiameter of the earth has little, if any, proportion with the distance of the solar epicycle from the earth. Around the sun, moving continually in this epicycle (its immobile palace) through the degrees of the anomaly, you can revolve, with motions proportionate to the system, the five planets: Mercury and Venus (the nearest barons of the sun), then Mars, Jupiter and, most remote, Saturn, with its respective satellites, etc., surrounding the earth itself and the moon in their immense ambit and wandering by their proper motions through the zodiac.
Nevertheless, not far from the earth you should imagine fabricated, as from most refined crystal, the heaven of the moon everywhere equidistant from the center of the earth and revolving separately on the same poles (prolonged even to this place) on which the Primum Mobile and the heaven of the fixed stars revolve. In the middle of this, that is, in some point equally removed from the poles, you place the center of the lunar epicycle, movable also by the common rotation of the lunar heaven. I refrain from the other movements of the moon in latitude, etc., as also those of the five planets, etc., which the theory in no way excludes, lest by a variety of congested motions explained too abundantly, either you might be confused about the fundamental concept of the system or, while adorning the theory and trying to embellish the least things more widely, you might reject also the things which are capital.
Here you already have the whole machine, but still inert and to be animated for the first time by motions accommodated to the system. Nevertheless, before I assign motion to the individual parts of the world, so that the thing might later appear more clearly to you, I arrange all things thus: first, as if by hand, I turn the Primum Mobile until the Boreal magnetic point comes to the level or the area of the semicircle described in the supreme immobile convexity; then I turn the heaven of the fixed stars until, for example, the heel of Castor (a star of the third magnitude), almost in the ecliptic and indeed in our time not far distant from the solstitial colure, likewise falls nearly at the level of the aforesaid semicircle. Later, I turn the lunar heaven until I bring the center of the lunar epicycle to the same level. Then, I turn the earth until some predetermined city, for example, Trent, situated in the northern zone with a latitude of about forty-six degrees, is brought to the oft-mentioned level.
From things arranged in this way and from what has gone before, it is evident (with the motions of the luminaries in epicycles left out, however, lest you be distracted by the explanation) that at Trent, just as in the whole northern hemisphere, it is the summer solstice; and, conversely, in the southern hemisphere, it is the winter solstice. The reason is because the northern magnetic point together with the northern half of the earthly axis is at its highest point towards the sun, immovably residing in a line sent through the level of the highest semicircle; and, conversely, the southern magnetic point with the corresponding half of the axis is most removed from the same. It further follows, that noonday and the new moon coincide, and the heel of Castor almost reaches the summit, etc.
Now, beginning from this hypothetical situation of the whole world as from the root of the motions, I move all things in their circles so the earth turns on its axis with a revolving motion from west to east in each 24 hours of median time. The lunar heaven completes one circle around its poles likewise from west to east in the time of 29 terrestrial revolutions, hours 22.214.171.124.1. The sphere of the fixed stars on the same poles revolves once from east to west within 365 revolutions of the earth, hours 126.96.36.199. The Primum Mobile on the poles (common to the heaven of the fixed stars and the heaven of the moon), is moved once in the same way from east to west, a little faster, however, than the heaven of the fixed stars, yet within 365 revolutions of the earth, hours 5.48.56; that is, within a median astronomical year.
Now, behold for yourself a new world supported on new poles and provided with new motions and laws. Now you, reader and lover of the stars, turn it, and revolve it as long as it pleases you, and compare it astronomically and physically with the Copernican or the Tychonian systems or with whatever one pleases you more, and judge which one seems more consonant with nature when all things are examined. But if you aren't able to reconcile this theory with some astronomical observations or physical experiments and think it should be[Pg 57] eliminated from the group of theories, see that I might know this while life is still my companion, so that I might think with you, if this is possible. Also, so that, in gratitude for the detected or perhaps hidden error, I might speak or write, and you won't have to shout in vain in bold ridicule and with no applause after the fleeing shades of the dead and the mute ashes. But, if you object that the daily motion of the revolving earth and the annual motion of its whirling axis do not sufficiently agree with certain texts of Sacred Scripture, and if those things which the Copernicans and the Longomontanists say do not convince you, then reject my whole system as an old wives' tale.
There is a break in the story of Borghesi and Bertolla for the next five years. The second clock may have been the last project on which the priest and the clockmaker worked together, for very good reasons. The two clocks must have represented a considerable financial investment in materials and in time, and neither of the men was in sufficiently affluent circumstances to undertake the luxury of such a hobby without some form of recompense. The publication of the two little volumes must have also been done at Father Borghesi's expense. The income of the parish priest in a small mountain village could not have been equal to the relatively great costs of the projects that had been completed. It seems probable that the priest attempted to sell his clocks to a wealthy patron, perhaps the Baron of Cles, or he may have attempted to obtain some form of recompense for the continuation of his research. However, no records can be found of such patronage if it existed. If Borghesi had received financial assistance while the projects were in progress, he would certainly have made adequate mention of the patron's name and assistance in one or the other of the two volumes which he published.
The next record relating to Borghesi which has been found is the description of a letter written by an anonymous mathematician late in 1768 or early in 1769. It was 28 pages in length, written in Latin, in the form of a reply to the writer's brother, on the subject of the clock invented by Borghesi. It consisted primarily of a criticism launched against Borghesi's first little volume published in 1763.
The anonymous letter is without date, place, or signature. This writer claimed that Father Borghesi had made many errors in his book, presumably in the description of the clock's functions, and in the basic theories upon which the priest had predicated his research. No complete copy of the letter's text has been found for study, although it is described at length in Tovazzi's Biblioteca Tirolese. Tovazzi noted that four copies of the letter existed at that time, and that he personally had filed one in the Biblioteca di Cles in Trent. However, every attempt to locate a copy at the present time has been unsuccessful.
If the anonymous letter was brought to the attention of Father Borghesi, it must have introduced a disturbing note into his life and cost the priest many unhappy moments. He was not, however, dissuaded from his preoccupation with horology. Several years later, in 1773, Father Borghesi was working on yet another astronomical clock, this time presumably without the assistance of Bertolla. This third clock was reported by Tovazzi to have been "of minimum expense but of maximum ingenuity."
No subsequent information relating to it has come to light, and there is no record that it was actually completed.
Again there is a period of silence in the life of Father Borghesi which no amount of research has yet been able to pierce. Whatever the circumstances may have been, it is reported by several of the sources noted that both the first and the second clock did, in fact, become the property of the Empress Maria Theresa in Vienna. The presentation was made sometime during the period between the completion of the second clock in 1764 and the year 1780. There is some discrepancy in the contemporary accounts as to whether Father Borghesi presented one or two clocks to the Empress, but all the sources with but one exception record that both clocks were acquired by the Empress.
It is doubtful that Father Borghesi had originally intended to give his clocks to the Empress at the time that they were made, for he would most certainly have made some mention of such an intention in the two little volumes which he published about them. If he saw the letter published by the anonymous mathematician in late 1768 or 1769, it is possible that he decided to make the presentation in expiation of his sense of guilt for the amount of his time which the creation of the timepieces had consumed. On the other hand, it is just as possible that Father Borghesi may have forwarded copies of his two little volumes to the Imperial Court at Vienna, and that the[Pg 58] Empress expressed a desire to acquire the clocks.
Father Tovazzi states that in 1780 "the clock invented by him [Borghesi] was preserved in Vienna, Austria, at the Imperial Court from which the inventor was receiving an annual pension of 400 florins." No records in the Palace archives relating to the clock have yet been found, nor records of payment of an annuity to Father Borghesi. However, a more exhaustive investigation of the Furniture Depository of the Imperial Court may bring forth related records. It was the implication in Father Tovazzi's account that the second clock had been presented to the Empress prior to the publication of the anonymous, critical letter in 1768 or 1769. He believed that it was envy of Father Borghesi's ingenuity, fame and financial benefit that had caused the anonymous mathematician to publish his letter, for Tovazzi asked "Who would have encountered opposition to such a marvel? Envy is not yet dead, and has always reigned."
This last-mentioned theory about the presentation may be the most likely one. Some evidence may be found in the second clock itself which bears out this assumption. The multiple chapter ring, with its many inscriptions, is engraved and silvered in a relatively crude manner, presumably by Bertolla himself. The main dial plate, however, which is of gilt brass, is engraved with the utmost skill by one of the great masters of the art. The inscription below the Imperial Hapsburg eagle relates to Francis I, Emperor of the Holy Roman Empire. It is entirely possible that although Father Borghesi originally had no intention of giving the clock to the Emperor or the Empress at the time that it was made, he later changed his mind. Accordingly, he may have commissioned a master engraver, possibly in Trent or in Vienna itself, to produce a dial plate which would be of such a quality as to be worthy of the Emperor himself. If so, this was done shortly after the clock was completed, for the Emperor died in August of the following year. Perhaps by the time that the clock was ready, the Emperor had already died, and Father Borghesi gave the clock instead to Maria Theresa without revising the inscription.
The acceptance of the clocks by the Empress, and the annuity which was his reward, would have constituted considerable honor even for one of the foremost clockmakers of the Empire, but for a humble parish priest in a little village, such notable Imperial recognition was overwhelming. Possibly as a result of it, a change was noted in Father Borghesi in the next few years. His conscience began to bother him, and he began to question whether he had done right in spending so much of his time and thought on his horological research. He became more and more confused in his own mind. Had he spent too much time in mechanical studies to the neglect of his ecclesiastical duties? If this had been the case, he had committed the most grievous sin.
Exaggerated though these thoughts may appear, they were undoubtedly of the most critical importance to the middle-aged priest. His mental turbulence and confusion increased daily, and it soon became apparent to others around him. By June 1779, he was completely in the grip of his obsession, and his parishioners began to whisper amongst themselves that their pastor was being tortured by the devil. They were unable to help him, and he became more and more preoccupied with his problem. The years passed slowly as the pastor became more vague and more tortured by his conscience.
There probably was continued contact between Father Borghesi and Bertolla for at least some time after the development of his illness. Bertolla had retired from active work, but continued to pursue his interests in his clockshop as much as his health and advanced years permitted. A clock which he made at the age of 80 survives and is described and illustrated in the following section on "The Clocks of Bartolomeo Antonio Bertolla." Finally, on January 15, 1789, Bertolla passed away and Father Borghesi was left alone, deprived of the companionship he had enjoyed with the older man for the past two or three decades. One of Bertolla's nephews continued to work in the master clockmaker's workshop, but there did not appear to be any association between the younger man and Father Borghesi.
At last, in 1794, Father Borghesi lost his sanity completely, and he was forced to relinquish his pastoral duties to a curate. For the remaining eight years of his life, he continued to live in the rectory of the little parish church in Mechel where most of his life had been spent, his needs undoubtedly attended by the parishioners he could no longer serve. During this period, until his death at the age of 79 on June 12, 1802, Father Borghesi lived on, oblivious of those around him. Seemingly, he retired to another world; perhaps to that universe which he had tried to reproduce in his second clock.
The ingenuity displayed in the Borghesi clock by its constructor, Bartolomeo Antonio Bertolla, requires a consideration of the other examples of his work that have survived. The most important of his clocks are probably the one in the Episcopal Palace at Trent and another made for the Baron of Cles.
The one which survives in the Episcopal Palace to the present time, is extremely tall and is housed in an elaborately decorated narrow case of black or ebonized wood approximately 9 to 10 feet in height. The upper part of the case is decorated with elaborately carved and gilt rococo motifs. The movement operates for one year at a winding, indicates and strikes the hours, and shows the lunar phases. It has an alarm, and will repeat the strike at will, indicating the number of the past hour and the quarters. The gilt brass dial is decorated with silver-foliated scrollwork in relief at the corners, inside the chapter ring, and within the broken arch. Featured above the chapter ring is the coat of arms, executed in silver, of the patron for whom the clock was made, Cristoforo Sizzo di Noris. Di Noris was Bishop of Trent for 13 years, from 1763 to 1776.
The clock which Bertolla made for the Baron of Cles is a tall, narrow, case clock of ebony or ebonized pearwood which is approximately 9-1/2 feet in height. The decoration of the case is considerably more conservative than the one made for Di Noris, but the black wood is decorated with silver trim and carved designs in the wood itself. The dial is decorated with silver scrollwork and spandrels within and around a raised chapter ring. The clock operates for one month at each winding, has an alarm, indicates and strikes the hours, and will repeat the quarters. This handsome timepiece is still in the possession of the descendants of the Baron of Cles.
According to Pippa, certain characteristics become apparent in a study of the surviving clocks by Bertolla. The tall-case clocks are narrow and range in height from 7-3/4 feet to 10-1/2 feet. The cases had this excessive height in order to obtain the greatest fall for the month and year movements which Bertolla constructed. For the weight assembly, he substituted a drum wound with a key at the point of the driving wheel in place of the customary pulley. The addition of an intermediate wheel augmented the drop of the weight.
Bertolla's movements were solidly constructed from well-hammered brass and iron. He favored the recoil anchor escapement in his clocks and the Graham dead-beat anchor escapement with a seconds' pendulum. The escapement was not always placed in the traditional location in the upper center between the plates. Bertolla occasionally displaced the pendulum to one side, to the lower part of the movement or placed it entirely between two other small plates.
He utilized every type of striking work, including the music-box cylinder common in the clocks of the Black Forest and the rack and snail. Bertolla most frequently employed the hour strike and grand sonnerie. He often used a single hammer on two bells of different sound with the rack and snail. An example of this type is the clock he produced at the age of 80. To achieve the necessary axis of rotation for the hammer, which is perpendicular to the plate when it strikes the hours, it moves to an oblique position and displaces one of the two long pins in an elongated opening.
Bertolla's dial plates were generally well executed,[Pg 63] with a raised or separate chapter ring applied to a brass or copper plate, such as a copper-plate repoussé and gilt with baroque motifs, or upon a smooth brass plate with spandrels of repoussé work usually of silver, in relief and attached. The engraving of the chapter rings was excellent. The hands were well executed in steel or perforated bronze, and occasionally of repoussé copper; gilt was applied to the hands made of forged steel.
In the course of time, Bertolla's home workshop passed from one generation to another within the family. Inevitably, it underwent many modifications until the only original part of the building that remained intact from Bertolla's time was his clockshop.
Within the last few years, the workshop room was acquired complete with contents from Bertolla's descendants, and installed in the Museo Nazionale della Scienza e della Tecnica in Milan as an exhibit of a typical 18th-century clockmaker's shop. The original workshop was dismantled in Mocenigo di Rumo and completely rebuilt in the museum, including the walls, ceiling and floor. The paneling and woodwork of the walls and ceiling, which have been preserved intact, are hand-cut fir, with columns, trim and moldings carved by hand. A small painting is featured in the center of the coffered ceiling. The original shop benches and chests of drawers are set around the reconstructed shop and Bertolla's tools and equipment laid out as they had been originally. Other clockmaker's tools and equipment in the museum's collection are also displayed. Approximately 40 percent of the tools are the original items[Pg 64] from Bertolla's shop. Parts of clocks and works in progress are on view on the benches as they were in Bertolla's time. Also preserved in the museum are sketches found in Bertolla's manuscripts, some of which are reproduced on the following pages.
The shop contains two completed clocks made by Bertolla. One is a weight-driven lantern clock typical of the 18th century, Italian style with brass dial, plates and posts, anchor escapement, and striking work. The dial is engraved in the usual style of Bertolla's baroque design, and the hands are of pierced bronze. Another clock associated with Bertolla and found in the shop, was made by his nephew, Alessandro Bertolla, who worked in Venice after his apprenticeship with his uncle had been completed. This clock is a regulator with a seconds' pendulum and sweep hand on an enameled dial. The original case has not survived.
One of the most interesting of Bertolla's clocks, and probably the last one which he produced, was found in his workshop. This timepiece indicates the hours, minutes and quarters by means of a single hand or index. The weight-driven clock strikes the hours and quarters on two bells with a single hammer. The chapter ring, which is soldered to the dial plate, is marked for the minutes on the outer rim and for the four quarters inside it. Over the center of it, is a semicircular opening in the dial plate through which is visible a revolving disk attached behind the dial plate. This disk is marked with the hours and revolves from right to left, the current hour being indicated by a projection from the minute ring. The brass dial plate is engraved with simple floral designs in the corners and around the broken arch. There is no comparison between this crude and simple decoration and the extremely fine quality of the engraving on the dial plate of the Borghesi clock, for instance. In the center of the dial plate is engraved the following:
"Questo orologio l'ideai e lo feci nella mia avanzata età d'anni 80. Barto Anto Bertolla"
(I designed and made this clock at my advanced age of 80 years. Bartolomeo Antonio Bertolla.)
 Borghesi, Novissimum Theorico-Practicum Astronomicum Authoma Juxta Pariter Novissimum Mundi Systema..., pp. 8-9.
 Wenham, "Tall Case Clocks," p. 33.
 Von Bertele, "The Development of Equation Clocks," parts 1 through 5.
 Engelmann, Philipp Hahn; Vischer, Beschreibung mechanischer Kunstwerke....
 Lloyd, Some Outstanding Clocks Over Seven Hundred Years, 1250-1950, pp. 116, 118, 120.
 San Cajetano, Praktische Anleitung für Künstler....
 Franch, La Valle di Non.
 Bonomi, Naturalisti, Medici e Tecnici Trentini, p. 16
 Ambrosi, Scrittori ed Artisti Trentini, pp. 132, 525.
 Pippa, "Antonio Bartolomeo Bertolla," pp. 22-23.
 Ibid., p. 22.
 Ibid., p. 23.
 The abbreviation in the inscription "pLan" is difficult to interpret. According to Father F. X. Winters, S.J., it may represent "sit planetis" or "sit planetarum." The use of an abbreviation was necessary to prevent the addition of another letter I or M, which would have disturbed the formation of the chronogram desired. Literally, "sit planetis" means "May he be eternal ruler by [or through] favor of the planets," while "sit planetarum" is to be translated "May he be eternal ruler of the planets." Father Winters considered both versions somewhat overexaggerated and proposed that the best translation might be "Long Live Francis I, Emperor."
 The word "Tempe" refers to the Vale of Tempe, in Thessaly, through which the Peneus River flows. It is between Mounts Olympus and Ossa, and is situated between the town of Larissa and the sea. In mythology, it is told that these mounts were originally joined and Hercules separated them to allow the river to pass between them. The word "Tempe" is also used to mean any pleasant place. Thus, the inscription "Tempe indesinenter clausa, Scaturigo signata" is literally translated "Tempe always closed, A fount of water sealed up" or, freely translated, as "A garden enclosed, a fountain sealed up."
 "Phoebi" or Phoebus, called Apollo, the sun god; Phoebes or Diana, the moon goddess, sister of Apollo.
 Pippa, op. cit. (footnote 11), pp. 23-25.
 Perini, Statistica del Trentino, Biblioteca Communale del Trentino, vol. 2, p. 57 (cons. 6, carta 9); Tovazzi, Biblioteca Tirolese, pp. 406-407.
 Pippa, op. cit. (footnote 11), pp. 24-25.
 Piamonte, La Nauna Descritta al Viaggiattore.
 Esposti, "La Sala 'Innocente Binda' al Museo della Scienza e della Tecnica di Milano," pp. 18-21.
[Translated from the section entitled "Synopsis Totius Operis Mechanici" in Francesco Borghesi's first book Novissima Ac Perpetua Astronomica Ephemeris Authomatica Theorico-Practica....]
Of three movable indices, the farthest from the center of the dial is fitted with an index on either side and marked with four segments of a circle. Immediately below are five numbers, divided into the days of setting the measure of the mean-synodic age of the moon, and into signs, degrees of the signs, and of the distance of the moon from the sun. These, in each revolution, revolve once around the solar disk superimposed on the mean synodic-lunar disk, and also around the lunar disk. The upper indices, meanwhile, in the two external greatest orbits, measure the time continuously, in the accustomed manner of the Germans—the middle index measuring by hours and the uppermost by the first minutes [of hours].
Inside these three circles, perpendicular above their center, is a small index of the seconds of minutes. At each first minute of time, being the fastest of all, it describes the smallest orbit. Next to this are two other slightly larger circles divided into 30 degrees, one [rotating?] from the right, the other from the left. These two indices are arranged in such a fashion that the one rotating from the observer's left completes its period 12 times during one, mean, solar-astronomical year. The one [rotating] from the right likewise completes its cycle 12 times during the period of one mean-synodic moon. In between these, there is placed another small sphere, divided into 40 arbitrary parts, whose dial does not move automatically, but is moved by hand for speeding up or slowing down the course of the time, or of the perpendicular.
Diagonally from the sides of the center of the three larger indices, six other indices revolve: three on the left from one center, and three on the right from another. The uppermost of the three which are on the right of the observer [and which are] decorated with a small disk of the sun, runs its cycle once during a mean solar-astronomical year. The second measures the distance of the sun from its apogee. The third revolves 12 times, with each lunar revolution from one node to the same [repeated] node. Under the point of the uppermost index, first lie the months of the year which are inscribed, and the days of each month, but having only 28 days assigned to February; then the signs of the zodiac, and their several degrees. The circle corresponding to the middle index, extending through the first semicircle from apogee to the lower perigee and returning through the second semicircle to the upper locations of apogee, shows the true equation or eccentricity of the sun, joined with the little equation of the moon in syzygy. [These equations are] measured by geometric-astronomic propor[Pg 72]tion for each distance of the sun from its apogee or perigee in degrees, and in sufficiently small parts of degrees, with the title added above in their proper places, whether an addition is to be made to the mean location of the sun or a subtraction from the same, so that the true longitude of the sun may be calculated. Three circles are assigned to the lowest index, of which 30 degrees of distance of the moon from its nodes comprise the larger. The middle circle is based on the hypothesis of the mean invariable diameters (that is, of the sun, the moon, and the terrestrial shadow), and is divided into hours and quarters of duration. The last circle is divided by the trigonometric laws into the inches of magnitude of lunar eclipses. Lying between these circles, there is another eccentric circle (black with a spot) exhibiting the shadow of the earth, in which the little moon sinks itself, carried by the lowest index. In any ecliptic full moons, the patent number of inches of immersion somehow affects the minds of the cultured, but also the scheme of maximum obscuration affects the eyes of the illiterate themselves.
Of the three indices which revolve from the left, the uppermost completes its cycle within 12 hours, just as the hour index. The middle one with two pointers on diametrically opposite sides, carries the marks of conjunction and opposition of the luminous bodies, with a movement equal to the course of the sun from lunar apogee or perigee. The lowest index, fitted with a single pointer, indicates the motion of the moon from its apogee or perigee. Under these three indices, there is situated a common circle, divided into 12 parts, each of which are further divided into 30 parts through its outer circumference. I have said a common circle, for, with respect to the first index, the division represents 12 hours, and the double subdivision representing the double set of minutes of the hours serves for an excitator for anytime at all, at will. For as often as the little index reaches the twelfth hour, first being moved by hand wherever you prefer, a little hammer strikes the little bell many times. But if you observe the second or the third index, the first division provides the signs, and the subdivision of the signs gives the individual degrees of the distance of the sun from the lunar apogee, or of the moon from its apogee, respectively. To this is added two other interior circles from the same center: to the larger is inserted the equation of the center of the moon in its conjunctions and oppositions; and on the smaller the equation of the same moon in its quarters, astronomically-geometrically proportioned to the distance of the moon from its apogee or perigee. In the first case, the equation is to be subtracted from the mean longitude of the moon, descending from apogee to perigee; in the second case, to be added to the mean longitude of the moon ascending from perigee to apogee; and, in the third semicircle of the index, as the rubric directs, common to both equations, added around the center.
Perpendicularly under the center of the machine, two other indices are carried about one and the same center. The one nearer to the observer—bearing in one of two points diametrically opposite the small disk of the sun, in the other the disk of the moon—runs a course equal to the motion of the sun from the head or the tail of the dragon (Draco). The other, of simple construction, marked with a small moon, signifies in like manner the motion of the moon from the head or the tail of the dragon.
Immediately below, there is a larger circle, common [referring] to both these indices, which is divided into 12 parts. Each of these parts in turn, in the outer periphery, is subdivided further into 30 parts, which are the 12 signs of the zodiac and the individual degrees of the signs of distance of the sun and the moon from the head of the dragon.
In the second circle is read the latitude of the moon, measured by degrees, etc., on a trigonometric scale, by signs and degrees of distance of the moon from its nodes, that is, from the head or tail of the dragon. When the second index is descending from the head of the dragon to the tail, the latitude will be to the north of the solar path; that is, the ecliptic. On the other hand, it will be south of the ecliptic when the same index is returning upward from the tail to the head of the dragon as advised by the title inscribed on the third circle.
Finally, on the fourth and last circle are seen more prime minutes of the circle for reducing the orbit of the moon to the ecliptic. That the true longitude of the moon may be obtained more accurately, these must be subtracted from the longitude of the moon[Pg 73] already calculated in the first and third quadrant of the circle of the second index. On the other hand, they are to be added to the same in the second and fourth quadrant, as is noted in their respective places, according to the theory of right ascensions.
Here, then, [you have] as finally completed, delineation of the great index which was partially described before in this book.
From two points of that index which perpendicularly correspond to the center of these circles, a pair of compasses, by an unvaried aperture up to the circumference of the first larger circle, has marked off four segments of a circle. The two larger segments, equal among themselves, in one aperture refer to the sun, and the two smaller in the other, likewise equal, refer to the moon. The one pointer is for determining the solar eclipses; the other, for lunar. Both segments of each division, like little wings of the index, stretch to the extent of the degree of distance of the moon from its nodes, and to which that determined latitude corresponds. On one side, that latitude precisely equals the radii of the earth, the sun, and the moon, as the termini of solar eclipses; and, on the other side, precisely equals the radii of the earth's shadow and of the moon, as the confines of lunar eclipses. The apexes of the last index, diametrically limited [opposite], indicate the age of the moon, and its mean distance from the sun; one pointer, upon which the sun sits, measuring the mean days and degrees from the full moon; the other, on which the moon sits, measuring the mean days and degrees from the new moon.
Besides the larger and smaller indices already mentioned, all [of which] revolve within the periphery of the three largest circles, six dials in this clock also revolve within the same circles which are to be seen through six openings of the frontispiece. The first of these, intended to indicate the phases of the moon by an unusual method (completely black, and decorated with the characters of the principal aspects of the moon) continually revolves interiorly around the center of the machine and at the new moon, it completely removes from sight the face of the moon through the round window. It continually recedes through the first half of the circle until, at the time of the full moon, it restores the moon, looking out with a full star. Soon again, too slow to be observed, it returns through the other half of the circle, so that in the next conjunction, the whole face of the moon may have a covering of darkness, once again to be removed.
The other dials are moved by spontaneous advances at stated times. The first of these shows, through a square opening, the day of the month; the second, through another opening, shows the current day of the week with the characters of the seven planets which, according to ancient superstition, preside over each day of the week (now, by a truer form of religion divided by the Church into ferias, etc.); that is, the sun, the moon, Mars, Mercury, Jupiter, Venus and Saturn, to which I have added the numbers of the ferias. These two little dials are advanced daily, by a sudden movement at midnight. The remaining three are changed automatically only once a year on the first of January.
The first of these dials contains five little cells, opening from a 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.
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.[Pg 74]
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[Pg 75] 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.
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.
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 Matthäus 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 à. Praktische Anleitung für Künstler, alle astronomische Perioden durch brauchbare bisher noch nie gesehene ganz neue Räderwerke mit Leichtigkeit vom Himmel unabweichlich genau auszuführen, sammt Erweiterung der Theorie des neuen Rädergebäudes. 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
Aristarchus of Samos, 54
Bertolla, Alessandro, 65
Brahe, Tycho, 54
Charles VI, Emperor of Austria, 32
Di Noris, Cristoforo Sizzo, 59
Evelyn, John, 32
Hahn, Father Philipp Matthäus, 33
Klein, Father ——, 33
Lippi, Fra Lippo, 42
Longomontanus, Christian Severin, 54
Quare, Daniel, 32
San Cajetano, Brother David à, 33
San Daniele, Father Aurelianus à, 33
Sully, Henry, 32
Tompion, Thomas, 32
Williamson, Dowe, 32
Williamson, Joseph, 32
Winters, Father S. X., S.J., 42