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., eccentrically 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 that 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 12.44.3.13.1. The sphere of the fixed stars on the same poles revolves once from east to west within 365 revolutions of the earth, hours 6.9.29.1. 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 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. [17]
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 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. [18]
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 Clocks of Bartolomeo Antonio Bertolla
Figure 21.—Tall-case clock by Bertolla in the Episcopal Palace in Trent, made for Bishop Cristoforo Sizzo di Noris. A striking and repeating clock with lunar phases. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
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 91/2 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, [19] certain characteristics become apparent in a study of the surviving clocks by Bertolla. The tall-case clocks are narrow and range in height from 73/4 feet to 101/2 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.
Figure 22.—Interior of Bertolla's workshop, showing detail of ceiling. (Courtesy Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 23.—Interior of Bertolla's workshop, showing the main workbench and the collection of clockmakers' tools. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 24.—Fusee cutter used by Bertolla. Now in the collection of the Museo Nazionale della Scienza e della Tecnica, Milan.
Figure 25.—Interior of Bertolla's workshop, showing details of paneling and floor case with Bertolla manuscripts. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
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. [20]
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, 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 from Bertolla's shop. Parts of clocks and works in progress are on view on the benches as they were in Bertolla's time. [21] Also preserved in the museum are sketches found in Bertolla's manuscripts, some of which are reproduced on the following pages.
Figure 28.—Detail of wall of Bertolla's workshop, with regulatory clock made by his nephew, Alessandro Bertolla of Venice. Note wheel layouts, etc., scribed in the paneling. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 29.—Table clock by Bertolla in the collection of Doctor Vittorio dal Lago of Bergamo. The dial indicates the days of the week and of the month, the names of the months and lunar phases. The clock strikes the hours and quarters and repeats. (Courtesy of Sig. Luigi Pippa of Milan.)
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.
Figure 30.—Layout of the wheelwork of a clock made by Bertolla for His Excellency Paulo Dona, inscribed "Design No. 1." (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 31.—Pendulum arrangement sketch for an unidentified clock found in Bertolla's workshop. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 32.—Striking clock sketch found in Bertolla's manuscripts. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
Figure 33.—Fifteen-day striking clock sketch, inscribed "Design No. 3," found in Bertolla's workshop. (Courtesy of Museo Nazionale della Scienza e della Tecnica, Milan.)
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.)
[1] Borghesi, Novissimum Theorico-Practicum Astronomicum Authoma Juxta Pariter Novissimum Mundi Systema…, pp. 8-9.
[2] Wenham, "Tall Case Clocks," p. 33.
[3] Von Bertele, "The Development of Equation Clocks," parts 1 through 5.
[4] Engelmann, Philipp Matthäus Hahn; Vischer, Beschreibung mechanischer Kunstwerke….
[5] Lloyd, Some Outstanding Clocks Over Seven Hundred Years, 1250-1950, pp. 116, 118, 120.
[6] San Cajetano, Praktische Anleitung für Künstler….
[7] Franch, La Valle di Non.
[8] Bonomi, Naturalisti, Medici e Tecnici Trentini, p. 16
[9] Ambrosi, Scrittori ed Artisti Trentini, pp. 132, 525.
[10] Ibid.
[11] Pippa, "Antonio Bartolomeo Bertolla," pp. 22-23.
[12] Ibid., p. 22.
[13] Ibid., p. 23.
[14] 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."
[15] 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."
[16] "Phoebi" or Phoebus, called Apollo, the sun god; Phoebes or Diana, the moon goddess, sister of Apollo.
[17] Pippa, op. cit. (footnote 11), pp. 23-25.
[18] Perini, Statistica del Trentino, Biblioteca Communale del Trentino, vol. 2, p. 57 (cons. 6, carta 9); Tovazzi, Biblioteca Tirolese, pp. 406-407.
[19] Pippa, op. cit. (footnote 11), pp. 24-25.
[20] Piamonte, La Nauna Descritta al Viaggiattore.
[21] Esposti, "La Sala 'Innocente Binda' al Museo della Scienza e della Tecnica di Milano," pp. 18-21.
Appendix
SYNOPSIS OF THE COMPLETE MECHANICAL WORKS OF THE FIRST CLOCK
[Translated from the section entitled "Synopsis Totius Operis Mechanici" in Francesco Borghesi's first book Novissima Ac Perpetua Astronomica Ephemeris Authomatica Theorico-Practica….]
I
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].
II
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.
III
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 proportion 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.
IV
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.
V
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 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.
VI
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.
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.
The following works have been used in compiling the material for this paper. They are frequently referred to in the text in shortened form.