From two points of that index which perpendicularly correspond to the center of these circles, a pair of compa.s.ses, by an unvaried aperture up to the circ.u.mference 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 lat.i.tude corresponds. On one side, that lat.i.tude 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 princ.i.p.al 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 superst.i.tion, 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 mult.i.tude 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 mult.i.tude 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 a.s.suming 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 s.n.a.t.c.hed 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 pa.s.sage 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 circ.u.mstances 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 bra.s.s throughout and further weighted with two bells and a rather large bra.s.s 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 G.o.d, thrice Best and Greatest, bless the undertaking and mercifully grant life and health--to whom be in, and from, and through all things, all honor and glory in eternity and beyond.

BIBLIOGRAPHY

The following works have been used in compiling the material for this paper. They are frequently referred to in the text in shortened form.

AMBROSI, FRANCESCO. _Scrittori ed artisti Trentini._ Trent: Giovanni Zippel, 1883.

BONOMI, L. _Naturalisti, medici e tecnici Trentini._ Trent: privately printed, 1930.

BORGHESI, FRANCESCO. _Novissima ac Perpetua Astronomica Ephemeris Authomatica Theorico-Practica._ Trent: Giovanni Battista Monauni, 1763(?).

---- _Novissimum Theorico-Practic.u.m Astronomic.u.m Authoma Juxta Pariter Novissimum Mundi Systema._ Trent: Giovanni Battista Monauni, 1764.

ENGELMANN, MAX. Philipp Matthaus Hahn. Berlin: Verlag Fischer, 1923.

ESPOSTI, ALFREDO DEGLI. La sala "Innocente Binda" al Museo della Scienza e della Tecnica di Milano. _La Clessidra_ (July 1960), anno 16, no. 7, pp. 18-21.

FRANCH, LEONE. _La Valle di Non._ Trent, 1953.

LLOYD, H. ALAN. _Some outstanding clocks over seven hundred years, 1250-1950._ London: Leonard Hill, 1958.

MOSNA, EZIO. _Trento._ Trent, 1914.

PERINI, AGOSTINO (compilatore). _Statistica del Trentino, Biblioteca Communale del Trentino._ Vol. 2, p. 57 (cons. 6, carta 9).

PIAMONTE, GUISEPPE. _La nauna descritta al viaggiattore._ Milan, 1829.

PIPPA, LUIGI. Antonio Bartolomeo Bertolla. _La Clessidra_ (January 1961), anno 17, no. 1, pp. 22-25.

SAN CAJETANO, DAVID a. _Praktische Anleitung fur Kunstler, alle astronomische Perioden durch brauchbare bisher noch nie gesehene ganz neue Raderwerke mit Leichtigkeit vom Himmel unabweichlich genau auszufuhren, sammt Erweiterung der Theorie des neuen Radergebaudes._ 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.