Tycho Speaks

Excerpt from chapter 2 of Progymnasmata

“There is also another method for determining the right ascension and declination of stars, and consequently, by means of spherical triangles, their longitude and latitude. This method is not very difficult and was also employed by modern scholars, particularly the Illustrious Prince Wilhelm, Landgrave of Hesse, which I myself have exercised on some occasions. It relies on the time when certain stars cross the meridian or occupy a known azimuth, with their simultaneous altitude measured, and the position of the Sun known beforehand. From this, their right ascensions and declinations, and therefore their longitudes and latitudes, can be calculated without much difficulty. But the main challenge of this procedure lies in the timing: the moment required, even to fractions of seconds, cannot be obtained with sufficient precision. Moreover, the position of the Sun is not known exactly, either by observation or by any reliable computation, as it was not determined previously. This complicates matters considerably. Hence, it is more appropriate to carry out this method around the equinoxes, when the Sun’s position, though variable in declination, can be more safely determined by observation. In other words, this is the time when the method can be most accurately put into practice.

And although both that most Illustrious Prince and I have labored greatly in this matter, so that we might have certain clocks constructed with the utmost accuracy, ones that indicate not only hours, but also minutes and seconds with a constant motion, of which I have three or four at hand, made with the greatest care, nevertheless, for many reasons, which I have also discussed with the most Illustrious Prince by letter, as will be shown in the book of Astronomical Epistles, these cannot be so precise as to correspond at all times, continuously and with uniform motion, to the celestial standard, as is required in so delicate a matter.

For no matter how skillfully and deftly those clocks are constructed by any mechanical craftsman, they are nevertheless subject to change because of variations in air and winds; nor is this defect sufficiently remedied if, during winter, they are kept in some heated room with as constant a warmth as possible. They also of themselves, from time to time, even if at first very carefully constructed, admit some alteration from various causes. And it can easily happen that a few teeth or wheels, being uneven in some part, slightly disturb the uniform and proportional harmony of the motion, and quietly introduce some inequality in the intermediate hours and in their most subtle divisions. Although the overall daily correction, whether compared with the Sun or with the stars, may be sufficiently accurate, yet even the cord itself to which the weight is attached, when it is let down more fully, adds somewhat more force, however slight, than when it is higher up and the weight has drawn it down less. And although this introduces only a very small difference in the motion of the clock, nevertheless, since what we seek is something extremely subtle, even an error of four seconds in the clock can produce an error of a whole minute in the position of a star, and thus it is not free from serious hindrance. There are also other factors which entirely undermine the reliability and precision required of clocks for this purpose.

Indeed, I also left no method untried by which I might mechanically measure the equality of time in agreement with the heavens themselves, namely by means of quicksilver, which chemists not inappropriately call Mercury (since it is the earthly analogue of that celestial star). I undertook to accomplish this in the following way, not without expense and labor. I sublimated many pounds of mercury, according to the method known to chemists, three or four times, removing its impurities, and each time I restored it by a certain method known to me, until it had cast off its coarser contaminants. When thus purified, I placed it into a large glass vessel prepared for this purpose, which had at its lower part a very narrow and round opening. Then, at the moment when the Sun or some star crossed the meridian, I allowed it to begin flowing, and this continuously, until that same celestial body again reached the meridian. At the same time, I took the precaution that, by means of another vessel placed above the first (supported in a suitable way), the lower vessel should remain as nearly as possible always filled to the same level, with the upper one dripping into it as much of the mercurial liquid as the lower lost by flowing out, so that the weight of the contained mercury would remain constant and thus drive the flow evenly. And so, after one full revolution, I collected the mercury and, placing it on a balance, weighed it. From this I determined proportionally, by weighing out other small portions, how much of the flowing mercury corresponded to each hour, minute, and second; so that in this way, whenever I wished, if a star were observed in the meridian at some intermediate time, I could, from the weight of the mercury that had flowed out since noon, determine how many hours, minutes, and seconds had elapsed from noon, and from this, with the Sun’s position taken into account, ascertain the right ascension of a given star. A laborious and costly undertaking indeed, so that the saying of the alchemical philosophers might be verified: “In mercury is contained whatever the wise seek.” Nor, even with mercury, though suited to all purposes and capable of being transformed into many forms, being satisfied, I also wished to try by means of lofty Saturn himself, that heavy old man (for thus the chemists rightly call lead), purified from its impurities by the force of fire and reduced to a most subtle powder by calcination, whether it too, as the highest and slowest of the planets, presiding over contemplation and higher wisdom, might through the metal corresponding to it on earth assist our difficult and arduous aim. And thus, with Saturn and Mercury joined in their operations, this investigation might be advanced, since, according to the Astrologers, their conjunction or mutual favorable influence, especially if accompanied by some configuration with the Moon, is believed above all other significations to contribute greatly to depth of intellect, ingenuity, contemplation, and steadfastness in labor.

But I made use chiefly of metals in this weighing of moments of time, because they are heavier than other substances and allow a large amount of weight to pass through a very small opening in a short time; and moreover, they are not so subject to changes of the air as those things which might be prepared from plants or animals for the same purpose.

But in truth, to say what the matter is, not only that crafty Mercury, just as he deceives Astronomers in the heavens and chemists on earth, also rendered our efforts fruitless; but even that heavy and otherwise constant Saturn did not abandon his subtle and hidden ways, and although he is laborious, he nevertheless evaded all labor.

I have recounted all these preceding matters at such length for this reason; that students of this art may understand how great a task it is to determine with exact precision the distance of even a single star in the heavens from the equinoxes or solstices, and how both the Ancients and even some of the moderns have failed in this endeavor; and at the same time, that I might show with what desire, effort, and labor, and by how many costly and difficult methods, I too have pursued this very goal for many years. From this they may also in some measure recognize how important it is to establish an accurate restoration of the fixed stars, at least so that even a single one may be precisely determined in both longitude and latitude.

But if anyone thinks that I have said anything here which would diminish or disparage the arduous efforts of the Ancients, efforts which I have always held in the highest regard, and without which now little or nothing could be accomplished in restoring this art, or likewise the praiseworthy attempts of the moderns, so that I might more arrogantly promote my own work, then such a person does me no slight injustice and shows himself not sufficiently devoted to that deeper Truth which alone we seek here, declaring nothing out of favor or hatred toward anyone, nor out of any kind of pride. For Truth ought to be dear above all things, the Queen of all virtues. But among those who understand and judge all things soberly and sincerely, such a defense (as I hope) will not be necessary.

Since, therefore, the precise restoration of the fixed stars to their proper places was found to be subject to so many and such great difficulties and obstacles, as I reflected long and carefully on what method might finally allow this task to be accomplished without any suspicion of error, behold, the heavens themselves, as if unexpectedly, generously offered a most excellent and sufficient opportunity for properly determining and arranging their stars. This occurred in the year 1582, when the star of Venus, in broad daylight together with the Sun, during a long period of very clear spring air, presented itself so visibly, both before and after noon, and even at noon, that its position and its distance from the Sun could readily and distinctly be measured with instruments. Therefore, since this opportunity, divinely offered from the heavens, was most suitable for fulfilling my long-held desire with certainty, safety, and minimal labor, I judged it by no means to be neglected. For I considered that to verify the fixed stars by means of Venus, with the Sun as intermediary, was far better, more convenient, and more certain than by means of the Moon, as had previously been attempted less successfully (for the reasons given above). For Venus, since it occupies only a small space in the sky in its visible diameter, and moves much more slowly than the Moon, its motion also being more clearly discernible, and is not entangled with such evident parallaxes as the Moon (although even here precautions must be taken regarding both parallax and refraction), seemed most suitable to be placed in charge of this task. Indeed, we rejoiced that she, by her favorable light and pleasing appearance, even when shown by day, did not disdain to favor, assist, and support our aspiring efforts. Thus, setting aside and abandoning that troublesome and difficult Saturn, together with the crafty and deceptive Mercury, I directed all my attention and effort toward the friendly and favorable light of Venus, which even by day supports our endeavors. For in this way she not only, in the heavens, by her bodily and visible presence, both by day and by night, but also on Earth, through a metal corresponding to her nature (namely copper, made purer and more shining by means of cadmium), from which instruments suitable and sufficient for this observation could be constructed, did not refuse, out of her benevolent disposition, to assist and to extend helping hands.

But lest what we intend be delayed too long, and lest we detain the attentive and eager reader longer than is proper, I shall now explain by what method, with the aid of the star ♀ through the Sun, I undertook the accurate verification of the fixed stars, and this not only for the year ‘82 (of which I have spoken), but also for several subsequent years.

I observed during the day, when the Sun and Venus were visible together, and were positioned as high above the horizon as possible, their mutual distance, and this by means of a certain special astronomical sextant instrument devised by us (the construction and form of which I shall explain later), which most precisely supplied all fractions of seconds, even down to very small parts of them, without any suspicion of error. This was done under the following arrangement: one observer would sight ♀ through certain small slits of a pinnacidium¹, aligned with the central axis of the instrument, along parallel lines fixed in place, while another observer (for two are necessary at the same time) would admit the shadow cast by ☉ from a cylindrical body into another movable pinnacidium, between two lines corresponding exactly to the shadow itself. In this way, by repeatedly aligning and sighting, the distance between ☉ and ♀ was measured with extreme precision through the adjustment of the two pinnacidia. The altitude of both ☉ and ♀, and sometimes also the azimuth in which they were situated, was noted simultaneously as required. Moreover, their declination was also measured by means of equatorial armillary spheres, in whatever position outside the meridian they were observed. Their meridian altitude was likewise obtained, when possible, by quadrants, thus completing the measurement.

Then at night, when the Sun had sunk below the horizon and the stars were visible, and when Venus still brilliantly shining, was glowing above the horizon between them, I investigated the distance of certain fixed and principal stars near the Zodiac from ♀, again using the same sextant instrument, and at that time also taking into account both declination and altitude of each body, and sometimes also its azimuth. In all cases, both by day and by night, the moments of time at which each observation was made were carefully recorded, so that, taking into account the motion of ♀ and correcting its position as seen from the Sun during the daytime, together with the proportional correction of the motion that had occurred in the meantime, we might determine the true position of the star under observation. This was done first with respect to right ascension in the equatorial circle, which, when combined with its declination, was easily resolved into longitude and latitude with respect to the ecliptic. And in this way I carefully investigated the positions of several fixed stars, and further examined them by their mutual distances. Finally, I reduced everything to that bright star which is above the head of ♈ [Hamal] so that from it the determination of the others might be derived, deliberately referring everything to the completed year 1585 as an intermediate epoch, setting aside that first star, numbered one, which Copernicus used [likely Sheratan], because it is too small and, especially when the Moon is shining brightly, not sufficiently accessible for observation. From more than a hundred observations made in that year using the above method, I shall present only three particular and select ones, and will set them out numerically and demonstratively, since upon these the whole foundation of the matter depends.

I also applied in these cases, where required, the correction and suitable adjustment of the parallax of the☉and ♀ and likewise of the complications of refraction, as one approaches the horizon.

So that these complications of parallax and refraction might not still leave some doubt in my mind as to whether they had been correctly corrected or not, thereby raising some suspicion even in the otherwise restored positions of the fixed stars, I undertook the matter by another method as well, one of a higher and more complete investigation, in certain later years.” - Tycho Brahe

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1. sights

2. For anyone who prefers the Latin https://archive.org/details/bub_gb_CVOItHLenPEC/page/n186/mode/1up