Letter against Werner - translation
Frombork, 3 czerwca 1524 r.
To the Reverend Bernard Wapowski, Cantor and Canon of the Church of Cracow, Secretary to His Royal Majesty the king of Poland, and my most highly esteemed patron, greetings from Nicholas Copernicus.
Some time ago, my dear Bernard, you sent me a little treatise on "The Motion of the Eighth Sphere," published by Johann Werner of Nuremberg. Your Reverence stated that the work was widely praised and asked me too to give you my opinion of it. I would surely have done so gladly to the extent that I too could have really commended it wholeheartedly. Yet I may laud the fellow's zeal and effort. Moreover, it was Aristotle's advice to be grateful not only to the philosophers who have spoken well but also to those who have spoken incorrectly because to those who wish to follow the right road, it is often no small advantage to have noted the blind alleys too. Besides, faultfinding is of little use and scant profit, for it is the very mark of a shameless mind to prefer the role of the censorious critic to that of the creative poet. Hence I even fear that I may arouse anger if I reprove another while I myself produce nothing better. Accordingly, I wanted to leave these matters, just as they are, to the attention of others, and I would have replied in such a way that your Reverence would learn my attitude expressed concisely. I am aware, however, that it is one thing to snap at a man and assail him, but another thing to set him right and redirect him when he strays, just as it is one thing to praise, and another to flatter and play the fawner. Hence I see no reason why I should not comply with your request or why I should appear to hamper the pursuit and cultivation of these studies, in which you have a conspicuous place. And therefore, lest I even seem to condemn the man gratuitously. I shall try to show as clearly as possible in what respects he erred regarding the motion of the sphere of the fixed stars and maintains an unsound position. This may perhaps even contribute not a little to the formation of a better understanding of this subject.
In the first place, then, he went wrong in his calculation of time. For he thought that the emperor Antoninus Pius' second year, when Claudius Ptolemy drew up the catalog of the fixed stars as observed by himself, was A.D. 150, when in fact it was A.D. 139. For in the Great Syntaxis, Book III, Chapter l, Ptolemy says that the autumnal equinox observed in the 463rd year after Alexander the Great's death fell in Antoninus' third year. But from Alexander's death to Christ's birth there are counted 323 uniform Egyptian years, 130 days, because from the beginning of Nabonassar's reign to Christ's birth 747 uniform years, 130 days, are reckoned. This is not questioned, I observe, certainly not by our author, as is evident in his Proposition 22, except that he adds one day, in accordance with the Alfonsine Tables. The reason for this [discrepancy of one day] is that Ptolemy takes noon of the first day of the first Egyptian month Thoth as the starting point of the years reckoned from Nabonassar and Alexander the Great, while Alfonso begins with noon of the last day of the preceding year, just as we compute the years of Christ from noon of the last day of the month December. Now from Nabonassar to Alexander the Great's death 424 uniform years are counted by Ptolemy, Book III, Ch. 8, with whom Censorinus, relying on Marcus Varro, agrees in his Natal Day, dedicated to Quintus Caerellius. [This interval of 424 years, when subtracted] from 747 years, 130 days, leaves a remainder of 323 years, 130 days, that is, from Alexander's death to Christ's birth. And from that time to the aforementioned observation of Ptolemy [there are] 139 uniform years, 303 days. Therefore, the autumnal equinox observed by Ptolemy, it is clear, occurred on the ninth day of the month Athyr, 140 uniform years after the birth of our Lord, but 139 Roman years, 25 September, Antoninus' third year.
Again, in his Great Syntaxis, Book V, Ch. 3, in his observation of the sun and moon in Antoninus' second year Ptolemy counts 885 years of Nabonassar, 203 days. From Christ's birth, therefore, 138 uniform years, 73 days, would have elapsed. The fourteenth day thereafter, that is, 9 Pharmuthi, when Ptolemy observed Regulus [in the constellation] of the Lion, was 22 February, in the 139th Roman year after Christ's birth. And this was Antoninus' second year, which our author thinks was 150 [A.D.]. Hence he went wrong by eleven years too much.
If, however, anyone is still in doubt and, not satisfied by the foregoing [criticism], wants to make a further test of this matter, he should remember that time is the number or measure of the motion in heaven considered as "before" and "after." For by this motion we determine our years, months, days, and hours. But the measure and the measured, being related, are mutually interchangeable. Besides, as far as Ptolemy's tables are concerned, since in addition they were built up on the basis of his own recent observations, it is unbelievable that they contain any deviation from the observations which is detectable by the senses, or any discrepancy that would make them inconsistent with the foundations on which they rest. Since this is so, if [our skeptic] consults Ptolemy's tables and computes the positions of the sun and moon with reference to Regulus as found by Ptolemy using the astrolabe in Antoninus' second year on the ninth day of the month Pharmuthi at 5 1/2 hours after noon, he will find these positions, not 149 years after Christ, but 138 years, 88 days, 5 1/2 hours, equal to 885 years after Nabonassar, 218 days, 5 1/2 hours. In this way the error is now exposed which frequently vitiated our author's investigation of the motion of the eighth sphere when he mentions time.
A second error, no less serious than the first, is involved in his hypothesis expressing his belief that in the 400 years before Ptolemy the fixed stars moved only with a uniform motion. For the purpose of further explaining and clarifying what will be said below, it should in my opinion be pointed out that the science of the stars belongs to the category of those [subjects] which we learn in an order contrary to nature. For example, first nature knows that the planets are nearer than the fixed stars to the earth, then as a consequence that the planets appear less radiant. We, on the other band, first see that the planets do not twinkle, and then we know that they are nearer to the earth. So, by the same token, first we perceive that the motions of the heavenly bodies seem nonuniform, then we conclude that there are epicycles, eccentrics, or other circles by which the bodies are carried in this way. And therefore I would like it to be said that, with the aid of instruments, the ancient scientists first had to mark the positions of the heavenly bodies together with the intervals of time, and with this [information] as a sort of guideline, they had to devise a precise theory of the heavenly motions, lest the investigation of these matters remain interminable. They appear to have found this theory when it matched, with a certain agreement, all the observed and noted positions of the heavenly bodies. Such is also the situation regarding the eighth sphere's motion, which the ancient astronomers could not pass on to us in its entirety on account of its extreme slowness. Those who wish to examine it must follow in their footsteps, however, and hold fast to their observations, bequeathed like a legacy. But if anyone, holding fast to his own view, thinks that they are untrustworthy in this regard, surely the gates of this art are closed to him. Lying in front of the entrance, he will dream the dreams of the deranged about the motion of the eighth sphere, and receive what he deserves for supposing that he should support his own hallucination by defaming the ancients. It is well known, however, that those who handed down to us many famous and praiseworthy discoveries made all these observations with the utmost care and expert skill. Consequently I cannot possibly be persuaded that in noting the positions of the heavenly bodies they erred by 1/4° or 1/5° or even 1/6°, as this author believes. [I shall say] more about this [subject] later on.
In addition, it must not be overlooked that in every heavenly motion involving an irregularity, what we want above all is the entire period during which the apparent motion is recognized as having passed through all its variations. For, an apparent irregularity in a motion is what makes it impossible for an entire revolution and uniformity of motion to be measured by their parts. But in their investigation of the moon's path Ptolemy, and before him Hipparchus of Rhodes, divined with keen insight that the revolution of a nonuniform [motion] must have four diametrically opposite points. These are the maximum swiftness and slowness, and the mean and uniform [motion] at both [ends of the diameter] intersecting at right angles [the diameter connecting] both maxima. The circle is [thereby] divided into four equal parts, with the result that in the first quadrant the swiftest motion diminishes; in the second [quadrant] the mean motion diminishes; on the other hand, in the third quadrant the slowest motion increases, [as does] the mean [motion] in the fourth [quadrant]. By this device they could infer from the moon's observed and examined motions in what part of the circle it was at any specified time. Accordingly, when a similar motion had recurred, they understood that a revolution of the nonuniformity had now been completed, as this was explained at considerable length by Ptolemy in his Great Syntaxis, Book IV. This [procedure] should have been adopted also in analyzing the eighth sphere's motion. As I said, however, its extreme slowness, on account of which the nonuniform motion quite clearly has not yet returned upon itself in thousands of years, does not permit an immediate solution of this [problem], because it transcends many generations of men. Nevertheless it is possible by a reasonable conjecture to attain a solution even now with the aid of some observations added since Ptolemy, observations which conform to the same pattern. For what is determinate cannot have innumerable explanations. For example, if a circumference is drawn through three points not located on a straight line, superimposition of another circumference greater or smaller than the one drawn previously is impossible. But in view of my discussion of these matters elsewhere, I may return to the point where I digressed.
Hence we must now see whether our author is correct in saying that in the 400 years before Ptolemy the fixed stars moved only with uniform motion. Besides, lest we be mistaken about the meaning of terms, by "uniform motion" I understand what we usually also call "mean" motion, which is halfway between the slowest and the swiftest. Let him not mislead us by his statement in Proposition 7, Corollary 1, that "the motion of the fixed stars is slower" where according to his own hypothesis he puts the uniform motion, the rest of it being swifter, just as if it would never be slower. In these respects I do not know whether he is consistent with himself when later on he adduces a much slower [motion]. He derives his measure of the mean motion, however, from the uniformity with which the fixed stars traversed equal distances from the earliest observers of the fixed stars, Aristyllus and Timocharis, to Ptolemy, and in equal periods of time, to wit, approximately 1° every one hundred years, as is quite clear in Ptolemy, cited by our author in his Proposition 6.
But being a great astronomer, he is not aware that around the points of uniform motion, that is, the intersections of the circles (the tenth sphere's ecliptic with [the circles] of trepidation, as he calls them), the stars' motion cannot possibly appear more uniform than elsewhere. Indeed, the opposite conclusion must be drawn: at those times the motion appears to vary the most, but the least when the apparent motion is swiftest or slowest. He should have seen this even from his own hypothesis and system as well as from the tables based on them, especially the last table, which he drew up to exhibit the revolution of the entire nonuniformity or trepidation.
In this regard, according to an earlier computation, for 200 years before the birth of Christ the apparent motion is found to be only 49' of 1° in the first 100 years, and in the second century 57'. Then after Christ's birth in the first 100 years the stars would have moved about 1 1/10°, and in the second 100 years about 1 1/4°. Thus in equal periods of time the successive motions increase by a little less than 1/6°. But if you combine the motion of the two centuries in either era, the first period's [total] will fall short of 2° by more than 1/5°, while the second [period's total] will exceed [2°] by about 1/4°. Thus again in equal times the later motion will exceed the earlier motion by about 1/2° + 1/15°. Yet previously in reliance on Ptolemy our author had reported that the fixed stars passed through 1° every 100 years. By the very law of the circles which he assumed, however, the opposite happens in the eighth sphere's swiftest motion, when a variation of scarcely 1' in the apparent motion is found in 400 years, as may be seen for the years A.D. 600-1000 in the same table, and likewise in the slowest [motion] also, as for the 400 years after 2060.
Now the reason for the nonuniformity is, as was said above, that in one semicircle of the trepidation, namely, that which [extends] from the maximum slowness to the maximum swiftness, there is always some increase in the apparent motion. In the other semicircle, which [is reckoned] from the maximum swiftness to the maximum slowness, the motion which had previously increased decreases steadily. The greatest increase and decrease occur at the diametrically opposite points of uniform motion. In the apparent motion, consequently, equal motions are not to be found in two continuous equal periods of time. One [of the two motions] becomes greater or smaller than the other, except in the vicinity of the maximum swiftness or slowness. Only there do [the motions] on either side traverse equal arcs in equal times; starting or ceasing to increase or decrease, at those times they counterbalance each other. Consequently it is by no means correct that the motion in the 400 years before Ptolemy was the mean motion. On the contrary, it was rather the slowest motion. Indeed I see no reason why we should speculate about another slower motion concerning which we have heretofore been unable to obtain any hint. For, no observation of the fixed stars made before Timocharis has come down to us, nor did any come down to Ptolemy. Besides, since the swiftest motion has already passed, we are now as a consequence in the second, post-Ptolemaic, semicircle, in which the motion decreases, and no small part of it too bas passed.
Accordingly it should not seem surprising that with these assumptions of his our author could not approach more closely to what was reported by the ancients, and that in his opinion they erred by 1/4° or 1/5° or even 1/2° and more. Yet nowhere does Ptolemy seem to have exercised greater care than in striving to pass on to us the motion of the fixed stars free from error. For this [precision] would have been available to him only in that restricted portion of [precision] would have been available to him only in that restricted portion of the motion from which he undertook to devise that entire revolution. An error, however imperceptible when occurring in the restricted portion, could undoubtedly emerge as significant in that whole immense framework. Ptolemy seems to have linked Aristyllus with his contemporary Timocharis of Alexandria, and Agrippa of Bithynia with Menelaus of Rome, in order in this way to have absolutely certain and unchallenged evidence in the agreement of these [observers] from such widely separated places. Hence it is unbelievable that such great errors were made by them or by Ptolemy, men who were able to understand many other even more difficult matters down to the last detail, as the saying goes.
Finally, nowhere is our author more foolish than in Proposition 22 and especially its Corollary. Wishing to praise his own work, he censures Timocharis with regard to two stars, namely, Arista in the Virgin, and the most northerly of the three stars in the Scorpion's brow, by claiming that in the first case Timocharis' computation falls short, and is excessive in the second case. Here our author prattles in an exceedingly childish way. For with regard to both of the stars under consideration, the displacement between Timocharis and Ptolemy is the same, namely, 4 1/3° in almost exactly the same time interval, and the numerical result of that computation is therefore practically identical. Yet our author completely fails to notice that adding 4°7' to the place of the star found by Timocharis in 2° of Scorpion could not properly fill out the 6°20' of Scorpion where it is found by Ptolemy. Conversely, the subtraction of the same number from 26°40' for Arista according to Ptolemy could not restore 22 1/3°, as it should, but remained at 22°32'. Thus our author thought that in the first case the computation was deficient by as much as it was excessive in the second case, as though this disparity were inherent in the observations, or as if the road from Athens to Thebes were not the same as the road from Thebes to Athens. Besides, had he either added or subtracted the number in both cases, as parity of reasoning required, he would have found that both computations proceed in the same way.
Moreover, between Timocharis and Ptolemy there were in fact not 443 years, but only 432, as I indicated in the beginning. Hence, the interval being shorter, the amount [of the precession] should be smaller, so that our author will deviate from the stars' observed motion not merely by 13' but by 1/3°. This is how he imputed his own error to Timocharis, while Ptolemy barely escaped. But while he thinks that their reports are untrustworthy, what else remains but to distrust his observations too?
So much for the eighth sphere's motion in longitude. From the foregoing [remarks] it can also be easily inferred what we should think about the motion in declination too. For our author complicates it with two trepidations, as he calls them, piling this second one on top of the first. But now that the underpinning itself has been destroyed, the superstructure must necessarily collapse, being weak and incohesive.
Lastly, what do I myself think about the motion of the sphere of the fixed stars? Since [my views] are to be stated elsewhere, I deemed it superfluous and improper to extend this communication further here. For it is enough if I satisfy your desire to have my opinion of this little work in compliance with your request. May your Reverence enjoy the best of health.
Nicholas Copernicus
Frombork, 3 June 1524
