INVITED DISCOURSES at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 06 Apr 2021 at 01:09:25, subject to the Cambridge Core terms of use, available https://www.cambridge.org/core/terms https://doi.org/10.1017/S1539299600004950 https://www.cambridge.org/core ASTRONOMY IN ANCIENT GREECE Michael Hoskin University of Cambridge Abstract: Science has spread from western Europe where it developed into recognisably-modern form in the seventeenth century, stimulated by Copernicus's claim that the Earth is a planet. Copernicus however was an astronomer in the Greek tradition, whose task was to reproduce the planetary paths by geometrical constructions using uniform circular motions. Eudoxus's attempt to do this with nests of concentric spheres had been superseded by the use of the more flexible techniques necessary to meet the observational standards of the Hellenistic era. Ptolemy's Almagest synthesised the Greek achievement but its shortcomings led Copernicus to make the Earth a planet. Our purpose this evening is to travel back in time for two thousand years and more, and to try to enter the minds of those men of the period who worked to understand the heavens and to explain and predict the motions of the stars and planets, and who communicated their conclusions to their fellow-men in the Greek language. And I shall outline reasons why their achievement was of decisive importance, not only for the history of astronomy but for the development of modern science as we know it. First, some general comments by way of orientation. Those like myself who spent most of their school years studying Latin and Greek were encouraged to think that Greek culture came to an end with the death of Alexander the Great in 323 BC and that of Aristotle the follow- ing year. But by then Greek astronomy was still in its infancy, and Claudius Ptolemy, the dominating figure in our story, died around 170 AD, some five centuries later. That is to say, major astronomers wrote in Greek for at least five hundred years after the decline of Athenian culture, and for our purpose the years after Christ are as important as those before. Nor, for the most part, was astronomy written on the main land of what is now Greece. Of where the great astronomers lived and worked we know extraordinarily little, but the places mentioned are mostly in 3 Richard M. West (ed.j. Highlights of Astronomy, Vol. 6,3-14. Copyright © 1983 by the IAU. at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. 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Carnegie Mellon University, on 06 Apr 2021 at 01:09:25, subject to the Cambridge Core terms of use, available https://www.cambridge.org/core/terms https://doi.org/10.1017/S1539299600004950 https://www.cambridge.org/core ASTRONOMY IN ANCIENT GREECE 5 copies of copies, laboriously and expensively made, and perhaps involv- ing one or even several translators. In most cases a work was never widely in demand, or if it was then the demand fell off with time, so that no copy has come down to us and the work is lost. This can apply even to works of the first importance, if their content is assimilated into a later and even more successful work. For then there is no longer any purpose in the potential reader's paying good money to recopy the earlier work, which therefore vanishes. This happened in Greek mathematics when Euclid's Elements synthesised the achievements of his mathematical predecessors: the writings of these predecessors thereupon vanished. But the historian of mathematics is lucky, in that Euclid wrote about 300 BC, when some of the greatest mathematicians of Antiquity were still to come. Ptolemy wrote his Almagest in the middle of the second century AD; he drew extensively on the work of his great predecessor Hipparchus, and so of the writings of Hipparchus we possess only one minor example. The very success of Ptolemy as a synthesiser, coming at the end of the high period of Greek astronomy, brought about the destruction of the works of even his greatest predecessors; and this apparent dearth of predecessors in turn enhanced Ptolemy's own stature in the eyes of later civilisations. With these preliminaries, let us quickly travel back in time from the present, beginning with a word about science and scientists in the modern world. We have at this General Assembly astronomers from every nation on earth, sharing in a common enterprise. There is world-wide agreement about what it is to be a scientist — what a scientist does, the questions he asks, the kind of answer that is acceptable, and the methods for arriving at such an answer and communicating it to other scientists. These agreements are inculcated in our education, and enforced by appointments committees to posts for teaching or research, by referees who control access to scientific journals, and by the electors to membership of scientific societies. Today this agreement is worldwide. But if we travel back in time to the year 1700, say, we find modern science only in western Europe. In England and France there are major scientific societies — the Royal Society and the Academie des Sciences — and scientific journals; scientific teaching posts in universities, and research institutions such as the Greenwich and Paris Observatories. Most important of all, there is the Principia of Isaac Newton which the eighteenth century would take as a model of a mature science. But the rest of the world has yet to learn from western Europe what science is. If we go back another hundred years, to 1600, we find no major scientific societies, no scientific journals, and only here and there a post where an astronomer or mathematician might make a career. But two men are at work whose achievements would set physical science on the path to Newton's Principia. Galileo would soon use the telescope to extend the range of the human senses, something no Greek would have envisaged, and he would become the first human being to see mountains on the Moon, and phases of Venus, the satellites of Jupiter, and so forth. Armed with this evidence against the old world-picture of at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 06 Apr 2021 at 01:09:25, subject to the Cambridge Core terms of use, available https://www.cambridge.org/core/terms https://doi.org/10.1017/S1539299600004950 https://www.cambridge.org/core 6 M. HOSKIN Aristotle and Ptolemy, he became a militant Copernican and set himself to create a physics in which it made sense for the Earth to be in motion about the Sun while we passengers on Earth are totally unaware of it. Kepler was a convinced Copernican from his youth, and he would soon use the accurate observations of Tycho Brahe to develope a profoundly new, dynamical astronomy within which each planet would orbit the Sun in a single curve, the ellipse studied by the mathematicians of Antiquity. In the work of Galileo and Kepler we find powerful new elements marking a fundamental advance beyond anything present in Copernicus only a few decades earlier. Copernicus's De revolutionibus (1543) is thoroughly Greek in spirit and method; it is very obviously modelled in layout on Ptolemy's Almagest, addressing the same problems and offering the same kind of answer by means of similar techniques. Indeed, in some ways it was more faithful to the totality of Greek natural philosophy and astronomy than was Ptolemy's Almagest. Copernicus was not the first of the moderns but the last of the medievals, and last of the astronomers in the Greek tradition; yet his claim that the Earth is a planet convinced both Kepler and Galileo and helped spark off the Scientific Revolution that taught first western Europe and then the whole world what science is. This, in brief, is why Greek astronomy is fundament- ally important in the whole history of science. The basic aim of Copernicus's De revolutionibus is to use combina- tions of uniform circular motions to provide geometrical constructions that would accurately reproduce the observed motion of each planet across the sky. He was, in fact, answering the challenge said to have been thrown down by Plato in the first half of the fourth century BC: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" The assumptions underlying Plato's question are very remarkable indeed. First of all, the universe is assumed to be a cosmos. Today we do not link the astronomical term 'cosmos' with the cosmetics that a lady uses to perfect the beauty and harmony and symmetry of her appear- ance, but the root word is the same. A cosmos is first of all a rational universe, one that the human intellect can penetrate. It is not the domain of the gods with their whims and fancies, their play- things and their enemies, gods whose behaviour a mortal man can neither control nor predict. There can be a science of the universe because the universe is a cosmos. But a cosmos is not merely rational; it has beauty and harmony and symmetry. Copernicus found Ptolemy's treatment of the planets one by one unsatisfactory because there was no perception of the unity of the universe; the result of assembling the various independent bits would be, he said, "monster rather than man". Kepler, in his first publication, believed he had penetrated the mind of the divine geometer who created the universe, when he found that the planet- ary orbits were spaced out on the pattern of a nest of regular solids and spheres. The cosmos had a long and important history, and the conviction on the part of the early Greeks that the universe is a cosmos set the scene for the science of astronomy. at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 06 Apr 2021 at 01:09:25, subject to the Cambridge Core terms of use, available https://www.cambridge.org/core/terms https://doi.org/10.1017/S1539299600004950 https://www.cambridge.org/core ASTRONOMY IN ANCIENT GREECE 7 At the outside of the cosmos was the sphere of the heavens. We are so used to working with spherical geometry that we think it self-evident that the heavens appear spherical to the observer, but a study of other early civilisations shows that this is far from being the case. Curiously, at the other extreme, many people today are convinced that the spherical shape of the Earth is an early modern discovery and that explorers like Christopher Columbus feared they would sail off the edge of a flat Earth. In fact, the spherical shape of the Earth was known to Pythagoreans long before Plato, and in the writings of Plato's pupil, Aristotle, which were so central to medieval education, we have several proofs of this: that the shadow of the Earth during an eclipse of the Moon is always circular in outline, and that the stars are seen differently as we travel north and south. Indeed Aristotle quotes a value for the circumference of the Earth that is too large, but only by a factor of less than two. The Greek sense of symmetry demanded that the spherical Earth be at the centre of the spherical heavens, and there was nothing about the appearances to contradict this. Plato's challenge, therefore, assumed a cosmos that was lawlike, and comprised a spherical Earth at the centre of a spherical heavens. Now the stars goes round us every day, and since the Greeks were the boldest, not to say the most irresponsible of speculative thinkers, a number of early philosophers suggested that the Earth itself might be spinning or otherwise in motion. Since Aristotle's method of exposition is to give the views of others before giving his own, he sets out these theories, thereby ensuring that every medieval and Renaissance student of astronomy considered them too. But Aristotle, like other Greek writers, has one especially decisive argument against the motion of the Earth; and although it is not the custom in Invited Discourses to perform experiments, I would like to reproduce the Aristotelian test, and prove to you experimentally that the Earth is indeed at rest. I take this heavy stone, and I throw it straight up in the air. You will see that it falls back into my hand, and this proves that my hand did not move during the time that the stone was rising and falling. If the Earth had been in motion, and I and my hand with it, then my hand would have moved on in the second or two that it took the stone to rise and fall back again to the place from which it had been thrown. Instead, when it arrived back again, there was my hand, ready to catch it. To quote Aristotle: "heavy bodies forcibly thrown quite straight upward return to the point from which they started" (De caelo, 296b). (It goes without saying that post-Newtonian science provides a theoretical frame- work within which the experiment by no means proves that the Earth is at rest. Modern theory benefits from the heroic efforts of Galileo and others to make dynamical sense of Copernicus's claim. But as historians we have to see the experiment through Greek eyes, and interpret it within the context of their theory, not ours. Within that context, the experi- ment decisively proves the Earth is at rest.) Aristotle, even more than Plato, emphasises for us the contrast between Earth and heavens. On Earth there is coming to be and passing away, life and death, and this is reflected in the fact that natural at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 06 Apr 2021 at 01:09:25, subject to the Cambridge Core terms of use, available https://www.cambridge.org/core/terms https://doi.org/10.1017/S1539299600004950 https://www.cambridge.org/core 8 M. HOSKIN movements (a stone in falling, smoke in rising) take place in a straight line, towards or away from the centre of the Earth, which is also the centre of the universe. And such movements are temporary: the stone stops falling when it has fallen as far as it can. By contrast, in the heavens everything is eternal, stars never appear or disappear, and this is expressed in their movements, regular uniform cyclic movements that of their nature continue endlessly without change. Mainstream Greek astronomy, then, accepted a spherical Earth at rest in the centre of a spherical sky, with almost all the stars rotating daily about the Earth with a common and unchanging cyclic motion. Almost all the stars, but not quite all. Seven stars seemed irregular, whimsical, lawless in their movements: namely, the Sun, the Moon, Mercury, Venus, Mars, Jupiter and Saturn. These were the 'wandering stars', in Greek planetes, 'planet'. These seven planets seemed exceptions to the otherwise regular and lawlike cosmos. Plato's challenge was to show that the seven wanderers are not true exceptions but are equally lawlike and geometrical and regular in their motions - in other words, that the regularity is there, though it is more complex than with the fixed stars. What kind of answer is Plato prepared to accept? The "uniform and orderly motions" he requires must in fact be combinations of uniform circular motions. Just as some recent cosmologists have insisted that a theory of the history of the universe must be without any special moment in time, because this is the way things must be, so Greek geometers and astronomers had a profound conviction that the heavens move with uniform circular motions: the cosmos simply is that kind of realm, and eternal, unchanging circular motions are the only motions so fundamental, so basic that of them no further questions can be asked. The challenge posed by Plato shows a mature attitude to astronomy as an intellectual enquiry: an apparent anomaly in an otherwise satisfactory theory is- to be resolved along agreed lines. The solution proposed by Plato's contemporary, the great mathematician Eudoxus, and preserved for us by Aristotle, is a brilliant mathematical tour de force; in that, although proceeding along what we know to be quite the wrong lines, Eudoxus generates the observed movements of each planet in qualitative outline by means of an elegant and simple geometrical construction. Each of the seven planets is thought of as attached to the equator of a sphere centred on the Earth and spinning about its poles with a uniform angular velocity. These poles are thought of as attached to a second sphere, outside the first and concentric with it, and spinning about different poles with a uniform angular velocity. The motion of the planet will of course be compounded from the motions of the two spheres. Outside the seoond sphere is a third, again centred on the Earth. The poles round which the second sphere spins are attached to the third sphere, which spins about yet another axis, and again with a uniform angular velocity. This completes the geometrical model for the Sun and at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1539299600004950 Downloaded from https://www.cambridge.org/core. 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X ! 4-1 1-4 cfl W cu .fi 4-1 4 H o C U 1-1 4-1 fi CU C J cu .fi 4-1 CO • H .fi C J • H X I Es C U CO S -i C U > •rH c 3 CU .fi 4-1 4 H 0 CU 1-1 4 -) C CU C J CU X 4-1 C U X I 4-1 * c o o s cu X ! 4-1 4 -1 0 CU C O CO C J C U X I 4-1 C M • U ) C U • H 4-1 • H C J O r-1 CU > 1-1 n i r-H 3 60 fi n) E >-i o C M • H C 3 X l 4 -1 • H ES 6 0 c •rH c c • M C X CO r H C fl • H 4 J CO C U i-l C U O C U X . 4 J C M 0 CO C U r M O C X CU X ! 4-1 4-1 3 o X i CO >> C O X ) cfl CU C J C o C O fi • H C X CO C U 1-1 CU X ex en 4 J CO O B M cu u 3 o C U C J c o CJ • H 4-1 P . •rH i-H O C U C U X I 4 -1 C M O CO C U r-1 o .*. u 3 CJ cu u >, 1 -1 1 -1 CO 3 CO 3 C O C U C O ex • H i-H a C U x: o • H e xx C U X I 4 -1 4-J 3 o X i CO CO C • H ex CO C U u CU X I ex CO C U r M X ) X ) • H B cu X I 4-1 .« 1-1 o 4 -1 CO 3 a" cu 3 c • H X i 4-1 • H Es X ) 0 • H 1-1 cu C X CO 0 U cfl i n cu X I 4 J «\ CO M CO C U s>, C O • oo r H >> u cu s> cu cu X I 4-1 CO C U • H M S H CO C J • 3 fi CO »* T 3 fi o C J cu C O cu X 4-1 o 4 -1 >. .-4 4-J X ! 6 0 • H .-4 CO T 3 C U C • M r-l C J C • H C O • H C U M CU X ex CO T 3 M •r4 X 4-1 C U X I 4-1 i X i-H 6 0 C • H CO •rH 1-1 C X 1-1 3 CO X I C U J* 1-1 O & i-4 CU X I o e CO • H X ! 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CO • fi u CU 4-1 4-1 CO a M (0 r-4 • M E • M en CO C O Es o 1 -1 1 -1 o C M X I C J • M X I & C 3 C O CU X I 4-1 C M O 4-1 CO X 4-1 C C O > s X 1-4 C U > CU &> E o fi 0 i-i 4 -1 CO cO fi • H 4-J o c C M •i-H A >̂ w 4 -1 C U E o C U C O c • H C O 3 X o T 3 3 W 14-1 o CU C J c CO • M i-H i— l •i-l 1-1 X i cu X 4-1 4-1 3 P Q C O C U 1-1 cu X I ex CO C U X 4-1 C M o 4-1 en o E l-i cu 4 J 3 0 cu X 4-1 *> c • H CO c • M ex en >-. i— i • M C O ••a C U X 4J C O CU C J 3 -a 0 u ex C U 1-1 •— V 4-J cu fi CO & 0 i - H < • en 4-J CU a CO r-l ex u CU X 4-1 O C U X 4-J M O C M en i— t C U -a o e en • M X C • M ex X I o CO CU u o C H l-l 3 O U -l % l-i 3 4-1 c cu C J cO C CO X 4-1 C O CO CU i-H X I CU M C U > 0 o cu 1-1 en CO Es en • H X 4-1 6 0 C • H X a cO cu o 4-1 >. i— i 4-1 X I 6 0 • H r-l CO X I C U C • M r-l C J C • M C U u C O fi • M ex C D en C U u cu X I ex en O E* 4 -1 CU P -.X I i— l 1-1 cu e X T 3 0 o i— i cu X I CO 1-1 6 0 O l-i 4-1 cu I-I G 3 CO C J • H 4-1 CO E cu X 4-J CO E 4-1 X CJ • H X I Es 4-1 3 o X CO CO CU X cO U cO i— l 3 60 C C O C U 4-J • M CO 0 ex ex 0 X I C C O i-H CO 3 • 4-1 0 1 fi cO r-l ex C U X i 4-1 C M o X I o • M S -l C U ex C J • M X ) 0 C >> CO CU trx ; 0 1 X I 4-1 • H Es cu 4-1 CO 4-1 O S -i CO C U S -i cu X I ex en O Es 4-1 C U X i 4 -1 X I C cO A S -l cu X 4-1 O 4-1 c • H c 0 • H 4-1 CO 4-> O u Ol c o 60 c • H 4-1 C U i-H & C M o X I C •i-l <̂5 cO en • M CO C o • H 4 -1 o E o Es 4-1 0 1 CO CU X 4-1 r - . X X I C U C J 3 X I 0 S -l ex CU > S -l 3 CJ cu X I 4 -1 4-1 CO E X I 0 C J r. en cu • M 4-1 • H C J O i— l 4-1 4 -1 3 o en fi l-i 3 4-1 4-1 M O 4 -1 4-1 c cu 6 0 C C O 4-1 u C U X I c • M r-l >» C J cfl X ) C CO CU r4 CU X i #• S -i C U 4-1 • M 0 1 X 4-1 6 0 C O e x i-i 3 i-> S -l o C M CO C U S -l C U X ex CO S -l 3 o 4 -4 CU e xx en CO C M O fi o •r4 4-1 U O J CO S -l 0 ) 4-1 c • H CU X 4-1 «t 4-1 X 60 • H CU 1 C M 0 | CU M 3 60 • H U -l 4-1 n 4-1 r-l 3 CO cu S -l CO en < • 4-1 C •i-4 O ex cu fi o 4-J cO CU S -l 0 ) X I ex en cu X 4-1 cO C o • H 4-1 o E C O 4-1 • H X ) c CO 4-1 0 1 G CO i— l a CU X 4-1 C M O G o • H 4-1 Q E 4-1 CU C cO i-4 ex cu X I 4 -1 CO C U > • M 6 0 4-1 CO X 4-1 4-1 X I 6 0 • M C U | C M O 1 C U S -l 3 60 • M C M U CO i-4 3 60 O ) 1-4 CO t-.X I r-l • H CO X I CU X i 4-1 CU C J 3 X I o S -l ex cu M n 4-1 • M Es X I C U X I c 3 o o 4-1 3! E • H 4 -1 E o u 4 -4 C U X J CO S -l 6 0 0 S-l 4-1 0 1 S-4 o 4-1 4-1 • M 6 0 fi • H C O 3 CO C J CO CO i-4 i-H CU Es CO CO C U X J 3 4-1 • M 4-1 CO C X r-l E o C J C J • M 4-1 ex • H > -, r H CO en C J C U c • M c o • H 4-J O E cO S -i cu X I 4-1 o cu X I 4 -1 S -l o C M X I C J CO 0 ) S -l 3 o 4 -1 *. fi o o g X ) fi C O c 3 C O cu X I 4-1 S -l o 4 -1 en 0 1 S -l 0 1 X I C X C O cu cu S -l X i 4-1 X 4-1 • 1-1 3 • cu E • H 4-1 C M o i-4 CO 4-1 o 4-1 CO X I C U X I cu C U c CO 3 X o X I 3 w A en S-4 C O 4-1 en X I C U X • M C M cu X 4-1 S -l o 4 -1 C U c o X ) fi CO ». C O 4-1 0 ) c CO 1— 1 cu X 4-1 X I 0 ) 4-1 C J cu r-l 4 -1 0 1 S -i >> i-H ex E • H en 4-1 X 60 • H cu G CO X 4-1 S -l C U s CU 4 -4 o G A 0 ) CO C U X 4-1 4 -1 o X ) c CO • »» C O 0 1 S -l 0 ) X I ex en r*- ex C M cu > •i-4 C M >, r H c o • X I 4 -1 S -l cO w CU X 4-J 4 -1 o c • H C X en ^ 1— 1 • H CO X I 1 -4 0 ) X ) o E 1 -1 CO C J • M u 4-1 0 ) E o 0 1 6 0 CO *. >. u o 4-1 en • M X fi •r-4 0 1 e •r-4 4-1 4-1 en S -l •r-4 4 -1 C U X I 4-1 S-4 o C M •V CU > C O X 01 Es cu S -l cu M r-l r-l CO S -i o C M CO 4-1 C U c CO 1 -1 C X cu X I 4-1 C H o en c o • H 4-1 o E cu X 4-1 CU C J 3 X I o S -i en •r-4 X I r-4 S -i o Es C U X I 4-1 4 -1 CO X 4-1 e S-l • H C M fi o CJ •• cu CO u 3 o o 4 -1 0 •\ ts X i C U S -l C U e xx CU S -i C U r-4 C X •r-4 C J c • H S-4 C X c •r4 X I r-l 3 o C J X I C J • H X I E* 4-1 X ) G CO 1 1 C U S -i 3 4 -1 3 C M cu X 4-1 c • H 0 1 E • M 4-1 r-l cO o •r4 4-1 CO E CU X 4-1 CO E cu X 4-1 X I O ) en en cu S -l ex X CU S J 0 1 4-1 2 B o 0 1 6 0 0 1 X I 4-1 en 3 X o X ) 3 pa • en o E CO o C J cu ^ • M r— 1 Es CO r— I CO X I 0 1 cu X I c • M CU X X ) 4-1 • M CO x i X 4 J cu X I O en >% 4-1 » • H r-4 r— 1 CO • M 0 1 X I U C O X ) ^ O r-l 1-4 r-4 ex co C J r-l - H r— i en CO i> . X i fi CX r-l en CO • e n 4 -1 4-1 O C U fi 4 J CO X I r-4 6 0 C X 3 o 0 ) X I X i 4 J 4-1 cu 4 -4 X o o en 4-J fi O en •r-l CU J J S -i o cu B x i ex C U en X I 4-1 CU en 6 0 C U C X I • M 4 -1 c S-l X I 0) fi > CU O 4-1 6 0 C • M en E $ 4-1 CO O r H . fi • en c cu > CO cu X I C U X 4-1 4 H o 01 S H 3 4-1 C J 3 S H 4-1 en r-4 cO • H S H C U 4-1 s E CU X 4-1 4-1 3 o X CO 6 0 c • H C O • M S H o cu X I 4-1 4-J o fi en CO Es >, r— 1 r H CO C J •r4 en > > X I C X CO cu u cu X I C X en 4 H o 4-1 C O cu fi X I C J CO C U 6 0 c • H r * CO E r. en •rH X 4J 0 X I 0 4-1 c 0 0 CO C O 9 Es C U r— 1 4-J 0 4-1 CO •rH S H < C U c o c cu 0 1 Es 4-1 C U X i en CU !H 0 1 X ex CO r 4-1 3 o 1 6 0 fi • M r H r H cu C J c CO o r. rH cfl c 0 •iH 4 J • H X ) X I C O 6 0 c •rH C J 3 X ) 0 S H 4 -1 c •rH X I c CO r— 1 CO cu SH g o X ) X ) cu 4-1 4-J • H s CO c CO S H 4 J C U X 4-> o c X ) r— 1 3 o Es CO fi o • M 4-1 o E X ) C U 4-1 c CO £ c 3 4-J cfl X 4-1 o en 4-1 X C U c CU X I 4-1 X I G CO 4-1 CO 0 1 G C O 0 1 S H cu X CX CO a • H S H 4-1 G C U C J c o C J C U en C U X I 4-J «l SH C U X I • • en o E CO o C J C U X 4-1 C M o G o • H 4-J cfl G cfl r-H C X X C U 0 1 exx: o CO o r H •rH X CX r— 1 CO SH 3 4-1 cfl G cu X I 4-1 o H • E cu 4-1 en 4 -1 SH o 4 H en •rH CO cfl X i cfl C O CO C U > •rH 4 J a cfl S H 4 -1 4-1 cfl >> > ^ r H CO C U X 4-1 X I 6 0 3 o M X I 4-1 X I G 3 0 C M o S H C X cu SH 0 1 Es s>» r-H S H cfl 0 1 r-H C J cu Es CO C O <*v X 4J SH cfl w . r H CO S H 4-1 c cu C J C U X I 4-1 4 J 3 0 X C fl r S r— 1 E S H o 4 H • H c 3 60 c • H G G • H S H cu X I 4-1 S H 3 4 H X I 0 1 X ) 0 1 C U fi i>. r-H X ) S H cO X i * c • H ex CO 0 4-J CO S -i cfl 4-1 en X I CU X •rH C M cu X I 4-1 4 H o 0 1 V 4 cu X CX en C U exx; C O en 0 ) S J CU X 4-1 O l > S H cu CO ex x CO o C M o M CO cu S H cu X 4-1 J3 4-1 •rH Es 0 1 X I 3 s en s s CU CO SH cu > •rH c 3 cfl X i C J 3 C O > . 4-1 c Q E u cfl X I c • H >, cu X I 4-1 0 1 S H S! 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