Airy on Thales' eclipse
On Friday 4 February 1853 George Biddell Airy addressed the Friday Evening Discourse in Physical Science at the Royal Institution in London. He addressed the audience On the results of recent calculations on the Eclipse of Thales and Eclipses connected with it. In the tradition of the lectures he assumed that members of the audience had no expert scientific knowledge. It is worth commenting on Airy's style, particularly the way he (rather charmingly) refers to himself as "The Lecturer".
On the results of recent calculations on the Eclipse of Thales and Eclipses connected with it.
G B Airy, Esq. F.R.S. Astronomer Royal.
The Lecturer commenced by remarking that he should not have thought the calculations connected with any other eclipse a subject worthy of his audience. The eclipse commonly called that of Thales is however one of extraordinary interest. It refers to a point of time which connects in a remarkable way the history of Asia Minor and the Greek colonies settled there with the history of the great Eastern empires. Its precise date has been for a long time a subject of discussion among the ablest astronomical computers and chronologers. It shows in a remarkable degree the power of astronomy; for it is no small thing that we are able to go back so many centuries and confidently to describe a phenomenon which then occurred, almost to its minutest features. But it shows also the weakness of astronomy. It requires the combination of theory and observation, with a full sense of the possible inaccuracies of both, and with an endeavour by the use of each to correct the failings of the other. It requires general criticism, history, tradition, and a careful examination of geographical and military circumstances. But when all these aids are properly brought to bear upon it, a conclusion is obtained upon which there appears to be no room for further doubt.
In the last century, the computations, or rather the assumptions, of distant eclipses, were extremely vague. The theory of the moon's motion, as applicable to distant eclipses, was imperfect; and it would almost seem that computers, under a sense of this imperfection, felt themselves free to interpret the calculations as loosely as they might find convenient. Eclipses were adopted by them, as corresponding to historical accounts, which did not represent the physical phenomena when visible; some were even taken which occurred before sunrise or after sunset at the places of observation.
The great step made in theory, in reference to these inquiries, was the discovery made by Laplace near the end of the last century, of the secular change in the moon's mean motion in longitude (accompanied by similar changes in the motion of the perigee and the node). In explanation of this, the Lecturer pointed out that the force which acts upon the moon tending to draw it towards the earth is not simply the attraction of the earth, but consists of that attraction diminished by a disturbing force which is produced by the sun's attraction. The sun sometimes attracts the moon towards the earth or the earth towards the moon, sometimes it produces the opposite effect; but on the whole it tends to pull the moon away from the earth. And this diminution of the earth's attraction is greater as the sun is nearer; and therefore, in an elliptic orbit such as the earth describes about the sun (or such as the sun appears to describe about the earth), the diminution of the earth's attraction is greater when the earth is nearest to the sun than when the earth is farthest from the sun. It might be supposed that one of these effects exceeds that which would happen when the earth is at its mean distance from the sun, as much as the other falls short of it; but in reality the excess is greater than the deficiency, and therefore the more eccentric the earth's orbit is, the greater is this disturbing force. So long as these circumstances remain the same, the magnitude of the moon's orbit will not be sensibly altered. But the fact is, that, in consequence of the perturbations produced by the planets, though the earth's mean distance from the sun remains unaltered from age to age, yet the eccentricity of its orbit is diminishing from age to age; the sun's disturbing force is therefore diminishing from age to age: and the real force which acts upon the moon as tending to draw it towards the earth is therefore increasing from age to age; and, from age to age, the moon approaches a little nearer to the earth and performs her revolutions a little quicker. This effect is extremely small. Between one lunation and the next (taken one with another) the moon's distance from the earth is diminished by about 1/14 of an inch; it would seem at first that this could produce no discoverable effect in the moon's motion: but one of the most wonderful things in the application of the laws of mechanics generally, and the law of gravitation in particular (where the magnitude of the force varies with the variation of distance), is, that the effect of a variation of a small fraction of an inch is as certain, in proportion to its magnitude, as that of a thousand miles. Still the effect produced in the moon's apparent motion is very small: in a century it amounts to only ten seconds; an angle which, when expressed in the usual way by the breadth of a known object as seen at a known distance, is less than the angle subtended by the human hand as seen at the distance of a mile. Yet in the course of twenty-four centuries the effect of this becomes so important as, in the case of eclipses, completely to change the face of the heavens; an eclipse might happen in Asia or Africa which, but for this consideration, we might expect to occur at that time in America.
Shortly after the discovery of this secular change, the French lunar tables (Bürg's) were constructed, the first which introduced this element. The late Mr Francis Baily soon made use of these in an investigation of the date of the eclipse of Thales, which deserves to be ranked among the most valuable that has been directed to that subject. The historical account of the eclipse is that the Medes attacked the Lydians, and that a war continued several years, until at length, when the two armies were preparing for battle, the day suddenly became night (an event which Thales is said to have predicted), and both parties were so much alarmed that they made peace at once. Mr Baily in the first place pointed out, from a collation of the beet accounts of total and annular and other partial eclipses, that nothing but a total eclipse could produce such a striking effect and that a total eclipse could do it. Mr Baily afterwards saw the total eclipse of 1842, but he saw it from the window of a house: the Lecturer, who had seen the total eclipses of 1842 and 1851, in each case from the top of a hill and in command of the open country, wished much that Mr Baily could so have seen it, when he could not have failed to be reminded of his former assertions with regard to the eclipse of Thales: the phenomenon in fact is one of the most terrible that man can witness, and no degree of partial eclipses gives any idea of its horror. Mr Baily then, using Bürg's tables, computed all the eclipses which could by possibility be visible in Asia Minor through a period of time exceeding that to which the eclipse of Thales is limited by chronological considerations, and found that only the eclipse of B.C. 610, September 30, could be total; and that the track of its shadow would pass across the mouth of the river Halys. He accordingly fixed upon that as the true date. But he then made a calculation which threw great doubt upon the result. Upon using the same tables to compute the eclipse of Agathocles (to be described shortly) he found that the track of the shadow would be nearly 200 miles in error; and, with a degree of good faith which was characteristic of him, he at once avowed his belief that if the elements of the tables were so altered as to make the eclipse of Agathocles possible, the eclipse of B.C. 610 could no longer be shown to be total in or near Asia Minor. He expressed his confidence however that no other eclipse could, under any possible change of the tables, have been total in Asia Minor. Mr Baily's conduct in this avowal was favourably contrasted with that of a German astronomer, Oltmanns; who, in one paper, using the same tables as Baily, fixed upon the same date as Baily for the eclipse of Thales; and in another paper, after alteration of the elements, showed that the eclipse of Agathocles was possible; but, although he then alluded to his own calculations of the eclipse of Thales, had not the courage to announce that his former conclusions must now be considered to be unfounded.
The Lecturer then proceeded to explain how it happens that there exists such a connection between two eclipses nearly 300 years apart, that the errors of calculation of one can have any influence upon the other. He explained that the moon's orbit is inclined to the sun's apparent orbit round the earth, but not always in the same direction, the line of nodes (or the intersection of the planes of the two orbits) revolving so as to complete a revolution in about 191 years; and that an eclipse of the sun can happen only when the line of nodes is turned nearly towards the sun (as, in other cases. the shadow falls above or below the earth). If for a given day of the year, (when the sun is in one certain position), the moon is in that part of its orbit most nearly in the direction of the sun, the shadow of the moon will fall upon a certain point of the earth; but now if the place of the node be changed, the effect will be that of driving a wedge under the moon, and she will be thrown further north or south, and the shadow upon the earth will be thrown further north or south. Thus the place of the node will define the part of the earth on which the shadow will be thrown; and conversely, a knowledge of the part of the earth on which the shadow is thrown will give information on the place of the node. Thus the alteration of the lunar elements, which is necessary to throw the shadow further north in the eclipse of Agathocles, consists in an alteration of the place of the node (other elements being supposed moderately correct); and this requires an alteration in the annual motion of the node, reckoning backwards from the present time when the position of the node is well known; and applying the same annual correction by the rule of three backwards to the place of the node at an assumed time of the eclipse of Thales, the corrected place of the node at, that time is found, and then the corrected track of the moon's shadow can be found.
Subsequently to the time of the calculations of Baily and Oltmanns, the improvements in astronomy haze been very great. Many advances have been made in theory, and one of the secular changes (that of motion of perigee) has been greatly modified. The Greenwich Lunar Observations from 1750 to 1830 (which are the foundation of Lunar Astronomy) have been completely reduced, on one uniform plan. Improvements have been made in the details of construction, but still greater improvements in the principles, of astronomical instruments. Our knowledge, also, of the geography of the countries to which the eclipses before us have relation, is much more accurate and extensive than it was.
Still there remain causes of uncertainty in the results of any calculations made for such distant periods.
First, in the theory. No person who has not fairly entered into the details of the Lunar Theory can conceive the complexity of the algebraical expressions and the operations which occur in it. Besides the usual chances of error from mistake of figures and mistake of signs, there is the risk of mistake in the selection of some terms to the exclusion of others, and the possibility of positive error in the metaphysical reasoning which guides some of the operations. And we are driven at last to admit that what is sometimes called mathematical evidence is after all but moral evidence. And thus it has happened that the conclusions of different theorists on some very important points are by no means accordant.
Secondly, in the observations from which are determined the elements that are to be combined with theory. Upon the same principle by which it was shown that the track of shadow in one eclipse depends upon the track of shadow in another eclipse, it will be easily seen that the track of shadow in a distant eclipse will depend upon the observed elevation of the moon in the beginning of the modem period of comparatively accurate astronomy; (for that elevation determines the place of the node; and an error in the elevation produces an error in the computed place of the node for that time; and this exhibits an error in the annual motion of the node; and that error carried through the long period to a distant eclipse produces a very great error in the place of the node there, and consequently in the track of the shadow). If a ladder of centuries- be constructed, each stave corresponding to a century, the extent of tolerably accurate and well-reduced observations of the moon (1750 to 1830) is represented by only 4 of an interval of staves. Thus it appears that an error of two seconds in Bradley's observations, (the angle which a finger-ring subtends at the distance of a mile, and which is smaller than can be perceived by the unassisted eye) would destroy our conclusions with regard to the distant eclipses in question. The fault in the principle of the Greenwich instrument used for observing the elevation of the moon (namely a quadrant, the use of which was for many years the bane of astronomy), and the slovenly way of using it in Bradley's time (no attention being given to the taking the elevation of the moon at the precise instant of her passing the meridian, though her elevation then changes rapidly) might well allow of this error. The Lecturer stated that both in the careful examination of the principles on which instruments are constructed, and in the rigorous attention to the proper rules for their use, it might be hoped that great improvement would be found in modem times.
In consequence of these causes of uncertainty, it becomes very desirable, in the investigation of the eclipse of Thales, to correct the elements of the moon's motions by some other well determined eclipse. Omitting the eclipses since the year 1200 A.D., and two in the second century B.C. which are somewhat discordant, there are two eclipses of peculiar value. One is the eclipse at the battle of Stiklastad at which Olaf king of Norway was killed, A.D 1030 August 31; in which the precise spot is known, and the precise position of the moon is known (the breadth of the shadow being very small, inasmuch as, when the eclipse commenced on the earth, it was annular). The only objection is, that if there is any uncertainty in the secular change of mean motions, the adjustment of the mean motions to represent the eclipse of Stiklastad will still leave a large uncertainty on an eclipse about 1600 years before it. Using the illustration of the ladder of centuries, it is like fixing the ladder at the bottom and at a point at one third of its height, which fastening, if the ladder is bent in some uncertain degree, still leaves great uncertainty in the place of its top. The other eclipse is that of Agathocles, B.C. 310, August 15, which will leave little uncertainty of that kind, if we can but determine its exact place upon the earth.
Agathocles, the Lecturer stated, being blockaded by the Carthaginians in Syracuse, placed men on board a fleet, ready to escape on the first opportunity; the approach of a provision-fleet drew off the Carthaginian ships, and Agathocles burst out of the harbour, and was pursued by the Carthaginians, but escaped. The next morning there was an eclipse of the sun which was evidently total. After six days he landed in the Carthaginian territories at a place called the Quarries, and, traversing their provinces, reduced the citizens of Carthage to the utmost difficulty, (in their terror they sacrificed 500 children to their god Kronos). The Lecturer acknowledged his obligations to Capt W H Smyth, R.N. who had called his attention to the enormous quarries at Alhowareah (Aquilaria) under Cape Bon, from which Utica and Carthage were built; which place appears to have been used by the Romans as a landing-place from Sicily; and which the Lecturer adopted without doubt as the landing-place of Agathocles. He then stated that from J W Bosanquet Esq., he had received the suggestion that Agathocles might have passed the Strait of Messina; and that gentleman had pointed out the passages in the historical accounts which indicated the belief of the sailors that they were going either to Italy or to Sardinia. The Lecturer stated that, on minute examination, he had found that only the city of Gela remained in alliance with Syracuse, and the provision-fleet must have come from Gela, and must have approached Syracuse from the south, and from this it followed that Agathocles must have escaped to the north. This brings the probable position of Agathocles at the time of the eclipse near to Messina; if it were still supposed (as had been formerly supposed) that be sailed to the south, his position would probably have been near to Cape Passaro. The Lecturer explained the small corrections which must be made in the Greenwich determination of the place of the moon's node to satisfy these two conditions: and these were then taken as bases for the investigations connected with the eclipse of Thales.
The armies which were confronted at the time of the eclipse of Thales were evidently large armies (from the circumstances that they were commanded by the kings in person, who were ready to make a treaty on the spot, and that their principal allies, Syennesis and Labynetus, were present). And the principal question to be answered is, where such armies were likely to march. The Lecturer called attention to the general form of Mount Taurus and Anti-taurus (as one part is sometimes called), ranging from the mountains in the south of Asia Minor, in a general north-eastern direction, till they joined the mountains about Trebizond and Erzerum; and stated that, according to the best information that he could obtain, (in which he had been materially assisted by W J Hamilton, Esq. and M Pierre Tchihacheff) the following were the principal roads through them. On the north coast there is one, of which the difficulties were well known from the retreat of the ten thousand Greeks. From Erzerum there are two roads towards Siwah (Sebaste) and Kaisarieh (the Cappadocian Caesarea), rugged, and passing through barren countries. There is one road from Kaisarieh falling on a branch of the Euphrates, which flows by Malatieh (Melitene); a rugged road parallel to it from Guroun; and finally, the road which is the best of all, descending from the southern mountains into the plain of Tarsus and Adana, then skirting the sea by Issus to Antioch. The Lecturer stated that on examining history he found no instance of an easterly or westerly march through the northern mountains: he had found one march of an army (under the Byzantine emperor Heraclius) from Trebizond to the south, which army however returned by Issus: one march by Melitene, where the last great battle of Chosroes Nushirvan with the Byzantine armies was fought: but, from the time of the younger Cyrus and Alexander, the marches by Issus are very numerous. Some of these lines of march are evidently very much curved out of their straight direction in order to take advantage of the pass of Issus: thus Alexander marched thither from Angora (Ancyra): Valerian entered by Issus to attack Sapor: Sapor, when in Armenia, and on his way to attack Caesarea, marched by Issus: Julian in return invaded Persia by the same road. From these circumstances it appeared most probable that the Medes entered by Issus to attack the Lydians, and that the battle-field would probably be included in the polygon whose angles are Issus, Melitene, Ancyra, Sardes, and Iconium.
The Lecturer then showed what would be the track of the shadow in the eclipse of B.C. 585, May 28, either on the supposition that the place of the Moon's node was that given by the Greenwich observations, or on the supposition that the motion of the node was so corrected as to make the shadow in the eclipse of Agathocles pass centrally over the assumed southern position of Agathocles, Or over the assumed northern position of Agathocles. The uncorrected Greenwich track, and the track over Asia Minor corresponding to a central eclipse on the southern position of Agathocles, though not inadmissible, are too far south to be accepted as probable; but the track over Asia Minor, corresponding to the elements which give a central or nearly central eclipse for the northern position of Agathocles (near the strait of Messina), would certainly pass over any probable position of the battle-field.
The conclusion as to the general fitness of the eclipse of B.C. 585 for representing the circumstances of the eclipse of Thales, by inference from modern elements of calculation, was first published by Mr Hind in the Athenaeum.
The Lecturer then stated that he had examined in greater or less detail every eclipse from B.C. 630 to B.C. 580, and that no other eclipse could pass over Asia Minor. That selected by Messrs Baily and Oltmanns, it was now shown, passed to the north of the sea of Azof.
In concluding this astronomical discussion, the Lecturer expressed his opinion that the date B C. 585 was now established for the eclipse of Thales beyond the possibility of a doubt.
The Lecturer then alluded to the tradition preserved by Sir John Malcolm from the poetical History of Persia, that Kai Kaoos (whom Sir John Malcolm considers to be the same as Cyaxares or Astyages, or possibly to represent both), having marched on a military expedition into Mazenderam, himself and his army were struck with sudden blindness; and that this had been foretold by a magician. Sir John Malcolm considered, and it appears most probable, that this is the record of a total eclipse of the sun; but no total eclipse near this time passed over Mazenderam. The Lecturer conceived therefore that it might refer to the eclipse of Thales, though with a strange perversion of the name of the province. Such perversions however occur in the Persian poetical history with regard to other names, which there is reason to believe are correctly given by the Greeks. The name Xerxes, for instance, has been found by Colonel Rawlinson in the Behistun inscriptions under the form Khshayarsha, of which the Greek Xerxes was probably a fair oral representation; whereas the name preserved in the poetical history is Isfundear. These confusions however are incidental to poetical history: thus if the Henriade of Voltaire should remain as the only history of the times to which it relates, the name of the king who preceded Henri IV would go down as Valois, instead of Henri III.
[G. B. A.]