was studying theology, to serve under the Prussian standard. He seems to have affixed to his offer of service a testimonial wherein Gauss certifies that Encke had "at first attended and afterwards borne an active part in his manifold astronomical occupations and labors, and had manifested throughout distinguished talent, great diligence, and uncommon knowledge." The brothers were required to undergo an examination, which, in the case of our astronomer, at least, was never repeated. He received, June 10, 1815, the commission of second lieutenant of artillery, and was first ordered to Thorn, and later to Graudenz.

Encke would, probably, like his brother, have still further pursued a military career had not Von Lindenau, the director of the Seeberg observatory, at the recommendation of Gauss and Gerling, offered him in the beginning of 1816 the place of adjunct therein. This induced him to ask a discharge from the army, which was accorded on the 8th of March. Hereupon he went once more to Göttingen, and remained there till July 5, 1816, when his nomination to the observatory was confirmed. The appointment was by no means dazzling. The salary was but $15 a month, and the place of service consisted of a garret so lowly that he touched the ceiling when he raised his hand above his head. Not the less did there go forth from hence such labors as soon turned the general attention on the young astronomer. With so much zeal did Encke apply himself to his duties that only once a week did he leave the observatory and go to Gotha.

He first occupied himself with the newly discovered small planets, especially Vesta, whose orbit he traced with superior accuracy, and of whose apparent motion he published the ephemerides. Another labor, if one of subordinate importance, was not without consequence by placing him in friendly correspondence with Bessel. The Fundamenta Astronomia had been printed at Gotha, and Lindenau, on whom the correction of the press devolved, transferred this task to his assistant. Encke, however, did not confine himself to a comparison of the manuscript with the impression, but repeated the calculations. Hence Bessel says, in the preface to his work, "Mr. Encke, who occupies the second place in the Seeberg observatory, but who would be an ornament to the first, has given himself with unsurpassed skill to the revision of the imprint, even to the detection and correction of the errors of the manuscript. I must acknowledge this with the more thankfulness, inasmuch as his time is worthily occupied with his own astronomical researches, and between us no other bond exists than that which embraces all who devote themselves with zeal to the same science."

The first of the more important labors of Encke relates to the comet of 1812.* This had been observed for two months at all the greater observatories. Encke had, at his first residence in Göttingen, and therefore immediately on the appearance of the comet, begun the calculation which, in the well-considered and careful employment of numerous observations and the exact execution of extended computations, takes rank with the most admirable investigations of this nature. It was crowned with a special result, since an elliptical orbit corresponded with the revolution of nearly 71 years.

How important this discovery was considered at that time is seen from a letter of Bessel's: "You have adduced the strongest proof for the shortness of the revolution of this comet, and placed the result in the clearest light. We have now, since we begin more narrowly to observe and to calculate the comets, quite other views to maintain. Halley's comet seemed only to be an exception. As regards that of Olbers, I scarcely trusted my own calculation, as this gave but a middling revolution. Yours is now the third. Our successors, through an exact investigation of the planet-masses, will be enabled to recognize the true movement of the heavenly bodies with a perfection of which we have scarcely an idea."

In the second volume of the Zeitschrift für Astronomic und verwandte Wissenschaften, p. 337 et seq.

Encke immediately thereafter addressed himself to a similar yet more troublesome inquiry. The editors of the Zeitschrift für Astronomie had chosen as the thesis for the prize offered by Cotta, the computation of the orbit of the comet of 1680. This comet, on account of its luminosity, the length of its tail, which comprised 80 degrees, as well as the duration of its visibility, had presented one of the grandest phenomena of which the history of the heavens makes mention. It had been extensively observed by the astronomers of the period, especially by Flamsteed, Newton, and Cassini, though the observations had been limited to the measurement of the distances of the fixed stars, and the comets' place had been in part only estimated, inasmuch as the observers had been content to suppose the body bisected by two great circles drawn through four neighboring stars, which circles only approximately touched it.

Encke wrote to Bessel that, at the special request of Lindenau, he would attempt the solution of the problem, and with this view requested the communication of a number of stellar positions from the catalogue of Bradley. With this request Bessel at once complied, but expressed the apprehension that the result would scarcely justify the expenditure of time, as he deemed the observations too uncertain. And, indeed, of so large a number of measurements there were but few that were available. In many cases it was even uncertain from what fixed stars the distances were measured. Nevertheless it was found, on critical examination, that Flamsteed's observations disclosed a high degree of accuracy, since their probable errors amounted to but 15 seconds of arc spherical. With due regard to planetary disturbances this orbit was also shown to be elliptical, and the period of revolution was found to be 8,813 years.

Gauss cordially congratulated Encke "on this admirable prize essay, to which he was indebted for so much pleasure." Bessel expressed himself in more specific terms: "It is without example that the more ancient observations have been reduced to so small a probable error. We learn from this, that to a good astronomical result there is indispensable, besides a tolerably good instrument and a capable observer, an able calculator also. If the last be wanting, the rest is little worth."

Together with these great labors Encke occupied himself in many ways with the incidental calculation of cometary orbits. As often as one was discovered, and had been for some time observed, he was accustomed to publish, not only its orbital elements, but, to facilitate further observations, its ephemeris as well. The constant practice and fine perception which guided him in the choice and grouping of the observations enabled him to arrive with wonderful certainty at a correct result. A remarkable example of this was furnished by the third comet of 1819, for which Encke, from some scanty Marseillese and a few Milanese observations, so accurately calculated the elements of an elliptic orbit and a revolution of 5 years, that on the re-discovery of the comet at the Bonn observatory after seven revolutions (in the year 1858) no important qualifications were admissible. This practical knowledge and perspicacity led, no doubt, to the discovery through which Encke's name is most generally known.

A comet was discovered November 26, 1818, by Pons at Marseilles, the path of which, as Olbers soon remarked, was nearly coincident with that of the comet of 1795 and 1805. It had been already surmised that the orbit was elliptical and the period of revolution short beyond example. The elucidation of this remarkable circumstance was probably undertaken by many astronomers, though it was Encke who first succeeded in shedding complete light upon it. The time of revolution amounted to 1,207 days, or nearly 3 years, and it was this comet respecting which Bessel had expressed a conjectural opinion that it moved in an elliptical orbit.*

In a communication on this comet Olbers extols "the skill, the care, and the

* In the Berliner Astronomiches Jahrbuch for 1822, which was published in 1819.

genius" which Encke had lavished on the calculations. Bessel, who had heard of the comet during an absence from Königsberg, wrote to one of his scholars: "It becomes clearer and clearer that this comet is the most important scientific discovery of the present century." Olbers also expressed himself in the same terms in a letter to Bessel.

Although the short period was in itself of the most pregnant consequence as affording the prospect of a more certain determination of the masses of the planets which exert an influence on the comet, yet further investigation soon led the way to another wholly unexpected result. Encke found, in effect, that this comet had been observed, also, in 1786, and hence four times in all, while no less than seven times in the interval its return had not been noticed. From a comparison of the three intervals between the observed transits it resulted, with all due allowance for the planetary disturbances, that each revolution, as regards the next preceding one, had been shortened by about three hours.

Olbers was the first to conjecture that the comet encountered a certain resistance whereby its approximation to the sun, and, consequently, the shortening of its period of revolution might be accounted for. Encke concurred in this view, while Bessel dissented from it. In the correspondence between the two, the reasons for and against the hypothesis were, for many years, fully discussed. In 1830 Bessel writes: "What admirable results are yielded by careful labor is now again seen in the conformableness of that unknown disturbance which you call resistance. Of the existence of such disturbance there can be no doubt, nor could there be long ago, but that it is a real resistance becomes more problematical to me the more I reflect upon it."

Encke continued assiduously to observe this comet, which he always called the comet of Pons, though his own name was, with perfect justice, commonly applied to it. Before each of its returns he made known its ephemeris in order to facilitate observation, and as the shortening of the period of revolution constantly recurred, in which fact he saw a confirmation of the above hypothesis, he developed, in 1831, his theory of the movement of heavenly bodies in the resisting medium. For the constants introduced, the values admitted of determination from foregoing observations.

Halley's comet, which re-appeared in 1835 after a period of 76 years, occupied very exactly the same positions which Rosenberger had previously calculated from the earlier observations. By this body, therefore, the hypothesis of the resisting medium was not confirmed, though it was by no means decidedly contradicted, because neither the earlier measurements nor the masses of the planets relied upon as a ground of calculation could be regarded as altogether certain; perhaps, also, this comet might have a denser mass, and the effects of resistance be on that account not so conspicuous.

The comet discovered still later by Faye seemed at last to remove the doubt previously existing. The period of this body, 7 years, was, according to Möller's computation, shortened at each revolution by about 17 hours, and Encke showed (Berliner Astronomisches Jahrbuch für 1864) that this acceleration could, with very close approximation, be explained by the resistance which the comet of shorter circuit had undergone. In the meantime Möller communicated the results of a more rigorous calculation, (Astronomische Nachrichten, vol. 64, p. 145,) in which were considered those quantities of the second order in the co-ordinates of the disturbances which arise from the changes sustained by the elements through the addition of new fundamental places at the more recent returns. By this it was found possible to bring all the three phenomena into harmony without the assumption of the resisting medium. The errors remaining over were, through this procedure, it is true, considerably greater than after the first calculation, but Möller entertained the hope of being able, by a renewed. and stricter calculation, to attain a still closer conformity. Whether, therefore, Faye's comet does or does not confirm the hypothesis of the resisting medium,

or, in more general terms, that of a yet unknown cause operating upon both comets, still remains undecided.

Two other important investigations of Encke related to the sun's parallax, as derived from the transits of Venus in 1761 and 1769, the last of which Cook had observed at Tahiti. After correction of the observations, revised by Father Hell in Vienna, Encke found the parallax to be 8.57 seconds. "You have turned to account," wrote Bessel, "what had been collected by the expenditure of vast sums and by the efforts of many, and thus those efforts have first achieved success and still point onward to a step in advance." This magnitude of the parallax was for a long time generally accepted; but subsequently, from the opposition of Mars and the disturbances of the moon, was estimated at 8.9 seconds. The difference between this value and that found by Encke arose from the circumstance that the position of the places of observation was not ascertained with the requisite precision. After a more accurate determination of this point in later times, the sun's parallax, as deduced from those old observations, has been shown by Powalky to amount to only 8.832 seconds.*

Encke's personal position had so far changed, soon after his accession to the observatory, that the charge of its management had devolved on him, at first partially, through the intermitting attendance of Lindenau, and soon wholly, from the absorption of the latter in administrative affairs. As no other duties claimed his time, Encke could now resign himself to scientific labor with free and entire devotion. The value which he placed upon this rare immunity is seen from a letter in which he declined an appointment tendered him of a professorship in the University of Greifswald. The chair of mathematics and astronomy had there become vacant by the death of Professor Droysen, in 1814, and for some years no successor was appointed. Bessel called Encke's attention to this, and as, in regard to external circumstances, the situation presented great advantages over that of Seeberg, proposed to recommend him for it. The philosophical faculty at the same time consulted both Gauss and Bessel in regard to a choice. The preference of Gauss fell upon Gerling, who had already approved himself as a teacher, though next he recommended Encke, whom, in regard to knowledge and capacity, he rated quite as highly. Bessel, on the other hand, named Encke in the first place: "He is a young man whose character is as amiable as his acquirements in astronomy and mathematics are distinguished; nor is his skill as a practical astronomer less so. Many are the admirable labors for which we are already indebted to him, evincing a diligence and conscientiousness beyond praise.""

To the question now addressed by the faculty to Encke, whether he would permit himself to be placed in nomination for the office, he replied, March 16, 1818, as follows: "My place here as adjunct of the observatory I have now occupied for two years, and must, in justice, regard it as eminently fortunate, seeing how much my student years were abridged by the distractions of the war, that I have been assigned to a position so wholly free from the demands of other business, provided with so excellent a stock of instruments, under a director (Herr Von Lindenau) whom Germany honors as one of its first astronomers, and where, in short, it is permitted me to live exclusively for science. This position has at present so far changed that the director, involved in many other affairs, and but just returned after a year's absence, has no prospect but to be again and repeatedly absent in the course of the current year. Under these circumstances my employers have taken occasion so clearly to indicate their wish that I should remain here, that I should little respond to their previous kindness were I not ready to forgo the great advantages proffered me by the Greifswald University.

* [This element has been recently investigated at the Naval Observatory, Washington, by Professor Newcomb, from all the more valuable data of recent times, and its value is thus fixed at 8".85, with a probable error of not more than two or three hundredths of a second. J. H.]

How highly soever, therefore, I may appreciate the honor of the proposal made to me, I am under the necessity of declining its acceptance."

We learn from a note by Gauss that the ducal government had taken the occasion of this call to increase the salary, and also to confer upon Encke the title of professor. Two years later he was named vice-director, and in 1822 director of the observatory.

In the last named year Walbeck died in Abo. Encke, though widely solicited to propose for the vacant place, could not be induced to comply, though here again the opportunity of greatly bettering his circumstances was presented to him. The grounds of his refusal were freely communicated to Bessel, and among them we find his recently contracted marriage: he was unwilling to transport his young wife to so northern a latitude.

Not the less did the discomforts and inconveniences of the residence at the observatory continue to be sensibly felt. During storms it was impossible to leave the building or have access to the city. Even with moderate winds the stroke of the pendulum clock could not be heard, and thus the observations were rendered difficult. Particularly annoying to Encke was the loss of the library, which belonged partly to Zach and partly to Lindenau, and which, in 1822, was withdrawn by both owners. At last, however, the prospect of a favorable change offered itself. Tralles, till then secretary of the physicomathematical class of our Academy, had died in 1822. Gauss was nominated as his successor, but at the close of 1824, after long negotiations, peremptorily declined the offer. At the same time Bode took his discharge, and it thus became practicable to unite with the above named place that of director of the academical observatory.

Bessel wrote to Encke, February 16, 1825, that this place had been offered to him, but that he had unconditionally declined, because he could not leave his own observatory. He had named Encke as the only one suited for it. The academy had approved of the proposition, and committed to him the negotiation respecting it. He goes on to say: "You will see what rare fruits will proceed from our co-operation. I know your modesty, and feared that you might not deem yourself qualified. To any such objection I oppose the firm conviction that you, and you alone, are fully qualified for the position; and I expect you on this point to believe me rather than yourself, which, in view of your modesty, cannot be so very difficult."

Encke answered that he hoped indeed that he was competent to the continuance of the journal (Jahrbuch) and the execution of astronomical calculations, though he must absolutely decline if the demands went any further. Bessel, who was just setting out on a journey to Berlin, wrote, March 20: "I will make inquiry about everything, and when I learn that your wishes in regard to the definite occupation can be complied with, and if a suitable provision be stipulated, I shall, in your name, say yes. Do not be startled at this liberty which I am taking. You can limit it by a letter which will reach me at Berlin."

Such a letter accordingly came, but it contained no decided refusal, and hence Bessel could write in reply: "You have not forbidden the agreeement, so I now hold you fast; you are now one of us."

The election which ensued in the academy was confirmed by the higher authorities, and Encke was named, June 21, member of the academy, secretary of the class, and director of the observatory. The ducal ministry, at the head of which Lindenau then stood, soon after accorded him a discharge from his previous situation, adding that "it dismissed so distinguished an official with regret, and only not to be a hindrance to his prospects in life."

Encke arrived at Berlin, October 11, 1825. He soon felt himself on a level with the duties devolved on him, and found complete satisfaction in their discharge. He was not bound to make reports to the university, but he voluntarily adopted the practice the following year. By the philosophical faculty of the university the honorary diploma of doctor was conferred on him, September 11,