1826, as a testimonial "to the sagacious mathematician and successful investigator of the cometary system"-mathematico sagacissimo, cometarum indagatori felicissimo.

Previously to these events an important scientific undertaking had been set on foot by Bessel-the editing, namely, of stellar charts, which should represent, in 24 sheets, the zones included between 15° north and 15° south latitude, with all the stars, to those of the 9th and 10th magnitude, which could be discerned with a Frauenhofer comet-searcher of 34 lines opening and tenfold magnifying power. Very soon after Encke's accession the academy invited the friends of astronomy to participate in the enterprise, stipulating a suitable honorarium for each available sheet. It was Encke who undertook the correspondence in regard to the repartition of the task, as well as the critical examination of the sheets and care of the engraving. The business part thus assumed, while in itself the most unthankful of the whole, was rendered more difficult because those who contracted engagements often failed to fulfil them, and sometimes what was produced did not answer to the requirements. At the close of 1858, and hence

after 33 years, the last sheet made its appearance. The results of this undertaking surpassed, even before its completion, all expectation. The first discovery of a new planet, Astræa, occurred in 1845, and others rapidly followed. At present, with the use of these charts, or in consequence of the completeness rendered attainable by them, 81 planets have been detected, while the discovery and observation of comets have been essentially facilitated.

The editing of the astronomical Annual (Jahrbuch) had still occupied Bode on his withdrawal from the observatory. The tables for 1829 had already appeared and the calculations for the following year been begun, when Bode died, November 24, 1826. Encke undertook the continuation, and as the tables in their then extent and precision no longer satisfied the new demands of science, it was found necessary to give them greater enlargement and completeness, as well as to employ a still more rigorous computation. If Encke in this labor availed himself of extraneous help, it was still so exacting that he was constrained at once to forego his lectures at the university.

*

What acceptance the new Annual found with astronomers may be gathered from Bessel's letters. "This is indeed an ephemeris," he said, "such as it should be. You make an offering of yourself for astronomy, and one can but wish that the progress which you aim at in doing so may indeed be realized, and that the result may correspond to the magnitude of the sacrifice. I have always thought that an ephemeris of this calibre must produce great results, but I had not believed that any one would subject himself to so great a trouble" * "I have been completely charmed with your work, and confess that I can imagine nothing more complete. It is all excellent. But explain to me, I pray, why it is that the French have not a Connaissance des Tems and the English a Nautical Almanac such as your Year-book affords, although both, and especially the latter, do not want for money to pay hosts of calculators. But what is absent, in fact, and is almost always absent, is the clear insight into science and its true wants." In the course of the following year many complementary improvements were introduced, the Annual for 1844 being especially enlarged, at the instance of the ministry of commerce, by several extensive tables for the use of mariners. These, however, were but little employed in the Prussian marine, chiefly for the reason that the sea charts were constructed with reference to another meridian, that of Greenwich, and the nautical tables in question were withdrawn from the Annual for 1852 and the following years.

The Berlin observatory, in Dorothea street, which Encke had undertaken to conduct, answered not long to the demands of the new astronomy. It had been erected in 1711, and was furnished with the instruments corresponding to that period. It was situated, at first, without the city, but Berlin had in the meantime spread so much in that direction that high buildings overtopped it. About the year 1800 the necessity was seen of adding an additional story, but the

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steadfastness of the instruments was thereby still more prejudiced, and the concussion of the intercourse in the streets hindered all exact measurement. this must be added the continued noise and the impurity of the atmosphere. Encke wrote, soon after his arrival, to Bessel, that the only serviceable instrument was the Frauenhofer heliometer, though this, too, could scarcely be used on account of the insecure stability. The best thing about the observatory was the library, limited as it was.

After Bode's death the erection of a new observatory was canvassed, and if at first Encke expressed himself with some humor about the proposed destination thereof, he nevertheless soon entered earnestly into the scheme. Bessel urged him to consider well "whether the satisfaction in the possession of an observatory or the hindrance to those labors to which he owed his renown, were greatest." In a following letter it is said: "I regard you as the astronomer on whom the superintendence of the calculations is obligatory. Others have other functions: you, my dear Encke, can undertake nothing new without neglecting what has earlier claims upon you, and is in reality of more essential importance. Be cautious, I pray you, in this matter."

Encke now addressed himself to Humboldt with the request that he would decide upon the proper objects of an observatory for this country. Ordinary observations, such as can here be scarcely conducted, are at present, he argued, without value. If it were proposed to afford opportunity for serviceable astronomical observations, a new observatory would be indispensable. This communication led Humboldt to second the movement for building a new observatory, which was authorized October 15, 1828, at the same time with the ordering of several important instruments from artists of the best repute. The purchase of a large refractor, which Frauenhofer had nearly finished, immediately followed. Encke's questions drew from Bessel a prompt answer respecting the judicious arrangement and equipment of the observatory, but still accompanied with precautionary counsels: "I think that neither your efficiency nor satisfaction will gain anything if you convert yourself into an observatory astronomer. In my opinion the observatory should not be the main point with you. An assistant, adjunct, or whatever you may please to call him, should do the work therein. Immeasurably more is to be done in order to save the material collected from being lost and suitably to use it. If this is once accomplished, it will be then for you to show to what ends further observations may be directed with the most fruitful results."

In the beginning of 1835 the building was finished, the instruments soon after put in position, and the activity of the new observatory commenced with the observation of Halley's comet. The observations which, since that epoch, have been instituted, partly by Encke himself and partly by his assistants, have been published in four volumes, which will soon be followed by a fifth.

How close were the friendly relations between Bessel and Encke is seen from the foregoing communications. They were knit still more closely when Encke took charge of the corrections of the press for the Fundamenta Astronomiæ. After Bessel, on a journey in 1819, had formed a personal acquaintance with Encke, he wrote to him: "I see in you not only a firm stay of astronomy in Germany, but a cherished and outspoken friend; both considerations prompt me to wish that you should continue to accord to me a portion of your affectionate regard." On his return to Königsberg Bessel spoke with enthusiasm of the gifted and estimable astronomer whose first labors had deservedly raised him to the highest consideration. The correspondence which followed was not restricted, like that between Olbers and Bessel, to scientific communications and the more serious affairs of life, but was rather a confidential intercommunion, which embraced at once their respective enterprises, whether begun or contemplated, and the frankest atterances on subjects of every nature. It is not to be disguised, however, that Bessel gave freer scope to his feelings, while Encke often observed a certain degree of reserve. This intercourse had already lasted some years, when we

find Bessel constrained, as it were, to beg of "the highly respected professor" that he would not allow their correspondence to languish. "You cannot do me the injustice to suppose that any one in the world is dearer to me and more highly confided in than yourself. Wherefore, then, a formality which, on my part, has been long ago discarded?"

That views and conceptions should sometimes have differed was, of course, evitable. The differences, however, were calmly discussed in the correspondence, but they failed not progressively to become more and more pronounced and frequent. The last friendly letter Bessel closed with the words, "I cannot imagine that different relations should find an entrance between us." Not the less, however, did such relations find entrance, and that immediately. The occasion was given far less by any single controverted points which had arisen in the course of astronomical journalism than by the contrast of personal position. Bessel, easily excited in oral as in written intercourse, as warmly maintained the opinions which he conceived to be right as he emphatically repelled those opposed to them, and so sometimes forgot that he who had begun earliest had not only erected himself into a master, but expressly assumed a higher and more influential position than was his due. Thus in one of the last letters Bessel styles himself "the experienced friend," and, as such, thought himself authorized to counsel and warn, whereupon Encke explained "that he could only take the course which alone was consonant to his nature."

Since 1837 only a few formal and professional letters had been exchanged. When Encke, however, in 1845, sought to obtain Bessel's views with regard to a new edition of the treatise of Olbers on the calculation of the orbits of comets, he made, as in earlier years, various communications respecting his own labors,' and added the assurance of his deepest concern for Bessel's afflictions. The answer, besides the desired opinion, conveyed a thankful acknowledgment. At the close of the same year Encke communicated the first result of the stellar' charts in the discovery of a new planet. A mutual approach was thus again in progress, when some months later the death of Bessel occurred.

The words which, from this place, Encke 20 years ago dedicated to the memory of Bessel, contain the fullest recognition of his great services in behalf of astronomy, but make no mention of the friendly relations which had existed between them. On that subject nothing could be ventured without, at the same time, recalling their later and well-known estrangement. However much that estrangement is to be regretted, it now no longer forbids us to recur to a friendship which not only endured with singular devotion for 30 years, but was of great importance for the advancement of science.

It only remains to recount the occupations of Encke's life during the last ten years. The extensive calculations for the Year-book, if, to a certain extent, devolved on the assistants, continually required his co-operation, and the more as the numerous newly discovered planets were to be taken into consideration. The academical functions connected with the editing of the stellar charts, the discourses before the university, the participation in the observations at the observatory, and in the accurate testing of the new and older instruments there deposited, together with his activity in the commission of studies for the military academy, and in the deputation respecting the calendar, to say nothing of the manifold inevitable demands which await the director of an observatory in a large city, all these appear so engrossing that we have only room for wonder that Encke should still have found time for the communication of so large a number of scientific papers to the transactions of the academy, the astronomical Year-book, and various mathematical and astronomical journals. Many of these relate to the execution of calculations, such as the method of least squares, interpolation, the mechanical quadrature and the like. They are chiefly of astronomical import, and bear relation to the parallax of the sun and moon, the dimensions of the terrestrial globe, the constants of the Berlin observatory, the masses of the planets, the determination of the orbits of planets and those

of comets; the latter as well with reference to parabolic as elliptical and hyperbolic orbits; the calculation of occultations and transits, the testing of different astronomical instruments, and in an especial manner the disturbances arising from the approximations of the heavenly bodies. Not only did he set forth in more than one treatise, and, with singular clearness, rules for the calculation of these disturbances according to the old method of Lagrange, as perfected by Gauss and Bessel, but almost simultaneously with the younger Bond at Cambridge, in America, he suggested a new method by which the calculation of the orbital elements of many of the recently discovered small planets was essentially facilitated. By this, instead of the changes which the disturbances produce in the elements of the orbits, it was proposed immediately to calculate those which the rectangular co-ordinates undergo. This method, if somewhat uncertain for long periods of time, was, on account of its convenience, extensively employed, till the later method devised by Hansen became more generally introduced. Encke also composed some physical treatises on dioptrics and the ballistic problem, as well as several popular lectures on different astronomical subjects. The latter, though but partially published, were distinguished for an ingenious co-ordination of facts, and were received with unqualified applause.

Towards his numerous friends and acquaintances Encke maintained that uprightness of intention which, with his sympathetic and open nature, his clear and unperverted judgment, won him the highest consideration and love. In his domestic circle the course of a serene life was disturbed by no loss until, in 1856, the news arrived of the death of his second son at Rio Janeiro.

On the 17th of November, 1856, Encke fell in the street from sudden vertigo. Although the apprehensions at first felt were not realized, yet the rare vigor of earlier years did not return. A new and severe loss befell him the next year in the death of his brother, the same with whom he had entered the Prussian artillery, 45 years before, and who had since been advanced to the rank of lieutenant general. A few years later he lost his sister, who had lived in his house. In February, 1863, he sustained an apoplectic attack, from which he so far recovered as to be able to return to his labors, and even to journey to Leipsic in order to witness the nuptials of his old scholar, professor Bruhns, but his condition remained so critical that soon all intellectual effort was forbidden him. He therefore spent the summer with his friends in Goslar and Wernigerode, and, on his return, was still bent upon resuming his labors, but his physician, the more effectually to prevent this, ordained him a new journey to Kiel; from Kiel he went with his family in December, 1863, to Spandau, where his eldest son was established. At his urgent and oft repeated request he was permitted by his medical adviser again to visit the observatory. Here he traversed with interest the observing rooms, and marked with particular attention the changed erection of the great refractor, which was now borne upon a stone pillar instead of the old wooden support. He soon tired, however, and returned contentedly to Spandau. From this time his bodily strength and mental activity continued to decline, until a second apoplectic attack occurred in July of the next year, and was followed by complete paralysis. A painless death released him, 26th August, 1865, from long sufferings.

If Encke's services in behalf of astronomy secure him an enduring remembrance, it continues also to survive in the grateful recollection of his numerous pupils. In the calculations for the Year-book, as well as in the prosecution of other astronomical labors, he delighted to find himself surrounded by young people, to whose instruction in all parts of knowledge he gave himself with a rare talent for conveying it; ever entertaining with them the most friendly relations, and thus winning to the pursuit of his science a number of pupils unequalled, perhaps, by any other astronomer. Among them may be counted the present directors of the observatories of Berlin, Breslau, Leipsic, Hamburg, Bilk, Copenhagen, Helsingfors, and Dublin, who, with many others, have contributed through their scientific labors greatly to extend his reputation.

MEMOIR OF EATON HODGKINSON,

PROFESSOR OF ENGINEERING, UNIVERSITY COLLEGE, LONDON.

BY ROBERT RAWSON.

(From the Transactions of the Literary and Philosophical Society of Manchester, England vol. II, third series, 1865.)

The subject of this memoir was born, of respectable parents, at the small village of Anderton, in the parish of Great Budworth, Cheshire, on the 26th of February, 1789; died at Eglesfield House, Higher Broughton, Manchester, June 18, 1861, in his seventy-second year, and was interred at his native village. His father died when he was about six years of age, leaving his mother with three children, whose education and maintenance depended upon her exertions and prudence. He left his native village, with his mother and sister, at the age of 22, and came to reside at Salford, Manchester, where he remained the greater portion of his after life. He was elected a member of this society in the year 1826, and he enriched the society's memoirs with the following important papers, thus laying the foundation of his reputation as a sound mathematician and an original thinker: "On the Transverse Strain and Strength of Materials," (read March 22, 1822.) "On the Chain Bridge at Broughton," (read February 8, 1828.)

"On the Forms of the Catenary in Suspension Bridges," (read February 8, 1828.)

"A few Remarks on the Menai Bridge," (read December 12, 1828.) "Theoretical and Experimental Researches to ascertain the Strength and best Forms of Iron Beams," (read April 2, 1830.)

"Appendix to the Paper on the Chain Bridge at Higher Broughton, Manchester."

"Some account of the late Mr. Ewart's paper on the Measure of Moving Force, and of the recent applications of the Principle of Living Forces to esti mate the effects of Machines and Movers," (read April 30, 1844.)

He occupied in succession the distinguished positions of vice-president and president of this society. He was a leading member of the British Association for the Advancement of Science from its commencement, and contributed greatly to the interest and efficiency of the mathematical and mechanical sections. He also gave active help to the association in several valuable reports on pure and mixed science. These reports, which have in a great degree assisted in maintaining the high scientific renown of the association, are as follows:

Third report, 1833: "On the Effect of Impact on Beams." "On the direct Tensile Strength of Cast Iron."

Fourth report, 1835: "On the Collision of Imperfectly Elastic Bodies."
Fifth report, 1835: "Impact upon Beams."

He held the distinguished position of vice-president of the association in the year 1861.

In the year 1841 he was elected a Fellow of the Royal Society, and contributed to its transactions two elaborate papers:

"Experimental Researches on the Strength of Pillars of Cast Iron and other materials," (read May 14, 1840.)

The aim of this paper was greatly extended in the second communication: "Experimental Researches on the Strength of Pillars of Cast Iron from various parts of the kingdom," (read June, 1857.)