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it each millimeter of the chart corresponds to the one-millionth of a millimeter of wave length. The probable error of measurement in determining the wave length does not usually exceed one or two ten-millionths of a millimeter, and the spectral lines have been ruled by a dividing engine upon the copper plate of the engraver so as to be correct in position to about one-tenth of a millimeter upon the chart. The substance generating each line is indicated by a dotted line and symbol as in Kirchhoff's chart, while the seven principal lines of Fraunhofer are denoted by the usual letters. In order to permit a comparison of the lines characteristic of different elements closely related to each other in their chemical properties, or belonging to the same natural groups, several impressions of the scale have also been printed upon a single sheet parallel to each other. Upon these the lines may be entered by hand. Copies of the scale have also been printed at the bottoms of large sheets so as to permit of the construction of dispersion curves. The comparison of the wave lengths of the spectral lines which characterize elements belonging to the same natural family may hereafter lead to interesting results, but at the present time it is difficult to institute such a comparison for the reason that we do not know all the lines which are produced by any one element. For the same reason it would probably be impossible at present to determine whether there is any law governing the wave lengths of the spectral lines belonging to the elements as regards their intervals or distribution over the spectrum. The conviction that precise knowledge of these and similar points must depend upon a knowledge of wave lengths and not merely of indices of refraction, has led me to make this first attempt to form a normal map of the spectrum. As a first attempt merely it is necessarily imperfect, but my object will be fully attained if I shall have succeeded in pointing out the path to be followed in the future discussion of the subject.

My grateful acknowledgments are due to Prof. J. E. Hilgard, under whose superintendence most of the curves which I have employed for interpolation have been drawn in the office of the Coast Survey. To Mr. S. P. Sharples I am also indebted for much assistance in the work of computation.

Cambridge, July, 1866.

Postscript.-Since the above was written I have received a second paper by Ditscheiner* on the wave lengths of the spectral lines, in which the author gives the results of a determination of the absolute value of the interval between two successive lines of the grating or ruled glass surface employed by him. When this value is used the wave lengths of Dẞ and Da become * Sitzungsberichte der kaiserlichen Akad. der Wissenschaften, Band lii, 289. AM. JOUR. SCI.-SECOND SERIES, VOL. XLIII, No. 127.—JAN., 1867.

respectively, as measured by Ditscheiner, 590-53 and 589-89, which are 049 and 0:46 higher than those of Angström as given in Table I. Ditscheiner in this second paper has recomputed the table given in his first memoir. The results are much higher than those of Angström or those given in my reduction of Ditscheiner's first measurements, the average difference being about 04 of one unit. The close agreement of the two sets of results given in Table I appears to me a sufficient reason for adhering to the values of the wave lengths employed in this paper as data for interpolation.

Cambridge, August, 1866.

ART. II.-John Francis Encke.*

JOHN FRANCIS ENCKE, born Sept. 23, 1791, was the youngest son but one of the deacon of the Jacobi Church in Hamburg. Four years after his birth his father died, leaving the care and the education of eight children to his mother, a lady of much worth, and happily possessed of great mental energy.

The first tutor of the boy was Mr. Hipp, a gentleman possess ing considerable aptitude for mathematical teaching; and to his honor be it spoken, a man who rendered valuable pecuniary assistance to the orphan and money less family. Hipp continued this material encouragement to young Encke even after the time that he entered the College at Hamburg, well known as the Johaneum. At this College, then under the directorship of Gurlitt, who enjoyed a high reputation for classical learning, the boystudent rapidly advanced, and in addition to considerable ability in Latin composition, his knowledge of Greek was sufficient to enable him to translate and enjoy the Lyricks of Pindar. Notwithstanding, however, this early classical training, when the time came for his entrance at the University, Encke resolved henceforth to devote his attention mainly, if not exclusively, to the study of astronomy.

But here came a very formidable impediment; there were ample funds at the disposal of a poor clergyman's son for a theological career, but none for the prosecution of so unusual a study. Nevertheless, such was the acknowledged ability, and so determined was the inclination, of young Encke, that, as is happily not unusual in such cases, all the difficulties yielded at length to perseverance, and to his great joy, in Oct. 1811, he found himself at Göttingen, and a student under the celebrated Gauss.

The very newspapers of Hamburg were at that day compulsorily printed in French; as a condescension, however, or as an insult to the inhabitants, a German translation was added; in a

From the Monthly Notices of the Astronom. Soc. of London, 1866, p. 129.

like spirit even the university matricula of the old "Georgia Augusta" of Göttingen had the image and superscription of Jerome Buonaparte printed upon it. No wonder then that neither Gauss nor astronomy could retain the young student at his books, but, obeying the impulse which animated the whole heart of Germany, in the spring of 1813 he took up arms and marched to Hamburg for the rescue of his country from the domination of the French. After the re-occupation of Hamburg by the foreigner, Encke entered the Hanseatic Legion, then in process of formation in Holstein and Mecklenburg, and there he served as a sergeant-major in the horse artillery until July, 1814. In the autumn of this year he returned to Göttingen and to his astronomical pursuits, and for nearly twelve months continued a diligent student of subjects far more peaceable, and far more congenial to his turn of mind. Nevertheless the return of Napoleon from Elba once more finds him in a soldier's uniform, but now only for a short period, and, happily, for the last time. Waterloo and its consequences restored peace to France and to Europe, and young Encke, who in peace had no taste for soldiership and a uniform, returned, for the third time, to Göttingen and to Gauss. It was thus in the midst of these stirring and troublesome events, that the spirits of such men as Franz Encke and Wilhelm Struve were disciplined and matured.

While Encke was serving as a lieutenant of artillery in the Prussian fortress of Kolberg, he became acquainted with the celebrated Lindenau, at once astronomer and statesman, and after the completion of his studies under Gauss, he was appointed, by the influence of the former, an sssistant in the Observatory of Seeburg, not far from Gotha. In 1820 he became Vice-director, and in 1822 he was appointed Director, in the place of Lindenau, who returned to his political career.

It was at Seeberg that Encke commenced and completed his important work on the "Transits of Venus in 1761 and 1769," published at Gotha in 1822 and 1824. He also matured his investigation of the comet of 1680, and of the remarkable comet of short period which bears his name. Zach's Correspondence and Lindenau's Zeitschrift, about this period, contain many evidences of his talents and his industry. During his directorship of the Observatory at Seeberg he was elected an Honorary Associate of the Royal Astronomical Society, and at the time of his decease was the oldest foreign member on our list. In 1824 the Council of our Society awarded to Encke their gold medal for what Mr. Colebrooke, the President of that day, properly designated as "the greatest step that had been made in the astronomy of comets since the verification of Halley's Comet in 1759." Encke had long been on the track of his comet. In 1818 he had succeeded in identifying it with the Comet of Mechain and Mes

sier in 1786, and again with the comet discovered by Miss Herschel in 1795, and with the comet of Pons in 1805. The result of his investigations was, that this comet, which astronomers have agreed to designate as "Encke's Comet" (although he himself always modestly calls it the Comet of Pons), would make its appearance again in 1822, although it would not then be visible in Europe. Accordingly our Society had the gratification of presenting to Mr. Rümker their medal for its discovery at Paramatta in 1822, on the same day when they bestowed a similar mark of approbation, as we have already stated, on Encke himself, for its prediction.

It was in these Memoirs, that Encke signalized himself by his systematic and most successful application of the principle of least squares to a number of astronomical observations. For the method itself we are mainly indebted to Legendre and to Gauss, but for the first exhibition of its vast practical value, we are indebted to the example of Encke. His mind, indeed, seems to have been preeminently arithmetical, delighting in the orderly and systematic development of what otherwise and to many would seem an inextricable maze of figures. Those who knew him. best consider that he probably injured the generality of his mathematical analysis by the fastidious care which he bestowed upon its symmetrical arrangement.

In 1825, at the recommendation of Bessel, Encke was appointed to the Directorship of the Observatory at Berlin; the Observatory itself was both improperly situated, and inadequately supplied with instruments, but ultimately, at the suggestion of Humboldt, a new Observatory was erected at the expense of the Prussian government, Encke superintending personally both its construction and its interior arrangements. And here, for eight or ten years after its completion, he continued with much assiduity to observe both with the Transit Circle and the Equatorial; but his natural tastes did not lie in instrumental observations, and after the discovery of numerous small planets by various observers, he devoted himself with much success to the investigation of planetary disturbances.

The labors of Encke in reference to the comet which bears his name have already been referred to. Having carefully taken into account the perturbing action of the planets on this comet during several successive periods, he established the remarkable fact that there is some extraneous cause in operation which continually diminishes the comet's periodic time. This is evidently the effect which would be produced if the comet suffered a resistance from moving in a very rare ethereal medium, and accordingly this is the explanation proposed by Encke, and at present generally accepted by astronomers.

Encke has also, as already mentioned, devoted special attention to the subject of the perturbations of the Minor Planets.

In the Appendix to the Berliner Jahrbuch for 1837 and 1838, he expounds in detail the method of calculating these perturbations which had been long used by himself and other German astronomers, and which was originally given by Gauss. In this method the perturbations of the six elements of the orbit are computed for successive equal intervals of time by means of mechanical quadratures, and from the values of the elements thus found for any given time, the co-ordinates of the body at that time are determined.

Now this method, although a very beautiful one in theory, is attended with the disadvantage of requiring the determination of double the number of unknown quantities that are really wanted, and the calculations which must be gone through consequently become excessively long.

As the number of the known minor planets became larger, the want of a readier method of computing their perturbations became more and more pressing.

Encke was thus impelled to devise a mode of applying the method of integration by quadratures directly to the differential equations of motion of the disturbed body, and he published an account of this new method in the Proceedings of the Berlin Academy for 1851. In this Memoir he refers the place of the body to rectangular co-ordinates, and he determines the perturbations of its movements during successive short intervals of time by a direct computation of the changes produced in the three co-ordinates by the action of the disturbing planet.

He estimates that the labor of computation is reduced by the new method to less than one-half of that required by the method previously employed.

It should be remarked that Prof. G. P. Bond, in a paper which was communicated to the American Academy of Arts and Sciences in 1849, had already briefly explained a method of calcu lating perturbations exactly similar in principle to that of Prof. Encke, but the latter was totally unaware of the existence of this paper when he published his own Memoir, which enters much more fully into the practical details of the method, and gives greater prominence to the importance of it as applied to the case of the minor planets.

By astronomers of the present day it is possible that Encke may be most highly estimated for the vast improvements which he introduced into the Berlin Ephemeris. The history of astronomical ephemerides is not a little varied and curious; a concise account of it will be found in the fourth volume of the Memoirs of the Royal Astronomical Society, on the occasion of the council of the Society presenting Encke, through their President,

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