619 



SIMROCK, KARL. 



SIMSON, ROBERT. 



520 



on Physical and Analytical Subjects," among which will be found an 

 investigation of the figure of a planet revolving on its axis, aud of the 

 foice of attraction at the eurfac. s of bodies which are nearly spherical; 

 al o a theory of the tides and of astronomical refractions. These 

 dissertations were dedicated to Martin Folkes, Esq., the president of 

 the Royal Society. 



'An Elementary Treatise on Algebra' was published in 1745; 'The 

 Elements of Geometry,' in 1747; and in the next year 'A Tract on 

 Plane and Spherical Trigonometry,' with the ' Theory of Logarithms.' 

 With the ' Elements of Geometry ' are given notes in which are sug- 

 gested improvements on some of the demonstrations of Euclid ; but in 

 making occasional observations on the notes given in the first editiou 

 of Dr. Robert Simson's ' Euclid,' for example on the note to the first 

 proposition of the eleventh book, he has fallen into some slight inac 

 curacies which have been remarked on in the succeeding editions of 

 the latter work. A second edition of Thomas Simpson's ' Geometry ' 

 was published in 170. 



In the year 1752 he published ' Select Exercises in Mathematics,' in 

 which are given many geometrical and algebraical problems, with th^ir 

 solutions, and a theory of puunery ; but his last aud most valuable 

 work was that which is entitled ' Miscellaneous Tracts ' (1754). This 

 consists of eight separate papers, four of which relate to pure mathe- 

 matics, and the others to physical astronomy. The first paper 

 contains investigations for determining the precession of the equinoxes 

 and the nutxtions of the earth's axis; the second contains equations 

 for correcting the place of a planet in its orbit on the hypotheses of 

 Bullialous and Seth Ward ; aud the third is on the manner of trans- 

 frrring the motion of a comet from a parabolical to an elliptical 

 orbit. In the fourth pap^r are explained the advantages, in point of 

 accuracy, which arise from using a mean of seveial astronomical 

 observations instead of one single observation. The fifth contains the 

 determination of certain fluents ; the sixth, the resolution of algebraic 

 equations by meaus of surd divisors ; and the seventh, a general rule 

 for the resolution of isoperiinetrical propositions. The eighth paper 

 contains the resolution of some important problems in astronomy ; the 

 propositions in the third and ninth sections of the first book of 

 Newton's 'Principia' are demonstrated, and the general equations are 

 applied to the determination of the lunar orbit. 



In order that the merit of this last paper may be rightly appreciated, 

 it is necessary to observe that about the year 1745 the modern 

 analysis was first applied to the determination of the elements 

 of tLe orbits of the earth, moon, and planets; these bodies being 

 supposed to perturbate each other's motions by their mutual attrac- 

 tions, as well as to be subject to the general attraction of the sun. 

 In the prosecution of the research, the mathematicians Clairaut, 

 D'Alembert, and Euler particularly investigated the effect of the 

 sun's attraction in causing a progression of the apogee of the moon's 

 orbit, which progression, being a remarkable consequence of perturba- 

 tion, was considered as a test of the correctness of the general principle 

 and law of attraction which had been assumed by Newton. The first 

 efforts of M. Clairaut showed an amount of progression in the period 

 of a revolution of the moon about the earth, equal to about half only 

 of tliat which had been determined from astronomical observations 

 ('Mdmoires de 1'Acad^mie,' 1747); and it is remarkable tbat both 

 DAlembert and Euler obtained at the same time a like erroneous 

 result. This circumstance at first caused some doubts to be ent-r- 

 tained of the truth of Newton's hypothesis, that the force of attraction 

 varies inversely as the square of the distance : but the process employed 

 by the three mathematicians being one of successive approximations 

 only, it was afterwards discovered by Clairaut that, on continuing the 

 process, the second step in the approximation produced a quantity 

 nearly equal to that which had been obtained by the first step ; and 

 thus the computed progression was found to coincide with the 

 results of observation. Now Simpson, employing a differential equation 

 of motion like that which had been used by the foreign mathema- 

 ticians, obtained the values of its terms by means of indeterminate 

 coefficients ; a method which entirely avoided the inaccuracy resulting 

 from the specirs of approximation which they had adopted; find thus 

 he arrived at once at the true value of the progression. 



The ' Tracts ' were not published till seven years after Clairaut's 

 ' Me'moire ' came out, and it appears that, in the interval, that mathema- 

 tician during a visit to England had an interview with Simpson ; the 

 latter states however, in the preface to his ' Tracts/ that previously 

 to having had any communication with M. Clairaut, he had discovered 

 that the movement of the moon's apogee could be accounted for on 

 the Newtonian law of gravitation. There is therefore no reason to 

 doubt that Simpson had the merit of arriving at a determination 

 which served to confirm the truth of that law by a process entirely his 

 own : the whole investigation exhibits profound mathematical skill, 

 and fully entitles him to the character of having been one of the 

 abk-st analysts, for all the purposes of practical science, of which the 

 country can boast. 



Mr. Simpson continued during the whole of his life his contribu- 

 tions to the ' Ladies' Diary,' of which work he was the editor from 

 1754 to 1760. 



*SIMROCK, KARL, was born on August 23, 1802, at Bonn, in the 

 Prussian Rhein Provinz, where his father kept a music shop. His 

 early education was received in the Lyceum established in Bonn by 



the French, when it formed a part of the Confederation of the Rhine. 

 After it again became a portion of the Prussian monarchy, he entered, 

 in 1818, the University there, and studied law, which study he con- 

 tinued at the University of Berlin in 1822, and in 1823 entered the 

 service of the Prussian government in the law department. His s'uly 

 of the law bad, however, not diminished his attachment to the stu'iy 

 of ancient German poetry and legends, and in 1827 he publi>hed 

 a translation of the ' Niebeluugenlied,' which has gone through several 

 editions : to this, in 1840, he added translations of 'Twenty Songs of 

 the Niebelungen,' which Lachmann had pronounced to be genuine. In 

 1830, he published a translation of the ' Armen Heinrich ' (Poor Henry), 

 of Hartmann von der Aue ; aud soon after, an original poem written 

 on the first intelligence of the French revolution iu that year, 

 occasioned his dismissal from the Prussian service. Since that time 

 he has devoted himself entirely to his favourite pursuit, for which his 

 poetical talents, his German predilections, and his deep philological 

 knowledge of the language used by the national poets iu the middle 

 ages, peculiarly fitted him. His information however is not confined 

 to this branch of literature or to his own tongue. In 1831, in con- 

 junction with Echtermayer and Henschel, was published. ' Quellen 

 des Shakspeare in Novellen, Mahrchen, und Sagen,' (' Sources of 

 Shakspeare's Plots in Novels, Tales, and Legends'). In this he had 

 the greatest share, and the remarks on the plots, in which he traces 

 them to their remotest sources (sometimes rathtr fancifully), aud 

 produces strong presumptive proof that Shakspere's knowledge of 

 languages must have been much more extensive than has been 

 generally supposed, was wholly his own. Tuey have been trans- 

 lated into English, edited by Mr. Halliwell, and published by the 

 Shakspere Society in 1850. In 1832 also he published a single volume 

 entitled 'Der Novellenschatz des Italiener ' ('The Novel- Treasure of 

 the Italians'). In conjunction with Wackernagel, he completed, in 

 1833, a translation, with explanations, of 'Gedichte Walthers von der 

 Vogelweide ' (' Poems by Walter of the Birdmeadow,' though Vogel- 

 weide is here a proper name), of which the valuable remarks at the 

 end of the second volume are all Simrock's. In 1835, he wrote an 

 original poem called 'Wieland der Schemed. Deutsche Heldensage' 

 (' Wayland the Smith, a German heroic poem '). It consists of twenty- 

 four adventures of the old German hero, written in the ballad style; 

 to which w*re added a few ballads and romances founded on other 

 legends, all deeply impressed with the spirit of the ancient lays, and 

 of great excellence. They were received with great favour : aa were 

 also his ' Rhein*agen aus dem Munde des Volks und Deutscher Dichter ; 

 fur Schule, Haus, und Wanderschaft' ('Legends of the Rhine, from 

 the Mouths of the People and from German Poets; for Schools, 

 Families, and for Travelling'), of which a third edition was published 

 in 1841. It follows the course of the Rhine from its mouth upwards, 

 illustrating the places by the legends conuected with them, some of 

 which are ancient, but the most either by himself or other modern 

 German writers. In 1839, he also wrote ' Das Malerische und Roman- 

 tische Rheiuland ' (' The Picturesque and Romantic Rhineland '), a 

 description of the district for the use of travellers and others. He 

 next resumed, and carried out to the extent of many small volumes, 

 'Die Deutscher Volksbiicher' ('Books for the German People'), 

 originally commenced by Marbach, which he continued from 1839 to 

 1847. The collection contains a large number of German tales aud 

 legends, and many which appear to be a common propi-rty of Europe, 

 such as ' Patient Grizel,' ' Tristan and Isolde,' &c. In 1842, he 

 published a translation of ' Purzival uud Triturel,' by Wolfram von 

 Eschenbach. And in order to give a poetical representation of 

 German heroic poetry, partly by translations and partly by his own 

 production?, he commenced in 1843, ' Das Heldenbuch ' (' The Book 

 of Heroes'), of which several volumes have beeu published. The 

 first contained a translation of 'Gudrun;' acd the fourth, filth, aud 

 sixth ' Das Amelungenlied,' an original poem which was opened iu his 

 ' Wieland.' In 1844, a collection of his own poems, ballads, aud 

 romances were published, which have become extensively popular. 

 Indeed, few poets have ever on so large a scale so thoroughly imbued 

 themselves with the spirit of ancient poetry, and so successfully 

 imitated its simplicity and energy. 



In 1850, he was created Professor of th German language and 

 literature in the University of Bonn. In 1851, he published a most 

 successful translation of the ' Lieder des Edda ' (' Lays of the Edda ') ; 

 a ' Haudbuch der Deutschen Mythologie,' in 1852; and an 'Altdeut- 

 sches Lesebuch in neu deutscher Sprache' ('Reading Book of old 

 German Authors in Modern Language '), in 1854. 



SIMSON, ROBERT, one of the many mathematicians who have 

 given a lustre to the universities of Scotland, was a son of Mr. John 

 Simson, of Kirton Hall in Ayrshire, and was born in October 16S7. 

 About the year 1701 he was sent to the University of Glasgow, wh<re 

 he acquired that proficiency in the learned languages which he 

 retained during all his life, and at the same time h^ made considerable 

 progress in moral philosophy aud theology, being destined by hia 

 father for the church. Young Simson soou however found a pursuit 

 more congenial to his taste in the study of mathematics, aud chiefly 

 of the ancient geometry : to this subject he applied himself at first as a 

 relief from what he considered as a more laborious occupation, and it 

 became at length almost the sole employment of his life. 



In 1710 Mr. Siuison made a visit to London, where he remained 



