m 



LA HARPS. 



LAIRESSE, GERARD. 



tut ion and Integration; on Iinary Root*; Astronomical Hrf mo- 

 tion ; InUjrration of Equation* of Partial Difference... 1773, On tha 

 llouiory Motion of Body ; on the Attraction of Elliptic Spheroid*; 

 on Triaiqrular I'ytnn.id* and Arithmetic. 1774, On the Particular 

 Integral* of Differt-ntial Equation* ; On the Motion of the Node* of 

 tlii> PlanrU' Orbit*. 1776. On KiniU DiflVrcnor*; the Attraction of 

 Kill | -lie Spheroid*, and Arithmetic, 1774, On the Change in tha Mean 

 Motion* of the Flaneta ; Continued Fraction*, and Spherical A*tronomy. 

 1777. 1 >k>ph.intina Analysis; On EKapatnenU; Determination of the 

 Imaginary Koota of Alge'bcaie Kquation* ; On the Mption of a SyaUca 

 at BodU* which mutually attract each other invenely u the aquare 

 of the dvtaooe. 1778, Determination of the OrbiU of Comet* from 

 thrreotvervations; Theory of Tclatoopem, 1779, On Particular Inte- 

 gral*; Conatruotion of Geographical Map*. 1780, Libration of the 

 Moon, and on other Problem* depending upon the Non-Sphericity of 

 that Planet 1781, Theory of the Motion of Fluids; Principlt-s and 

 general Formula; for determining the aecular variation* of the Planet*' 

 OrbiU ; Report of M. LagraDge on a Method proposed for finding the 

 Quadrature of the Circle. 1782, Continuation of the preceding Memoir 

 on Secular Variation* ; Report of Lagrange on a Method proposed for 

 determining whether the Earth is flattened at the poles. 1783, On the 

 Periodical Variation* in the Planetary Motions ; Secular Variations in 

 the Mean Motion* of the Planet* ; Correction* of the common Methods 

 of Approximation for Integrating the Equations of the Planets' Mo- 

 tions ; A particular Method of Approximation and Interpolation ; A 

 New Property of the Centre of Gravity ; Third Memoir on the deter- 

 mination of the Orbita of Comet*. 1784, Theory of the Periodical 

 Variation* in the Planet*' Motions, independent of the Inclinations 

 and Excentricitiea, for each of the ix principal planets. 1785, Partial 

 Differential Equation*. 178, Geometrical Theory of the Motion of 

 the Aphelia, to serve a* an addition to Newton's Principia; Correction 

 of tboee parts of Newton's Principia relative to the Propagation of 

 Sound and the Motion of Wave*. 1792-93, Solution of a Problem in 

 Life Annuities ; Determination of the general term of a recurring aerie* 

 when Generating Equation contains equal roots ; On Elliptic Sphe- 

 roids ; On Interpolation ; On the Secular Equation of the Moon ; Addi- 

 tion to a Memoir by M. Duval-le Roi oil the Secular and Periodical 

 Variations of Herechel, printed in the Memoirs of the year 1787. 

 1803, On a General Law of Optic*. 



ilemoirt in the Trantactiom of the Academy of Parit. 1764, On the 

 Libration of the Moon (thi is the memoir for which the medal wa< 

 awarded to M. Lac range by the Academy, and in which he first employs 

 the principle of Virtual Velocities). 1760, On the Inequalities of 

 Jupiter'* Satellites. 1772, On the Formation of Tables of the Planets ; 

 On the Problem of Three Bodies. 1774, Oil the Motion of the Nodes 

 and the Inclinations of the OrbiU of Planet*. 



.Si ran* EtraiHjm. Tome 7, On the Secular Equation of the Moon. 

 (Prize Memoir for the year 1774) ; tome 10, On the Perturbation* of a 

 Comet which passe* near to a Planet. 



French Intliiute. Memoir* of the First Clot*. 1808-9, On the 

 Variation of the Elements of a Planet, and more particularly the 

 Variation of the Major Axis of their OrbiU; Theory of the Varia- 

 tion of Arbitrary ConxtanU in all Mechanical Problems (two memoirs). 

 Journal of the Polytechnic School. Tomo 2, On the principle of 

 Virtual Velocities; Etsayon the Transformation of Fraction*; Theory 

 of Analytical Function* ; Analysis of Spherical Triangles ; tome 5, On 

 the Calculus of Analytical Function* ; tome 7, Supplement to the same; 

 tome 8, On the Attraction of Spheroid*. 



Connaiuancet da Tem$. 1814, On the Origin of Comet*. 1817, On 

 the Calculation of Eclipses. 1819, Remarks on the Method of Pro- 

 jection in the Calculation of Eclipse*. 1821, Method of determining 

 the Orbit of a Comet from Observation. 



M. Carnot, while Minister of the Interior, recommended to his 

 government the purchasing of the manuscripU of Lagrange. and, at 

 his suggestion, the mathematical and physical class of the Institute 

 nominated a commission to select tmch as were in a state for publication ; 

 the rest are arranged nnd deposited in the library of tho Institute. 



(Koye de M. JJelambre ; Memoirtt de I'lntlitut, 1812; Lagrange, 

 Mtcanique Anaiytique, 1815 ; Thforie del Ponctimi Analytit/ue, 1813 ; 

 MiictUanta Taunnentia, 1759-61 ; Optucvlei Mathcmati'/uet de JU. 

 fAlembert, 1761-69; tiotict of the Life of Lagrange, by Maurice; 

 B\og. i'niver$elU ; Professor Hamilton, Memoir on a General Hethoil 

 i Dynamic*, in Phil. Tram., 1834; Uictionnaire Biblioyrajihique. de 

 QtUrard.1829.4c.) 



LA HAHl'K. [HARPB, LA.] 

 LAHIRK, PHILIPPE DK, wa* born at Paris March 18th, 1640, 

 in which city he also died April 21 Ft, 1719. Up to the age of twenty- 

 four year* he followed the profession of hi* father, who had acquired 

 considerable reputation aa a profotsor of pnintini; and sculpture to the 

 Royal Academy. In 1660 he visited July, partly for the improvement 

 of hi* health, and partly with a view to the completion of his pro- 

 fessional education. While at Venice ho applied himself to the itudy 

 of geometry, and more particularly to the conic sections of Apollo- 

 nins ; and a few yean after hi* return to Paris he published several 

 treatises upon tboae subjects, which fully t-sUblithcd his claim to the 

 reputation of a profound geometrician. In 1679, Colbert having aug- 

 gri'ed the construction of a general map of France, Picard and De 

 Labire were nominated by the king to conduct certain surveys along 



the coast of Qaaeony, and in 1683, De Lahire, in conjunction with 

 Dominic Caaaini, wa* instructed to proceed with the measurement 

 of the meridian, which bad been oomnienoed in 1669 by Picard. 

 [ PICARD.] The death of M. Colbert having put a *top to this import- 

 ant undertaking, he wa* next employed in determining the difference 

 of level of the river Eure and the reservoir of Versailles, preparatory 

 to the construction of an aqueduct for the supply of the oapiUI, which 

 he effected to the satisfaction of tha kin?, and of Louvoia, the then 

 minuter. The other public works in which M. Da Lahire wa* suc- 

 cessively engaged were numerous and important, but our limiU will 

 not permit u* to notice them more particularly. lie was twice married, 

 and "each of hi* marriages," aays U. Fontenelle, " furnished an 

 Academician." 



Although he doe* not appear to have been altogether unacquainted 

 with the infinitesimal calculus, the whole of the subjects upon which 

 he has written are treated lynthetically. In hi* manner* he wai more 

 reserved than the generality of his countrymen, but the uprightnea* 

 and disinteraatednes* of hi* conduct were most exemplary. A pur* 

 piety, free from superstition and singularity, characterised the whole 

 of his life. 



For further information the reader may advantageously consult the 

 ' llcanoires de Niceron,' torn. v. and x. ; ' 1'Histoire du College Royal,' 

 by Qoguet; and the 'Eloge de Lahire,' by Fontenelle ('(Eiivrei 

 Diverse*,' folio, 1729), from which this notice is chiefly drawn. Hi* 

 published works are ' Treatise on Conical and Cylindrical Section*,' 

 Paris, 1673. 4to; 'De Cycluide Opusculum,' 1676; 'Conic Sections 

 and Geometrical Loci,' 1679 ; ' Gnomonics, or the Art of making Sun- 

 dials,' 1682; Conic Sections,' 1685, folio; ' Tabulso Astronomicte,' 

 1702, 4to; 'Treatiso on Surveying,' 1689; ' Mechanics,' 1675; 

 Description of the Globes in the Pavilion of the Chateau de Marli,' 

 1704; besides numerous memoir* in the public journals of the day, 

 and more particularly in the ' Transaction* of the Academy of Sciences,' 

 from 1666 to 1718. 



LAING, MALCOLM, an historian, was born in Orkney, where he 

 possessed a small patrimonial estate, in 1762. He received the rudi- 

 nents of education at Kirkwall, and afterwards studied at Edinburgh, 

 where he was one of the most active members of the ' Speculative 

 Society,' an association in which many young men who became distin- 

 guished in after life first tried their prowess. In 1785 lie joined the 

 Scottish bar. He does not appear to have obtained much practice as 

 a lawyer, and the only conspicuous occasion in which he was pro- 

 fessionally employed seems to have been in the defence of some of the 

 partie* tried for sedition in Scotland between 1793 and 1795. He is 

 one of the many instances where lawyers lmv in their works displayed 

 peculiarly hi_r!i forensic abilities, without being able to rise in their 

 profession. His first known literary effort was editing the lost volume 

 of Henry's ' History of Britain,' in 1793, after the author's death. Ho 

 was charged with having spoiled the harmony of tho work, as Henry's 

 opinions were all in favour of despotic principles, while the addition* 

 made by Laing were of a democratic tendency. In 1800 he pub 

 'The History of Scotland from the Union of the Crowns on the 

 accession of James VI. to the throne of England, to the Union of the 

 Kingdoms in the reign of Queen Anne.' This was published along 

 with two other works, the names of which appearing on the title of 

 the ' History,' with which the subjects of neither of them were in any 

 way connected, are very characteristic of Lain< '* propensity to enter 

 on disputed points in history or criticism with the spirit of a lawyer. 

 The ' History ' as published in two volumes was accompanied by ' Two 

 Dissertation*, Historical and Critical, on the dowry Conspiracy, and 

 on the supposed authenticity of Ossian's Poems.' To the second 

 edition of his 'History,' published in 1804, ho added ' A Preliminary 

 Dissertation on the Participation of Mary Queen of Scots in the Murder 

 of Darnlry.' He was a sagacious, honest, and able historical critic, 

 but too much inclined to take up a side in any question, and to keep 

 perpetually in view the circumstance that he wa* bound to defend 

 that side. His style was harsh and formal, and sometimes ob-curo. 

 He wa* for some time member of parliament for Orkney, and enjoyed 

 the confidence and esteem of Fox. He died in 1818. His brother 

 Samuel Lain?, the author of the valuable ' Notes of a Traveller,' 

 ' Travels in Norway,' &c., succeeded to his property. Mr. Samuel 

 Laing, late chairman of the Brighton Railway and Crystal Palace 

 Companies, and a conspicuous member of the railway interest in the 

 House of Commons, is the son of Mr. Laing the traveller, and nephew 

 of the historian. 



LAIKESSE, GERARD, an eminent painter, was born at Lie"ge in 

 1640. He acquired his knowledge of the art from liis father; but 

 there is reason to believe that be also htuilied under Hartolet, from 

 whom he prohuMy derived the Uste for the antique which appears in 

 his works. He first followed his profession at Utrecht, where be met 

 with little encouragement; but having born advised to send one of his 

 pictures to the famous picture-dealer Vylenburg, at Amsterdam, he 

 wa* so pleased with it that he prevailed nn Laircaie to remove to 

 Amsterdam, which proved the mean* of raising him from poverty 

 and obscurity to fortune and reputation. Having a lively 

 nation, great rapidity of execution, and great industry, tho number 

 of painting* which ho executed wa* very great They are of very 

 unequal degree* of merit, but all bear marks of considerable ability. 

 Hi* expression is generally good, hi* colouring true and glowing, and 



