L A N L A N 271 primogeniture, with the additional objection that it tends to limit the growth of population. Parents who are com pelled to give an equal portion to every child avoid the risk of subdivision by not having many children, a course which, if commendable when the Old World seemed in peril of over-population, is a source of national impoverishment when the world affords profitable employment for hundreds of millions more than exist. Among the children them selves the certainty of succession abates the sentiment of filial duty, and the desire to bestow a special bounty on one child who is favoured above the rest may sometimes induce the parents to spend less than they otherwise would in the improvement of the whole estate. Subdivision of property may, however, be gradually effected by prohibiting excessive bequests. It has always been recognized that the state has an unquestionable right to deal with property at the moment of its transmission from the dead to the living, and no objection could be made to a rule that no one should leave by will or through intestacy more than a certain sum, or land of equivalent value, to one individual. This would not generally affect the desire during life to amass and improve property, because the improved value would still be available for division among all whom the owner wished to benefit. But it would in one generation reduce all estates of abnormal size to properties of such dimension as in the opinion of parliament would be most serviceable for cultivation, and consequently most conducive to national benefit. The abolition of the right to raise money by mortgage of land would also tend to promote its subdivision, since an owner in debt would be obliged to sell a portion of his estate in order to pay his debts. The improvement of conveyancing, which would follow from the general aboli tion of all interests in land except that of simple and absolute ownership, would also facilitate the sale of land. The leading principle which should guide legislation is in short that land should be made capable of the easiest trans mission from one owner to another, and of the fullest use by him to whom for the time it belongs. The ordinary motives of human nature will then concur in transferring it from those who are least to those who are most capable of making it productive, and of inducing each successive owner to bestow on it the labour and outlay by which the maximum of beneficial production will be secured, See Mommsen, History of Rome ; Yon Maurer, Geschichtc der Markenverfassung in Dcutschland ; Id., Geschichtc der Dorfverfas- sung ; Id., Geschichtc der Stddtcverfassung ; Id., Gcschichte der Frohnhofe, der Bauerhofe, und der Hofvcrfassung ; Nasse, Ucber die Mittelalterliche Feldgemcinschaft in England ; Landau, Die Territorial in Bczug auf ihre Sliding ; You Haxthausen, Ueber die Afjrarverfassung in Nordcutschland ; Laveleye, Primitive Pro perty ; Maine, Village Communities in the East and West ; Cobden Club, Systems of Land Tenure Reports of H.M. Representatives on Tenure of Land, Parl. Papers, 1860-1 ; Statistique de la France; Marx, Das Capital ; Herbert Spencer, Social Statics ; George, Pro gress and Poverty ; Brodrick, Land in England ; Boyd Kinnear, Principles of Property in Land. LANDAU, the chief town of an official district in the Palatinate of the Rhine, Bavaria, is situated on the Queich, about 18 miles north-west of Carlsruhe. 4mong its various interesting buildings are the Gothic church, dating from 1285, and the monastery, founded in 1276, and now con verted into a brewery. There is a considerable trade, and some manufacture. The population in 1875 was 7579. Landau was taken no less than seven times in the Thirty Years War. At the peace of Westphalia it was ceded to the French, and was generally held by France till 1815, when it was restored to Germany ; in 1816 it was annexed to Bavaria. In 1871 its forti fications were finally destroyed. LANDEN, JOHN, a distinguished mathematician of the 18th century, was born at Peakirk near Peterborough in Northamptonshire in 1719, and died 15th January 1790 at Milton in the same county. Most of his time was spent in the pursuits of active life, but he early showed a strong talent for mathematical study, which he eagerly cultivated in his leisure hours. In 1762 he was appointed agent to the Earl Fitzwilliam, and held that office to within two years of his death. He lived a very retired life, and saw little or nothing of society ; when he did mingle in it, his dogmatism and pugnacity caused him to be generally shunned. He was first known as a mathematician by his essays in the Ladies Diary for 1744. In 1766 he was elected a Fellow of the Royal Society. He was well acquainted and au courant with the works of the mathe maticians of his own time, and has been called the English D Alembert. In his Discourse on the " Residual Analysis," in which he proposes to substitute for the method of fluxions a purely algebraical method, he says, "It is by means of the following theorem, viz., xl + . . (m terms) (where m and n are integers), that we are able to perform all the principal operations in our said analysis ; and I ain not a little surprised that a theorem so obvious, and of such vast use, should so long escape the notice of algebraists." The idea is of course a perfectly legitimate one, and may be compared with that of Lagrange s Calcid des Fondions. His memoir (1775) on the rotatory motion of a body contains (as the author was aware) conclusions at variance with those arrived at by D Alembert and Euler in their researches on the same subject. He reproduces and further develops and defends his own views in his Mathematical Memoirs, and in his paper in the Philosophical Transactions for 1785. But Landen s capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs. To find this, he integrates a differential equation derived from the equation interpreting geometrically in an ingenious and elegant manner three integrals which present themselves. If in the foregoing equation we write m= 1, g = k 2 , and instead of t consider the new variable y = 1 4- ( 1 - ), then which is the form known as Landen s transformation in the theory of elliptic functions ; but his investigation does not lead him to obtain the equivalent of the resulting differential equation dti (l + k )da 1-fc L -- , where = . , Vl - y 2 . 1 - A 2 ?/ Vl due it would appear to Legendre, and which (over and above Landen s own beautiful result) gives importance to the theorem as leading directly to the quadric transforma tion of an elliptic integral in regard to the modulus. The list of his writings is as follows : Ladies Diary, various com munications, 1744-1760 ; papers in the Phil. Trans., 1754, 1760, 1768, 1771, 1775, 1777, 1785 ; Mathematical Lucubrations, 1755 ; A Discourse concerning the Residual Analysis, 1758 ; The, Residual Analysis, book i., 1764 ; Animadversions on Dr Stewart s Method of computing the Sun s Distance from the Earth, 1771 ; Mathematical Memoirs, 1780, 1789. LANDER, RICHARD (1804-1834) and JOHN (1807- 1839), two brothers, African explorers, were natives of Cornwall. Richard Lander accompanied the Niger expedi tion of 1825-27 as Clapperton s attendant, and on the death of his master at Sokoto on the Niger in April 1827,
