774 



MKNSKS MENTZ. 



fluence of Menschikoff that Catharine was raised to 

 the throne, and that affairs were conducted during her 

 n-iini. (See Catharine /.) When Peter II. suc- 

 ceeded her on the throne, Menschikoff grasped, with 

 a bold and sure hand, the reins of government. In 

 1727, when his power was raised to the highest pitch, 

 he was suddenly hurled from his elevation. Havinj 

 embezzled a sum of money which the emperor hai 

 intended for his sister, he was condemned to perpe- 

 tual exile in Siberia, and his immense estate was con- 

 fiscated. He passed the rest of his life at Berezov, 

 where he lived in such a frugal way, that, out of a 

 daily allowance of ten roubles, he saved enough to 

 erect a small wooden church, on which he himsell 

 worked as a carpenter. He sunk into a deep melan- 

 choly, said nothing to any one, and died in 1729. 

 Menschikoff was selfish, avaricious, and ambitious, 

 implacable, and cruel, but gracious, courageous, well 

 informed, capable of large views and plans, and per- 

 severing in the execution of them. His services in 

 the promotion of civilization, commerce, the arts and 

 sciences, and in the establishment of Russian respec- 

 tability abroad, have been productive of permanent 

 effects. 



MENSES. See Catamenia. 

 MENSURATION, is the art of ascertaining the 

 contents of superficial areas, or planes ; of solids, or 

 substantial objects ; and the lengths, breadths, &c., 

 of various figures, either collectively or abstractedly. 

 The mensuration of a plane superficies, or surface, 

 lying level between its several boundaries, is easy : 

 when the figure is regular, such as a square, or a 

 parallelogram, the height multiplied by the breadth, 

 will give the superficial contents. In regard to 

 triangles, their bases, multiplied by half their heights, 

 or their heights by half their bases, will give the 

 superficial measure. The height of a triangle is taken 

 by means of a perpendicular to the base, let fall from 

 the apex or summit. Any rectangular figure may 

 have its surface estimated, however numerous the 

 sides may be, simply dividing it into triangles, by 

 drawing lines from one angle to another, and taking 

 care that no cross lines be made ; thus, if a triangle 

 should be equally divided, it may be done by one line, 

 which must, however, be drawn from any one point 

 to the centre of the opposite face. A four-sided 

 figure will be divided into two triangles, by one 

 oblique line connecting the two opposite angles ; a 

 five-sided figure (or pentagon) by two lines, cutting, 

 as it were, one triangle out of the middle, and mak- 

 ing one on each side ; a six-sided figure (or hexagon) 

 will require three diagonals, which will make four 

 triangles ; and so on, to any extent, and however 

 long or short, the several sides may be respectively. 

 The most essential figure is the circle, of which ma- 

 thematicians conceive it impossible to ascertain the 

 area with perfect precision, except by the aid of 

 logarithmic and algebraic demonstration. It may be 

 sufficient in this place to state, that 8 1 ? of the 

 diameter will give the side of a square, whose area 

 will be correspondent with that of a circle, hav- 

 ing ten for its diameter. Many circular or cylin- 

 drical figures come under the measurer's considera- 

 tion mirrors, arched passages, columns, &c The 

 contents of a pillar are easily ascertained, even though 

 its diameter may be perpetually varying ; for if we 

 take the diameter in different parts, and strike a 

 mean between every two adjoined measurements, 

 and multiply that mean area by the depth or interval 

 between the two, the solid contents will be found. 

 The contents of pyramids are measured by multi- 

 plying the areas of their bases by half their lengths, or 

 their lengths by half the areas of their bases. Cones, 

 whose sides are straight, are equal to one third the 

 solid contents of cylinders, equal to them in base 



and altitude. Solids having a certain degree of re- 

 gularity, may be easily measured : thus a cube is com- 

 puted by multiplying first its width by its length ; 

 then their product by its height: thus a cube, measur- 

 ing four feet each way, would be 4x4=16x4=64. 

 This is the meaning of what is called the cube root. 

 (See Cube.) Parallelopipedons, or solids of a long 

 form, such as squared timbers, are measured by the 

 same means. For the mensuration of growing tim- 

 ber, various modes have been devised. After a tree 

 has been felled, its girth is usually taken at each end, 

 and at the middle, when there is no particular swell, 

 or the top extremity does not suddenly decrease, 

 But where the irregularity is great, it is better to 

 take many more girths, and, summing up the whole, 

 to divide their amount by the number of girths taken, 

 so as to establish a mean measurement. Divide that 

 mean measurement by four, to find the side of a 

 square to which the tree will be reduced when 

 prepared for the sawyer. If the whole solid contents 

 are to be estimated, divide by three, instead of by 

 four, and taking the third part, thus given, for a 

 diameter, proceed in the way already shown, to find 

 the side of a square, equal to the circle of which 

 that ascertained third part is the diameter. Solid 

 bodies, or areas, such as hay-stacks, interiors of barns, 

 granaries, &c., come under the rule laid down for 

 cubes, &c. When any sides fall in regularly, as in 

 garrets, &c., the inclined part must be treated as a 

 pyramid, or as a quoin (or wedge), and the whole be 

 summed up together. The contents of casks, tubes, 

 &c., are found by the process of gauging. For that 

 part of the subject which appertains to the admeasure- 

 ment of lands, as also to the distances, heights, 

 &c., of remote objects, accessible or otherwise, see 

 Surveying. 



MENTAL DERANGEMENT. See Insanity. 

 MENTCHIKOF. See Menschikoff. 

 MENTOR, son of Alcimus, the confidential friend 

 of Ulysses, who intrusted to him the care of his do- 

 mestic affairs, during his absence in the war against 

 Troy. The education of the young Telemachus fell 

 to his charge, and when the latter set out on his 

 voyage in search of his father, Minerva accompanied 

 lim under the form of Mentor (Odyssey, ii. 390; iii. 

 12, &c.), acting the part of a prudent and experienced 

 counsellor to the young hero. This character of a 

 sage adviser is more fully developed in the Tele- 

 maque of Fenelon, in which Mentor plays a conspicu- 

 ous part. Mentor has thence acquired the meta- 

 phorical sense of a wise and faithful counsellor or 

 nonitor. 



MENTZ, or MAYENCE, or MAINZ ; a city of 

 ermany, in Hesse-Darmstadt, formerly capital of 

 an electorate and archbishopric, situated at the con- 

 flux of the Rhine and Maine, called in Latin Mo- 

 guntia, or Moguntiacum ; Ion. 8 E. ; lat. 49 59' 

 . ; population, 25,251. It is the strongest town in 

 ermany : towards the river less defence is necessary, 

 nit on the land side the works are extensive and 

 (implicated. The fortress belongs to the Germanic 

 :onfederation. The town is built nearly in the form 

 of a semicircle, the Rhine forming the base. The 

 nterior is by no means handsome. The streets are 

 irooked, narrow, and gloomy, and the houses mostly 

 ild fashioned. It contains a cathedral, a lyceum, 

 chools of medicine, a cabinet of coins and medals, 

 i cabinet of natural history, a gallery of paintings, 

 ind a library of 90,000 volumes. The trade consists 

 >artly in wine, and partly in commission business, 

 connected with the navigation of the river. The town 

 s famous for the beauty of its environs and prospects. 

 A university was founded here by Charlemagne in 

 800, and re-established in 1482, by the archbishop 

 Diether, of the house of Isenburg, but has been since 



