Page:Encyclopædia Britannica, Ninth Edition, v. 16.djvu/23

Rh M E N M E N 13 seeing the youth at Lefort s, was also delighted with him, and took him to be his page. Menshikoff soon became indispensable to the czar, assisting him in his workshop, and displaying signal bravery in the company of his master at the siege of Azoff. He formed one of the suite of Peter during his travels, and worked with him at Saardam and Deptford. Throughout his wars with the Swedes, Men shikoff was the companion of the czar, and greatly distin guished himself. For his gallantry at the battle of the Neva, on the 7th of May (o.s.) 1703, he received the order of St Andrew. In 1704 he was made general, and at the request of the czar created a prince of the Holy Roman Empire. His house on the Vasilii-Ostroff was magnificent ; there ambassadors were received, and banquets were given gorgeous with gold and silver plate. Unfortunately there is a dark side to the picture, and the favourite was guilty of extortion to such an extent as to bring him under his master s censure. On the death of Peter the position of Menshikoff became very perilous ; his successes had raised about him a host of enemies eager for his downfall. The Golitzins, Dolgoroukis, and all those who formed what may be called the Old Russian party, wished to proclaim the son of Alexis emperor. Those, however, whose aggrandize ment was bound up with Peter s reforms Menshikoff, Apraksin, Bontourlin, Goloff kin, and others were in favour of giving the crown to Peter s widow, who accordingly ascended the throne as Catherine I. During her reign the influence of Menshikoff was unbounded, and he virtually governed the country; but the empress died in 1727, after a reign of two years. She had made a will, no doubt at the instigation of the favourite, to the effect that Peter, her grandson, was to be czar under the guardian ship of Menshikoff, whose daughter Mary was to be married to the youthful sovereign. Under pretence of taking care of the young czar, Menshikoff caused him to be removed to his house and surrounded him with his creatures. He was now at the height of his power ; foreign ambassadors remarked that even the great Peter himself was never feared so much. The young czar, however, showed no affection for Mary Menshikoff, and the girl was equally apathetic towards her betrothed, being in love with a member of the family of Sapieha at the time her father had forced her into the engagement. The Dolgoroukis used the aversion of the young prince to his fiancee as a means of creating dislike to the father. A chain of events was gradually leading to the downfall of the favourite. He was soon refused admittance to the summer palace, whither the young czar had retired. Next he was arrested, and so overpowered was he at his disgrace that he had an apoplectic stroke. In vain did he address letters both to the emperor and his sister. Shortly after, by order of the czar, the fallen magnate departed from St Petersburg, but more like a nobleman retiring to his estate than a culprit going into exile. The people regarded him with dislike, and most of them rejoiced over his fall. On his way a courier arrived with orders to take the czar s ring of betrothal from his daughter Mary and give her back her own, which had been worn by Peter II. Menshikoff was not permitted to pass through Moscow, but was conducted to Oranienburg, in the government of Riazan, and there placed under strict surveillance. Soon afterwards the whole family was banished to Siberia, and arrived at Berezoff towards the end of 1727. Menshikoff .s wife died on the journey, and was buried near Kazan. On the arrival of the prisoners they were lodged in a wooden house, consisting of four rooms. But Menshikoff did not long endure the horrors of exile in this inclement region. According to Mannstein, he died (November 12, o.s., 1729) of an apoplectic stroke, because there was no one at Berezoff, as he himself remarked, who understood how to open a vein. The young czar ordered the release from exile of the two remaining children of Menshikoff, his daughter Mary had died at Berezoff in the same year as her father, and restored some of their property to them. MENSHIKOFF, ALEXANDER SERGEIEVICH (1 787-1 869), great-grandson of Peter s favourite, born in 1787, entered the Russian service as attache&quot; to the embassy at Vienna. E o accompanied the emperor Alexander throughout his cam paigns against Napoleon, and attained the rank of general, but retired from active service in 1823. He then devoted himself to naval matters, and put the Russian marine, which had fallen into decay during the reign of Alexander, on an efficient footing. On the outbreak of the Crimean War he was appointed commander-in-chief, and suffered a severe defeat at the Alma. On the death of the emperoi Nicholas in 1855 he was recalled, ostensibly on account of failing health. He died in 1869. MENSURATION ~ /TENSURATION, or the art of measuring, involves _LVJ_ the construction of measures, the methods of using them, and the investigation of rules by which magnitudes which it may be difficult or impossible to measure directly are calculated from the ascertained value of some associated magnitude. It is usual, however, to employ the term mensuration in the last of these senses ; and we may therefore define it to be that department of mathematical science by which the various dimensions of bodies are calculated from the simplest possible measurements. The determination of the lengths and directions of straight lines, including what are familiarly known as problems in heights and distances, generally depends on the solution of triangles, and will be discussed in the articles TRIGONOMETRY and SURVEYING. The remaining portions of the subject are the determinations of the lengths of curves, the areas of plane or other figures, and the volumes and surfaces of solids ; and it is of mensura tion as thus restricted that the present article will discuss some of the more important problems. 1. Units of Length, Area, and Volume. In measuring any magnitude we select some standard or &quot; unit &quot; to mea sure by. Thus in measuring length we take for unit an inch, a foot, or a yard. From the unit of length we derive the units of area and volume. Thus we define the unit of area to be the area of the square described upon the unit of length, and the unit of volume to be the volume of the cube whose edge is the unit of length or whose side is the unit of area. For example, if an inch be taken as the unit of length, the square whose side is 1 inch is the unit of area, and the cube whose edge is 1 inch is the unit of volume. The length of a line, the area of a surface, and the volume of a solid are then expressed by the numbers, whole or fractional, of units of length, area, and volume which they respectively contain. Hence, if I denote the linear unit, the length of a line which contains a units is af, or simply a since I is unity ; similarly the area of a surface which contains b units of area is bm, or simply b, where m is the unit of area. 2. Commensurable and Incommensurable Magnitudes. When two magnitudes have a common measure, that is, when another magnitude can be found which is contained in each an exact number of times, they are said to be &quot;commensurable.&quot; Thus a line 4i and another 3i inches