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 UNITED STATES NAVAL ACADEMY, an institution for the education of officers of the United States Navy, at Annapolis, Maryland, occupying about 200 acres on the banks of the Severn. Its principal buildings are the marine engineering building, the academic building (containing the library), the chapel, the gymnasium, the physics and chemistry building, the auditorium, the armoury, the power-house, the administration building, Bancroft Hall (the midshipmen's quarters), officers mess and club, and Sampson Row, Upshur Row and Rodgers Row, the officers' quarters. By an Act of Congress passed in 1903 two midshipmen (as the students have been called since 1902; “naval cadets” was the term formerly used) were allowed for each senator, representative, and delegate in Congress, two for the District of Columbia, and five each-year at large; but after 1913 only one midshipman is to be appointed for each senator, representative and delegate in Congress. Candidates are nominated by their senator, representative, or delegate in Congress, and those from the District of Columbia and those appointed at large are chosen by the President; but to be admitted they must be between sixteen and twenty years of age and must pass an entrance examination. Each midshipman is paid $600 a year, beginning with the date of his admission; and he must bind himself to serve in the United States Navy for eight years (including the years spent in the academy) unless he is discharged sooner. The course of instruction is for four years—“final graduation” comes only after six years, the additional years being spent at sea—and is in eleven departments: discipline, seamanship, ordnance and gunnery, navigation, marine engineering and naval construction, mathematics and mechanics, physics and chemistry, electrical engineering, English, modern languages, naval hygiene and physiology. Vessels for practice work of midshipmen in the first, second, and third year classes are attached to the academy during the academic year, and from early in une to September of each year the midshipmen are engaged in practice cruises. The academy is governed by the Bureau of Navigation of the United States Navy Department, and is under the immediate supervision of a superintendent appointed by the secretary of the navy, with whom are associated the Commandant of Midshipmen, a disciplinary officer, and the Academic Board, which is composed of the superintendent and the head of each of the eleven departments. The institution was founded as the Naval School in 1845 by the secretary of the navy, George Bancroft, and was opened in October of that year. Originally a course of study for five years was prescribed, but only the first and last were spent at the school, the other three being passed at sea. The present name was adopted when the school was reorganized in 1850, being placed under the supervision of the chief of the Bureau of Ordnance and Hydrography, and under the immediate charge of the superintendent, and the course of study was extended to seven years; the first two and the last two to be spent at the school, the intervening three years to be passed at sea. The four years of study were made consecutive in 1851, and the practice cruises were substituted for the three consecutive years at sea. At the outbreak of the Civil War the three upper classes were detached and were ordered to sea, and the academy was removed to Fort Adams, Newport, Rhode Island (May 1861), but it was brought back to Annapolis in the summer of 1865. The supervision of the academy was transferred from the Bureau of Ordnance and Hydrography to the Bureau of Navigation when that bureau was established in 1862; and, although it was placed under the direct care of the Navy Department in 1867, it has been (except in 1869—1889) under the Bureau of Navigation for administrative routine and financial management. The Spanish-American War greatly emphasized its importance, and the academy was almost wholly rebuilt and much enlarged in 1899–1906.

UNITS, DIMENSIONS OF. Measurable entities of different kinds cannot be compared directly. Each one must be specified in terms of a unit of its own kind; a single number attached to this unit forms its measure. Thus if the unit of length be taken to be L centimetres, a line whose length is l centimetres will be represented in relation to this unit by the number l/L; while if the unit is increased [L] times, that is, if a new unit is adopted equal to [L] times the former one, the numerical measure of each length must in consequence be divided by [L]. Measurable entities are either fundamental or derived. For example, velocity is of the latter kind, being based upon a combination of the fundamental entities length and time; a velocity may be defined, in the usual form of language expressive of a limiting value, as the rate at which the distance from some related mark is changing per unit time. The element of length is thus involved directly, and the element of time inversely in the derived idea of velocity; the meaning of this statement being that when the unit of length is increased L] times and the unit of time is increased [T] times, the numerical value of any given velocity, considered as specified in terms of the units of length and time, is diminished [L]/[T] times. In other words, these changes in the units of length and time involve change in the unit of velocity determined by them, such that it is increased [V] times where [V]=[L][T]". This relation is conveniently expressed by, the statement that velocity is of + 1 dimension in length and of − 1 dimension in time. Again, acceleration of motion is defined as rate of increase of velocity per unit time; hence the change of the units of length and time will increase the corresponding or derived unit of acceleration [V]/[T] times, that is [L][T]” times: this expression thus represents the dimensions (1 in length and −2 in time) of the derived entity acceleration in terms of its fundamental elements length and time. In the science of dynamics all entities are derived from the three fundamental ones, length, time and mass; for example, the dimensions of force (P) are those of mass and acceleration jointly, so that in algebraic form (P)=[M][L][T]−2. This restriction of the fundamental units to three must therefore be applicable to all departments of physical science that are reducible to pure dynamics.

The mode of transformation of a derived entity, as regards its numerical value, from one set of fundamental units of reference to another set, is exhibited in the simple illustrations above given. The procedure is as follows. When the numerical values of the new units, expressed in terms of the former ones, are substituted for the symbols, in the expression for the dimensions of the entity under consideration, the number which results is the numerical value of the new unit of that entity in terms of the former unit: thus all numerical values of entities of this kind must be divided by this number, [in order to transfer them from the former to the latter system of fundamental units.

As above stated, physical science aims at reducing the phenomena of which it treats to the common denomination of the positions and movements of masses. Before the time of Gauss it was customary to use a statical measure of force, alongside the kinetic measure depending on the acceleration of motion that the force can produce in a given mass. Such a statical measure could be conveniently applied by the extension of a. spring, which, however, has to be corrected for temperature, or by weighing against standard weights, which has to be corrected for locality. On the other hand, the kinetic measure is independent of local conditions, if only we have absolute scales of length and time at our disposal. It has been found to be indispensable, for simplicity and precision in physical science, to express the measure of force in only one way; and statical forces are therefore now generally referred in theoretical discussions to the kinetic unit of measurement. In mechanical