DIVISION, a general term for the action of breaking up a whole into parts (from Lat. dividere, to break up into parts, separate). Thus, in political economy, the phrase "division of labour" implies the assignment to particular workmen of the various portions of a whole piece of work; in mathematics divi sion is the process of finding how many times one number or quantity, the "divisor," is contained in another, the "dividend" (see ARITHMETIC and ALGEBRA) ; in the musical terminology of the i7th and 18th centuries, the term was used for rapid passages consisting of a few slow notes amplified into a florid passage, i.e., into a larger number of quick ones. The word is used also in concrete senses for the parts into which a thing is divided, e.g., a division of an army, an administrative or electoral division; similarly, a "division" is taken in a legislative body when votes are recorded for and against a proposed measure.
In logic, division is a technical term for the process by which a genus or wider class is differentiated into its sub-classes or species. Thus the genus "animal" may be divided, according to the habitat of the various kinds, into animals which live on land, those which live in water, those which live in the air. Each of these may be subdivided according to whether their constituent members do or do not possess certain other qualities The basis of each division is called the fundamentum divisionis. It is clear that there can be no division in respect of those qualities which make the genus what it is. The various species are all alike in the posses sion of the generic attributes, but differ in other respects; they are "variations on the same theme" (Joseph, Introduction to Logic, 1906) ; each one has the generic, and also certain peculiar, qualities (differentiae), which latter distinguish them from other species of the same genus. The process of division is thus the obverse of classification (q.v.) ; it proceeds from genus to species, whereas classification begins with the particulars and rises through species to genera. In the exact sciences, and indeed in all argument both practical and theoretical, accurate division is of great im portance. It is governed by the following rules. (i) Division must be exhaustive; all the members of the genus must find a place in one or other of the species. Rectilinear figures are not cor rectly divided into triangles and quadrilaterals because there are rectilinear figures which have more than four sides. On the other hand, triangles can be divided into equilateral, isosceles and sca lene, since no other kind of triangle can exist. (2) Division must be exclusive, that is, each species must be complete in itself and not contain members of another species. No member of a genus must be included in more than one of the species. (3) In every division there must be but one principle (f undamenturn divi sionis) . The members of a genus may differ from one another in many respects; e.g., books may be divided according to external form into quarto, octavo, etc., or according to binding into calf, cloth, paper-backed and so on. They cannot, however, be divided logically into quarto, paper-backed, novels and remainders. When more than one principle is used at the same time in a division it is called "cross division." (4) Division must proceed gradually ("Divisio non facit saltum") ; i.e., the genus must be resolved into the next ("proximate") species. To go straight from a summum genus to very small species is of no scientific value.
It is to be observed that logical division is concerned exclusively with universals or concepts; division is of genus and species, not of particulars. Two other kinds of division are recognized : meta physical division, the distinction in thought of the various quali ties possessed by an individual thing (a piece of lead has weight, colour, etc.), and physical division or partition, the breaking up of an object into its parts (a watch is thought of as being com posed of case, dial, works, etc.) . Logical division is closely allied with logical definition (q.v.).
In military science, "division" is the term which is given to a higher formation of an army. The infantry division is a perma nent formation of all arms, and it is provided with all the necessary means for subsisting, marching, and fighting inde pendently of any other formation. Divisions as we know them to-day were first formed by the French in 17 7o ; but it was not till a hundred years later that they became a permanent part of the army in peace time. At the opening of the World War the French division, which may be taken as typical of European prac tice, comprised two infantry brigades, each of two 3-battalion regiments, a cavalry squadron, two artillery groups each of three 6-gun batteries, engineer, medical and administrative units, in all 12,000 men and 36 guns. The Prussian army introduced the divisional system at the opening of the Wars of Liberation in 1813, and it was adopted for the whole German army after the war of 1866, and continued in essentials unchanged down to 1914. Other European armies were slower to follow suit, but by the end of the 19th century practically all had done so.
In the British army the division had been the highest tactical and administrative unit throughout all the wars from the Penin sular to the Boer War; but it did not really become a part of the peace-time organization till the period of Lord Haldane's reforms in 1906. At the opening of the World War the British division differed in some important particulars from its continental counterparts, consisting as it did of three infantry brigades, each of four battalions, four artillery brigades, each of three 6-gun batteries, one 6o-pdr. battery, three field companies of engineers, three field ambulances, a signal company, and administrative units such as the divisional ammunition column, a supply train and a veterinary section. Numerically it was considerably stronger than the average Continental division.
During the World War in all the belligerent armies the division became the tactical and administrative unit. Various modifications took place in its internal composition : by 1918 the strength of the infantry had been greatly reduced, though the number of machine guns and automatic weapons had increased; divisional cavalry had disappeared; and the proportion of artillery and administrative units was larger. The majority of the remodelled armies of the post-war period show similar tendencies in the composition of their higher formations. The division tends more and more to become the kernel of peace-time armies. The numerical reduc tion of the infantry has gone hand in hand with a re-armament which has greatly increased its fire power and its potentialities for attack and defence, including defence against tanks. Divisional cavalry on the other hand has been generally reintroduced; while the lavish artillery allotment necessary for position war has been reduced to an amount considered more suitable for mobile opera tions. Finally, the mechanization of transport has considerably increased the radius of action of the whole formation.
In the British army, however, these tendencies have perhaps been less marked than elsewhere. The 4-battalion infantry bri gades have been retained; the artillery, signal, engineer and medical units remain much as before the war, and no divisional cavalry has been allotted. The great increase in infantry fire power has, however, been fully maintained, and the mechanization of transport has proceeded further than in any other army; so that though the framework of the British division has changed but little in broad outline, it is to-day a far more powerful engine of war than its prototype which took the field in Aug. 1914.
Cavalry divisions were first formed in war in the time of the first Napoleon; but though they became part of the French peace-time organization in 1875, the Germans, in common with the majority of European armies, had few or none in peace, and formed them as required on the outbreak of war. They usually comprised six regiments, organized in two or three brigades, with horse artillery and ancillary units. Since the World War, in which, after the early stages, at any rate in the European theatres, cavalry were rarely able to carry out their normal functions, the general tendency has been to remodel them as light divisions, of which cavalry form only a proportion of the combatant strength ; mechanized units, such as armoured cars, motor machine-guns, cyclists, artillery and mechanical transport, have been added to increase mobility and fire power. (See ARMY.) United States Army.—The division is at present the highest tactical and administrative command in the United States army in time of peace. Prior to the World War the regiment was the highest. Provisional manoeuvre divisions were assembled in Texas in 1911 and again in 1913, largely under the influence of conditions on the Mexican border. Theirs, however, was only a transitory existence. The 1928 divisional organization of the army of the United States is a World War development. It preserves on the one hand the designations which have become historic on the battlefields of France and Flanders, and on the other hand embodies the results of World War experience. The actual strength of the army necessitates, however, the mainte nance of these divisions in highly skeletonized form. The com mand consists of two infantry brigades of two regiments each ; a field artillery brigade of two regiments, with a total of 48 French 75 mm. guns; one regiment of engineers; a medical regi ment ; an observation squadron ; division trains and special troops, such as military police, tank, signal, ordnance and head quarters companies, complete the organization of an infantry division which is commanded by a major general. The total war strength of this organization is 20,030 officers and enlisted men. In a single column it occupies 28.1 m. road space and requires standard type railway trains for its transportation.