by the last digit, the last two digits, or the last three digits is divisible liy 2, 4, or 8 respectively; (b) a number is divisible by 5 if it ends in 0 or 5, by 10 if it ends in 0; (c) a number is divisible by 9, or by 3, if the sum of its digits is divisible by 9, or by 3, respectively, and by 6 if it is even, and the sum of its digits is divisible by 3; (d) a number is divisible by 11 if the difference between the sum of the digits in the odd and in the even places is divisible 11. The simplest test of the divisibility by algebraic binomials is that of the remainder theorem (q.v.). The division of large numbers is generally facilitated by the use of logarithms (q.v.). For the origin of the present method of division and for improved forms, see Arithmetic.
DIVISION. In military organization, a com- ponent part, consisting usually of two or more brigades. The term is .sometimes used as a classifying title, as 'the cavalry division.' 'infan- try division,' etc. The strength and composition of a division vary in times of peace according as alterations are made in tactical or organization dispositions and in time of war according to the needs of the work for which the division is formed. In the United States Army, a division consists of two. three, or four brigades, including all branches, under the command of a major gen- eral. In Germany, an infantrj- division consists of two brigades to which, under the command of the general commanding, are attached four .squadrons of cavalry, four batteries of artillery, each of six guns, and a battalion of riflemen, or. in some instances, pioneers. A division ililTers from the corps d'armre in that the latter is invariably complete in itself, wliile the former is only oc- casionally so, and then on a very much smaller scale. See Army OBn.vxizATiox. In naval usage, a division is a group of ships constituting a part of a fleet, or one of the parts into which the crew of a man-of-war is divided. See Ship's Comp. y.
DIVISION OF LABOR. In political econo- my, an expression desijjiiating. somewhat awk- wardly, the fact that in modem production each workman performs a part only of the process of manufacture. His work is coiirdinated with that of others to complete the wliole. The fact of division is dependent on the fact of coiiperation, which is the essential feature. Foreign econo- mists have deemed it wise to use the more general temi 'coiiperation,' but in English econo- mics the term division of labor has become consecrated through the labors of .dam Smith, and it would be idle at this late day to substi- tute the more exact formulation. .dam Smith drew attention to the increased productiveness which results when, in the process of manufac- ture, the .several operations are apportioned to different workmen, so that each workman shall perform continually one operation, instead of per- forming several in succession. This is the nar- rowest view of the division of labor, and sub- sequent writers have extended the term so that it includes not only the separation of proce-scs in one employment, but also the separation of employments. The fact that one man is exclu- sively a carpenter and another exclusively a smith enhances their combined production over what it would l)e if each were a jack-of-alltrades. Other writers have still further extended the notion, and speak of a national division of labor. by which they would designate the peculiar apti- tudes of certain nations for certain branches of production, and which under a system ol un- restricted couniicix-e would probably promote a contrast lietween the economic activities of the several parts of the world. The division of labor has become one of the commonplaces of modern industry,, and we do not perhaps sutheiently realize how entirely the effectiveness of modern production rests upon it. It nuiy be well to re- view brielly the advantages of the division of labor set forth with so nuich skill by .dani Smith, which subsequent experience has so amply verified. In the first place, it promotes in a high degree tlie skill of the laborer. Hy devoting his energies solely to one operation, he acquires in it a dexterity which could not have been obtained if his attention had been given to many tilings. The hand that daily performs the same task comes to do it almost automatically. W ith the better separation of labor, it is possible to em- ploy persons according to their capacities. While some operations require great strength, others demand nicety of touch and extreme delicacy of handling. The weak, wlio lin<l no place in the ruder labors of agriculture or mining, tiud in manufacturing a place for their labor. Without discussing at this point whether the increase of the labor of women and of young persons has been a social benefit, we can readily see that the division of labor which has made it possible has increased the national production by ))ractieally increasing the number of laborers, and diminish- ing the relative number of dependent persons. Another advantage of division of labor lies in the saving of labor and of time. The skilled work- men make better use of the materials intrusted to them than do those who are not trained, and thus prevent waste: while the continuity of em- ployment practically increases working hours by saving the time which would otherwise be spent in passing from one employment to an- other. To realize what this means, one has only to compare the labors of the agricultural population, where division of labor is not prac- ticable to the same extent as in other forms of production, with those of the artisan classes. Xot the least advantage resulting from the divi- sion of labor is the stimulus which is given to in- ention by the concentration of energies upon distinct and definite processes. While it may be true that learned men have made some of the most noted inventions of our time, it is equally true that the many thousands of modifications of tools and maeliines which have made them feasi- ble and workable have come largely from those who have l>een in daily contact with their opera- tion. The discussion which has been given here has been in view of the separation of employment in the operations of a workshop or a factory, hut it must be equally obvious that like gains result from the dilTercntiation of functions among the people generally from the increase of specialism, not only in trade and eomnierce, but also in pro- fessional and scientific ai-tivities. Xor need space be given to the denmnstralion of the fact that the division of labor between localities and between nations creates in each special aptitudes which might not otherwise be awakened, and thus increases the sum of firatifications which are in the reach of mankind at large. To offset these advantafres. which are almost self-evident, there
