POSITION, is the name of a rule in arithmetic, by means of which an unknown number is determined by means of one or more suppositions or assumed values of it. Position is'clivided into single and double.
In single position, the false conclusion is to the false position, as the number given is to the number sought. Thus, Ex. A manufacturer being asked how many workmen he had, replied, that, if he tripled the number he had, and added one-eighth of his number to that, he would have 150.
Let us suppose 32 to be the number, then 32 x 3 -I 4=100 instead of 150. Consequently, 100 the false con clusion, is to 32 the false supposition, as 150 is to 48, the true number of workmen.
In double position the answer is obtained by two suppo sitions. The rule, therefore, is to assume two different numbers, and subject them to the conditions given in the question. Then the difference of the results thus obtain ed, is to the difference of the assumed numbers as the dif ference between the two results, and either of the others is to the correction to be applied to the assumed number, from which the result was obtained. This rule was given by Mr. Bonnycastle in his arithmetic, published in 1810.
The following more general rule, has been given by Mr. Thomson of Belfast, in his very useful on the theory and practice of Arithmetic.
" Having assumed two different numbers, perform on them separately the operations indicated in the question, and find the errors of the results. Then as the difference of the errors, if both results be too great, or both too little, or as the sum of the errors if one result be too great, and the other too small, is to the difference of the assumed numbers, so is either error to the correction to be applied to the number that produced that error." As all the questions that are capable of being solved by these rules, can be done with more facility by the simplest rules of algebra, it is needless to occupy any more space with their illustration. The principle on which they rest is quite correct, for all questions which can be resolved by a simple equation, but in relation to other equations, the rules give only approximate results. See ALGEBRA.