ent of some end, the mind does not
simply keep itself focused on the particular problem. For instance, in
attempting to solve the problem that the exterior angle of a triangle
equals the sum of the two interior and opposite angles, no progress
toward the attainment of the end in view could be made by merely holding
before the mind the idea of their equality. It is, in fact, impossible
for the attention to be held for any length of time on a single topic.
This will be readily seen if one tries to hold his attention
continuously upon, say, the tip of a pencil. When this is attempted,
other ideas constantly crowd out the selected idea. The only sense,
therefore, in which one holds his attention upon the problem in an act
of voluntary attention is, that his attention passes forward and back
between the problem and ideas felt to be associated with it. Voluntary
attention is, therefore, a mental process in which the mind shifts from
one idea to another in attaining to a desired end, or problem. In this
shifting, or movement, of voluntary attention, however, two significant
features manifest themselves. First, in working forward and back from
the problem as a controlling centre, attention brings into consciousness
ideas more or less relevant to the problem. Secondly, it selects and
adjusts to the problem those that actually make for its solution, and
banishes from consciousness whatever is felt to be foreign to obtaining
the desired end.

=Example of Controlled Attention.=--To exemplify a process of voluntary
attention we may notice the action of the mind in solving such a problem
as:

Two trains started at the same moment from Toronto and Hamilton
respectively, one going at the rate of thirty miles an hour and the
other at the rate of forty miles an hour. Supposing the distance
between Toronto and Hamilton to be forty miles, in how many minutes
will the trains meet?

Here the pupil must first fix his attention upon the problem--the number
of minutes before the trains will meet. This at once forms both a centre
and a standard for measuring other related ideas. In this way his
attention passes to the respective rates of the two trains, thirty and
forty miles per hour. Then perhaps he fixes attention on the thought
that one goes a mile in two minutes and the other a mile in 1-1/2
minutes. But as he recognizes that this is leading him away from the
problem, resistance is offered to the flow of attentio