n in this
direction, and he passes to the thought that in a _minute_ the former
goes 1/2 mile and the later 2/3 of a mile. From this he passes to the
thought that in one minute they together go 1-1/6 miles. Hereupon
perhaps the idea comes to his mind to see how many miles they would go
in an hour. This, however, is soon felt to be foreign to the problem,
and resistance being set up in this direction, the attention turns to
consider in what time the two together cover 40 miles. Now by dividing
40 miles by 1-1/6, he obtains the number 34-2/7 and is satisfied that
his answer is 34-2/7 minutes. The process by which the attention here
selected and adjusted the proper ideas to the problem might be
illustrated by the following Figure:

[Illustration]

Here "P" represents the problem; a, b, c, d, and e, ideas accepted as
relevant to the problem; and b', d' ideas suggested by b and d, but
rejected as not adjustable to the problem.

=Factors in Process.=--The above facts demonstrate, however, that the
mind can take this attitude toward any problem only if it has a certain
store of old knowledge relative to it. Two important conditions of
voluntary attention are therefore, first, that the mind should have the
necessary ideas, or knowledge, with which to attend and, secondly, that
it would select and adjust these to the purpose in view. Here the
intimate connection of voluntary attention to the normal learning
process is apparent. The step of preparation, for instance, is merely
putting the mind in the proper attitude to attend voluntarily to an end
in view, namely the lesson problem; while the so-called
analytic-synthetic process of learning involves the selecting and
adjusting movements of voluntary attention.

=Spontaneous and Voluntary Attention Distinguished.=--In describing
voluntary attention as an active form of attention, psychologists assume
that since the mind here wills, or resolves, to attend, in order to gain
a certain end in view; therefore voluntary attention must imply a much
greater degree of effort, or strain, than other types. That such is
always the case, however, is at times not very apparent. If one may
judge by the straining of eye or ear, the poise of the body, the holding
of the breath, etc., when a person gives involuntary attention to any
sudden impression, as a strange noise at night, it is evident that the
difference of effort, or strain, in attending to this and some selected
problem may not, dur