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 attention 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.