Of these characteristics, the first is what the word directly expresses—­zealous exertion on the part of the student’s own intellectual powers, a zeal literally pre-venting all other incentives, or, at the least, subordinating them, through pure love of finding out that which is new and curious, or true.  In two words, this first essential of study, and fraught with all the desirable results of study, is genuine INTELLECTUAL WORK.  It is the nisus of the intelligent principle to bring itself into ascertained and well-ordered relations with the facts, agencies, and uses of nature, alike in her physical and spiritual domains.  The bright-minded boy or girl who may not comprehend the feeling or thought when so uttered, nevertheless knows it, and, for his or her range of effort, as keenly as does the adult explorer.

But, when a mind thus works, the truth that it can never advance beyond missing or unfound links in the chain of thought does not need to be taught to it.  The impossibility of so doing has become a matter of experience and of certain conviction.  The mathematician knows, that, beyond that form of his equation containing an actual mis-step, or a positively irresoluble expression, all subsequent forms or values involving that step or expression are vitiated, and the results they seem to show substantially worthless.  Now, every actually working mind, and at every stage, from schoolboy perplexities over algebraic signs, up to philosophic ventures in quest of one remove further of solid ground, in respect to the interrelations of physical forces, or the law of development of organized forms, finds itself in precisely the predicament of the mathematician:  it feels no footing and accomplishes no advance beyond that link in the chain of fact and thought, which, to its comprehension, stands as uncertain, erroneous, wanting, or inexplicable.  This is so from the very nature of our knowing faculties and of knowledge.  The true intellectual worker, encountering interruption through any of these conditions, goes back to view his difficulty from a better vantage ground, or attempts to approach it from either side, or, failing these resources, bows to the necessity, and suffers no harm, other than stoppage and loss of time.  Thus, the second characteristic of true study is in the rigidly natural and unfailing CONSECUTION of the steps and processes by which the intellectual advance is made.  A mind so advancing never flatters itself of being able to grasp that which, in the nature of knowledge, must be a consequent truth, until the antecedent or antecedents german to the question in hand have first been possessed by it.  But in our schools, how vastly much is supposed to be taught, in which consequents come before antecedents, or are promiscuously jumbled up with them, or assert themselves, without so much as the grace to say to antecedents of any sort, ‘By your leave.’  Obviously, however, such could not be the character of so much of our teaching, did not the character of most of our books for schools exactly correspond with it.  And the books do correspond:  they not only give to a faulty teaching its cue, but, now that the theory of education is being so much discussed, and in good degree improved, they constitute one of the most influential causes of the almost hopeless lagging of its practice.