2.  The development of the mind, as all other development, is an advance from the indefinite to the definite.  In common with the rest of the organism, the brain reaches its finished structure only at maturity; and in proportion as its structure is unfinished, its actions are wanting in precision.  Hence like the first movements and the first attempts at speech, the first perceptions and thoughts are extremely vague.  As from a rudimentary eye, discerning only the difference between light and darkness, the progress is to an eye that distinguishes kinds and gradations of colour, and details of form, with the greatest exactness; so, the intellect as a whole and in each faculty, beginning with the rudest discriminations among objects and actions, advances towards discriminations of increasing nicety and distinctness.  To this general law our educational course and methods must conform.  It is not practicable, nor would it be desirable if practicable, to put precise ideas into the undeveloped mind.  We may indeed at an early age communicate the verbal forms in which such ideas are wrapped up; and teachers, who habitually do this, suppose that when the verbal forms have been correctly learnt, the ideas which should fill them have been acquired.  But a brief cross-examination of the pupil proves the contrary.  It turns out either that the words have been committed to memory with little or no thought about their meaning, or else that the perception of their meaning which has been gained is a very cloudy one.  Only as the multiplication of experiences gives materials for definite conceptions—­only as observation year by year discloses the less conspicuous attributes which distinguish things and processes previously confounded together—­only as each class of co-existences and sequences becomes familiar through the recurrence of cases coming under it—­only as the various classes of relations get accurately marked off from each other by mutual limitation, can the exact definitions of advanced knowledge become truly comprehensible.  Thus in education we must be content to set out with crude notions.  These we must aim to make gradually clearer by facilitating the acquisition of experiences such as will correct, first their greatest errors, and afterwards their successively less marked errors.  And the scientific formulae must be given only as fast as the conceptions are perfected.

3.  To say that our lessons ought to start from the concrete and end in the abstract, may be considered as in part a repetition of the first of the foregoing principles.  Nevertheless it is a maxim that must be stated:  if with no other view, then with the view of showing in certain cases what are truly the simple and the complex.  For unfortunately there has been much misunderstanding on this point.  General formulas which men have devised to express groups of details, and which have severally simplified their conceptions by uniting many facts into one fact, they have supposed must simplify the conceptions of