6. Each experiment should be associated with some truth expressed in words. The experiment should be remembered in connection with a definite statement in each case. The memory of either the experiment, or the principle apart from the experiment, is a species of half knowledge which should be avoided. An unillustrated principle must, when the necessity arises, be stored in the memory; and in the systematic study of books this necessity will often come. But we should never crowd this abstract work on the memory unassisted by the suggestive concrete, when the concrete aid is possible. 7. All that is taught should be true. It is not necessary to attempt to exhaust a subject, nor to attempt to teach minute details regarding it to the pupils in our schools, but it is necessary that every statement given to the pupil to be learned and remembered should contain no element of falsehood. The student in mathematics experiences a feeling of growing strength and power when he finds, in algebra, that the formula he used in arithmetic in extracting a square root has grown in importance by leading indirectly to a theorem of which it is only one particular case--a theorem with a more definite proof, and a larger capability for use than he had thought possible. When he finds a still simpler proof for the binomial theorem in his study of the calculus, his feeling of increasing power and the desire for still greater results deepens and intensifies. Were he to find, on the contrary, that from a false notion of the means to be used in making a thing simple, his teacher in arithmetic had taught him what is false, we should approve his feeling of disgust and disappointment. Early impressions are the most lasting, and the hardest part of school work for the teacher is the unteaching of false ideas, and the correcting of imperfectly formed and partially understood ideas. I took a case from mathematics, the exact science, to illustrate this point. But I must not neglect to notice the difference between that subject and physical science. The latter consists of theories, hypotheses, and so-called laws, supported by _observed facts_. The facts remain, but time has overthrown many of the hypotheses and theories, and it will doubtless overthrow more and give us something better and truer in their place. While a careful distinction between what is known and what is believed is necessary, I should always class the teaching of accepted theories and hypotheses with the teaching of the true. But teachers, with more of imagination than good sense, teach distinctions which do not exist, generalizations which do not generalize, and do incalculable mischief by so doing.