224. Decimal arithmetic no pupil would be likely to think out by himself; he would very certainly not invent Bible history. Both must accordingly be regarded as belonging preëminently to the province of synthetic instruction, which always involves the difficult problem of how to assure its entrance, as a potent factor, into existing masses of ideas. As to this, it would be a blunder to conclude that, since Bible history and history as a whole, arithmetic and mathematics as a whole, hang together, there is also a corresponding pedagogical connection (219). But so much is certain, that the efficiency of a group of ideas increases with expansion and with multiplied association. It will be an advantage, therefore, to Bible history and to arithmetic, if as wide a range is given to historical and mathematical teaching as circumstances and ability permit, even if the conditions should be such that a many-sided culture is not to be expected. 225. The subjects next to be considered in the choice of material for instruction are poetry and natural history, great care being taken not to disregard the necessary sequence. The time for fables and stories should not be curtailed; it is important to make sure that boys do not lose the taste for them too early. The easiest and safest facts of zoölogy will have been presented already in connection with the picture-books of childhood. The right moment for introducing the elements of botany has arrived when the boy is collecting plants. Foreign languages would be assigned the lowest place, if particular circumstances did not in many cases lend them a special importance. The ancient classical languages, at any rate, form to such an extent the basis of the study of theology, of jurisprudence, and of medicine, they are so necessary to all higher scholarship, that they will always constitute the fundamental branches of instruction in academic preparatory schools. It is obvious, however, that the extent of instruction depends too much on external conditions of rank and means to permit a definite prescription of instruction-material for all cases. Far less dependent is the development of many-sided interest in its relation to branches of study. If the limits set to the latter are narrow, it is still the business of instruction to secure an approximation to many-sided culture; while under highly favorable circumstances the very abundance of educational help must put the teacher on his guard against losing sight of the real aim of instruction.