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 True Order of Studies. 
 
 BY 
 
 THOMAS HILL. 
 
 NEW YORK : 
 
 G. P. PUTNAM'S SONS. 
 
 Fourth Ave and 230 St. 
 1876. 
 
• • • » • t • 
 
 • • 
 
 • • • 
 
 • • • • 
 
 • • • . - 
 
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 Copyright : 
 
 G., P. PUTNAM'S SONS. 
 
 1S75. 
 
PREFACE. 
 
 THE hierarchy of sciences adopted as the basis 
 of this work, was first perceived by me one night 
 about the first of February, 1843, while attempting to 
 answer a chance question. Four years afterwards I 
 be2:an to use it as the basis of lectures on a revised 
 scheme of Common School Education, nearly identical 
 with that presented in this volume. In May, 1853, 
 the hierarchy was first pubHshed in an address deliver- 
 ed before the Harvard Natural History Society. I 
 used it in a P. B. K. address at Cambridge, in 1859 ; 
 and have, since that time, used it repeatedly in address- 
 es, lectures, and magazine articles, and especially in a 
 series of four communications to Barnard's Journal 
 of Education for 1859, bearing the same title as 
 
 this book. 
 Portland, Me. August, 1875. 
 
 5J.M37 
 
CONTENTS. 
 
 CHAPTER PACK 
 
 Preface 5 
 
 I.— The Child 7 
 
 II. — The Hierarchy of Sciences 11 
 
 III. — Geometry 24 
 
 IV. — Arithmetic 39 
 
 V. — Algebra " . . 51 
 
 VI.— Physics 54 
 
 VII.— Chemistry 65 
 
 VIII. — Mineralogy 69 
 
 IX.— Physiology 71 
 
 X.— Botany 74 
 
 XL— Zoology 79 
 
 XIL— Geology 91 
 
 XIIL— Commodity 94 
 
 XIV.— Art 99 
 
 XV. — Language 103 
 
 XVL— Law 123 
 
 XVII. — Political Economy 127 
 
 XVI 1 1.— Psychology ly^ 
 
 XIX.— Aesthetics I34 
 
 XX.— Ethics 139 
 
 XXL— Theology 142 
 
 XXIL— Scholia I49 
 
 XXIIL— A Curriculum I59 
 
1 ■> 
 > ■> 
 
 > J 
 
 1' 
 
 
 THE 
 
 TRUE ORDER OF STUDIES. 
 
 CHAPTER I. 
 
 THE CHILD. 
 
 A THOROUGH and complete education ought to 
 preserve and increase the pupil's bodily health 
 and strength ; give him command of his own muscu- 
 lar, and mental powers ; increase his quickness in per- 
 ceiving through his five senses, and quicken his men- 
 tal perception ; form in him the habit of prompt and 
 accurate judgment ; lead to delicacy and depth in 
 every right feeling ; and make him inflexible in his 
 conscientious and steadfast devotion to all his duties. 
 In other words an integral education must include at 
 least these four branches : — gymnastics, or care of the 
 body ; noetics, or training of the mind ; aesthetics, or 
 cultivation of the tastes ; and ethics, which shall include 
 religion as well as duty. And in every part of each 
 branch of education, there will be a.double end in view, 
 namely, the increase of knowledge, and the increase 
 of skill. Each study may be made the object of 
 
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 ,■, TRtJE ORDER OF STUDIES. 
 
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 thought, or the object of action ; in the one case it is 
 pursued as a science ; in the other case as an art. 
 
 In the present Httle book, I occupy myself chiefly 
 with the second branch, the education of the intellec- 
 tual powers ; not, by any means, because I consider it 
 as more important than the others ; but simply be- 
 cause I have something to say upon it. 
 
 The intellectual powers may be roughly, but con- 
 veniently divided into three groups, the perceptive, the 
 imaginative, and the reflective. 
 
 By perception I mean the direct vision of truth, 
 whether by outward or by inward sense. By the five 
 senses we have a direct perception of the presence of 
 colors, sounds, odors, flavors, variations of temperature, 
 and other tangible and visible things. By the inter- 
 nal powers of consciousness we have a direct percep- 
 tion of our own feelings, and know that we love, hate 
 fear, are glad or sad ; and by internal sense we also 
 know the existence of space, time, power, thought. 
 
 By imagination I mean the reproduction, or imita- 
 tion, in the mind, of the impressions previously made 
 by direct perception. When imagination is confined 
 to a simple reproduction of the impressions made 'in 
 perception, it is usually called memory ; and the term 
 imagination is by most persons confined to the cases in 
 which the remembered impression is variously modi- 
 fied, or merely imitated. The word fancy is by many 
 writers applied to the cases in which the imagination is 
 occupied with inventing imitations of external things, 
 and the word imagination confined to inventions of 
 character or of spiritual attributes. 
 
THE CHILD. 
 
 By reflection I mean the act of comparing, by help 
 of the imagination, the truths of perception, or the 
 creations of the imagination. When this comparison 
 of truths eUcits new truths of relation, between the 
 compared truths, it is called reasoning. Thus reason- 
 ing may be considered as an art of bringing truths into 
 a position to be perceived by the internal sight. 
 
 It may be observed that the words imagination, 
 reason, and perception, are also used to denote the 
 faculties of the mind by which we perform the acts of 
 imagination, reasoning, and perception. 
 
 The first act of the mind must always be the direct 
 perception, of some truth, as the necessary prelude to 
 any act of reason or imagination. In the history of 
 any child's intellectual development it is always the 
 case, also, that his powers of external perception give 
 the earliest evidence of activity. For the first seven 
 years of his life, his chief intellectual occupation is the 
 reception of impressions from the senses ; and by the 
 age of fourteen years the powers of seeing, hearing, 
 tasting, smelling, and feeling are in their fullest per- 
 fection. 
 
 The power of imagination does not betray any ac- 
 tivity until the child is more than a year old, and it is 
 later in attaining its full vigor, which it seldom reaches 
 before the age of twenty-one. The reasoning power 
 lies half dormant still later than the imagination; and 
 seldom shows activity till after the seventh year ; nor 
 develops its full strength until after the twenty-first. 
 The will comes to its maturity of power, with the de- 
 velopment of reason. 
 
 I* 
 
10 TRUE ORDER OF STUDIES. 
 
 Nature thus indicates that a teacher in educating 
 a child, should give his earliest attention to the devel- 
 opment of the child's perceptive powers. Moreover, 
 among these powers, those of external sense should be 
 the first to receive a careful training, such as is given 
 in the admirable Kindergarten system of Froebel. 
 Afterwards, when the child has learned to perceive 
 with every sense, the imagination must be systemat- 
 ically cultivated. In learning to observe, he will learn 
 to remember what he has observed, and this is an in- 
 cidental culture of the imagination ; but he must also 
 be regularly trained to invention. This is admirably 
 done by some of the Kindergarten gifts ; and I the 
 more cordially express my approbation of the treat- 
 ment of the child by Froebel's system, because I dis- 
 agree so totally with him, in some of the considera- 
 tions by which he would explain and justify his treat- 
 ment. 
 
 Nature further indicates that a child should not be 
 expected, or required to reason at an early age. Any 
 direct training of the logical powers, before the age of 
 twelve years, is premature ; and, in most cases, a posi- 
 tive injury to the scholar. The common sense view 
 would give facts before reasoning. Reasoning upon 
 the facts is the work of a maturer mind. The play of 
 the imagination should from the beginning be com- 
 pared with or contrasted with facts ; and, in the later 
 stages of education be carefully guided by reason and 
 conscience. 
 
THE HIERARCHY OF SCIENCES. II 
 
 CHAPTER II. 
 
 THE HIERARCHY OF SCIENCES. 
 
 IT is evident that we cannot teach a given subject 
 to a child, before he is old enough to comprehend 
 it, nor before he has acquired the necessary prelimin- 
 ary knowledge. In order to learn a given thing, he 
 must be sufficiently mature, and sufficiently well in- 
 formed. It would, for example, be folly to attempt to 
 teach a boy of six years how to measure heights and 
 distances, by a theodolite and steel tape ; or to teach a 
 boy of any age, who was ignorant of the four simple 
 rules in arithmetic. 
 
 It is the object of the present chapter to inquire 
 whether there is any comprehensive order, embracing 
 all the objects of human knowledge, which can serve 
 as a guide in the selection and sequence of studies ; 
 that is, which will help us in deciding what are the 
 proper preliminary studies requisite for the pursuit of 
 any branch, or in deciding which of two given studies 
 ought to be placed first in the curriculum of a school. 
 If the discussion should appear, to any reader, dry and 
 abstract, he may be assured it will be brief ; and that 
 the subsequent chapters shall be occupied with more 
 practical and easily intelligible details. 
 
 In attempting to analyze and classify the great 
 
12 TRUE ORDER OF STUDIES. 
 
 field of human knowledge, we obtain, at first, a separa- 
 tion into four elements, viz. Space and Time, Matter 
 and Spirit. There is nothing, existent or non-existent 
 possible or impossible, which we do not include in some 
 sense, under one of these four heads ; while, on the 
 other hand, there is no one of these four which we 
 can clearly bring under another. It is true that we 
 might, in some phases of mind, be tempted to consider 
 Time as a mere abstract notion, formed from our per- 
 ception of the permanence of Space; it is true that 
 some men have suspected, from the marvellous divers- 
 ity of the powers of matter, that thought is but a mode 
 of motion ; it is also true that the obedience of Matter 
 to Spirit leads a majority of men to believe that Mat- 
 ter is a creation of Spirit ; but these opinions are not 
 scientific certainties, like the existence of the four 
 elements. 
 
 Of these four. Space and Time are the earliest ob- 
 jects of distinct intellectual action. The attention is 
 called to them by the phenomena of motion and the 
 shapes of material things. The forms, and motions of 
 things, are the food of much thought, and the objects 
 of lively attention and intellectual action, years before 
 the other myriad problems of matter begin to suggest 
 themselves ; still longer before spiritual character and 
 the nature of the mental processes, receive any atten- 
 tion. It is true that, to a certain degree, all these ele- 
 ments enter into some of the earliest states of con- 
 sciousness ; so that it might be thought that the knowl- 
 edge of them is gained simultaneously. But they are 
 evolved out of the mist of the child's consciousness 
 
THE HIERARCHY OF SCIENCES. 1 3 
 
 one by one ; and become the themes of distinct men- 
 tal efforts, in the order in which I have named them. 
 The child's knowledge and recognition of things by 
 their shapes long precedes any definite recognition of 
 time or rhythm ; and becomes varied and exact to a 
 marvellous degree, while as yet there has been no dis- 
 tinct introversion of consciousness, and no distinctly 
 intellectual appreciation of character. 
 
 Whether Spirit created Matter, as is generally be- 
 lieved, or not, this at least is certain ; that the advanc- 
 ing science of our century tends rapidly towards prov- 
 ing that our only knowledge of Matter is gained through 
 its being the realization of thought, in Space and Time. 
 Sound, color, temperature, and other sensible proper- 
 ties of Matter, are revelations to us of modes of 
 motion in the bodies about us. It is probable that 
 without motion there could, not be any sensation ; cer- 
 tainly the human imagination tries in vain to imagine 
 the communication of sensation without motion. But 
 •all the motions thus revealed to us, through our sensa- 
 tions, prove on examination to be rhythmical in time, 
 and symmetrical in space. The body which by its 
 motion reveals its existence to our senses, is moving: 
 by intelligible law ; it is moving in consonance with 
 a geometrical and algebraical thought. Thus the 
 sensible properties of matter, through which alone the 
 existence of matter is revealed to us, reveal to us di- 
 rectly the existence of thought, anterior to the present 
 state of matter, ruling and guiding all the present 
 manifestations of matter. Thus the beins: of God is 
 manifest through the existence of the world ; and the 
 
14 TRUE ORDER OF STUDIES. 
 
 world can be apprehended by our intellect, even in its 
 simple sensible properties, only because those proper- 
 ties are the work of intellect. And this creates a 
 strong «/;7^nprobabiHty that matter is an absolute 
 creation ; not a fashioning of original material. 
 
 We awake to consciousness, through the fact of 
 motion, which reveals to us an outer world, and a uni- 
 verse of Space and Time, in which that world of mat- 
 ter moves. These space and time relations are the 
 earliest objects of distinctly conscious intellection ; the 
 first objects concerning which our knowledge takes a 
 scientific form. This was true of the race, and it is 
 true of the individual. Before the child has a clearly 
 intellectual life on any other subjects, it attains a very 
 definite power to distinguish the square, the circle, the 
 oval, the spiral ; to recognize, by approximate likeness ... 
 of outline, even rude drawings of men, dogs, horses, 
 cats, cows, trees, and various articles of furniture ; — 
 and also to recognize the rhythm of verse and music. 
 
 Out of space and time (which have by some wri- 
 ters been classed, erroneously as I think, among ab- 
 stract notions, as though mere abstract ideas of exten- 
 sion and duration) arise, through the suggestions of 
 the material world, three principal sciences : — Geome- 
 try, Arithmetic, and Algebra. Geometry deals purely 
 with space, and considers it as divided, and portions of 
 it as bounded, by surfaces ; the surfaces divided and 
 bounded by lines ; the lines by points. Space being 
 in itself indivisible, except in imagination, we are led 
 to that act by the perception that matter is not amor- 
 phous ; in other words, we are led to imitate the act of 
 
THE HIERARCHY OF SCIENCES. 1 5 
 
 the Divine Intellect, which has geometrized from 
 eternity. No thoughts enter, indeed, the human 
 mind, except at the suggestion, reverently followed, or 
 wickedly perverted, of nature. The forms of material 
 things, conforming to the Divine Geometry, suggest 
 to us the study of pure forms in space, and thus lead 
 us to create human Geometry, the earliest and simplest 
 of all possible sciences. 
 
 But the earliest abstraction from the idea of form 
 is that of number ; and out of this idea is evolved the 
 earliest of the truly abstract sciences, namely Arith- 
 metic ; which thus becomes the second branch in 
 the hierarchv. 
 
 The earliest suggestions of motion reveal to us 
 time as well as space ; and although these two ele- 
 ments are indissolubly joined in every phenomenon of 
 external nature, they cannot by any exertion of our 
 intellect be made to appear to have any property in 
 common. Space is external to the mind ; time enters 
 into our spiritual consciousness, and measures our flow 
 of thought. Space stands immovable, and we can 
 move our bodies through it, or transfer our attention 
 from place to place in it, at our own will. Time 
 sweeps past us with irresistible flow ; and it is with the 
 greatest difficulty that we can arrest our attention, 
 even for a few moments, upon an absolutely instanta- 
 neous epoch, a point in time. Rhythmical miOtion con- 
 nects, however, the abstract idea of number as readily 
 with time as with space ; and time, in its turn, gives 
 flexibility to the idea of number, connecting it more 
 intimately with continuous quantity ; from which con- 
 
l6 TRUE ORDER OF STUDIES. 
 
 nection springs the third science ; that of pure Algebra. 
 Out of these three, by combination and development, 
 have sprung the wonderful forms of the Calculus, 
 which have shed such lustre upon the i/th and 19th 
 centuries. 
 
 The physical properties of matter, which thus sug- 
 gested to man his earliest sys-tematic study of space 
 and time, next call his attention to matter itself, and 
 the laws under which it moves. From the study 
 of motion, recognized as such, was developed the sci- 
 ence of mechanics, following long after the mathemat- 
 ics, but being developed with greater rapidity after it 
 had sprung into life. Parts of this general science, 
 such as acoustics, and optics, were not recognized at 
 first in their true relation to motion, and held there- 
 fore, for a time, an apparently independent existence. 
 Certain of the phenomena of the world, which modern 
 science declares must be expressions of particular 
 modes of motion, suggest, however, the idea that mat- 
 ter exists in different original forms. It combines, and 
 separates, into apparently new substances ; and the laws 
 by which it thus apparently multiplies, or divides, con- 
 stitute chemistry. Other phenomena in nature lead 
 us to separate certain bodies into a class by them- 
 selves and call them living. They are to all appear- 
 ance, not under the strict laws of mechanics and chem- 
 istry, but rather use those laws to attain their indi- 
 vidual ends; each growing 'nto an individual form of spe- 
 cific likeness ; o-rowino:, not by a mere mechanical aggre- 
 gation of particles, nor simply by a chemical separation 
 of kindred particles, but growing by a compound pro- 
 
THE HIERARCHY OF SCIENCES. 1/ 
 
 cess of chemical analysis and synthesis, and mechanical 
 building according to a complicated intellectual plan. 
 The study of matter in this third, most exalted stage 
 of its action is Physiology ; which completes the divi- 
 sion of Physics ; constituted of the three sciences. 
 Mechanics, Chemistry, and Physiology, which mani- 
 festly stand related to each other in the order in which 
 I have named them. 
 
 Geometry is necessarily the first study. Arithmetic 
 the second, Algebra the third ; as 1 have defined these 
 studies, they must be understood, in some degree be- 
 fore it is possible to understand anything further ; and 
 the three physical branches, mechanics, chemistry^ 
 and physiology must follow in that order. Many per- 
 sons may be unconscious of possessing any knowledge 
 of either of these sciences, except arithmetic ; simply 
 because their knowledge has not been acquired from 
 text books, and is not arranged in their minds in a sys- 
 tematic or scientific order. Nevertheless, any skilful 
 questioner could draw out of them, a confession of 
 acquaintance with fundamental facts in each one 
 of these six branches ; and thus convince them that 
 they had learned, at first hand, perhaps, from nature, 
 many valuable truths concerning relations of space, 
 time, and number ; mechanical force, chemical changes, 
 such as combustion, oxidation, fermentation, and de- 
 cay ; and physiological truths, concerning the growth 
 of plants and animals, their food, poisons, sleep and 
 rest ; and these have been acquired in their due 
 order ; the knowledge of each requiring some previ- 
 ous knowledge in the preliminary branches. 
 
1 8 TRUE ORDER OF STUDIES. 
 
 The more extensive physical sciences such as ge- 
 ography, or astronomy may be considered as built up 
 of the simpler, in much the same manner as the wider 
 mathematical studies are a combination of the three 
 elements of geometry, arithmetic and algebra. 
 
 After acquiring some knowledge of material things, 
 the pupil naturally turns his mind towards an investi- 
 gation of the uses to which man has put this world in 
 which he has been placed. The attention is first 
 caught by tools and machines, fabrics for clothing, 
 houses, and other external things ; by the mastery, 
 one might say, of man over the material world and its 
 subjection to the uses of the human body. Next in 
 order the child observes the manner in which man 
 uses matter as a natural vehicle for the expression of 
 his thought and feeling, as in statues, paintings and 
 music. After this he begins to give consciously his 
 attention to the wonderful manner in which men ex- 
 press thoughts, by conventional modes ; which may 
 originally have been but abbreviations of more natural 
 expressions, but have now become, like the clicking of 
 Morse's telegraph, merely conventional modes of ex- 
 pressing propositions of the intellect or emotions of 
 the heart. Finally, among the actions of men, he rec- 
 ognizes the crowning greatness of statesmanship, of 
 the formation of States, and constitutions, the. estab- 
 lishment of government and laws. These studies I 
 call in a large sense of the word, historical ; and con- . 
 sider them as coming under four heads, for which 
 there are no thoroughly satisfactory names. The first 
 head embraces manufactures, commerce and agricul- 
 
THE HIERARCHY OF SCIENCES. 1 9 
 
 tiire, with all their subsidiary mechanic arts. The 
 second embraces the fine arts, — the third deals with 
 language and literature in every form. The fourth 
 embraces jurisprndence, constitutional law, compara- 
 tive legislation, etc. The larger sciences created by the 
 combination of these heads are Political Economy, 
 Social Statics and Dynamics, and History in its or- 
 dinary sense. Thus we have found three great divi- 
 sions of the hierarchy, the mathematical, the physical 
 and the historical. 
 
 But when the child is mature enough so to do, he 
 begins to introvert his attention upon himself, he in- 
 vestigates his own powers, and does for himself, more 
 or less correctly, and more or less thoroughly, what I 
 have attempted to do in the introductory chapter of 
 this book ; he analyses and studies the powers of his 
 own soul, and developes for himself an intellectual 
 philosophy, a doctrine of his emotions, and a code of 
 natural ethics. 
 
 Nor can he stop here, — he inevitably pushes his 
 thoughts upwards, and enters upon theological specu- 
 lations. The relation of the Universe to its Creator 
 is a problem that no man of any intellectual develop- 
 ment can put aside. Even Herbert Spencer, who has 
 been in our day famous for the strength with which 
 he has maintained that we can assign to the First 
 Cause of the Universe no attributes whatever, asserts 
 with equal strength and emphasis that the existence of 
 that First Cause is forced constantly on our attention, 
 and avouched to us with a certainty that is attained by 
 no other truth whatever. He deprecates theological 
 
20 TRUE ORDER OF STUDIES. * 
 
 discussion but, nevertheless regards himself as taking 
 the most preeminently religious view of the origin of 
 things ; and of course can defend this claim only by 
 theological argument. I shall, therefore, continue to 
 count Theology as the head of the Hierarchy of 
 Sciences. 
 
 The fivefold division at which we have thus 
 arrived may be set forth in several other modes. The 
 mode in which it first presented itself to me was this ; 
 God is the uncreated Creator ; He has made us in 
 His own image, as inferior, created creators ; we have 
 made many uses of this world, and enacted quite a 
 history upon it; the world itself is deserving of our 
 study, independent of its uses to us; and we find it 
 can exist, and manifest itself to us, only as it floats in 
 space and endures in time. This gives the hierarchy 
 in its descending order; but in education we need its 
 guidance in the ascending order. In that order it 
 agrees with the expanding powers of the child's mind 
 and with the logical sequence and dependence of 
 thoughts. 
 
 We can form dim conceptions of the spiritual 
 attributes of the Deity, only in proportion as we 
 understand our own faculties, in which lies our like- 
 ness to Him ; we can understand the human faculties 
 and human nature only as we observe and study the 
 words and deeds, the achievements of men ; we can 
 understand the achievements of man only as we 
 have a knowledge of the theatre wherein he has 
 wrought, and the material he has had to work upon ; 
 and we can understand this heaven and earth, only 
 
THE HIERARCHY OF SCIENCES. 21 
 
 in proportion to the clearness and profundity of our 
 knowledge of the laws of space and time in which 
 they exist. 
 
 In every school, therefore, and in every private 
 tuition of a child, the question must constantly be 
 asked, not only whether the child is old enough to 
 learn what you are attempting to teach him, but 
 whether he has the requisite knowledge of the pre- 
 liminary branches. There is no single fact, or 
 doctrine, in Theology or in Psychology, which does 
 not require from the pupil, some definite preparation 
 in historical, physical and even mathematical studies. 
 What that preparation ought to be, is an important 
 question ; and, in seeking an answer, the Hierarchy 
 of Science is a valuable guide. The scheme, carried 
 more into detail, will be found in the following table. 
 
22 
 
 TRUE ORDER OF STUDIES. 
 
 SCIEIVCE, 
 
 
 
 
 The Infinite 
 
 Religion, 
 
 
 
 
 
 Spirit, 
 
 
 
 
 THEOLOGY, 
 
 B 
 
 the 
 Unlimited Will; 
 
 Natural Theo 
 
 logy, 
 
 - 
 
 
 
 
 
 « Ethics, 
 
 
 
 
 o 
 
 The Finite Spirit, 
 
 
 
 
 PSYCHOLOGY 
 
 a 
 » 2 
 
 the 
 
 ^ Esthetics, 
 
 
 
 
 
 Limited Will ; 
 
 0) 
 
 ■5 Mental PhilO' 
 
 
 s 
 
 
 
 
 o sophy. 
 
 
 
 
 re 
 
 
 .S 
 
 .*3 
 
 Pi 
 
 
 o 
 
 
 
 2 
 
 11 
 > 
 
 
 m 
 
 
 .s Law, 
 
 13 
 
 
 o 
 
 
 o 
 
 The Acts of Man, 
 
 nT 
 
 .3 
 
 .S 
 
 *t3 
 
 
 the 
 
 -^ Language, 
 
 rt 
 
 '0 
 
 '7^ 
 
 HISTORY, 
 
 0) 
 
 
 E 
 
 w 
 
 
 
 (U 
 
 Creations of the 
 
 S Art, 
 
 S 
 
 ■-s 
 
 
 In 
 
 
 ^ 
 
 i 
 
 o 
 
 
 'S 
 
 Finite Will ; 
 
 s 
 
 
 rQ 
 
 
 M 
 
 
 M Trades 
 
 
 
 
 *3 
 
 
 
 -3 
 
 s 
 
 
 
 
 ^ - - - 
 
 S? 
 
 o 
 
 
 H-1 
 
 
 CO • • - 
 
 rt 
 
 c" 
 
 
 <1> 
 
 
 OJ 
 
 Ji 
 
 
 
 ■4-J 
 
 The Material 
 
 1 Biology, 
 
 H 
 
 CO 
 
 rt 
 
 
 .5 
 
 World, 
 
 rt 
 
 a. 
 
 
 hH 
 
 NATURAL 
 
 rt 
 
 
 
 
 ►*< 
 
 HISTORY, 
 
 
 the 
 
 ^ Chemistry, 
 
 
 
 
 
 Creations of the 
 
 0) 
 
 
 
 
 ;> 
 
 
 ^ 
 
 
 « 
 
 
 
 Infinite Will ; 
 
 Z Mechanics, 
 
 
 
 
 
 or, The 
 
 Algebra, 
 
 
 
 
 
 Field of Time 
 
 
 
 
 MATHEMA- 
 TICS, 
 
 
 and Space 
 
 in which Creation 
 
 is wrought ; 
 
 Arithmetic, 
 Geometry, 
 
 
THE HIERARCHY OF SCIENCES. 
 
 23 
 
 The Relations of God to 
 tlie Human Soul and 
 to Finite Spirits, 
 
 Investigation of particular 
 Fielda of Religious In- 
 quiry, 
 
 Evidences of Chris- 
 tianity, 
 
 Dogmatic Theology, 
 
 His Relations to the Jg 
 World and to History. ^ 
 
 Investigation of particular 
 Fields in Natural The- 
 ology, 
 
 The Will and the Ideas 
 of Duty, &c.. 
 
 The Emotions and Ideas 
 of Beauty, &c., 
 
 The Mind and Ideas of 
 Truth, <S:c., 
 
 o 
 
 <v 
 cu 
 (A 
 
 Discussions of particular 
 Relations in an Ethical 
 Light, 
 
 Analysis of particular 
 Classes of Emotions, 
 
 INIetaphysics, 
 Logic, 
 
 Theory of Education, 
 
 The Attempts of Man to 
 enforce his Ideas on his 
 Fellows. 
 
 The Use of Symbols to 
 express Ideas. 
 
 The Material World as 
 naturally expressive of 
 Thought and Feeling. 
 
 The Material World in 
 Material Uses. 
 
 > 
 'to 
 
 c 
 
 c 
 
 £ 
 
 c 
 o 
 
 P4 
 
 
 Law of Nations, 
 
 Constitutional Law, 
 
 Jurisprudence, 
 
 Philology, 
 
 Rhetoric, 
 
 Poetry, 
 
 Music, 
 
 Painting, 
 
 Sculpture, 
 
 Architecture, 
 
 Commerce, 
 
 Manufactures, 
 
 Agriculture, 
 
 CI 
 
 "o History, 
 pq 
 
 4) 
 
 > Social Science, 
 
 Political Economy, 
 
 Plants and Animals, or 
 Matter as living. 
 
 Matter as 
 into Kinds 
 
 distinguished 
 
 « 
 
 c 
 o 
 
 Matter as the subject of Q 
 ^lotions. b 
 
 Zoology, 
 
 Botany, 
 
 Phj^siology, 
 
 Organic Chemistry, 
 
 Inorganic Chemistry, 
 
 ElectrioSj 
 
 Thermotics, 
 
 Optics, 
 
 Acoustics, 
 
 Dynamics, 
 
 Statics, 
 
 ^ Geology, 
 
 Geography, 
 
 Astronomy,' 
 
 The Ideas of 
 Progression. 
 
 Time 
 
 or 
 
 Number and Ratio. 
 
 J3 
 
 Theory of Functions, 
 Theory of Equations, 
 
 Theory of Probabilities, 
 Theory of Numbers, 
 
 Kinematics, 
 The Calculus, 
 
 Space, Distance, and Di- 
 rection. 
 
 Analytical Geometry, 
 Trigonometry, 
 Descriptive Geometry, 
 Plane and Solid Geometry 
 
 Quaternions, 
 Stigmatics, 
 
24 TRUE ORDER OF STUDIES. 
 
 CHAPTER III. 
 
 MATHEMATICS. GEOMETRY. 
 
 WE liave endeavored, in the preceding chap- 
 ter, to show, that all possible objects of 
 human thought are comprised under one or another of 
 these five heads : Mathematics, Physics, History, 
 Psychology and Theology. In making these the objects 
 of study, mathematics must precede physics, because 
 conceptions of form, time and number must precede 
 conceptions of material phenomena. For example, me- 
 chanics treats of motion, in straight or curved lines, 
 of the parallelogram of forces, and direction of reflect- 
 ed and refracted motion, of the strength of materials 
 as dependent on form, of the equilibrium of the arch ; 
 and in these and other problems, demands a prelimin- 
 ary knowledge of geometry. Chemistry deals with 
 definite proportions, atomic weights, permutations of 
 combinations, multiples in series, and other matters, 
 necessarily involving a preliminary knowledge of 
 arithmetic. Botany and zoology in their morphology 
 require geometry ; in their physiology, chemistry ; in 
 both departments, mechanics. 
 
 As mathematics thus necessarily precede physics, 
 so physics must precede history. All that men do in 
 
MATHEMATICS. — GEOMETRY. 25 
 
 this world, must be done upon the materials set before 
 us, and under the conditions imposed by physical 
 laws. Our thoughts can find expression only through 
 outward symbols, in things built or made, in imitative 
 arts, or in language ; which, when verbal, was all 
 originally figurative, and when musical, is subject to 
 laws of rhythm and elasticity. The history of human 
 thought must also include, as one of its most import- 
 ant chapters, the history of the physical sciences, and 
 thus demand some knowledge of those sciences. 
 
 Moreover, Psychology can be advantageously 
 studied, only by one acquainted to some extent with 
 physiology, and with history. We know nothing of 
 the powers of the soul, except as we manifest them, or 
 see them manifested by others ; and in judging of the 
 soul from our external action as interpreted by con- 
 sciousness, we must also learn what allowance to 
 make for the automatic action, under physiological 
 laws, of the body in which we dwell. 
 
 Lastly, we have endeavored to show that Theology 
 requires a knowledge of all the inferior branches. 
 We can know, by nature, nothing concerning the 
 Creator, in whose image we were made, except by 
 studying his works, and especially by studying that 
 image of Himself which He has placed within us. 
 We may have religion with very little theology ; but 
 we cannot have any theology at all without some 
 previous knowledge of the lower branches, and espe- 
 cially of psychology. 
 
 Thus it is evident that the mathematics take 
 logical precedence, as the great and indispensable foun- 
 
26 TRUE ORDER OF STUDIES. 
 
 dation of all learning. It is not only impossible to dis- 
 pense with them, but impossible to place them any- 
 where else than at the beginning of all intellectual 
 education. All intellectual life upon our planet begins 
 with geometry ; it was so with the race ; it is so with 
 the individual. A man's geometrical knowledge may 
 have been learned unconsciously, as M. Jourdain's 
 prose ; but it is no less a real knowledge of space and 
 form,, and no less the real foundation for all the other 
 knowledge he possesses ; first, for his knowledge of 
 number, of rhythm, of time ; then for his knowledge of 
 business, morals, politics, and religion. 
 
 A natural method of education requires us, there- 
 fore, to pay our earliest attention to the development 
 of the child's power to grasp the truths of space and 
 time, his mathematical power, 
 
 The three great branches of the mathematics are 
 Geometry, Arithmetic and Algebra. If the reason 
 for arranging them in this particular order is not clearly 
 apparent, on a consideration of the sciences them- 
 selves, it may become clearer on considering the 
 sequence in the development of the child's power of 
 thought. Number, although an abstraction very 
 early made from the contemplation of forms in space 
 is manifestly subsequent to the perception of the 
 forms themselves. The child recognizes hundreds 
 of objects from their shapes long before he could be 
 taught to count them ; therefore, geometry precedes 
 arithmetic in education. Again, time is much more 
 difficult to see, than space ; it requires a riper effort of 
 the imagination to separate time from the succession 
 
MATHEMATICS. — GEOMETRY. 2/ 
 
 of events, than to separate space from the extension 
 of bodies. Space remains, so to speak, visible, to the 
 mental eye ; but time cannot, by any device of the 
 imagination, be made to appeal to sense. Algebra, 
 therefore, the science of time, follows arithmetic, as 
 arithmetic follows geometry. Every day, from the 
 hour of birth, a new knowledge of forms developes 
 new power in numbers ; and that again, new power in 
 the consideration of flowing or changing quantity ; 
 and thus the child runs its round ; from geometry to 
 Theology, and then to a higher point in geometry, and 
 round again to Theology ; in ever recurring five-fold 
 cycles, as long as it continues its intellectual develop- 
 ment and growth. 
 
 Until the age of four or five years, the child is 
 seldom at school, and seldom directed at all with a 
 view to intellectual education. The best parents, 
 usually, content themselves with looking after its 
 physical health, and its habits of obedience and order 
 in the house. Nevertheless the education of the first 
 years of life is, in many respects, more important 
 than any which follows. There can be no doubt that 
 early impressions are very deep, and exert great power 
 over the subsequent life, physical, intellectual and 
 moral. Every observer knows the difficulty of cor- 
 recting the moral habits of a spoiled child. The 
 difficulty of correcting his intellectual habits, although 
 less apparent, is as real. For this reason, I have 
 endeavored to persuade the school committees with 
 which I have been connected, to secure the highest 
 talent and pay the highest wages in the schools for 
 
28 TRUE ORDER OF STUDIES. 
 
 the youngest pupils ; convinced that this would in the 
 end, most truly elevate the character of the whole 
 community. 
 
 For the geometrical education of children under 
 five years of age, the early kindergarten gifts are 
 admirably adapted. Picture books, provided the 
 drawing is good, are also valuable ; and many of the 
 toys given to children serve a good purpose in this 
 direction. 
 
 We must, however, remember that the great ends 
 to secure, by early geometrical culture, are accuracy 
 of observation, and definiteness of imagination. These 
 uses of geometry have been strangely neglected by 
 both friends and foes of this intellectual gymnastic. 
 The admirers of geometry have contended themselves 
 with showing that no other study holds the student to 
 such continuity of thought, to such extended series of 
 consecutive, dependent arguments. And in Sir 
 William Hamilton's plea against the use of geometry 
 in education, he contents himself with showing, as he 
 thinks, that other sciences afford better training for 
 the powers of logical thought. 
 
 But the powers of perception, and the powers of 
 imagination, or conception, are of even greater 
 importance than those of reasoning ; they give us the 
 facts of nature, and definite theorems in science, 
 without which reasoning is vague and worthless. The 
 early studies of the child, therefore, while seeking to. 
 develope his ideas of space, and time, must do so by 
 training him to rapid and exact observation, clear and 
 definite conception. • 
 
MATHEMATICS. GEOMETRY. 29 
 
 Miss Edgeworth, in one of her invaluable stories, 
 describes small wooden bricks ; rectangular parallelo- 
 pipeds, whose dimensions are in the ratio 1:2:4. In 
 the public schools of Waltham, we used to supply the 
 scholars, under 10 years old, with such bricks, made 
 of birch or maple, two inches long, one inch wide? 
 half an inch thick ; with a small percentage of double 
 length, and half length. Each scholar, when playing 
 with these bricks in school, had his desk covered with 
 a piece of dark cotton velvet, to prevent noise, and 
 prevent slipping. For younger children before they 
 come to school the bricks may be larger, and of lighter 
 wood. A child of eighteen months old will find amuse- 
 ment in them. The variety of structures, all beautiful 
 and symmetrical, which an ingenious boy, of ten years* 
 will make with a few dozen of such bricks, would 
 astonish the unitiated. Square and circular build- 
 ings, pyramids, crosses, gateways, columns surmount- 
 ed by crosses, and natural arches of various forms, 
 will be devised by the child, and combined in a variety 
 of modes. For the building of real arches, centerings 
 must be provided, and also a substitute for mortar in 
 the shape of numerous little sticks, like Vienna matches 
 without phosphorus, one to be inserted in each joint 
 of the arch, before the centring is removed. This 
 process, as well as the breaking of joints, binding of 
 crosses together, erecting of the long cross-bar in 
 crosses, etc., will give incidental instruction in 
 mechanics, as well as in geometry. It will also give 
 valuable lessons on the importance of precision, and 
 promptness in action and observation. 
 
30 TRUE ORDER OF STUDIES. 
 
 The Chinese tangram consists of seven pieces of 
 flat metal or wood : — five isosceles right triangles, a 
 rhomboid and a square. The area of the seven pieces 
 being called unity, the areas of the square, the 
 rhomboid, and one of the triangles, are each one- 
 eighth ; two of the remaining triangles one-sixteenth 
 each ; and the other two one-quarter each. They are 
 accompanied by a book containing hundreds of oddly 
 shaped rectilinear figures ; any one of which may be 
 made by putting all the seven pieces together. 
 Learning that Archimedes had invented a similar 
 game, and ascribed to it an educational value ; but 
 feeling that the Chinese tangram was too difficult for 
 beginners, I published in 1848 a much simpler form 
 and introduced it into the schools of Waltham, where 
 it was used for many years. Two hundred and four 
 figures were given, each capable of analysis into three 
 isosceles right triangles ; and the area of these 
 triangles were either the ratio i : i or i : 2. These 
 "puzzles to teach geometry," cultivate the habit of 
 exact observation, and of the rapid analysis of forms. 
 They may also be made of curvilinear figures. I 
 have frequently used, instead of triangles, trigonoid 
 figures, each being enclosed in three arcs, one of 120°, 
 and two of 60°. Two varieties of the trigonoid are 
 procured by having, in some, both arcs of 60° con- 
 cave, in other only one. 
 
 At the earliest stage of schooling the child may 
 be taught also to derive instruction from his slate and 
 pencil. Agassiz is reported to have said, in regard to 
 observation in Natural History, that a lead pencil is a 
 
MATHEMATICS. — GEOMETRY. 3 I 
 
 very good microscope ; and the slate pencil serves the 
 same purpose for the younger pupil, in the more 
 fundamental study, of geometrical forms. When the 
 child can use the pencil, he can also use the crayon 
 upon the blackboard ; and the ingenuity and skill of 
 men in Waltham, have brought white crayons of the 
 best quahty within the reach of every school. As a 
 suo-o-estion of the mode in which the pencil and 
 crayon may be made to conduce, rapidly, to accuracy 
 and quickness in the perception of geometric form, 
 take the following exercise. 
 
 Let the teacher have cards or tablets each con- 
 taining one clearly drawn simple figure. For younger 
 classes these figures may be ; a horizontal straight 
 line, a vertical line, a line slanting to the right, a line 
 slanting to the left, a St. George's cross, a St. 
 Andrew's cross, an arrow head, an arc in one position 
 or another, etc. For classes a little older the figures 
 may be triangles in different forms and positions, 
 circles, circles with a diameter in different positions, 
 ellipses of different forms and positions, capital 
 letters, etc. Classes still more advanced may take 
 lower case letters, Roman and Italic, outlines of 
 forest leaves, profiles, outlines of familiar animals, 
 utensils, etc., Gothic arches, numerals, etc. These 
 cards, or tablets may be permanently printed, or they 
 may be made extempore by the teacher, a slate with a 
 crayon drawing will answer every purpose, in the 
 hands of a teacher who can draw rapidly and correctly. 
 The class being ready with their slates, or at the 
 blackboard, the teacher calls their attention, and ex- 
 
32 TRUE ORDER OF STUDIES. 
 
 poses her card for a few seconds, longer to absolute 
 beginners in the exercise, but afterwards for still 
 shorter times, until it is reduced to a minimum ex- 
 posure. Then each pupil draws immediately from 
 memory a reproduction of what was shown, and ex- 
 hibits it for criticism. This will be found an admir- 
 able preparation for subsequent observation of objects 
 of natural history. 
 
 When the child is able to analyze figures com- 
 posed of three or four triangles ; and to copy triangles 
 and rectangles with approximate similarity to his copy, 
 he will be ready for conversations upon geometrical 
 theorems. The steady aim of the teacher in these con- 
 versations must be to lead the child to see for himself; 
 not to learn words by rote ; much less to learn reasons 
 for belief; but to see the truth, directly, without the 
 intervention of reasoning, and without appeal to rea- 
 soning for verification. Whatever proposition you an- 
 nounce to him, announce to him as known, and to be 
 received by him, for the present, simply as food for his 
 imagination ; do not attempt, nor lead him to attempt 
 to prove it, nor to use it as proof ; that exercise of 
 logic belongs to a later period in his course. If the 
 child asks for proof, and the demonstration is fully 
 within the grasp of his mind, it may do no harm to 
 give it ; — but it will be an exceptional case ; there are 
 very few children under twelve years of age, capable 
 of understanding the simplest geometrical demonstra- 
 tion. On the other hand I have seen scores of child- 
 ren in the primary schools of Waltham, under ten 
 years of age, who by familiar oral instruction on the 
 
MATHEMATICS. GEOMETRY. 33 
 
 part of the teacher, had been made well acquainted 
 with the leading truths of the geometry of the trian- 
 gle and the circle ; many also under twelve years, who 
 had in like manner attained a clear knowledge of the 
 relations of the cycloidal curves, and their evolutes ; 
 and of many theorems concerning the conic sections 
 and the catenary curve. 
 
 The ease of imparting such information, or lead- 
 ing the child's imagination into such exercises is greater 
 than the teacher who has not tried it would imagine. 
 Take any clear-headed boy of ten or twelve, and sup- 
 pose to him the case of a goat on a plain, tethered 
 to a ring, sliding on a cord, fastened at either end to 
 one of two stakes, whose distance apart is less than 
 the length of the cord. Question him about the goat's 
 liberty of movement, and you will very readily lead 
 him, by questions only, to see that the ring is confined 
 to an oval, which is symmetrical on two rectangular 
 axes (he of course will not use these technical phrases of 
 words but he will describe the facts), the longer diam- 
 eter passing through the stakes, and that the sum of 
 the distances from any point in the periphery to the 
 two stakes will be constant, and equal to the longest 
 diameter. Then imagine a dove for the goat, a finger 
 ring and thread tied to the tops of two tall poles and 
 you can lead him to discern the form and some of the 
 properties of the prolate ellipsoid. 
 
 Now if it be asked of what value are these geo- 
 metrical conceptions to the scholars who have thus 
 early attained to them, I answer that the uses of the 
 knowledge will be manifold. It has already afforded 
 
34 TRUE ORDER OF STUDIES. 
 
 to each of them an excellent culture in the power of 
 clear and definite conception ; it has enlarged their 
 sphere of thought, and linked the higher mathematical 
 truths with their playthings, — the hoop, the swing, the 
 jumping rope, the ball, and its movements ; it has 
 made them partakers in the fruit gathered by the 
 highest spirits of our race. 
 
 The clearness and precision of observation and 
 imagination, cultivated by these early geometrical 
 studies, will be of use in every occupation of life ; 
 and render the student's testimony and his judgment 
 of more value in after life, both to himself and to 
 other men. Even the powers of the eye and of the 
 hand will be more likely to be cultivated with care, 
 for uses of industrial art, by one whose imagination 
 has been thus developed and strengthened. And if 
 there chance to be, among the children thus early im- 
 bued with the germs of geometry, any scholar whose 
 natural gifts peculiarly fit him to advance its progress, 
 or to use the higher mathematics to advantage, noth- 
 ing could more surely lead him to application, and im- 
 provement of his gifts, than to set before him at an 
 early age some of the curious and interesting results 
 that have been attained by the labor of his predeces- 
 sors. As the visible forms of nature stimulate the 
 imagination, so the creations of the imagination stimu- 
 late the reason. 
 
 The sight of a hanging chain, for example, may 
 stimulate the imagination to conceive of a chain 
 formed of infinitesimal links, producing a uniform 
 curve. This conception arouses the logical powers to 
 
MATHEMATICS. GEOMETRY. 35 
 
 inquire into the relations of the parts of such curve 
 to each other, and to the forces which hold it in equi- . 
 librium. A boy of ten years old playing with such a 
 chain, may readily learn some of the truths which 
 such inquiries bring to light. He may roughly test by 
 his muscular exertion, or more accurately test by a lit- 
 tle mechanical ingenuity and measurement, the truth 
 of your assertion, that the length of a piece, of the 
 same chain, equal in weight to the horizontal tension, 
 will strike, used as radius, a circle just large enough to 
 fit exactly the lower part of the chain ; and may easily 
 be led to draw the corollary that no amount of 
 power can draw a horizontal flexible thread perfectly 
 straight. The marvellousness of this corollary will 
 fix the theories ineradicably in his memory, and he ^ 
 will, years afterward, when he begins to learn how to 
 demonstrate the theories of geometry, wish to prove 
 the proposition. But he finds that simple geometry 
 is not enough. He takes up algebra, learns to apply 
 it to geometry ; but the problem is still too difficult for 
 him ; he adds the resources of trigonometry, bu-t is 
 no nearer the proof that he desires. He enters col- 
 lege, learns the marvellous uses of Descartes' coordi- 
 nates ; but finds his chain still hangs beyond the 
 reach of their magic. Nor is his curiosity, aroused at 
 so early an age, gratified until, perhaps in his senior 
 year, having learned something of the wonderful cal- 
 culus of Leibnitz and Newton, something of the an- 
 alytical mechanics of Lagrange, he takes up the discus- 
 sion of the catenary curve. 
 
 The student who has in childhood become familiar 
 
36 TRUE ORDER OF STUDIES. 
 
 with the facts of geometry, approaches, when nearer 
 manhood, higher mathematical studies under less dis- 
 advantage than others. The student who betakes him- 
 self, as preparatory to higher engineering or architec- 
 ture, to the study of the conic sections, the arch of 
 equiHbrium, and other transcendental curves, has usu- 
 ally a twofold difficulty ; he is receiving novel and be- 
 wildering ideas, at the very time that he is also learn- 
 ing a new language in which to express them. But if 
 he has already become familiar with the properties of 
 the curve, and easily form a clear picture of it in his 
 imagination, he can give his whole attention and whole 
 strength to the mastery of the language, the analytical 
 key that unlocks the hidden treasure-houses of the 
 Science of Space. 
 
 In order to facilitate the formation of habits of 
 precise imagination at the beginning of the course, we 
 introduced into the Waltham Schools, to be used upon 
 the teacher's desk, several pieces of home-made ap- 
 paratus, for the mechanical production of curves and 
 illustrations of theorems. 
 
 When he attains the age of 12 or 13 years, the 
 pupil having learned a little arithmetic also, may be- 
 gin problems of geometrical construction. I have 
 known boys, at that age, who made quadrants, and 
 horizontal circles for themselves, and solved graphic- 
 ally, problems in heights and distances, and surveying ; 
 and who habitually carried in their breast pockets, sun- 
 dials of their own construction, which by a thread 
 and plumbline, gave them the hour of the day. 
 
 A year or so later, the pupil will be mature enough 
 
MATHEMATICS. — GEOMETRY. 3/ 
 
 to comprehend geometrical reasoning. The ordinary 
 text-books on geometry fail, as I think, in their adap- 
 tation to children from three circumstances. First, 
 in not explaining the object of reasoning. The child 
 plunges into demonstrations, without having any con- 
 ception of what demonstration is, or what it proposes 
 to do ; and he not unfrequently passes through his 
 whole course of mathematical instruction in a state of 
 bewilderment, never having clearly perceived the 
 force of a Q. E. D. Secondly, the ordinary text-books 
 give their propositions in a disconnected manner, so 
 that it is only by accident that some scholar, brighter 
 than the average, perceives that to attain to some of 
 his propositions in isoperimetry he must weave a con- 
 nected series of two or three hundred propositions, 
 not one of which can be omitted, or transposed, with- 
 out destroying the validity of the whole argument. 
 Thus geometry loses much of the very excellence for 
 which it is commonly extolled, the teaching of a pa- 
 tient continuity of attention, of a close adherence to 
 the logical sequence of thought. Thirdly, the usual 
 treatises confine themselves to the demonstration of 
 theorems and solution of problems ; — giving no ex- 
 ercises to be solved by the pupil, as in arithmetic and 
 algebra, and in various arts of mensuration. In my 
 '' Second Book in Geometry " I endeavored to reme- 
 dy these three defects, by explaining carefully, in pre- 
 liminary chapters, the object of demonstration ; by 
 giving demonstrations of only two theorems, but 
 selecting such as required the demonstration of about 
 two hundred preliminary propositions ; and by ap- 
 
38 TRUE ORDER OF STUDIES. 
 
 pending unsolved theorems and problems to some of 
 the chapters. I have been partially followed in the 
 second and third of these reforms, by William F. 
 Bradbury, and hope that other writers on the subject 
 will be led into the same path. 
 
ARITHMETIC. 39 
 
 CHAPTER IV 
 
 AR ITHMETIC. 
 
 AT the same time that the child is expanding his 
 powers of geometrical conception, — let us say 
 from the age of five or seven, to that of eleven or 
 twelve, according to his natural ability, — he should 
 also be gaining simple ideas of numbers. Before he 
 enters school he has usually gained, without effort or 
 intention on the part of his parents, sufficient knowl- 
 edge of shapes and forms, to serve as the basis of a 
 partial knowledge of numbers under five. Let his 
 schooling in arithmetic begin with developing, and 
 making clear, these partial and confused ideas. The 
 order of nature requires that this should be done at 
 first by concrete illustrations ; beans, grains of corn, 
 marbles, pencils, buttons, blocks, or counters. On 
 the whole beans are, when we wish to illustrate large 
 numbers, the best ; being at once cheap and clean. 
 
 The method of teaching which has always seemed 
 to me the most natural and effective, is substantially 
 that which has recently been called Grube's method ; 
 but which has probably suggested itself, independ- 
 ently, to many thoughtful educators. A number is 
 the answer to the question how many ; but the usual 
 
40 TRUE ORDER OF STUDIES. 
 
 method o£ teaching a child to count is apt to produce 
 a confusion in its mind between ordinal place and 
 numbers. Counting, or naming numbers in their 
 order, should not be taught until the child has learned 
 to recognize the numbers themselves. Expose suc- 
 cessively, in front of a little book or slate, the fore- 
 finger, little finger, ring finger, middle finger ; — asking 
 each time, " How many fingers do I show," and 
 dictating, if the child cannot answer, the answer, one. 
 In like manner, show successively fore and middle, 
 fore and ring, fore and little, middle and ring, middle 
 and little, ring and little ; asking at each exhibition, 
 the same question, and dictating, if the child hesitates, 
 the answer, two. Exhibit in like manner, first one, 
 and then two, beans, pencils, marbles, books, chalk 
 marks, chalk crosses, letters of the alphabet, etc., 
 varying the position and direction of the couples, until 
 you are assured that the child really knows the mean- 
 ing of the words, two, and one. But do not yet begin 
 to teach him to count, i. e., to say one, two. Expose 
 now three fingers, three beans, three books, etc., etc., 
 in various collocations, until he recognizes a triplet, 
 under any disguise of form ; and to the question how 
 many, always promptly answers three. Review now 
 his knowledge of two, and one ; and when there is no 
 doubt in your mind that he knows one, three, or two, 
 objects of any kind, in any position to be one, three, 
 or two, you add a new element as follows : — 
 
 Place a finger of the right hand in front of one 
 little book, of the left hand in front of another ; ask 
 separately concerning each, then bringing the books 
 
ARITHMETIC. 4I 
 
 and hands together ask of both. Then put the ques- 
 tion in concrete form, one finger (showing the right 
 hand), and one finger (bringing up the left) make how 
 many fingers ? If the child does not say, at once, 
 two ; it shows that he had not learned perfectly the 
 distinction between one and two, and you must begin 
 again with the first exercise. But if he answers 
 promptly, then is your opportunity to put your first ab- 
 stract question, then one and one make how many ? 
 and he will answer, two. You may then ask ; And if 
 I take one away from two (suiting the action to the 
 word) it will leave how many ? 
 
 Many teachers will pursue this method of nature thus 
 far ; but its great value can be really appreciated only 
 by one who will follow it carefully up, at least as far 
 as to the number thirty. This will require time and 
 patience, — months and years will elapse, — but the 
 labor will be abundantly rewarded. The process at 
 first should be very slow, and the child should be led, 
 somewhat in the manner I have indicated above, to 
 see for himself that two beans and one bean make 
 three beans ; one from three leaves two ; two and one 
 make three, two from three leaves one ; one and one 
 and one make three. Treat each number successively 
 in the same manner until you have reached six. You 
 may now arrange a series of little parcels of beans, or 
 groups of chalk dots, in order, and lead the child 
 by judicious questions to see that the numbers four 
 and six can be divided into twos, and the number 
 six into threes. You may also ask him to name 
 them in order, and lead him to perceive that 
 
42 TRUE ORDER OF STUDIES. 
 
 each is formed by adding one to the preceding. Then 
 giving him a handful of beans you may let him drop 
 them one by one in a place by themselves, naming as 
 each one drops, the number which he thus doles out. 
 Proceed now to twelve, slowly and gradually. Great 
 quickness in counting may be produced, without strain 
 on the child's mind, by a process similar to that 
 named under geometry ; expose, successively, — for a 
 few seconds to the youngest, for a fraction of a second 
 to the older pupils — three, two, five, six, four, one, five, 
 seven, etc., objects, and see who can, a moment after- 
 wards name the number. 
 
 By the time that you have reached the number 
 twelve, your division of numbers into classes may be- 
 gin to receive names. The numbers that can be 
 divided, into couples of beans, without leaving an odd 
 one, are called even numbers ; those that leave an odd 
 one, are odd numbers. Even numbers increase by 
 twos, and so do odd numbers. The numbers above 
 twelve being too large to be recognized at sight, may 
 be counted by addition of twos, threes, or fours — and 
 the child will probably find that he has been thus re- 
 co2:nizino; the numbers between six and twelve, by ad- 
 dition. The commutative principle of arithmetic may 
 be shown by dividing six into three twos, or two threes, 
 still using beans. With the same illustrations, before 
 you have reached the number thirty, you may lead the 
 child to see for himself the difference between prime 
 and composite numbers ; the meaning of equal factors; 
 the nature of powers and roots ; the value of Eratos- 
 thenes' sieve, and its defects ; the distinction between 
 
ARITHMETIC. 43 
 
 the two factors, that one is abstract and the other 
 concrete, etc., etc. 
 
 The Httle j^rimary arithmetics which the dihgence 
 of our writers has produced, endeavoring to substitute 
 pictures for real objects, in giving the first lessons in 
 numbers, are of little value to the pupil, and do much 
 harm to the teachers, by deluding them into an en- 
 tirely false view of the functions of their office — a view 
 which is hardly caricatured in the jocose anecdote of 
 the teacher who gave a boy, of four years, the three 
 first letters of the alphabet to commit to memory and 
 recite at the next hour, — the boy never yet having heard 
 the names of the mysterious symbols. Text books 
 are the incubus on our New England schools, turning 
 the attention of the teacher and the child away from 
 nature and from truth, to fix it on the errors and weak- 
 ness of men. Arithmetic is taught backward, begin- 
 ing with reasoning instead of with observation, and 
 is hampered with factitious difficulties or artificial 
 rules and processes. I have known but three really 
 good treatises on arithmetic published in this country, 
 in my day ; one of these, Warren Colburn's First Les- 
 sons, has been abused, by being put into the hands of 
 children too early, and has thus been productive of 
 almost as much harm as good ; a second was promptly 
 suppressed by legal proceedings, because it infringed 
 on Pliny E. Chase's copyright ; and Chase's Arith- 
 metic has gone out of print, and the stereotype plates 
 have been melted, because the popularity of a text 
 book in America is in inverse proportion to its real 
 merits. All other school arithmetics now in the 
 
44 TRUE ORDER OF STUDIES. 
 
 market have a great similarity to each other ; the 
 best differing but shghtly from the average. 
 
 Very soon after the child has become familiar with 
 the names of the first half dozen numbers, and can 
 instantly name, without conscious counting, any num- 
 ber of beans under six, he should be taught the Arabic 
 figures representing them, and from that time should be 
 taught to write, instantly, the figure representing the 
 number of beans exposed to view. Quickness in 
 writing numbers should now be cultivated by requir- 
 ing the children, pencil in hand, to write the Arabic 
 figures on the slate, as you successively expose for 
 a second each small number of objects. 
 
 Two or three hundred beans may now be arranged 
 in heaps of ten, and those heaps in groups of ten, and 
 the mysteries of decimal notation be thus made 
 clear to sight. The rapidity with which the value of 
 the units in the different places increase as you go to 
 the left will never be distinctly appreciated until the 
 child sees for itself, in the heaps of beans, how few 
 figures are needed to express the largest quantities. 
 When he has perceived this he will comprehend why 
 men need names only as high as millions. 
 
 Then break up a few dry beans and select pieces 
 that shall average about one-tenth of a bean each, and 
 some also to represent hundredths, and he will see in 
 the rapid decrease of size, why we so seldom need 
 decimals beyond millionths. Teach him from this 
 point the mode of writing decimal fractions, without 
 any allusion to vulgar fractions. He is now ready for 
 addition, subtraction, multiplication and division, in 
 
ARITHMETIC. 45 
 
 both whole numbers and decimal fractions, and can 
 learn them both at once, as easily as he can one of 
 them. For the first two years after he has thus 
 begun to cypher, let your whole aim be to make him 
 expert in performing these four operations. Do not 
 ask him to commit any rules to memory, do not ask 
 him to explain or understand the reasons for his oper- 
 ations, but simply keep him at work on simple ex- 
 amples in numbers, whole and decimal. Avoid even 
 giving him problems that shall require any ingenuity 
 in reducing them to form ; — but give him figures to 
 operate upon, and tell him what to do, until the mere 
 addition, subtraction, multiplication and diviston of 
 whole numbers, or decimals, and the correct pointing 
 and reading them, shall be an automatic process, like 
 the reading of the easiest story book. 
 
 The teacher who has been accustomed to the 
 modern erroneous method of teaching a child to reason 
 out his processes from the beginning may be assured 
 that this method of gaining facility in the operations, 
 before attempting to explain them, is the method of 
 nature ; and that it is not only much pleasanter to 
 the child, but that it will make a better mathematician 
 of him. In this work of cyphering fast, dictation ex- 
 ercises, like Walton's, are of great value. Especial 
 attention should be given to the addition of columns, 
 that being the place in which arithmetical blunders 
 most frequently occur. A convenient method is to 
 give to the class from your extempore invention, any 
 odd number of numbers, each beginning in the same 
 place, keeping a record of them ; for example, 248, 
 
46 TRUE ORDER OF STUDIES. 
 
 751.6, 842, 943, 851.7: then give the arithmetical 
 complements of all, except one ; for example, give all 
 but the second one above, 752, 158, 57, 148.3 ; and 
 then say, add. The class, not knowing your key, can 
 add the numbers quicker than find the key ; you, 
 knowing the key, write the omitted number, 75 1.6, and 
 prefix to it the number of complements, 4, giving 
 instantly the sum, 4751.6; and you are ready to test 
 at once the accuracy of the swiftest computer. 
 Similar methods are easily devised for the other rules. 
 There is a difficulty in a child's mind, not 
 usually recognized by the teacher, in passing to the 
 application of number to continuous quantity ; 
 and one of the minor advantages of introducing 
 decimal fractions into the very beginning of written 
 arithmetic, consists in its affording a ready means of 
 introducing the idea of an arbitrary or artificial unit. 
 Arrange the number 123.45 for example in this way; 
 First place to the child's left a group of ten heaps, ten 
 beans in a heap : then passing to the right, making 
 another group of two heaps ; still further to his right 
 place three beans ; then four pieces averaging a tenth 
 of a bean each ; and lastly to the right lay five frag- 
 ments of bean dust for hundredths. Now lead him to 
 see that these 123.45 beans may be written as 1.2345 
 groups, or as 12.345 heaps, or as 1234.5 tenths of a 
 bean, or as 12345 hundredths of a bean. 'Repeat this 
 lesson, varying the numbers, day after day, week after 
 week, until the pupil has become perfectly familiar 
 with the conception of varying the unit from groups, 
 to heaps, to beans, and to hundredths. Lead them by 
 
ARITHMETIC, 4/ 
 
 judicious questions and the actual exhibition of coin, 
 to see that ^12.375 may in like manner be called 
 1.2375 eagles, or 123.75 dimes, or L237.5 cents, or 
 12375 mills. Next give them a meter stick, and show 
 them its division into ten decimeters ; 100 centime- 
 ters ; and its possible division into 1000 millimeters, 
 and measuring the length of books, tables, window 
 seats, &c., in the school room, show them how each 
 can be expressed in terms of either of these units ; — 
 and the passage from the natural to the artificial unit 
 will have been made unconsciously. The process 
 should however be continued further, by learning, from 
 good maps, not otherwise, the distance from the 
 school house of prominent objects in the neighbor 
 hood, other schools, churches, banks, hotels, cross- 
 roads, bridges, &c., and requiring the children to ex- 
 press- the kilometers as meters, centimeters, and by 
 moving the decimal point. Be careful that the child 
 has a definite conception or image of the length of 
 the metre, and its parts. One mode of doing this 
 is to allow the stholars to estimate the length of 
 various objects, and then test the accuracy of the 
 estimate by applying the meter stick. A little rivalry 
 in this matter is of great benefit in sharpening the 
 powers of observation and judgment. 
 
 The passage from linear to square and cubic 
 measure is also accompanied with more difficulty, in 
 a child's, mind, than the teacher is usually aware of. 
 Indeed we seldom find even an adult, except in certain 
 professions, who has a really practical appreciation of 
 the different rates of increase in linear dimensions, 
 
48 TRUE ORDER OF STUDIES. 
 
 surface, and solidity. To assist the pupil in gaining 
 this appreciation it is well to have a square meter 
 permanently marked upon the blackboard ; and also 
 to furnish the school with pieces of card, one 
 decimeter square ; and other pieces one centimeter 
 square. Five of the larger pieces of card will thus 
 give the means of making a litre measure in cubic 
 form, which ought to be the first form in which solid 
 measures are introduced to a child's attention. 
 
 We are thus particular, and emphatic, concerning 
 the early steps of mathematical education, because it 
 is " the first step which costs." Much more labor is 
 requisite to unlearn than to learn. As we have be- 
 fore said, the younger the class of pupils, the more 
 need of a high moral and intellectual character, and 
 of peculiar aptness for teaching in the teacher. The 
 teachers of the youngest classes ought to deserve and 
 to receive the highest wages. 
 
 Fifty years ago the treatises on Arithmetic were 
 blind guides, giving very imperfect announcement of 
 rules, and no explanations. In the modern reaction 
 the opposite extreme has been reached. Explana- 
 tions, and reasons, and pictured illustrations, have 
 expanded the course of Arithmetics, until the un- 
 fortunate pupil is lost in a wilderness of words, and 
 does not find his way through in time to learn to 
 cypher. The science of Arithmetic receives so much 
 attention, that the art is neglected ; and the elements 
 of the science are so much expanded that its higher 
 parts are never reached. I The primary object in the 
 earlier years, from 7 to 12, should not be to develop 
 
 
ARITHMETIC. 49 
 
 the reasoning power, but to give familiarity with the 
 forms of calculation ; — so that when a child is asked a 
 question, he should not begin a course of analysis and 
 reasoning based upon a model in the text book, or 
 given by the teacher ; but should begin instantly to 
 add, subtract, multiply, divide the numbers themselves, 
 and give the answer in numbers instantly. After the; 
 age of 12 he may begin to learn to explain, using 
 Warren Colburn's First Lessons. Life is not long 
 enough, to spend so large a proportion of it on 
 Arithmetic as is spent in the modern system of teach- 
 ing it ; and Arithmetic is too valuable an art, to have 
 our children neglect to acquire facility in it, while 
 they are being stupified, and disgusted with prema- 
 ture attempts to understand it as a science. "" 
 
 The fewer the artificial rules in Arithmetic, the 
 better. Vulgar fractions must always be retained ; 
 and for the next fifty years we shall need English 
 tables of weights and measures ; after that it is to be 
 hoped that they will drop into disuse, as the shillings, 
 ninepences, fourpence-halfpennies, fips and eleven- 
 penny bits of fifty years ago have given place to 
 dollars and cents. Square root and cube root must 
 also be retained ; and it were very desirable to re- 
 introduce into the school books the rule of Double 
 Position, as a natural introduction to the larger 
 methods of modern mathematical science. If, at the 
 same time, four place logarithms could be introduced, 
 a great variety of problems could be solved interesting 
 to the pupil, and stimulating him to a thirst for higher 
 knowled^re. Loe:arithms could be used to advanta^re 
 
50 TRUE ORDER OF STUDIES. 
 
 in many operations of business life, where they are 
 now neglected : and would be used, did the pupil learn 
 in the common school how rapidly and easily he 
 attains accurate results by them. For the child's use 
 , three place tables might be large enough, and the 
 cost would be trifling. The labor of using tables in- 
 creases very rapidly with the increase of decimal 
 places ; and it is a point of practical wisdom to use 
 tables of a size proportioned to the nature of your 
 work. Six place tables seem the most ill-judged of all ; 
 being too unwieldy for ordinary problems, and not 
 nice enough for nicer operations. 
 
ALGEBRA. 5 1 
 
 CHAPTER V. 
 
 ALGEBRA. 
 
 ALGEBRA was originally considered an exten- 
 sion of Arithmetic ; and its essence was 
 supposed to consist in representing numbers by 
 letters ; so that we could represent- an unknown 
 number by a letter, and work upon it as if known. 
 This is still the best way of introducing the pupil to 
 this study. And it were well if part of the time saved 
 by reducing Arithmetic to reasonable bounds, were 
 given to acquiring this art. There is no difficulty in 
 teaching the scholars in the Grammar school, as they 
 are finishing their arithmetic, the meaning of the 
 signs, +, — , =, (), 0", and the like ; nor in teaching 
 them to perform their arithmetical examples not only 
 on the numbers given, but then upon letters ; obtain- 
 ing thus formulae, in which again they may substitute 
 numbers. 
 
 But Sir Isaac Newton, and long afterwards, in more 
 distinct form. Sir William R. Hamilton, have shown 
 that there is a deeper, a more vital distinction between 
 algebra and arithmetic, than the mere ability of alge- 
 bra to deal with the unknown ; it deals with the varia- 
 ble ; it introduces conceptions of flowing, changing 
 quantity ; it is in fact a science of Time. Leibnitz 
 
52 . TRUE ORDER OF STUDIES. 
 
 then introduced what Peirce, in his Linear Associative 
 Algebra, has shown to be a new algebra, to deal with 
 the infinitesimal. The increase of power given by 
 the three gifts, Neper's logarithms, Newton's doctrine 
 of fluxions, and Leibnitz's algebra of the calculus, has 
 been incalculable. Their gifts have, however, been 
 but scantily used by the compilers of elementary 
 books, until within the last half century. They could 
 be advantageously carried much further ; and, in spite 
 of the famous denial, a royal road to geometry, in its 
 widest sense, could be constructed by the labors of 
 these three kings ; a road which would lead to new 
 treasures of art and science for the benefit of the 
 whole race. 
 
 A few writers on geometry have followed Peirce 
 in introducing the infinitesimal into the elementary 
 treatises on that science ; it is to be hoped that others 
 will follow him and go beyond him in introducing the 
 idea of flow or change into algebra. An anecdote will 
 illustrate the advantage thus to be derived. A pupil of 
 mine had labored for several days in vain to under- 
 stand the demonstration of the binomial theorem. I 
 took out my watch, and said : Now give me undivided 
 attention for five minutes, and I will give you an easier 
 demonstration. At the expiration of the five minutes, I 
 was through ; and he was repeating with all the de- 
 light of success, my demonstration. In those five 
 minutes I had begun de novo, from first principles, and 
 given him a simplification of Peirce's demonstration 
 of Arbogast's Polynomial Theorem, based on deriva- 
 tives, which are the same as differential coefficients, 
 
ALGEBRA. 
 
 53 
 
 or fluxions. I had avoided every new technical term, 
 and given him the ideas. 
 
 In like manner by introducing the idea of flow, 
 early, and teaching Leibnitz' calculus with the ordinary 
 algebra, the whole mysteries of trigonometry and an- 
 alytical geometry could be brought within the range 
 of High School instruction ; what might be done 
 with Hamilton's Quaternions, and Ellis's Stigmatic 
 Geometry I have not examined. The mathematical 
 sciences are advancing with wonderful rapidity in this 
 nineteenth century; — but our American common 
 school education has as yet, hardly felt even the discov- 
 eries of the seventeenth. I would at least bring them 
 up to the position of that era. 
 
54 '*' TRUE ORDER OF STUDIES. 
 
 CHAPTER VI. 
 
 Physics. 
 
 THE CHILD learns from its earliest experience 
 some of the mechanical properties of matter ; 
 his muscular movements, which are the earliest phe- 
 nomena to call his attention to the existence of Space 
 and Time, are accompanied also by a sense of the ex- 
 ertion of power, and of an external resistance to that 
 exertion. The introversion of consciousness upon his 
 exertion does not take place until after his distinct ap- 
 prehension of the resistance. The degrees of resist- 
 ance soon give him conception of the gaseous fluid 
 and solid states of the body ; its fixity or mobility, 
 rest or motion. At the same time, sight, touch and 
 hearing are giving him with his primary conception of 
 the shape of different objects, ideas also of light, dark- 
 ness, and color ; of heat and cold also ; and of smell, 
 taste and flavor. All these sensations lead to new 
 knowledge, capable of scientific development ; which, 
 however, comes later than that in mathematics. 
 
 Frobel's kindergarten gifts are excellent in giving 
 the first ideas of physics as well as mathematics. All 
 good things are, however, capable of perversion, and 
 there is danger in his system, as in all others, of fall- 
 ing into a routine ; endeavoring to bend nature to our 
 
PHYSICS. 55 
 
 system ; instead of making our practice conform to 
 nature. The teaching of nature is incidental and 
 infinitely varied. By incidental I mean what may 
 be, less reverently, called accidental ; it is teaching by 
 the occurrences of the hour. The mind naturally 
 passes from this to regular and systematic study ; and 
 we obey the law of our native intellectual power, in 
 preparing scientifically arranged elementary text books. 
 Nevertheless the earliest teaching of nature is inciden- 
 tal, and it will be found that in no other way can we 
 begin the study of the sciences successfully in our 
 schools than by incidental teaching ; teaching in which 
 the teacher's active and trained mind leads the child 
 to gain knowledge from the passing events of each 
 moment. This is the true spirit of what has been 
 called object teaching ; which I have seen degenerate 
 in the hands of a dull and lifeless teacher, into a 
 routine as worthless, as any stereotyped text book. 
 
 When the child of seven or eight years old is 
 building with Httle wooden bricks, upon his covered 
 desk, the teacher will, for example, have the oppor- 
 tunity to make clear, to the school, some of the principal 
 properties of the centre of gravity, and of the states 
 of stable and unstable equilibrium. He will not give 
 the children those phrases, but will lead them to see 
 that if the centre of a brick, or of a mass of bricks, is 
 not supported by something directly under it, it must 
 fall ; he can make them see that if this support is 
 narrow, the mass is easily overthrown, if broad it 
 stands. He also will lead them to a practical recogni- 
 tion of the analytical condition of stable equilibrium ; 
 
56 TRUE ORDER OF STUDIES. 
 
 that if on a slight disturbance, the building returns to 
 its former position, it is stable. 
 
 The laws of elasticities also, and the reflection of 
 motion, may be exemplified by the rebound of balls, 
 the return of echoes, and the use of mirrors. At the 
 age of eight or ten years, the average pupil will see 
 and appreciate the difference between the more per- 
 fect elasticity of his marbles, and the less perfect of 
 his balls ; the perfect reflection of light in straight 
 lines, and the readily refracted ray of sound. The 
 games with balls and marbles, illustrating geometri- 
 cally the parabola, and the ellipse, give us also the 
 opportunity for incidental instruction concerning the 
 composition of forces, the effects of an accelerating 
 force, the ratio of momentum to velocity, and the like. 
 We have referred to the effect upon a boy's mind of 
 the truth that a chain supported by its ends can be 
 straight only when vertical ; a similar effect is pro- 
 duced when he is led to see that the path of a pro- 
 jectile can be straight only when it is a perpendicular 
 straight line. 
 
 Some of the principal laws of optics, of acoustics, 
 and of thermotics can be advantageously given to the 
 child in this incidental way. The optical toys, which 
 are in almost every household ; musical instruments, 
 burning glasses, and the phenomena of dew, rain, 
 frost, and snow, give the teacher abundant opportu- 
 nities. The lightning, the refractory state of the hair 
 in dry cold weather, toy magnets, the electric fire 
 alarm, — give occasions for incidental instruction in 
 electricity and magnetism. 
 
PHYSICS. 57 
 
 In giving this instruction tell the child only what 
 you really know, and never be ashamed to confess 
 your ignorance. Lead him, if possible, by judicious 
 questions to see for himself ; — when not possible, tell 
 him clearly, what is clear to you, and confess ignor- 
 ance as to the rest. A popular scientific chattering 
 upon a subject is worse than a total neglect of it. 
 I have heard a lecturer, to whom a hundred dollars 
 was paid for his evening's instruction, tell an audience 
 that zinc was decomposed by sulphuric acid, and 
 hydrogen evolved ; that a certain insect in the sea 
 ran a circular saw at 60,000 revolutions a second, to 
 cut up its prey ; that he had made a gyroscope, 
 weighing a pound, run so fast as to weigh but five 
 ounces. A text book on Familiar Science, said to 
 have sold to the amount of nearly 200,000 copies in 
 the United States, gives, among other trash, as an ex- 
 planation why soap destroys grease, the statement 
 that grease consists of oleine and stearine, and that 
 " when soda or potash is mixed with it, the oily 
 principle flies off, and the stearine is converted into an 
 oxide of potassium, which is perfectly soluble in 
 water." Such instruction as this would be improved 
 by the substitution of Foote's celebrated passage ;• 
 " So she went into the garden to cut a cabbage leaf to 
 make an apple pie, and, at the same time, a great she 
 bear, coming up the street, pops its head into the shop. 
 What, NO SOAP ? So he died, and she very impru- 
 dently married the barber ! " The absurdity of this 
 would be laughable ; of that, is lamentable. 
 
 One of the earliest studies^ commencing perhaps 
 
58 TRUE ORDER OF STUDIES. 
 
 at the age of seven years, should be geography. Two 
 modes of beginning are open to you. The first 
 was developed in Woodbridge's geography. You 
 begin with the school room and draw a plan of it on 
 the blackboard, being careful to put the north side of 
 the plan up, as that is the mode universally adopted 
 in maps. While looking at the plan, and when study- 
 ing maps, the young child should always turn in his 
 seat until he faces north ; the older child, who has 
 learned to " orient himself " may face in any direction. 
 When the plan of the school room is understood, 
 draw around it the plan of the school yard ; let the 
 children copy it ; question them upon it, and be sure 
 that it conveys to them the correct impression. Let 
 them measure the dimensions of the room and yard, 
 and draw the plan to various scales. Add now, to 
 the plan drawn on a small scale, the map of the 
 neighboring roads and streets, and let the pupils indi- 
 cate on the map the position of their own houses. 
 Proceed thus gradually to show them the map of the 
 county, of the state, of the United States and of 
 North America, and then lead them to the globe. 
 
 The ether method is the one which I have usually 
 pursued, which is, to begin with astronomy. The 
 heavens catch the child's attention early, and he wishes 
 to know about the sun, moon and stars. The only 
 answer that can be made to his inquiries, in this age 
 of the world, is to explain to him that they are large 
 balls, and to tell him of the points of resemblance, of 
 the moon and planets to this terrestrial ball. Then 
 show him a globe, (being careful to have the pole 
 
PHYSICS. 59 
 
 pointing towards the real pole in the heavens, and your 
 own meridian uppermost,) and lay a marble upon it. 
 Explain to him that the earth is a large ball or globe, 
 under the little globe, as that is under the marble. 
 The immense magnitude of the great globe he cannot 
 as yet imagine ; and at first you must be content to 
 see that he understands its form and motion. Set the 
 globe (rectified as before) with the marble upon it, in 
 the window seat, where the sun may shine upon it, 
 and draw his attention to the fact that the light and 
 shadow on the marble and on the globe are similarly 
 situated, then tell him that the light and shade 
 fall on the earth as they do on the marble and 
 on the globe, making night in the shadow, and day in 
 the sunshine. Explain how the reflection from the 
 globe diminishes the intensity of shadow on the 
 marble ; that reflection from the window seat partially 
 enlightens the under side of the globe. Make the 
 amount of reflection from the window seat more ap- 
 parent by conveying it alternately with a black veil, 
 and a white handkerchief. Now explain to them that 
 "the earth hangeth upon nothing," floating free in 
 space like a bird in the air ; and that is the reason 
 why the night is so much darker than the under side 
 of the little globe ; namely, because there is no win- 
 dow seat under the earth to cast a reflection upon 
 our antipodes ; except when the moon acts in that 
 office. Take the children out, (in the morning, when 
 the moon is in its last quarter ; or afternoon, when she 
 is in the first quarter) and placing a globe, ball, or 
 marble, in the sunshine, on top of a fence or post, let 
 
60 TRUE ORDER OF STUDIES. 
 
 the children successively place their heads in a posi- 
 tion to project the globe against the moon ; they will 
 then see the light on the globe will take the shape of 
 the moon. Call also their attention to the fact that 
 the moon is of the same brightness, by day, as a white 
 cloud. This will give them a visible demonstration 
 that the sunlight falls on the planetary bodies, as it 
 does on the marble and the globe. 
 
 Now explain to the child the figures on the globe ; 
 which is meant for land, which for water : and show 
 him his own country and the situation of his own 
 town ; — still remembering never to direct his atten- 
 tention to the globe until it is rectified, (bringing the 
 school house to the top of the globe, and making the 
 North Pole point north). Give him brief descriptions 
 of the character of various nations, and the climate of 
 their countries, and show him how to point towards 
 them, by putting a pencil point on top of the globe 
 pointing through it to the given country, and explain- 
 ing that the pencil also points through the real earth 
 to the real country. The magnitude of the world may 
 also be given, (the great circle being 40,000 kilometers, 
 and the diameter being 12725 kilometers) by showing 
 how long it would take for an express train at 50 
 kilometers an hour to go round ; and how long to go 
 at a slow walk of 5 kilometers. Invite the children 
 also to go with you to the point where the most dis- 
 tant point can be observed, and show them on your re- 
 turn to the school house, that the panorama seen from 
 that place is covered by a very small spot on the 
 globe. Describe to them the highest mountains in 
 
PHYSICS. . 6l 
 
 the world, and when you have led them to their live- 
 liest conceptions, take them up the steepest possible 
 hill, and climbing far enough to show them some 
 town 1 2 or 1 5 miles distant, point out to them how small 
 upon the globe would be the circle of their vision. 
 [The square root of seven quarters of the elevation 
 of the eye, in feet, is the radius of the circle of vision 
 in miles. The square root of fifteen times the eleva- 
 tion in metres is the radius in kilometers]. 
 
 Place again the marble upon the surface of the 
 globe, (choose a mottled or marked marble,) and hold- 
 ing it there, show them that the rotation of the globe 
 rotates the marble with reference to the sun, but not 
 with reference to the globe ; that the marble is, like 
 the globe, now this side up, now that, as the globe 
 rotates ; but the marble keeps always the same side to 
 the globe. Show them that in like manner if the 
 globe stands with the same side constantly down, that 
 is, towards the earth, then if the earth rotates, spins 
 round, the globe, and the marble, balanced on top of 
 it by aid of a few grains of dust or crayon, will spin 
 with it. Propose now to see whether the earth is 
 rotating ; by placing the globe (always rectified) in 
 the sun shine, noting where the sun light falls, 
 and coming at the end of the next half hour or hour 
 to see whether it has moved. When the children 
 have thus seen for themselves that the little globe is 
 rotating under the sun at the rate of 15^* an hour, and 
 the marble at the same rate, show them that the cause 
 of it lies in the great globe rotating at the same 
 velocity. But let them see that this angular velocity 
 
62 TRUE ORDER OF STUDIES. 
 
 implies a greater speed in the surface of the great 
 ball, 1 200 kilometers an hour, or nearly that, accord- 
 ing to the latitude, — forty times railroad speed ; so 
 fast is their school house constantly whisking east- 
 ward. 
 
 Now show them that by placing the globe, (rectified) 
 in the sunshine they can see for themselves just 
 where the sun is rising, where it is setting, where it is 
 on the meridian, where vertical, and so on ; see it on 
 the globe, and thus know it concerning the earth ; 
 they will be greatly charmed, if you are fortunate in 
 having a position for the globe in which it can remain 
 some hours in the sun, showing them from hour to 
 hour, as they return to it after other occupations, what 
 countries are having sunrise, and what sunset. Their 
 attention should always be called to the poles, one 
 lying in darkness, the other in light, all day long. 
 These lessons, with the smallest kind of globe, should 
 be repeated in every month of the school year ; and 
 thus the scholars would gain precise conceptions of 
 the meaning of the arctic circle, the tropics and 
 equator, the causes of the changing seasons, and other 
 matters of astronomical geography, more surely and 
 accurately than in any other way. Especially care 
 should be taken, for this end, to give the lesson at the 
 equinoxes and solstices. 
 
 From the globe, the transition to maps, and to 
 detailed geography or topography is easy ; and in 
 country schools may be made intensely interesting to 
 children by occasional walks. The natural objects 
 actually found are the best text books ; the brooks 
 
PHYSICS. 63 
 
 and rivers, the various soils, and rocks, the diverse 
 kinds of vegetation, the roundness of the earth as 
 seen in the curve of water Unes, and the dip of the 
 horizon if you cHmb a hill ; these and many other 
 points will readily be observed by a child when 
 pointed out; and they may early be taught also to 
 perceive the increased beauty given to the landscape 
 by the illusion which invariably exaggerates vertical 
 heights andunder-estimates horizontal distances. Show 
 them that this makes the relief maps, with their ex- 
 aggerated elevations, so true to the feeling of nature. 
 Let them also learn a similar lesson by building clay 
 models of the hills in their neighborhood, upon a true 
 and then on an exaggerated vertical scale. 
 
 Further lessons in Astronomy should be given by 
 procuring a ball, of a little over one quarter the 
 diameter of the globe, and holding it about no times 
 its own diameter from the globe. At this distance, 
 it will appear to an eye held close to the globe, of the 
 same size as the moon, and held in the sunshine may 
 be made to imitate the moon's changes. The en- 
 deavor, both in geography and astronomy, should be 
 to lead the child's mind away from the illustration to 
 the thing illustrated. It is annoying to see, in some 
 of the best geographies, a picture of the earth float- 
 ing among clouds, some of which are larger than the 
 diameter of the earth. Such a picture will make it 
 more, instead of less, difficult for the child to get a 
 vivid conception of the real facts, — that the atmos- 
 phere and clouds make a covering about the earth, 
 about as thick in proportion as the coating of varnish 
 
64 TRUE ORDER OF STUDIES. 
 
 about his globe ; that the highest mountains, and the 
 deepest deep-sea soundings, are but like the uneven- 
 nesses in the grain of the paper with which the globe 
 is covered. Astronomy is the most powerful among 
 the sciences, in developing clearly the imagination in 
 space, and its primary facts may therefore be given 
 to children many years before they can understand 
 the processes by which we have arrived at a knowl- 
 edge of these facts. 
 
CHEMISTRY. 6$ 
 
 CHAPTER VII. 
 
 CHEMISTRY. 
 
 CHEMICAL relations are evidently more ab- 
 struse than mechanical. It requires some 
 maturity of mind to distinguish chemical compounds 
 from mere mechanical mixtures ; and yet the simplest 
 chemical phenomena begin to excite a child's curiosity, 
 by the time that he is ten or twelve years old ; and it 
 will be greatly to his advantage if his curiosity is 
 gratified by correct explanation and sound principles, 
 instead of being lulled by plausible pretences at ex- 
 planation. Oxidation, especially in its two forms of 
 the combustion of fuel and the rusting of metals, is 
 the most prominent instance of chemical metamor- 
 phosis that the child will notice. A skilful teacher 
 will find in the famiUar examples of this metamor- 
 phosis almost daily opportunity for incidental instruc- 
 tion in the fundamental principles of chemical 
 affinity, atomic proportions, stability or instability of 
 compounds, &c. We acknowledge that this implies 
 a large amount of intellectual life in the teacher, but 
 one who is intrusted with the direction of these 
 earliest movements of the expanding mind should be 
 a person not only of some acquirements, but of some 
 intellectual vivacity ; of ability to seize upon the right 
 
^^ TRUE ORDER OF STUDIES. 
 
 occasion and right moment to make permanent 
 lodgment of a truth in the child's mind, and give the 
 child a new ability to find truth for itself. There is 
 always danger of a bungling teacher's extinguishing the 
 child's thirst for knowledge. This may be done by 
 diverting the attention at the moment when interest 
 has been aroused ; by discouraging with difficulties, 
 by disgusting with tedium ; or by puffing the child 
 into a conceit that he has learned all, when he had 
 really only mastered the merest rudiments. The 
 great art in instruction is the same as, in letter writing, 
 according to Weller, to make the recipient "wish 
 there was more of it." 
 
 A boy leaves his knife out in the rain, and brings 
 it in red with rust, another takes a nail out of the fire, 
 and finds it nearly all converted into black scales. 
 The anthracite is converted, in the fire, into a color- 
 less air which flies up the chimney, and a few ashes ; 
 but about the fire blue blazes are seen. The com- 
 bustion is effected by a double process on part of the 
 coal, first converting it into one kind of gas, then into 
 another. The iron is oxidized, into black scales by 
 the fire, into red powder by the dampness. The child 
 has thus before him two examples in which two differ- 
 ent compounds are made with the same simples, and 
 can readily deduce from them important corollaries. 
 First, that the same element, iron for example, may 
 be concealed under various forms ; he sees the metal, 
 the black oxide, and the red ; and can readily under- 
 stand when you show him pyrites, copperas, black ink, 
 and other instances in which iron lies in a concealed 
 
CHEMISTRY. 6/ 
 
 form. Secondly, that substances diverse in appear- 
 ance, may consist of precisely the same elements, in 
 different proportions. Thirdly, that the variation of 
 proportion is not unlimited, but limited to a few 
 definite proportions ; the black oxide always contain- 
 ing 777 per cent, of iron, and the red oxide always 70 
 per cent. Fourthly, he can be told and understand 
 that the element which is united with the iron in 
 these oxides, is the same as that which unites with 
 the coal and burns it, that rusting is a slow burning. 
 By dropping iron filings in the candle blaze he can 
 see that the iron may be made to burn fast, and 
 brilliantly. The old fashioned flint and steel, may 
 show the same thing, and also illustrate and demon- 
 strate that heat is a mode of a motion ; the friction of 
 the flint scraping off a fragment of steel, so rapidly that 
 the motion of the flint produces a violent vibration in 
 the little particles of the fragment, which vibration is 
 heat. Fifthly, he can see that a gas, like oxygen, 
 may make a solid compound with iron, a gaseous 
 compound with coal. Sixthly, he can thus rise to the 
 generalization that all bodies may be considered, like 
 water, capable of existing in the three forms; solid, fluid 
 and gaseous. Seventhly, he can be told how univer- 
 sally and abundantly diffused is this element of 
 oxygen, constituting one fifth of the air, eight ninths 
 of the water, and one half of the solid crust of the 
 earth. Such are a few of the chemical lessons which 
 the young child can be led to be interested in, and to 
 learn, from the familiar incidents of burning and 
 rusting. Many other daily occurrences may lead to 
 
6S TRUE ORDER OF STUDIES. 
 
 as valuable incidental instruction on other chemical 
 facts ; and prepare the pupil for the higher branches 
 which are to follow. 
 
 It will be observed that all these lessons concern- 
 ing difference and identity, unity and multiplicity, 
 definiteness of proportion, and limited numbers of com- 
 pounds, imply clear arithmetical conceptions, and 
 that therefore arithmetic precedes chemistry in 
 the hierarchy. The higher branches of chemical 
 philosophy will also demand geometry. Few bodies, 
 for example are absolutely amorphous, and the know- 
 ledge of crystalline forms, if nothing else, is required 
 in distinguishing chemical compounds. Remember, 
 in every branch to teach humility, and let the child see 
 that he is getting only glimpses of a boundless field. 
 
MINERALOGY. 69 
 
 CHAPTER VIII. 
 
 MINERALOGY. 
 
 A PRELIMINARY knowledge of the meaning 
 of chemical relations having been acquired, the 
 pupil is ready to classify the substances actually found 
 in nature. In the " Evenings at Home " of Dr. Aiken 
 and his sister, are some admirable examples of early 
 lessons in mineralogy, botany and zoology. The 
 " Harry and Lucy " of Maria Edgeworth contains 
 equally valuable lessons, and a school teacher may 
 find aid in learning how to present scientific truths to 
 the child from these works. 
 
 Among the early incidental teaching in miner- 
 alogy will be the introduction to the group of metals ; 
 those anciently known, together with the modern 
 platinum, nickel, antimony, bismuth, and aluminium, 
 can readily be furnished to every school house. 
 Alloys may be shown in sufficient number to illustrate 
 their nature; especially brass, bronze, pewter, and 
 other commercially important mixtures. The mode 
 of obtaining these metals, from their ores, and the 
 chemical nature of their ores ; mechanical properties, 
 uses in the arts, and in medicine ; history of their 
 discovery, and the like will furnish many topics for 
 conversation. The usefulness of iron alone, will 
 
70 TRUE ORDER OF STUDIES. 
 
 furnish food for many hours at different times. The 
 rarer metals may less seldom be shown ; but some 
 of them, as sodium, potassium, calcium, lithium, 
 osmium and iridium, will be so naturally suggested 
 to the teacher's mind, by familiar objects in the school 
 room that she can hardly avoid telling the children 
 something about them. 
 
 When a school is situated in the country, especi- 
 ally when that country is rich in a variety of minerals, 
 the scholars should be invited to bring, to the school 
 room specimens of all that they can find in their 
 Saturday rambles. The different kinds of rock and 
 earths, should be referred to their nearest species ; 
 and the uses of each kind, in building, plastering, 
 making brick, farming, and so on, should be explained. 
 There will always be some one in the school district 
 or in the town to whom the teacher can apply for 
 information if the child chances to bring in an un- 
 recognised specimen. When the mineral is crystal- 
 line in its form, be careful to draw the attention of the 
 pupil to its precise shape, even to the minutest 
 feature. When the mineral is amorphous call attention 
 to that fact. 
 
 Gases do not present, in visible natural forms, any 
 great variety ; but the four or five elements constantly 
 found in the atmosphere, with one of which his 
 chemical studies began, may be described. 
 
PHYSIOLOGY, 71 
 
 CHAPTER IX. 
 
 PHYSIOLOGY. 
 
 THE legislatures of our various States, and even 
 their Committees on Education, are not infallible. 
 To require instruction in physiology in the common 
 school, as ordinarily constituted, is to require babies 
 to make bricks, and that without straw. The super- 
 ficial thinker, readily perceiving the mode in which 
 arithmetic is applicable to practical life, exaggerates 
 the value of the study as a means of education, and 
 defeats his own end ; not even teaching the child to 
 cypher as well as he would do, were arithmetic con- 
 fined to its proper narrow boundaries. In like man- 
 ner because the application of human anatomy and 
 physiology to the practical care of the health, is ob- 
 vious, many teachers and legislators have pressed with 
 great zeal the introduction of those studies into the 
 primary schools. But the study of the human body 
 and its functions can be made much more effective, 
 more interesting, and more valuable, if it is preceded 
 by lessons upon zoology and botany. In the order of 
 nature, the plant lives upon inorganic food, and the 
 study of vegetable physiology, must come after the 
 study of mineralogy ; the animal lives upon the plant, 
 and vegetable physiology must precede animal. In 
 
*J2 TRUE ORDER OF STUDIES 
 
 the order of nature the child's attention is most forcibly 
 attracted by what is external ; and by what is foreign 
 to his own body, before it is by his own members. It 
 is an unnatural, an injurious thing to turn the child's 
 attention too early to the functions of his own organs. 
 A better result, both intellectually and morally, will 
 be attained, if the teachers and parents take care of the 
 diet and exercise of the child ; his clothing, and the 
 temperature and ventilation of the rooms in which he 
 'sleeps and studies ; at least until the age of thirteen 
 to fifteen years. It must be confessed that teachers 
 and parents are themselves sometimes terribly ignor- 
 ant, or perverse, upon such subjects. I have seen, 
 highly educated and cultivated people urging mere in- 
 fants to eat rich cakes and scalloped oysters ; and 
 giving cakes and candies to older children between 
 meals. Nevertheless the cure for such terrible abuses 
 is not to be found in teaching physiology to children, 
 but in teaching it to young men and young women, 
 before they have the care of children providentially 
 intrusted to them. 
 
 The mind must be prepared for understanding 
 physiology, by previous instruction in botany and 
 zoology ; and the observing powers being at the same 
 time thus developed, will prevent the danger that the 
 introduction of anatomy and physiology will lead to 
 premature and excessive habits of mental introversion. 
 The study of one's own body approaches nearer to 
 psychology, forming a natural introduction to it ; and 
 should, therefore, come last among the studies of 
 Natural History. I mean to say that the study of 
 
PHYSIOLOGY. ;r3 
 
 human anatomy and physiology naturally and inevit- 
 ably leads a child to make psychological investigations 
 into the facts of consciousness, involved in the exer- 
 cise of the functions of his own frame ; and this is not 
 a wholesome process for him before the age of four- 
 teen or fifteen years, if even so early. 
 
 4 
 
74 TRUE ORDER OF STUDIES. 
 
 CHAPTER X. 
 
 BOTANY. 
 
 INASMUCH as botany, although it depends upon 
 chemistry in its physiological department, classifies 
 plants solely by their texture and form, some knowl- 
 edge of the common weeds, and flowers, the trees, 
 grasses, mosses and Uchens, of the neighborhood, may 
 advantageously be given to a child as soon as it is old 
 enough to distinguish them. Even in the cities the 
 shade trees, gardens, and yards offer an opportunity 
 for gathering specimens. In walking from Franklin 
 street, through Arch to Summer street, Boston, — not 
 more, I suppose, than 125 or 150 meters, in thickly 
 frequented streets, — I saw thirteen different species 
 of plants, crouching against the foot of the walls, and 
 rooting between the bricks of the pavement. It was 
 thirty years since, and I do not recall them, but pre- 
 sume there were two or three mosses, two or three 
 lichens, as many grasses, and perhaps shepherds' 
 purse, knot grass, wild pepper grass and plantain, with 
 one or two clovers. Linnaeus is said to have found 
 8 1 species in a square yard. One might say of plants 
 what Professor Cleveland used to say of minerals : 
 " You can find almost any species in Topsham, if you 
 will look for it." 
 
BOTANY. 73 
 
 From the day that a child enters the sub-primary 
 school, I would have it receive oral instruction in 
 botany ; illustrated when possible, by living plants ; 
 if not, by pressed plants, or even by good drawings. 
 At first the child may be simply taught to recognize 
 different species at sight ; just as he knows a man, a 
 woman, a horse or a dog ; that is, he may simply learn 
 to say on seeing the plants : This is a sugar maple ; 
 this a Norway maple ; this is a lilac ; that a white birch; 
 this a white pine ; that a yellow pine ; this a sweet 
 violet ; that a bird-foot violet. Afterwards he may 
 have a sprig of sugar maple, and one of Norway 
 maple, given to him to study. Let the class look long 
 and carefully at specimens of two allied species, and 
 then try which one can point out the most, or the 
 most important, of the differences between the two. 
 
 In the first volume of Agassiz's Contributions to the 
 Natural History of the United States, he gives an 
 essay on the principles of zoological classification. 
 He shows that the animal world is first of all divided 
 into four distinct plans of structure. Zoologists who 
 believe in gradual evolution attempt to belittle the im- 
 portance and accuracy of this division into four plans, 
 but it rests on necessary mathematical foundations ; 
 and the glory of Cuvier will not pale before that of 
 Darwin. Each of these four great branches is, ac- 
 cording to Agassiz, divided into classes, according to 
 the means employed in carrying out the plan of its 
 structure. Each class is again divided into orders, 
 according to the general degree of complexity or sim- 
 plicity of the organization. Each order is again 
 
y6 TRUE ORDER OF STUDIES. 
 
 divided into families, distinguished from each other by 
 the general outline of their external form. Each 
 family is divided into genera, distinguished from each 
 other by the anatomical detail of the feet and mouth. 
 Each genus is divided into species, distinguished from 
 each other, by the difference of their relations to the 
 external world, and to members of their own species. 
 
 No botanist has done for plants what Agassiz has 
 thus done for animals. Yet there is, doubtless, a close 
 analogy in the principles of classification that must be 
 adopted in botany to those that hold in zoology. And 
 as in animals the easiest division for a child to recog- 
 nize is that of families, because it depends upon ex- 
 ternal form ; so among plants, the child will more 
 readily appreciate the likeness among members of a 
 well defined natural family, or tribe, than any other 
 botanical likeness. I have known a child of very 
 tender years, and not at all distinguished for accuracy 
 of observation, call a succory flower, at first sight, a 
 blue dandelion. 
 
 When, therefore, the child is able to point out 
 similarities and differences, from its own independent 
 observation, between different flowers which it brings 
 in, it may be taught to observe family likenesses ; to 
 see, for example, the relationship of the oak to the 
 hazel, in their catkins of staminate flowers, and the 
 involucre surrounding the nut ; or the kindred of the 
 alder to the birch in having both kinds of flowers in 
 scaly catkins, with two or three flowers under each 
 scale. The greatest care must be taken not to allow 
 the child to think that a few words embody all the 
 
BOTANY. TJ 
 
 points of resemblance which characterize a family. 
 He must ever be led to perceive the unity of each 
 organism ; that the oak and the hazel, for example, 
 differ from each other in every single point wherein 
 they can be compared ; yet have also a certain family 
 likeness in every part ; and his definitions simply 
 seize upon the likenesses that are easiest to describe, 
 not upon those which are most vital. 
 
 Much less should the child be encouraged or even 
 permitted to repeat formulas on such subjects by rote. 
 The very objects for which such studies are intro- 
 duced into our schools is defeated when the children 
 are allowed to commit the words of the text book to 
 memory. Yet so accustomed are some teachers to 
 this mode of instruction ; so incapable, apparently, of 
 conceiving of any better plan, that I have known 
 teachers to require their pupils to repeat the very 
 words of Dr. Gray's " How Plants Grow," and of my 
 own " First Lessons in Geometry." I have no doubt 
 that Miss Hale's "Our World," Miss Youman's 
 " First Lessons in Botany," and Prof. E. S. Morse's 
 "First Book of Zoology," are abused in the same 
 manner, so difficult is it for teachers to understand 
 that the natural objects themselves are the true text- 
 books ; and that the words written by men are 
 nothing in comparison with the lines of nature, whence 
 the true man of science gets all that he can record. 
 
 By having the children collect and bring to the 
 school-room the common flowers and weeds of their 
 neighborhood ; and by leading them to examine and 
 compare the flowers and seed vessels (and to some 
 
yS TRUE ORDER OF STUDIES. 
 
 extent the foliage also), they can, without the slightest 
 strain upon their mind, or memory, before they are 
 fourteen years old, be taught to recognize at sight any 
 one of three or four hundred common species ; and to 
 refer the greater part of them, at once, to their natural 
 families, and recall the principal characters of the 
 family and its uses in the arts and in medicine. No 
 book need be placed in their hands. The teacher 
 should have Dr. Gray's books, and any others as ad- 
 juncts, to refer to as a basis of oral instruction ; but 
 the child should study the living plants, or dried ones, 
 or good drawings. I am speaking of the sub-primary 
 school ; the instruction of older pupils is less difficult 
 and less important. 
 
ZOOLOGY. 79 
 
 CHAPTER XL 
 
 ZOOLOGY. 
 
 ZOOLOGY is not forced upon the child's atten- 
 tion by nature so constantly as botany. The 
 plants stand to be examined at every step of his path- 
 way. Yet the motion of animals, and still more, their 
 intelligence, makes them more interesting and fascin- 
 ating to most children than plants. And although 
 physiology demands a knowledge of chemistry, yet the 
 classification of animals, like that of plants, depends 
 primarily upon their organic structure, their external 
 form, and upon their manifest relations to the exter- 
 nal world. A child of five years old is interested in 
 watching animals ; and I have even known a child of 
 half that age to watch insects and toads with the 
 closest attention, again and again, patiently observing 
 their habits ; and he may readily be taught to dis- 
 tinguish and name many of the creatures which he 
 thus observ^es. 
 
 In a country school-house, in the month of May or 
 June, it frequently happens that the notes of thirty or 
 forty different species of birds are heard in the course 
 of a single day. It would be no waste of time, but on 
 the contrary, a thing of inestimable value, should the 
 teacher enable his pupils to recognise each species by 
 
80 TRUE ORDER OF STUDIES. 
 
 teaching them to learn their appearance also and hab- 
 its ; and perhaps tell them the family to which each 
 belongs. 
 
 In teaching the names of birds and flowers there 
 is a great difficulty which we may as well boldly face. 
 When the child has learned to recognise a plant or an 
 animal at sight, it becomes almost a necessity to give 
 him a name for it ; if you do not, he will name it for 
 himself. But many of our familiar weeds and birds 
 have no common names ; the common names of many 
 are also very inappropriate. English names are given 
 to our American objects ; and when the child reads, 
 in his school-books, selections from English literature, 
 he brings up a wrong picture of American instead of 
 English scenery. Adults of some culture, are con- 
 stantly subjected to the same cause of error. In one 
 of Wilson Flagg's interesting volumes he confuses the 
 Roxbury Waxwork {Celastrus scandeiis) with Bitter- 
 sweet iySolamiht didcamara), attributing the medical 
 properties of the latter to the former ; and I have 
 known others hearing the Bittersweet (5. dulcamara) 
 called Deadly Nightshade, immediately assume that 
 it was Belladonna. Thus, also,' the name of Wood- 
 bine (fragrant monthly honeysuckle) is in this country 
 given to the Virginia creeper, which is a sort of five- 
 leaved grape ; the name robin is given to a thrush ; 
 the name ivy to a poisonous climbing sumac ; the 
 name pennyroyal to a plant which smells like it. 
 Other common names are worthless from either being 
 local, or from being differently applied in different 
 States of the Union. Thus, our American plant 
 
ZOOLOGY. 8 1 
 
 Gaultheria, is called in some sections Wintergreen, in 
 others Chequerberry, in others Pine Ivy, in others 
 Partridge-berry, in others Tea-berry. And the English 
 word honeysuckle is applied not only to the genius 
 and family of the Woodbine ; but in various parts of 
 the United States is given to Azaleas, Diervillas, Colum- 
 bines, and Clovers. In one of Emerson's poems he 
 speaks of " blinding dogwood " ; by which, as a New 
 England man, he means the poisonous Swamp Sumac ; 
 but a man of the middle Western States would be 
 greatly perplexed to know why Emerson should call 
 the beautiful flower and cornel "blinding." 
 
 The common names of fishes, and of birds are in 
 this country in the same state of confusion ; the fishes 
 perhaps even worse. Care should be taken with child- 
 ren to give them from their earliest acquaintance with 
 the plant or animal, a name which will not thus mis- 
 lead. Let them understand that our pennyroyal is 
 " American " and different from the European ; that 
 our lark is not the singing lark of which English poets 
 speak ; that our robin is not the robin-redbreast of the 
 old world, but is more like a thrush ; and that our blue 
 bird is nearer being a blue-breasted robin. I hardly 
 need say that the child should be taught to call a 
 columbine by its name ; and reserve the word honey- 
 suckle for the genus Lonicera and its closest con- 
 geners. Nor need the teacher fear giving, where there 
 is no good common name, the scientific name. Many 
 scientific names, (such as geranium, fuchsia, eschscholt- 
 zia, clarkia, abutilon, althea, syringa, rose, violet, 
 crocus,) are as familiar to lovers of flowers as any com- 
 
82 TRUE ORDER OF STUDIES. 
 
 mon names can be. If the child hears no other than 
 the scientific name he remembers it as readily as he 
 will an English name. 
 
 Poets have sometimes expressed the fear lest a 
 scientific acquaintance with nature should destroy its 
 beauty ; lest the song of the bird might seem less 
 melodious if you called the songster by a barbarous 
 Latin name. On the contrary, a closer acquaintance 
 with nature only increases the pleasure of one who 
 truly loves her. The beautiful in nature is always 
 more beautiful than it at first appears to us ; and if 
 we lose our appreciation of it, the fault is in us and not 
 in the object. '' Nature," says the Concord seer, 
 " never became a toy to a wise spirit." The wisdom 
 and beauty embodied in each specimen of organic life, 
 is "not only vast, but infinite"; so that there is no 
 possibility of the closest study exhausting it. 
 
 The insects in any given country are usually more 
 numerous, in species, than the plants. The mysteries 
 of insect transformation, the wonderful mechanical 
 instincts that many of them display, the brilliancy of 
 the colors of some, and the pertinacity with which 
 others thrust themselves upon the attention of man, 
 render insects peculiarly fitted to engage a child's at- 
 tention, and to serve as a basis for *' incidental " in- 
 struction in zoology. In this class of animals the 
 orders are more conspicuously distinguished than the 
 families ; and for conv^enience, in talking about the 
 specimens which are brought in, it may be best to 
 group them at first simply in orders. They are, in • 
 general, easily preserved, and I would have, in every 
 
 4* 
 
ZOOLOGY. 83 
 
 primary school, a collection of the most common 
 species of the neighborhood, scientifically arranged in 
 boxes with cork bottoms and glass tops. These would 
 be better than books, to serve as a reference for any 
 insects which the children might catch and bring in. 
 
 The field of zoology is vast, and even entomology 
 is more than sufficient to occupy a lifetime. Yet on 
 account of this very magnitude of the field, the child's 
 attention should be early directed to it ; so that, if it 
 be one for which he proves peculiarly adapted, he 
 may have the advantage of an early beginning. But 
 whether he pursue it in after life or not, the study of 
 zoology and botany in the earliest years is important 
 for the intellectual disciphne which it gives. In the 
 erroneous education of the present day, intellectual 
 discipline is supposed to be needed only for the 
 reasoning powers ; whereas it is needed for all the 
 faculties ; the observing and the imaginative as well 
 as the reasoning; and should be given in that order, 
 the child being first of all taught to observe, to see 
 with the outward eye. The main object of these first 
 lessons in natural science is to induce the spirit of 
 patient exactness in observation ; calling the child's 
 attention to differences as carefully as to likenesses, 
 and to the fact that likeness in one part my co-exist 
 with diversity in another ; that the likeness may be 
 conspicuous and the difference obscure ; or on the 
 other hand, the differences obvious, and the likeness 
 in miniature. Nevertheless, while the main object is 
 to cultivate a spirit of observing patiently and accu- 
 rately for oneself, a second object is not to be lost 
 
84 TRUE ORDER OF STUDIES. 
 
 sight of ; which is to place incidentally,, as opportunity 
 offers, before the mind of the pupil, general principles, 
 already discovered, and firmly established by the 
 inductive philosophy ; principles which may assist the 
 pupil in the guidance of both his sense and his reason, 
 in his future studies, and in his daily business. 
 
 The evils of introducing the child too early to the 
 consideration of human physiology have been already 
 mentioned. Comparative anatomy will be usefully 
 introduced to his notice much earlier. The homology 
 of the parts in vertebrate animals with those of his 
 own body, forces itself on the attention of the youngest 
 child who plays with a kitten, or watches a toad. He 
 may readily be led to see the homology in the more 
 remote forms, even in the fishes, while the difference 
 between the limbs of the vertebrates, and the organs 
 of locomotion in the invertebrates must also be care- 
 fully pointed out. Thus these studies will gradually 
 develope, without conscious effort on the part of pupil 
 or teacher, a power of judgment and of reasoning in- 
 dependent of forms of language. 
 
 Prominent among the reasons why the studies of 
 Natural History should be introduced into the primary 
 schools, is the fact that it accords with the usual tastes 
 of children, as well as with the natural order of intel- 
 lectual development. Children are always interested 
 in looking at crystals, plants, flowers, insects, shells, 
 birds, and beasts ; they are interested in intellectual 
 and spiritual truths only when dressed in living 
 figures. They cannot understand the thing signified 
 unless they first know the facts through which it is 
 
ZOOLOGY. 85 
 
 signified. Nature, like the Gospels, speaks in para- 
 bles to those who cannot understand the truth in other 
 forms ; and children are pleased and instructed when 
 allowed and encouraged to read those parables for 
 themselves. Nor is there any purer, or more perman- 
 ent source of happiness and of wisdom that can be 
 opened to them, than this habit of reverently reading 
 for themselves, the lessons of nature. 
 
 The principles which I am endeavoring to apply in 
 what I say of the subprimary and primary schools, are 
 easily applied to the whole course of liberal education; 
 — by liberal education I mean that education which 
 fits one for the social and • political duties of a free- 
 man ; without rigorously excluding every thing that 
 might be considered as professional training. For 
 liberal education, the course of physics should, in 
 proportion as the pupils mind enlarges, deal gradually 
 more with general laws, and less with the details by 
 which those laws are established. The ability and 
 habit of patient and exact observation having once been 
 gained, then the wider and more general the princi- 
 ples which you give your pupil, the more practically 
 useful will your teaching be. This is the true method 
 of the Novum Organum ; asceiidendo ad axiomata, de- 
 scendendo ad opera. Physics and Natural History were 
 thirty years ago unjustly neglected in our general 
 education ; there is danger to-day lest, in the reaction, 
 they are allowed to claim an unjust portion of atten- 
 tion. They belong, as means of liberal education, to 
 the schools more truly than to the colleges ; in the 
 latter their place is rather as a part of philosophy. 
 
S6 TRUE ORDER OF STUDIES. 
 
 than as a training in observation. History, literature, 
 politics, psychology and theology are the more appro- 
 priate studies for a collegiate course. 
 
 In the grammar and high schools, after a proper 
 preparation in the younger grades, we can readily give 
 as much of the mechanical sciences, and sciences of 
 natural history, as it is profitable to teach to those 
 who have no special aptitude for the studies. I ac- 
 knowledge that this is impossible with the prepara- 
 tion now given in the primary and subprimary 
 schools ; and that, therefore, a part of the collegiate 
 course is necessarily occupied in giving instruction in 
 the physical sciences, better adapted to children than 
 to youth. The preparation of such excellent text 
 books as Guyot's Earth and Man, and of Agassiz and 
 Gould's Zoology is thus rendered a thankless task ; 
 these books, adapted for the widest usefulness in high 
 schools, are, by the insufficient preparation of the 
 younger scholars, confined to a few of the most ad- 
 vanced institutions. Within a few years past, good 
 text books have been prepared in Geography, Botany, 
 and Zoology, for younger children, — very good, if they 
 be used, as some of the best were meant to be, by the 
 teacher alone, and the child have the globe, the plant 
 and the animal put into his hands for study. It is 
 absurd to attempt to teach from text books alone ; 
 and in the most modern style of text book, each sub- 
 ject is expanded so fully that the child who studies 
 his school text books has no time left in which to 
 play, much less any time to study nature ; and the 
 teacher who examines the pupil, in so called recita- 
 
ZOOLOGY. 87 
 
 tions, sufficiently to know whether it has studied the 
 whole of the text book, has no time left in which to 
 teach anything. 
 
 Changes in the system of public education are 
 usually made with difficulty ; and it is, doubtless, well 
 that it is so ; since, otherwise, our schools would 
 suffer, even more than at present, from the eccentri- 
 cities and errors of those who have control over them. 
 At present, the legal guardians of the school, the 
 teachers, the scholars, and the parents, constitute 
 four classes, who resist every change, whether for 
 better, or for worse. In the changes which I have 
 been advocating now for thirty years, the difficulty 
 has been greater from the fact that the proposed 
 alterations require an alteration from the very begin- 
 ing of the course, in the alphabet school. It must be 
 confessed that my scheme of high school instruction 
 is impracticable, unless the pupils have been from 
 their first entrance into the lowest school, trained in 
 habits of exact observation, and rapid, accurate con- 
 ception ; and taught to grasp and become familiar 
 with the results of sound inductive reasonino-s 
 
 So far from this being the case in ordinary schools, 
 we might more truly say that there the child is taught 
 to neglect observation, to withdraw his mind from any 
 healthy interest in things around him, to value 
 words above ideas, to repeat phrases to which he 
 attaches no meaning, to adopt the results of hasty and 
 unsound speculations. Even to the present day there 
 are very few schools into which minerals, plants, or 
 
88 TRUE ORDER OF STUDIES. 
 
 animals are ever brought for examination ; very few 
 teachers who themselves know the difference between 
 a moss and a lichen, a bug and a beetle, a moth and a 
 butterfly, or who would not reprove a child for bringing 
 such things into the school room ; in nearly all schools 
 the pupil is taught to spell, that is to deny the truth 
 of his own sense of hearing ; and this is done so per- 
 tinaciously and thoroughly that by the time that he 
 leaves the high school he hears in a spoken word 
 sounds that are not there, and fails to hear sounds 
 that are. Drawing has been largely introduced into 
 the schools within a few years, but not for the reasons 
 for which the soundest writers on education- have 
 urged it. Commercial, financial reasons have led to 
 its introduction ; in a form which, however valuable, 
 fails to give it its highest value ; it is drawing from a 
 copy, and thus but feebly exercises the observing 
 powers ; or it is inventive drawing, which does not 
 develop the observing powers at all. l^rithmetic was" 
 after a long struggle against the tyranny of grammar 
 introduced into schools, and has now become a king 
 stork more intolerable than a king log. It owes its 
 popularity to the obviousness of its practical applica- 
 tions ; but it is pursued, at the present day, princi- 
 pally as a premature drill of the reason, and thus the 
 practical end of learning to cypher is lost, with no 
 counter-balancing advantage ; and the study occupies, 
 in the ordinary school, at least double the time in 
 which it could be thoroughly acquired, if it were made 
 first a matter of direct sight, secondly, practised as an 
 
ZOOLOGY. 89 
 
 art, and lastly studied as a science. Geography is 
 the only study in the ordinary school which can be 
 called a science of observation, and even that is taught 
 as a matter of imagination, the things seen in the 
 ordinary school being words and maps, not the real 
 earth and sky. All these points show that the ordi- 
 nary schooling in the primary school gives no sort of 
 adequate preparation for scientific instruction in the 
 high and grammar schools. 
 
 For this reason, I occupy myself more especially 
 in indicating what I conceive to be the true time and 
 mode of beginning each branch of study. I pass by 
 the studies of the high school and the college, not from 
 want of interest in them, but from a conviction that he 
 who would produce the highest educational effect must 
 begin with the youngest pupils. Each days mental 
 state depends, in part, upon our previous education, the 
 mental development of to-day, depends in part upon 
 the education of yesterday ; and that of yesterday, 
 upon that of the day before. We must acknowledge 
 this, even if we do . not, with Herbert Spencer, con- 
 sider our mental development as the culminating 
 •result of the education of our ancestors through 
 countless generations. Moreover we must acknowl- 
 edge that a stronger impression is made upon a young 
 person than upon an old ; that, although one is never 
 too old to learn, he soon becomes too old to learn 
 easily. I simply would express my earnest conviction 
 that the best time for the cultivation of geometric 
 ability, and the power of observation, is in very early 
 
go TRUE ORDER OF STUDIES. 
 
 childhood ; that we do a grievous wrong to our young 
 children by drawing their attention from objects of 
 natural history, and things which they can handle, and 
 by forcing them to pore over a false alphabet, and 
 Arabic figures which have no interest for them. 
 
GEOLOGY. 91 
 
 CHAPTER XII. 
 
 GEOLOGY. 
 
 WHEN the pupil has some clear ideas concern- 
 ing the present condition of the earth and 
 the solar system, his natural instincts will lead him to 
 inquire concerning the ancient history of these bodies. 
 The majority of school-houses in the United States 
 are built upon the drift, or upon alluvial deposits. A 
 child of any activity of mind, brought up upon the 
 drift, will at a very early period perceive that the peb- 
 bles around him are fragments of rock, rounded and 
 worn smooth, by some, to him, unknown agency. The 
 boys with whom I played in my childhood were con- 
 tinually speculating concerning the rounded pebbles 
 of silex and jasper scattered over the red sandstone of 
 Central New Jersey. The children of Norfolk county, 
 Massachusetts are forever questioning concerning the 
 great lumps of pudding stone scattered over the 
 ground. In Ohio and other Western States, the 
 children, playing in the streets of the cities, stop to 
 ponder over the fossil imbedded in the Hmestone slabs 
 with which the sidewalks are paved. 
 
 It is only within forty years that any very satis- 
 factory answer could be given by teachers or parents, 
 to children questioning them upon these things. 
 
92 TRUE ORDER OF STUDIES. 
 
 When Agassiz first gave a rational answer to inquiries 
 concerning the drift, even the most learned geologists 
 refused to accept it, and clung to their inadequate, and 
 confused notions of water and floating ice ; which the 
 healthy intellectual instincts of children rejected as 
 wholly inadequate to explain the problem. But twenty 
 years of battle for the obvious truth was at length suc- 
 cessful, and the existence of a glacial period, as the 
 immediate precursor of the present epoch, is so well 
 established now, that there need be no hesitation in 
 o-iving; it to children as a fact. In like manner the 
 older truths, of the long succession of preliminary 
 ages, and of the deposits of mud, afterwards hardened 
 into stone, around animals which have long since 
 perished from the earth, may safely be given as facts, 
 more interesting than any fictions — 
 
 Through the window we are peering 
 
 Into ancient realms of shade ; 
 Lo ! instead of ghosts appearing, 
 
 Creatures, like the present made. 
 
 None of Pluto's fabled terrors, 
 
 Neither Sphynx, nor Harpies dire ; 
 
 Nor Chimaeras, (fearful errors !) 
 Lick up hell-born flames of fire. 
 
 No ! within these quiet places, 
 
 Daemons foul no vigils keep; 
 But a thousand dreaming races 
 
 Lie in an eternal sleep. 
 
 In old time, the Sun arisen 
 
 Made, for them, the world shine bright; 
 
 Now the rocks their forms emprison, 
 Closed in everlasting night. 
 
GEOLOGY. 93 
 
 So sings Oswald Heer ; and the child is as much 
 entranced with the new stories as with the old. Only 
 let due care be taken to distinguish as accurately be- 
 tween facts and imagination in the new forms* as in the 
 old. In Darwin's " Voyage of the Beagle " he closes 
 with an emphatic warning, which, it seems to me, he 
 himself, thirty years afterwards, entirely disregarded ; 
 an emphatic warning against the temptation, which 
 constantly assails the student of geology, to bridge 
 over the gaps of knowledge by loose and unfounded 
 speculations. His warning needs to be earnestly re- 
 peated at the present moment, to the teachers of the 
 young ; since his enthusiastic followers are constantly 
 assuming that his recent speculations are established 
 inductions and have the authority of science. There 
 are facts enough established in this science, — the 
 origin of fossils, the formation of ancient and modern 
 rocks, the origin of the drift, and of alluvial deposits, 
 the nature of the various coals, and coal oils, the for- 
 mation of continents, the direction of the great moun- 
 tain chains' and coast lines, and its connection with 
 the obliquity of the Ecliptic, the duration of the pre- 
 sent epoch, — to give to the child as incidental oppor- 
 tunities occur ; facts which will enlarge the scope of 
 his thought and imagination, and prepare him to re- 
 ceive new truths as they may be presented to him in 
 after life. 
 
94 TRUE ORDER OF STUDIES. 
 
 CHAPTER XIII. 
 
 COMMODITY. 
 
 OUR third great division of human science in- 
 cludes all that is historical, — all that relates to 
 man's action, what he has said and done. This di- 
 vision, as we have already said (p. 1 8 ) may be roughly 
 divided in four groups ; the first treating of man's use 
 of nature for commodity ; that is, for purposes of agri- 
 culture, manufactures or commerce. The second 
 embraces the fine arts ; the third, language ; and the 
 fourth, social life, custom, and law. The reasons for 
 this subdivision, and for the order in which the groups 
 are arranged, will be evident on a moment's thought. 
 The use of the world for our bodily needs is first in 
 order of time and of simplicity ; the earliest knowledge 
 that a child has of the work of man, as distinguished 
 from the work of nature, consists in knowing to what 
 uses man puts the material things furnished by nature. 
 We must, however, confess that this precedence is 
 logical rather than chronological ; since the child has 
 been in the world but a year or two before it uses 
 dolls, and pictures, that is, works of art, as naturally as 
 it does food or clothing. The invention of language 
 is more manifestly subsequent to the use of material 
 things ; and it is also manifest that the ability to com- 
 
COMMODITY. 95 
 
 mimicate ideas by language must precede every at- 
 tempt at social order or law. 
 
 Without historical knowledge, a child would grow 
 up a barbarian. The educated man, and the highly 
 civilized nation, are chiefly distinguished by their ad- 
 ding to the inheritance received from their fathers, a 
 knowledge of what that inheritance is, and how it was 
 gained by those who have transmitted it down the 
 ages. Yet the history of manufactures, commerce 
 and agriculture is seldom taught in the schools. Books 
 on trade, on commerce, on the economy of manufac- 
 tures, although recommended by many of the best 
 writers on education, have never enjoyed a wide popu- 
 larity. The great obstacle here, as in all the historical 
 branches, consists in the multiplicity of details which 
 seems to be involved. It is with difficulty that the 
 good teacher finds general principles cover the facts 
 of agriculture, manufactures and commerce ; and he 
 knows that a knowledge of general principles is the 
 only knowledge practically useful in the highest sense. 
 Instruction upon these matters remains, therefore, at 
 present, almost wholly '' incidental " ; and is received 
 in the family more than at school. A very young 
 child, is, however, greatly interested in, and benefited 
 by, even such instruction. In the cities, let him see 
 the planting of seeds and bulbs in pots, and watch the 
 growth of the plants in the school-room window ; in 
 the country let the same lesson be given in a bed in 
 the school yard. The processes of planting, watering, 
 weeding, loosening the surface, manuring, (in the city 
 with nitrate of ammonia), pruning, collecting the 
 
96 TRUE ORDER OF STUDIES. 
 
 seed, etc., will furnish abundant opportunities for the 
 most valuable incidental instruction ; concerning the 
 dependence of man and animals upon plants ; the uses 
 of the atmosphere and rains ; the right of man to re- 
 move plants when out of place ; the ethical objection 
 to a needless destruction of them ; the nature of the 
 dew, and of evaporation ; the arrangement of the leaves 
 to catch the light, the necessity of light for green- 
 leaved plants ; the adaptation of different plants to 
 different climates and situations ; the various parts of 
 plants used by man ; the modes of increasing the 
 yield, and of arresting the deterioration of soils. 
 
 Again, every one of the articles in household use 
 may furnish lessons concerning the mode in which 
 men bring the raw materials into subservience to 
 man's needs. The processes of grinding and bolting 
 wheat ; of fermenting and baking bread ; of planting, 
 tending, gathering, cleaning, carding, spinning, weav- 
 ing, bleaching, dyeing or printing cotton ; of tending 
 sheep ; of shearing and cleansing wool ; of spinning, 
 dyeing and weaving yarn into the various kinds of cloth 
 and carpeting ; of tanning leather and making boots 
 and shoes ; of manufacturing glass ; of digging and 
 smelting ores and working metals ; — in short, of pro- 
 ducing from the raw material any one of these articles 
 which the pupil daily sees and handles, — will furnish 
 subjects for valuable instruction ; even if the details 
 are forgotten, the general impression remains, of the 
 multiplicity of human industries, and the utter lack of 
 excuse for any man being a drone in this busy hive, 
 the earth. 
 
COMMODITY. 97 
 
 If the teacher is ignorant concerning such matters, 
 the school ought to be furnished with reference books, 
 Hke the Penny Encyclopedia, or Chambers', or the 
 American Encyclopedia, or at least with smaller books 
 prepared expressly for the young. Undoubtedly the 
 best mode of instructing a child concerning any of the 
 operations of the useful arts, is to allow him to see the 
 process going on ; and, whenever practicable, this 
 course should be adopted. It is not, however, always 
 convenient for a manufacturer to be interrupted by 
 visitors ; and in some places it would be dangerous to 
 allow children to pass among machinery arranged for 
 work, and not for show. But advantage should be 
 taken of those places where work can be seen without 
 interruption to the workmen ; and especially of indus- 
 trial exhibitions, and mechanics' fairs. 
 
 Beside the enlargement of mind, the extension of 
 the circle of ideas, the increase in the power of con- 
 ception, — which a child must gain from the examina- 
 tion of agricultural tools, labor-saving machinery, and 
 processes of manufacture — he will be likely to choose 
 his occupation in life more intelligently, and with a 
 more just reference to his own powers. The attrac- 
 tion which figured so prominently in the socialist's 
 theories, cannot have fair play and bring the young 
 man into his appropriate sphere of labor, if this op- 
 portunity has not been afforded him of knowing what 
 spheres are open to him. A history of inventions, a 
 book containing the first rudiments of agriculture, 
 " Babbage's Economy of Manufactures," and similar 
 works ought to be embraced in the child's reading. 
 
98 TRUE ORDER OF STUDIES. 
 
 Miss Edgeworth's " Harry and Lucy " answers toler- 
 ably in school iise ; also, the " Evenings at Home " ; 
 but I am not acquainted with any modern imitations 
 that handle these subjects well, although there are 
 several treatises which are better than nothing. 
 
ART. 99 
 
 CHAPTER XIV. 
 
 ART. 
 
 THE moment that man's bodily needs are satisfied, 
 he begins to express his feeUngs in art. Music, 
 and dancing, sculpture and painting, are as natural to 
 man as eating and drinking. The child of two years 
 old makes anything into a doll, and recognizes in the 
 rudest picture the designed resemblance to man or 
 dog, tree or house. Even the likeness to individuals, 
 in the photograph, is thus early recognized. At three 
 years old, the child begins to sing ; and readily 
 catches a melody. 
 
 In the kindergarten, the child begins at an early 
 age to model in clay ; and it would be a great boon 
 to our children could something cleaner than clay be 
 invented, sufficiently cheap to allow this feature of 
 Frobel's system to be adopted in all the public pri- 
 mary schools. 
 
 Drawing has of late years received increased at- 
 tention, and Walter Smith's system of instruction 
 seems to leave nothing to be desired as an introduc- 
 tion to drawing as an industrial art. For the pur- 
 poses of intellectual and artistic education it needs, 
 however, to be supplemented by drawing from 
 
100 TRUE ORDER OF STUDIES. 
 
 nature ; else it fails to exercise its peculiar power as 
 a stimulus to observation, to purity of taste, and to 
 appreciation of natural beauty. The leaves brought 
 in for botanical study, or even the pressed leaves, 
 kept in the school-house for types of reference, make 
 excellent copies for the young draughtsman ; as do 
 also the shells and insects, which ought to make part 
 of the common school furniture. The young ob- 
 server will not see the peculiarities of the natural 
 object, nor its graceful beauty, until he attempts to 
 copy it with the pencil. I have alluded to Agassiz's 
 saying that a lead pencil is an excellent microscope ; 
 Professor E. S. Morse, in his admirable First Book of 
 Zoology, expands the idea by saying that " a specimen 
 or figure may oftentimes be carefully studied, and yet 
 only an imperfect idea be formed of it ; but when it 
 has once been copied, the new points gained repay all 
 the trouble spent in the task.'' 
 
 The first lessons must, of course, be in copying 
 the simplest forms of leaves and shells ; afterwards, 
 the more complex forms ; then the insects. When 
 considerable facility in drawing has been obtained, 
 and the power of accurate observation gained, — 
 greater quickness of perception may be formed by a 
 process similar to that recommended in Arithmetic 
 and Geometry. A new leaf, or shell, may be ex- 
 posed to full view for a short time, shorter in propor- 
 tion to the proficiency of the class, and then covered, 
 while the class copy the outline from memory. 
 Drawing thus from nature, and especially from fresh. 
 
1 1, 1 5 > ) 
 
 1 l\ ' ' 1 J 
 
 ART. ^ \ ^ ^'A i ^ i'lo'i^^!: i\i J 
 
 living plants and animals, stimulates the pupil's 
 powers of observation and conception to vastly higher 
 activity, than drawing from copies ; giving him 
 greater pleasure, and greater increase of power. By 
 this means, progressive courses in drawing from copy, 
 and in invention from the suggestions of nature, will 
 be made much more profitable. 
 
 The real order of procedure in education has 
 never been so much neglected in music, as in the 
 other arts ; yet great advances have been made within 
 the past twenty years, and the most admirable results 
 obtained. Singing has been very extensively intro- 
 duced into public schools ; and, although in many 
 places a mischief has been done by requiring the 
 children to scream, and by misleading their ears with 
 a pianoforte, always out of tune, the mischief has been 
 overbalanced by the good. In other places, and 
 especially in Boston, the advantages have been gained 
 almost without a mixture of evil. The pupils are 
 taught to depend upon their own ears, to keep the 
 tones pure, soft and natural, to read the musical staff 
 as easily as a printed page, and to give the absolute 
 pitch as easily as they give the true vow^el or conso- 
 nant sounds of the language. The selections also in 
 the Readers aje made with correct taste, from stan- 
 dard authors. Were such instruction as that given 
 by Luther W. Mason in Boston, given in the schools 
 generally, it would be impossible to circulate the 
 books of psalmody and Sunday School hymns which 
 are now by their popularity a disgrace to our country, 
 and to our race, — from the flatness of their words and 
 
:I02 TRUE ORDER OF STUDIES. 
 
 their music. The great end of teaching art in the 
 public schools is not to create artists, but to give all 
 the pupils more enjoyment in a true appreciation of 
 art and of nature. 
 
LANGUAGE. 103 
 
 CHAPTER XV. 
 
 LANGUAGE. 
 
 THE Study of the very extensive group of histori- 
 cal sciences included under the name of lan- 
 guage, logically follows the study of labor and of art ; 
 we must know things before we can talk about them ; 
 and language logically precedes the study of law ; we 
 must communicate our ideas before we seek to enforce 
 them. But practically, in chronological order, the study 
 of language begins at the moment after birth, and 
 by the time that a child enters the public school, he 
 can talk somewhat fluently. The first point of in- 
 struction will naturally be to teach him to read and 
 to write the language which he has already learned 
 to speak. 
 
 The words which he uses are in his mind signs of 
 things, and he has no more analysed the parts of a 
 word than he has analysed the parts of the thing it 
 stands for. At first this is the best method of intro- 
 ducing him to the printed language, not to its letters, 
 but to its words as wholes. As when you hold up the 
 picture of a dog, and ask what it is, you do not wish 
 him to say, " It is the picture of a dog," nor that "it 
 is one side of the head, one hind leg, and both fore 
 legs of a dog," but when he sees the picture, you wish 
 
104 TRUE ORDER OF STUDIES. 
 
 him to say, it is a dog ; so when he sees the printed 
 word, you wish him to say, not dee oh jee, but dog. 
 Teach him thus to read very simple sentences, con- 
 taining only the most common words, by pronouncing 
 at sight each word, and continue at this for some 
 months, until the child recognizes instantly, at sight, 
 about a hundred words of our language, such as are 
 used in his primer, and have been copied in writing 
 text upon the blackboard. 
 
 When this point is thus practically established in 
 his mind, that written and pri-nted words are individ- 
 ual pictures of spoken words, we may begin the an- 
 alysis of the words into their elements. If now the 
 primer has been in the Cincinnati Phonotype, your 
 task is delightfully easy ; if in Dr. Leigh's Pronounc- 
 ing Orthography, it will present some difficulty ; and 
 if you have only had the ordinary type the difficulties 
 will be greater than in any part of the whole course 
 of education. 
 
 The first step, in either of the three cases, is how- 
 ever the same, and is easy ; the child must be taught 
 to analyze by his ear, the spoken word, which he can 
 do by simply pronouncing it very slowly. He will 
 soon discover that all the sounds of our English 
 speech can be divided into about forty classes, each 
 one of which may be called an elementary sound. 
 This sounds learned, and beyond a child's reach ; but 
 practically the best way to teach a child of three 
 years old, to pronounce a difficult word, is to make 
 him pronounce the phonic elements of it separately 
 and successively, and then blend them. This is pho- 
 
LANGUAGE. 
 
 105 
 
 netic spelling, and a child of five or six years old will 
 grow enthusiastic in such spelling, as an amusement, 
 before he knows a single letter of his alphabet. 
 
 When the pupil can with facility analyze the 
 spoken words into their phonic elements, he must be 
 taught that alphabetic writing originated in an attempt 
 to represent each element by a letter. With the Cin- 
 cinnati alphabet this is done for English ; and the 
 child has but to learn the sound of each letter, in 
 order to read. With Dr. Leigh's type, or with com- 
 mon type, the child must now be taught that this 
 original attempt of alphabetic writing is very imper- 
 fectly carried out in English ; that he will find each 
 letter has various sounds, or is sometimes silent ; and 
 that each sound has various modes of being repre- 
 sented in words. Great care must be taken not to 
 let him use, or even know, at first, the names of the 
 EngHsh letters. For instance, A must be named as 
 it is pronounced in at ; B must be named simply as 
 pronounced in hub, whispering inaudibly the hu, and 
 pronouncing aloud the mere end of the word ; C as 
 in the end of music ; D as at the end of had ; G as at 
 the end of hag, &c. Not until the child is perfectly 
 familiar, by many months practice, with the fact that 
 H signifies a slightly roughened breathing, ought it 
 to be allowed to call it aitch. 
 
 Unfortunately the English alphabet contains but 
 twenty-six letters, three of which, c, q, and x, are 
 superfluous ; while the sounds which ought to be 
 represented are from 34 to 40. And in addition to 
 this necessity for using the same letter to represent 
 
I06 TRUE ORDER OF STUDIES. - 
 
 different sounds, (as for example, t in bat, bath, bathe) 
 we add the unnecessary use of various letters and 
 combinations to represent the same sound, (as for ex- 
 ample, nay, neigh, nail, nation, they, fete, and other 
 ways of writing the sound a). Some writers have 
 maintained that there are but trifling exceptions, and 
 that the mass of our language is truly phonetic. But 
 this is a mistaken view ; the exceptional words occur 
 so frequently that not only is a child unable to pro- 
 nounce a new word by the aid of his alphabet, but no 
 scholar of whatever ability can tell the pronunciation 
 of an English word, which he has never chanced to 
 hear, or to see printed with diacritic signs. It may 
 therefore be justly said, that English is, like Chinese, 
 not alphabetic in its dress, but logographic ; and there 
 is no man living, in England or America, who has 
 learned, or can learn to read it ; that is to pronounce 
 anything and everything written in it. 
 
 For this reason learning to read, being the attempt 
 to accomplish an impossible thing, is the most diffi- 
 cult task undertaken by an English child. A tough 
 constitution resists a great deal of hardship and 
 abuse ; a vigorous intellect frequently survives the 
 labor of learning to spell in the ordinary mode. A 
 man who has lived through a course of bad diet, and 
 inattention to the laws of health, is apt to regard at- 
 tention to such matters as a mark of effeminacy ; and, 
 in like manner, those whose love of literature has not 
 been quenched, and whose power to see truth has not 
 been wholly blinded, by the ordinary mode of learning 
 to read, -suppose that there is no urgent need for im- 
 
LANGUAGE. 10/ 
 
 provement. He who will reflect, however, seriously, 
 upon the absurdities of English orthography, and 
 upon the gravity, with which those absurdities are 
 usually introduced to the child as reasonable things, 
 must perceive that such instruction has an injurious 
 effect upon the child's mental powers, and upon his 
 love of truth. The boy may survive it ; as he sur- 
 vived in olden days compression of swathing bands, 
 drenching with herb-teas, and drugging with cordials ; 
 I will even allow that, in the case of great native 
 vigor of mind, the injurious effect may be small : but 
 it is always pernicious ; and in the case of persons of 
 small intellectual ability, disastrous. The child is told 
 to spell a word, and then expected to pronounce it ; 
 as though the spelling were a guide to the pronuncia- 
 tion. I remember hearing a schoolfellow hesitate 
 when he came to the word " business." Spell it ! 
 said the teacher. Be you ess eye n e ess, — double 
 ess, rephed the boy. Well ! and what does that spell ? 
 asked the teacher. As he paused for a reply to this 
 unanswerable question, he espied a larger boy doing 
 something wrong, and looking sternly at him, uttered 
 his name, in tones of reproof, — Chris top Jier Frazer ! 
 The little fellow thought this was the pronunciation 
 of his " be you ess eye, &c.," and meekly repeated, 
 Christopher Frazer. We laughed, — and yet that 
 jumble of the names of the letters sounds as much 
 like Christopher Frazer as it does like business. 
 
 Even if it be not desirable to change the printed 
 form of our language, for ordinary purposes in books 
 and newspapers ; it is extremely desirable that the 
 
 5* 
 
I08 TRUE ORDER OF STUDIES. 
 
 books for the first two or three years of school life 
 should be in phonetic print. The saving of time thus 
 effected for the child, if the Cincinnati phonotype be 
 used, has been experimentally demonstrated to be more 
 than a year ; and with Leigh's type more than six 
 months ; but the saving of time, although very valu- 
 able as giving more opportunity for geometrical plays 
 and puzzles, and for the examination of objects of 
 natural history, is not worth so much, as the increased 
 happiness of school life, the increased sense of truth- 
 fulness, the increased accuracy of ear, and spirit of 
 general accuracy, produced by it. The objection, 
 made by those who have not tried the experiment, of 
 the difficulty of transition from phonotype to common 
 print, is of no weight. The pupil who reads phono- 
 type fluently, can in one fortnight, without appreci- 
 able labor, learn to read common print; as well as it 
 is possible for any human being to do what cannot be 
 done. 
 
 The child who learns to read in phonotype, will 
 learn common orthography more rapidly, because he 
 perceives more clearly its oddities and anomalies ; 
 and that fixes them on his memory. Experiments in 
 Waltham upon many hundreds of pupils, continued 
 through a series of six or seven years, showed that 
 those who had learned phonotype, or even phono- 
 graphy, were better in spelling than other scholars. 
 Bad spelling, indeed, usually arises from an attempt 
 to spell phonetically with the common alphabet ; so 
 that we might say that the cause of bad spelling is 
 that children are taught to spell. For this, and for 
 
LANGUAGE. lOQ 
 
 Other reasons which I shall presently mention, I re- 
 gard spelling books as mischievous ; a hindrance, not 
 a help to learning. A child accustomed to associate 
 phonetic values only with a peculiar type, and know- 
 ing that the common spelling is traditional and 
 anomalous, will not attempt to use the ordinary alpha- 
 bet phonetically, and will thus avoid the most common 
 source of errors. The use of a phonotype, or even 
 pronouncing type, has also the advantage of giving 
 unceasing instruction in accuracy of enunciation ; and 
 no other method has been so successful in removing 
 from a school provincialisms, brogues, and vulgarities 
 of pronunciation. 
 
 For fixing the orthography of words in the memory, 
 no practice is more useful than constant reading, with 
 frequent writing from dictation ; but the latter adjunct 
 cannot be employed at the earliest age. When we 
 have a phonotype in ordinary use in our literature, the 
 child will learn the current hand writing at the same 
 time that he learns print; but with the present 
 heterotypy (as it has been facetiously called,) we must 
 be content to begin writing at the time of transition 
 from phonotypy ; when, of course, the progress in 
 writing will be much slower than in reading. 
 
 These two fundamental arts do not receive in our 
 ordinary schools their due attention. To read, to 
 write and to cypher are the three most valuable 
 accomplishments taught in our public schools, and 
 should take precerlence in importance over all the rest. 
 Not that more time is to be given to them ; too much 
 time is given already ; what is needed is more thought 
 
no TRUE ORDER OF STUDIES. 
 
 and attention, good judgment and good taste. What 
 Luther W. Mason has done with music in the Boston 
 schools, can be done with these three humbler arts in 
 every school. All art is imitative, it cannot be taught 
 scientifically, but only by example. Precepts, direc- 
 tions, principles, are of value only to the student who 
 is actually trying to imitate a model. To learn to 
 cypher the child must see the teacher perform an 
 arithmetical operation ; and then repeat it himself, 
 until it is familiar, and he can do it with ease ; then, 
 and not until then, is the time to explain to him the 
 reasons for what he has done. To learn to read, and 
 write, the child must hear the teacher read, and see 
 the teacher write ; and then himself go over the sam« 
 sentence, with his pencil, and with his lips, until he 
 reads it readily. It is idle to tell a little child to let 
 his voice fall at a period, to stop long enough to count 
 two at a semicolon, and so on. Let the teacher read 
 the sentence in easy natural tones, in such wise as to 
 bring out the meaning ; and let the pupil repeat by 
 ear. 
 
 Pains should be taken from the very beginning to 
 cultivate pure and natural intonation ; smooth and 
 melodious sounds. This is as important in reading 
 and speaking as it is in singing. And yet I have been 
 for fifty years hearing school teachers teach their 
 children directly the reverse ; constantly saying, 
 "speak up, let out your voice," and forcing the little 
 thin2:s to shout, and scream, in harsh unnatural tones. 
 Distinctness of articulation can be best gained by a 
 careful drill on the phonic elements of the language, 
 
LANGUAGE. I I I 
 
 particularly the consonants ; and sufficient force must 
 of course be given to make the reading audible. But 
 a boy of eight or ten years should not be required to 
 speak loud enough to be heard by a, school of 150 
 scholars ; nor should a child of any age be allowed to 
 go on through a single line of his reading book, in a 
 strained, unnatural voice. Few scholars of American 
 schools, as far as my observation goes, are at present 
 allowed to read in any other than strained tones. 
 
 Nothing but practice can give ease and facility in 
 an art, and practice takes time. This is a second 
 mode in which the spelling book is injurious, it takes 
 up time which would be much more usefully occupied 
 in reading. It is reading which actually does the 
 work, with which the spelling book has usually been 
 credited. When a scholar has learned to read with 
 perfect facility, so that the printed page is just as in- 
 stantly intelligible to him as spoken speech, (and in- 
 deed a good reader can take in words silently from a 
 printed page more than thrice as fast as by the ear), 
 then the forms of the whole words of the language 
 are as familiar to him as the letters of the alphabet, 
 and he cannot spell a word in any other way than 
 that which the tyranny of lexicographers and proof- 
 readers has fastened upon him. No student of Greek, 
 or of Latin, or of a modern tongue, uses a spelling 
 book in acquiring the new language ; yet in precise 
 proportion to his acquaintance with its literature, he 
 can spell it. It is so with the vernacular ; and all 
 spelling books are hindrances to learning to spell, 
 they take up time which ought to be occupied in 
 
112 TRUE ORDER OF STUDIES. 
 
 reading ; the method of learning what we, with curious 
 perverseness, call English orthography. 
 
 The character of the books put into the child's 
 hands is an important matter. By the modern 
 method of using in schools text books written with 
 profuse explanations, as if for scholars without a 
 teacher, the time of the pupil is very largely occupied 
 with reading his text books, and he gets little time 
 for reading literature. The reading books in schools, 
 which were formerly made by compilation of classic 
 authors, are now too largely original compositions ; 
 or compilations from inferior writers ; or when con- 
 taining selections from classic writers, those selections 
 are mangled and weakened. These inferior books 
 are read again and again by the scholar. When at 
 home, many children have, at the present day, a 
 superabundance of books, written for children, and 
 not always by authors of the highest merit. There is 
 danger therefore, real and imminent, lest our children 
 fail to enjoy the best results of modern thought ; and 
 fail to acquire the capacity for the enjoyment ; by en- 
 joyment I, of course, do not refer simply to the pleas- 
 ure received from art and literature ; but also to the 
 power of using them in any and every direction. 
 
 A plan which was tried in Waltham, to obviate 
 these evils, succeded so well that it deserves to be 
 more widely adopted. First selecting the briefest 
 and most condensed books in mathematics and the 
 sciences, (and producing thereby better results in 
 those branches also,) we next provided, at the expense 
 of the town, classic authors as reading books, only 
 
LANGUAGE. II3 
 
 lending them to the scholars while in actual use. 
 The books were kept in good order, and lasted for 
 many successive classes, and we were enabled to give 
 the children a greater variety than usual. For the 
 younger scholars we had, for example, Mrs. Barbauld's 
 Hymns in prose, and Maria Edgeworth's Early Les- 
 sons, while in the High School we had Shakspeare, 
 and other standard writers, English and American ; 
 introducing some books of a scientific character, like 
 Guyot's Earth and Man. 
 
 The approach to ordinary orthograpy through 
 phonetic type, (and no other approach ought to be 
 permitted) will very naturally lead to questions of 
 etymology : which will interest a child several years 
 before he is old enough to have any power to under- 
 stand the analysis of sentences, or any form of syn- 
 tax. Words themselves must be understood before 
 they can be intelligently classified. When a word is 
 introduced to a child in its orthographic dress ; and 
 he laughs, as well he may, at the oddity of this cos- 
 tume ; we may tell him of its gradual growth into its 
 present form ; children's and foreigners' mispronun- 
 ciations will illustrate to a young pupil the way in 
 which words may change ; and we can show him how 
 the silent and mispronounced letters in a word are a 
 record of its ancient pronunciation, or of its deriva- 
 tion, or of an ancient error in regard to its supposed 
 derivation. This will lead us to explain to him the 
 conventional element in language ; that usage is the 
 law and rule in speech ; and to define to him usage as 
 the usage of a majority of the best educated ; and to 
 
114 TRUE ORDER OF STUDIES. 
 
 show him in what instances a usage creeping in 
 ought to be strenuously resisted by the educated 
 classes. When a geographical name, for example, is 
 on all the maps and charts, it is an offence against 
 morality, akin to removing a neighbors landmark, to 
 attempt to change it. Holmes' Hole, Roxbury, Bangs 
 Island, Pequawket Mountain, are geographical names 
 on all maps and charts until after 1850, which ought 
 not to be given up in favor of the much inferior sub- 
 stitutes recently invented, Vineyard Haven, Boston 
 Highlands, Cushing's Island, Kiarsarge Mountain. 
 To the last there is a third objection, namely, that it 
 sounds so much like Kearsarge that it has already 
 produced great confusion as to the identity of two 
 mountains, fifty miles apart. 
 
 We may then go further back with our pupil, and 
 show him that a part of our language is, in its origin, a 
 natural attempt to represent the thing of which we 
 speak. We may show him how a sound has, in a 
 number of words, the same meaning ; the compound 
 element i"/^, for example, imitates a sneeze and seems 
 to call attention to the nose, (in which word the ele- 
 ments are inverted) ; and the nasal element can fre- 
 quently be detected in words containing this sound. 
 The younger classes can see that the word nose can 
 easily be introduced into the definition of such words 
 as sneeze, snore, snarl, sneer, snicker, sniff, snivel, 
 snort, snooze, snout, snub, snuff, snuffle ; and even of 
 such as snail, snake, snap, snare, sneak, snipe. The 
 older classes can see how frequently an initial th points 
 the forefinger ; it is demonstrative, — as in this, that, 
 
LANGUAGE. II5 
 
 these, those, then, there, thither, thence, thus, thou ; 
 while the initial wJi is relative, that is, it is a tJi pre- 
 ceded by a conjunction ; and can be translated by 
 and tJi or and h. Thus : " I saw a man who, etc.," 
 is equivalent to " I saw a man and he." A similar 
 force is in what, when, where, whence, which, whither, 
 etc. Still older classes will be interested to see that 
 the relative is an interrogative ; a question always im- 
 plying a previous thinking, with which the conjunctive 
 part of the relative connects the demonstrative part. 
 Such plums out of the pudding of grammar, will awak- 
 en, in some pupils, a taste for this fascinating study. 
 
 The forms of even the individual letters may be 
 made the occasion of incidental instruction upon the 
 origin of written languages ; the probable develop- 
 ment of Semitic alphabets from phonetic hierogly- 
 phics ; and of the European alphabets from those of 
 Phenicia. If such instructions fail to awaken a 
 scholarly turn of mind, and to lead to literary taste, 
 they will at least relieve the dryness of learning to 
 spell, and give the learner some glimpses of the numer- 
 ous and subtle ties which bind us to all the generations 
 which have preceded us. 
 
 The study of grammar, and of composition, does 
 not belong to an early period in education. Grammar 
 is the study of a maturer mind, and may be wisely de- 
 ferred to the high school ; or at least to the last year 
 of the grammar school. It is an analysis of the usages 
 of language, and requires the pupil to have become 
 familiar with those usages. 
 
 It is also an inversion of the true order of educa- 
 
Il6 TRUE ORDER OF STUDIES. 
 
 tion to give a child an abstract theme to write upon, 
 before he is old enough to think upon such themes of 
 his own accord. In like manner, it is not in the true 
 course of nature to set a child to declaim before he 
 has any ambition or desire to speak for himself, his 
 own thoughts. 
 
 The most instructive reading, for a person of any 
 age, old or young, is that in which the author's tone 
 of thought is above the average tone of the reader's 
 thought, and yet not beyond his grasp. The best exer- 
 cise for a child is to commit to memory, to repeat, but 
 not to declaim, such selections, of poetry or prose, as, 
 although not altogether above his comprehension, are 
 worth being treasured forever in remembrance. As 
 a general rule the child should be even discouraged 
 from committing to memory anything except passages 
 from the Scriptures, and passages of sterling poetry. 
 The Scriptures he may commit to memory ; not only 
 for their intrinsic value, but because they are often 
 appealed to as authority, and when so used should be 
 quoted with verbal accuracy. Good poetry may be 
 also committed to memory, because a part of its value 
 lies in its felicitous choice of expressions, and in the 
 melody of its rhythm ; and these are lost unless it is 
 quoted, or recalled to memory, in the poet's own 
 language. But the committing to memory of the 
 words of ordinary text-books, or of inferior poetry, or 
 of school dialogues for exhibition, should be indulged 
 only at the rarest intervals ; and the teacher who re- 
 quires it frequently does a harm to the pupil far 
 greater than he imagines. 
 
LANGUAGE. II7 
 
 The best exercise in composition is to read good 
 autiiors ; that is the only real '' Aid to Composition." 
 All art is imitative, and the great essential in teach- 
 ing it is to set good models before the pupil. When 
 the pupil has read something which is worth reading, 
 let him close the book, and tell what he has been 
 reading about. When he is old enough to write 
 legibly, let him write upon his slate some brief anec- 
 dote from memory, after reading it. Let him with a 
 ballad before him, tell the tale in good prose ; — let 
 him write in prose the ideas of a piece of poetry lying 
 before him. The student who is old enough to write 
 upon a given theme, will find after reading or reflect- 
 ing upon his subject, no preparation for writing upon 
 it, so effective as reading, for an hour immediately be- 
 fore taking up his pen, some particularly well written 
 essays upon similar themes. It is in this way that an 
 inferior poet can write sometimes an admirable 
 parody, or imitation, of a superior one ; by reading 
 Shakspere, or Milton, or Tennyson, for an hour or 
 two, he is able to write a poem of his own in the style 
 of the selected author. Indeed, it is thus that all 
 oratory and poetry, even among the princes of litera- 
 ture, has grown ; each building upon, and stimulated 
 by, the labor of his predecessors. And it is for this 
 reason, as well as others, that it is so important that 
 the child should have before him in the books which 
 he reads at home, and in schools, the best models of 
 pure English and of elevating thought ; to give him 
 the ability to express himself gracefully, that is to say, 
 with ease and strength. 
 
Il8 TRUE ORDER OF STUDIES. 
 
 The French and German languages, and also 
 Latin and Greek are taught in many schools in this 
 country. Of late years there has been some return 
 to rational methods in teaching languages ; and yet the 
 mania for educational drill prevails, even now, to such 
 an extent, that I may be pardoned for speaking freely 
 upon it. Twenty years ago the fashionable mode of 
 learning a language was to begin by committing some 
 text book upon its grammar to memory. In the 
 case of Latin this grammar involved the grammar 
 of the whole literature from the oldest writers, 
 to the most recent ; in Greek it involved all the 
 various dialects of the different countries, as well 
 as the changes in the more recent forms, from the 
 more ancient. After this feat of memory, the pupil 
 began to study very critically some author, pausing 
 over each sentence and word to apply his grammar to 
 the explanation of the construction. Finally, if his 
 life and his patience, were long enough, he began to 
 read the literature of the language. 
 
 The more natural method is more agreeable, and 
 more rapid in producing results. The pupil begins 
 by reading the literature, then analysing the lan- 
 guage, and studying its grammar. The pronuncia- 
 tion is first to be determined ; if Greek or Latin, some 
 fixed principles must be adopted ; if a modern lan- 
 guage, we should get as nearly as possible the actual 
 present usage of the best speakers. This is to be 
 gained by the ear, listening to native speakers ; al- 
 though great aid may be had I hope in the not 
 distant future from Bell's Visible Speech. While 
 
LANGUAGE. HQ 
 
 learning to pronounce, you also are to learn to trans- 
 late ; and the first essay is to be upon a sentence, not 
 merely upon a word. Professor Sauveur's method in 
 teaching French conversation is a perfect method of 
 nature. But if you have not the living teacher, and 
 are obliged to use books, begin at once with classic 
 authors and translate them, without grammar or 
 dictionary. The object at first is to learn the lan- 
 guage ; to get if you can the meaning of the particu- 
 lar page before you, not for its own sake, but for the 
 sake of learning the meaning of the words. Now, 
 the meaning of the frequently occurring words will 
 be fixed in the memory more surely by repetition of 
 them, in reading, than by looking them out in the 
 dictionary. Skip, therefore, the words and sentences 
 whose meaning is not clear to you after a moment's 
 thought ; read the chapter through a second time, and 
 it may come to you. Your clew to the meaning is to 
 be found in the similarity of the words to the cognate 
 words in the vernacular ; and this method, therefore, 
 can be wholly adopted only in the case of the modern 
 tongues of Western Europe. If the reader of this 
 chapter has never tried it, he will be astonished to 
 find how readily an intelligent American boy, know- 
 ing only English, will pick out a part of the meaning 
 of a page in French, German, Danish, Swedish, 
 Italian, Spanish or Portuguese, and how rapidly, if he 
 continues the trial always on the same language, half- 
 an-hour every day, the proportion of the page which 
 is intelligible to him will increase. 
 
 When the pupil can thus read the language, and 
 
120 TRUE ORDER OF STUDIES. 
 
 understand nearly the whole of what he reads, he 
 may begin to look out in the dictionary the meaning 
 of the few words which he does not know ; and then, 
 also, he must begin to study the grammar ; after 
 which as a final thing he may begin to translate 
 from the vernacular into the foreign tongue, and to 
 write in it original compositions. But this should 
 not be done until the scholar can easily read and 
 understand the new language without a conscious 
 translation of it into the vernacular. This, however, 
 is to be obtained by keeping up, even after beginning 
 to study critically with grammar and dictionary, the 
 habit of daily taking up, also, books which you are not 
 studying, and readmg them. 
 
 There are two entirely distinct objects to be kept 
 in view while studying a foreign tongue ; the acquisi- 
 tion of a new language, and increased mastery over 
 your own. For the first end, you need to pay close 
 attention to the minutest details of the construction 
 and order of the words of the author whom you are 
 reading ; for the second, to express his thoughts (oc- 
 casionally, at least, and in his finest passages), in the 
 best and most idiomatic English. When reading 
 Plato, Cicero, Goethe, or Moliere, you wish to seize 
 their thoughts precisely as they uttered them, with 
 the words in their very order, and with a perception 
 of the ideas direct from their words, without even a 
 mental translation into your own tongue. This 
 power is acquired by the combination of the critical 
 study of some one or two select works with a rapid, 
 extensive reading of the other writings of your author. 
 
LANGUAGE. 121 
 
 In this reading for the sake of learning the new 
 language, the translation, if one occurs to your mind, 
 will be slavishly literal, and if you should utter it would 
 be less intelligible than the original ; like Thomas 
 Taylor's translation of the Divine Dialogues, in which 
 he follows the author so literally, that the English is 
 harder, for an Englishman, than the Greek. But if 
 you would have the study aid you in expressing your 
 own thoughts, you must also at times accustom your- 
 self to translate, from the original, the thoughts alone ; 
 putting them, with fidelity to the thought, into 
 English entirely remote from the forms of your 
 author, and peculiar to our own best writers. 
 
 These directions are not inapplicable to schools. 
 In the Waltham High School we had for several years 
 a teacher whose classes would bear the most vigorous 
 examination in all the niceties of philological and 
 grammatical analysis, and would also read, from a 
 Latin or French author, so fluently and in such easy 
 and idiomatic English, that, as a member of the ex- 
 amining committee, I not unfrequently felt obliged to 
 inform visitors that the class were not reading from a 
 written or printed translation. The teacher should 
 require, in a spoken or written translation, one thing 
 or the other, either extreme literal accuracy, or else 
 good idiomatic English. Next to the ability to act 
 well, must be placed the ability to speak well ; indeed, 
 so interwoven are the functions of the human being, 
 that the ability to express thought increases the 
 ability to think ; and the power to think increases the 
 
 power to act. 
 
 6 
 
122 TRUE ORDER OF STUDIES. 
 
 That which pertains most strictly to the general 
 purpose of the little volume, however, is to lay 
 emphasis upon the fact that in the order of nature a 
 child hears music and spoken language long before it 
 has the power to study and analyse them. Whatever 
 language we are considering, it is better for the child 
 to be taught to read and understand it in its larger 
 scope and meaning before he begins to give it a criti- 
 cal and thorough study. He must learn to sing and 
 play, before he is ready for thorough bass and counter- 
 point. He must read and write English, before he is 
 ready for grammar and rhetoric. He must in like 
 manner be able at least to read easily any other 
 tongue before he takes up its grammar. And in learn- 
 ing to speak and write it, he must confine himself to 
 the best models of native writers and speakers until 
 he is perfectly familiar with them ; before he begins 
 himself to use it in expressing his thoughts. 
 
LAW. 123 
 
 CHAPTER XVI. 
 
 LAW. 
 
 THE word law as used in the title of this Chapter 
 has a wide significance, including the whole 
 history of the state ; of both the military and civil 
 powers; the mode in which human society has been 
 governed, or endeavored to govern itself in all ages. 
 
 The child is born subject to his parents ; and the 
 parental government has always been a type ; perhaps 
 suggesting and leading to the government of tribes 
 and nations. At all events, there are no savages to be 
 found without some traces of government ; and in all 
 civilized countries, there has been developed the idea 
 of impersonal law; through the organization of a 
 community whose associated wisdom shall decide 
 upon what is right, and what is for the best interests of 
 the whole ; whose associated power shall enforce the 
 right, and develop the good, so far as the limits of its 
 ability extend. The historical study of these relations 
 of men to each other is necessary, not only to the full 
 development of the student's mental powers ; but as 
 a preparation by which he is fitted for an intelligent 
 participation in the rights and duties of those relations; 
 which is by definition the chief end of a liberal edu- 
 cation. 
 
124 TRUE ORDER OF STUDIES. 
 
 The method of nature, in this branch of discipHne, 
 is sufficiently obvious. The child is born into a 
 family, and is subject to his parents; they require of 
 him obedience before he can understand the ground 
 on which the authority rests. No disciplinarian of the 
 modern school has as yet, I beheve, published a text 
 book for infants, explaining and proving to them, 
 while yet in the nurse's arms, the logical foundations 
 on which they are required to submit to and- obey 
 their parents. Here is one retreat, where nature and 
 common sense retain some hold. In a well ordered 
 family the child learns by subjection to his parents, 
 the duty of subjection to just authority, and forms a 
 habit of obedience. He is brought under the order 
 and discipline of the family, before he can rise to the 
 perception of that vast scheme of universal order, 
 planned by Infinite wisdom, in obedience to an im- 
 pulse of unfathomable love, and carried into execution 
 by Almighty Power ; — that Universal Order, after 
 which all wise legislation strives ; according to which 
 all just judicial decisions are framed ; and which all 
 righteous executive power seeks to embody. 
 
 Thus also in the school. The first and most im- 
 portant ideas of law, gained there, come not from 
 histories and constitutions, political essays or orations; 
 but from the wise and just discipline of the school 
 room ; from the rules of play observed in the games 
 of the school children ; and from the perception that 
 the parents and teachers are also the subject, even in 
 school matters, to the regulations of the committee, 
 the votes of the town, and the laws of the common- 
 
LAW. 12$ 
 
 wealth. The judicious teacher, by occasional words, 
 rightly directing the child's attention, for a moment, 
 to such themes, giving an incidental instruction in 
 politics and law, does an important work for the State, 
 and for her children. 
 
 Under this department comes also History in the 
 ordinary sense of the word. The " History of the 
 World" is too vast a field for survey as a mere 
 part of liberal education. In selecting nations and 
 periods which shall be most useful to the general 
 student, it is manifest that we should confine ourselves, 
 principally, to the direct line of spiritual inheritance, 
 the sources whence we derived our science and laws. 
 The United States, particularly in the periods when 
 the Colonies were taking consolidated form, and when 
 they were achieving their independence, and becom- 
 ing a nation : Great Britain, especially in the sixteenth 
 and seventeenth centuries ; Rome in the age of Caesar 
 and Augustus ; Greece just before, and during the 
 age of Pericles ; and Israel from the days of Moses to 
 those of Solomon ; these are topics on which every 
 man, who takes any interest in the welfare of our dear 
 land, ought to be early well informed. They all bear 
 directly upon the questions of to-day in a Republican 
 Government. Before the young man leaves the High 
 School he should also take a brief course of study in 
 constitutional law ; comparing the constitutions of our 
 States, and of the United States, with those of Great 
 Britain, Rome, Greece, and the early Hebrew Com- 
 monwealth. The simplicity of our constitution brings 
 this study within the reach of all minds ; and the im- 
 
126 TRUE ORDER OF STUDIES. 
 
 portance to the nation of having the knowledge of the 
 constitution diffused among the people makes it an. 
 imperative duty for every High School graduate to 
 have read carefully some simple and sound commen- 
 tary upon it. 
 
POLITICAL ECONOMY. 12/ 
 
 CHAPTER XVII. 
 
 POLITICAL ECONOMY. 
 
 BESIDES the government of man by man, the 
 older pupil will see that men's affairs are also 
 governed by laws not altogether under their control. 
 He will find at one time the community apparently 
 prosperous, and after a year or two will hear 
 that business is dull. He will hear allusions 
 made to the time when gold and silver coin were 
 used freely, as the fractional paper currency is to-day. 
 At the time when elections for Congress are about 
 to take place he will hear earnest debates concerning 
 the currency, or concerning protection and free trade. 
 It is not well that the young man in the public 
 school should have angry political passions aroused ; or 
 become a partisan upon either side, blinded to all con- 
 sideration of truth as held by his opponents. But 
 there are fundamental truths, established by the clear 
 thought of Adam Smith, and Henry C. Carey (the 
 two most solid thinkers upon these subjects), which 
 are valuable to every citizen ; and no sound decision 
 concerning such debatable questions can, except ac- 
 cidentally, be reached by one who does not learn these 
 truths. Some of these vital propositions are perfectly 
 within the comprehension of children, and ought to be 
 
128 TRUE ORDER OF STUDIES. 
 
 taught in the public schools, as a protection against 
 multiform errors introduced by English writers, and 
 poj^ularized in tales and newspapers of the present 
 day. 
 
 The government of man by men is, of course, liable 
 to error ; mistaken legislation and arbitrary acts of 
 military and executive power, may therefore occasion- 
 ally interfere with the operation of the natural and 
 wholesome laws of commerce. Persons living in 
 countries in which the course of legislation, and of 
 custom, has long been in an erroneous direction, will 
 be likely to mistake, and misunderstand, the natural 
 laws ; and this, as we Americans think, is the condi- 
 tion of persons living in Great Britain, where laws of 
 primogeniture, entailment of estates, difficulties in 
 conveyancing, guilds and trades unions, so utterly 
 prevent freedom of trade in the two prime raw 
 materials, land and labor, as absolutely to prevent an 
 Englishman from knowing what freedom means. We 
 draw from our fatherland a rich inheritance of political 
 and civil freedom ; but we also draw, at the present 
 day, many false opinions in specious dress. The 
 firmness with which an Englishman adheres to a 
 theory, or to a custom, or to a supposed right, is an 
 excellent element in his character, making the pro- 
 gress of the nation stable ; but it is an inconvenient 
 element, when he gets started in a wrong direction. 
 
 The youngest child may be taught how to place a 
 just estimate upon the worth of things ; that a thing 
 is useful in proportion as it gratifies, or enables you to 
 gratify, healthy human desires ; and thus promote 
 
POLITICAL ECONOMY. 1 29 
 
 hiiman happiness. Thus an article which can be used 
 for an indefinite time, and by a multitude of persons, 
 (for example, a book, a picture, a statue), is worth in- 
 comparably more than a thing which is used but once, 
 and that only by a single person ; even if the price in 
 money be the same. The usefulness of a thing is its 
 ability to serve human needs, and may exist in the 
 highest degree in things like air and sunshine that are 
 generally without price. Price is the measure, in gold 
 or silver, of the commercial value. Value is the 
 measure of the difficulty of reproducing a useful 
 thing. Wealth consists in the ability to command the 
 services of natural agents. The whole life of a civilized 
 community depends upon commerce ; upon the inter- 
 change of men's services, by which each does some- 
 thing that others desire him to do, and receives from 
 them in return what he desires. The instrument by 
 which this is accomphshed is coin. The persons 
 through whom the commerce is effected are trades- 
 men, or merchants, and common carriers. The fewer 
 of these, and the nearer that producers and consumers 
 are brought together, the more advantageous is the 
 commerce. No country on earth is, or probably ever 
 will be, over populated ; and the poverty, vice, and 
 crime of nations ; their decay ; and the depopulation 
 of countries, arises from misgovernment, tyranny 
 legislation to encourage foreign trade ; and other 
 errors of men. Such truths as these, and others 
 equally valuable, may be incidentally presented, and 
 illustrated by occurrences in the course of the school 
 life, or by passages ir^ the school histories ; and wilj 
 
 6* 
 
130 TRUE ORDER OF STUDIES. 
 
 enlarge the minds of the young men, and prevent their 
 being afterwards ensnared by the sophisms of those 
 who still re-echo Ricardo and Malthus, or still hold 
 that foreign trade is more important than internal 
 commerce. 
 
PSYCHOLOGY. 131 
 
 CHAPTER XVIII. 
 
 PSYCHOLOGY. 
 
 A CHILD of six years old recently asked " How- 
 do you know that any thing is there, where 
 you see it ? " The question seemed to indicate 
 precocious metaphysical development; and there can be 
 no question that a precocious metaphysical spirit of 
 psychological introversion, is as much to be deprecated, 
 as the premature study of physiology. But the 
 anecdote shows that such questions arise at a very 
 early age, and the judicious teacher may find some 
 better way of quieting the doubts and conflicts than 
 by absolute silence, or by laughing. Children suffer 
 very much from dreams, and from waking visions in 
 the dark ; especially if they have been unfortunate 
 enough to hear or read stories of elves, witches, 
 ghosts, dragons, and the like. They are afraid to 
 speak of the matter, and endure the agony in silence. 
 Many an otherwise sunny childhood has been clouded 
 by these visions ; the child being haunted at night by 
 a fear that the vision was, after all, a finer reality ; or, 
 like the boy whom I have mentioned, that the 
 realities of the day were as unsubstantial as the 
 visions of the night. " Mother," said another child, 
 on awaking, " I thought that this world was God's 
 
132 TRUE ORDER OF STUDIES. 
 
 dream." I could give many anecdotes to a like im- 
 port. And some children still retain the faith which 
 men formerly held, that dreams are visitations by 
 night, of spiritual beings. Even at the present day 
 there are men who hold that view. 
 
 It has seemed to me that, in consideration of the 
 great suffering of childhood from that which Hamlet 
 so much dreaded, bad dreams, we might, quite early, 
 give the child enough of psychology to explain to him 
 the harmlessness of these monsters. He knows, be- 
 fore he goes to school, that there are brains in his 
 skull. He might upon some incidental opportunity 
 be told that when he is thinking, he is moving his 
 brain, as truly as that when walking he is moving his 
 legs. And that as sitting still is resting the legs, so 
 stopping all thinking, which is sleeping, is resting the 
 brain. Then he may have observed in himself, or in 
 a very tired dog, on dropping asleep, a twitching of 
 the legs ; so in a very tired brain, there is a twitching, 
 a motion ; and that partially arouses it, and sets it to 
 half conscious imaginations, which are dreams or 
 visions ; they are his own fancies and imaginations 
 when he is so nearly asleep, that he does not know they 
 are his ; but they cannot really hurt him, any more 
 than his playful make believes when awake. 
 
 This explanation will still leave certain points con- 
 cerning dreams as great a mystery as ever ; they may 
 be, as Emerson has pronounced them, an inexplicable 
 one ; but this partial explanation, not carrying the 
 child into much introversion, may yet enable him to 
 bear with more composure this annoying symptom of 
 
PSYCHOLOGY. 
 
 133 
 
 fatigue, of over excitement, of too heavy a supper, or, 
 still more frequently, of a slight cold disturbing the 
 digestion. 
 
 Truly metaphysical inquiries belong to so late a 
 period of the course of education that I do not care to 
 speak of them in this book, which is principally taken 
 up with the studies of the younger pupils. 
 
134 TRUE ORDER OF STUDIES. 
 
 CHAPTER XIX. 
 
 AESTHETICS. 
 
 THE perception of beauty shows itself at an early- 
 age. I have known a child whose first articu- 
 late word was the exclamation " pretty ! " on seeing a 
 bright nosegay. The analysis of beauty, as the em- 
 bodiment of a simple law in a variety of details, is the 
 work of a mature mind. Erasmus Darwin attributes 
 the sense of beauty to the association of the ideas of 
 the pleasures of satiety in the infant, with the curved 
 outlines and soft contour of the mother's breast. 
 
 This theory would deprive the infant brought up 
 by hand, of all appreciation of beauty ; therefore the 
 modern followers of that eccentric philosopher, 
 supply an inheritance of instinctive ideas derived 
 from grandparents who were more fortunate in their 
 infancy. This discussion of the nature of the sense 
 of beauty is not required for education ; but the 
 culture of that sense is requisite ; and if the child's 
 taste is properly cultivated, and he have native deli- 
 cacy of perceptions, and depth of feeling, he will when 
 old enough to think for himself give a very different 
 account of the origin and nature of the perception of 
 beauty. He will discover then that the sense of 
 beauty is awakened only by those objects which show 
 
AESTHETICS. 1 35 
 
 a thought, simple in itself, embodied in variety of de- 
 tail ; so that it is an intellectual pleasure in the 
 presence of a work of intellect. 
 
 To cultivate the taste for beauty, care should be 
 taken in the furnishing of the school house, the hang- 
 ing of its walls ; and if it be a country school-house, 
 in the arrangement of its grounds. Of two text books, 
 in other respects equal, that is to be preferred which 
 has a well proportioned page, and that in which the 
 illustrations are well drawn. In the selection of copies, 
 whether drawn or natural objects, choose those which 
 are of normal and beautiful forms. If you have 
 chromos, or paintings, on your walls, let them be not 
 only beautiful scenes, but well and harmoniously 
 colored. 
 
 Frobel's gifts are arranged with reference to color 
 as well as form. I have for twenty-five years past 
 been accustomed to try direct experiments on the 
 beauty of form and color as perceived by scholars. 
 For example I place a long rectangle in sight, (say of 
 stiff paper tacked on the blackboard) and covering one 
 end, (say by a slate without a frame) I shorten the 
 rectangle, and ask the pupil to decide at what length 
 it is of best proportions. In the judgment of seven 
 out of ten, the best proportion is that in which the 
 diagonal divides the right angle in the ratio of very 
 small integral numbers. To give another example, I 
 have taken two circles of card of equal size, and drawn 
 in each a central circle of just half the area. In one 
 I paint the central circle purple, the outer ring yellow ; 
 in the other, the centre yellow, the outer part purple ; 
 
136 TRUE ORDER OF STUDIES. 
 
 ■being careful to use precisely the same shades on each 
 card. I ask the pupil to compare the effect on his 
 feelings produced by looking at the one, and at the 
 other. Nearly every child will, without knowing what 
 others have said before him, say that the one is con- 
 strained, sad, depressing, autumnal ; the other free, 
 cheery, summer-like. 
 
 A series of experiments of this kind awakens in 
 the pupils a new interest in the beauty of nature and 
 of art, and rapidly cultivates and improves the taste. 
 Of course this is merely rudimental, and not to be 
 considered as taking the place of the higher art cul- 
 ture which should follow in those who have the taste 
 and the means. At every step in the course of draw- 
 ing lessons, a judicious teacher may by skilful ques- 
 tions or suggestions lead the pupil to a keener appre- 
 ciation of the beauty of form. But let the criticism be 
 always guided to the perception of beauties, not to the 
 exaggeration of defects. 
 
 The lessons in singing give also constant oppor- 
 tunities for aesthetic reading. First in regard to mere 
 purity and smoothness of tone ; it should be remem- 
 bered that there is a beauty in the mere quality of 
 a monotone, just as there is beauty in mere purity of 
 color ; and this is not a matter of whim or association 
 of ideas ; but, both in sound and color, arises from 
 what may be called an unconscious perception of the 
 rhythmical character of the motion. The greatest 
 pains should be taken to check all loudness, harsh- 
 ness, roughness : natural smoothness in the early at- 
 tempt to sing being much more important than 
 
AESTHETICS. 13/ 
 
 correctness of integrity or of harmony. Secondly, 
 pains should be taken to have the melodies and the 
 words adapted to each other, and that both are good. 
 The Music Readers for the Boston Schools are com- 
 mendable in this respect, as are also many of the older 
 collections of Church music. But there is also a style 
 of music and of hymns popular in the churches and 
 Sunday Schools to-day, to which I have already 
 alluded, as having a debasing, demoralizing effect. 
 The words are vapid, or strained, not in idiomatic 
 English ; and the music is of the same character, a 
 mere haphazard writing of the notes, and subsequent 
 division into measures. We have in these instances 
 neither English melody nor German harmony ; but a 
 composition which has been well described as having 
 the flavor of boiled water.* 
 
 I have found it advantageous to ask pupils to give 
 their opinion on the meaning of a melody, new to 
 them, and of which they knew nothing, except as they 
 heard it for the first time upon a piano ; and I have 
 
 * Lest I seem to strike in the dark, let me quote, first an en- 
 tire chorus from a popular hymn to the Saviour : — " Ever near 
 us, guide and cheer us, Touch our eyes that we can see; If 
 thou charm us, naught can harm us. Still the Father calls 
 through thee." The meaning of the word " charm " in this 
 chorus, and the connection of the fourth line with the other 
 three, passes my comprehension ; as does the following popular 
 illustration of the aphorism that " Bright things can never die " : 
 *' Many a happy thing, Many a daisy spring, Float o'er time's 
 ceaseless wing. Far, far away." May such poetry keep far away 
 from me and mine. What a contrast between these two stanzas, 
 and the songs of Watts, or Mrs. Follen. 
 
 «* 
 
138 TRUE ORDER OF STUDIES. 
 
 heard of a good teacher, who always required her 
 pupils thus to judge of a piece, before they heard its 
 name, or attempted to play, or sing it. Every melody 
 has an expression of its own, heightened and modified, 
 but not essentially altered, by harmony, and by orches- 
 tration. The melody thus answers to outline, har- 
 mony to light and shade, orchestration to coloring. 
 Bring into the school frequently the portraits, photo- 
 graphed, engraved, or lithographed, of various persons 
 of marked character known to you ; and let the 
 scholars without hint or clew, tell you how the face 
 impresses them. They will doubtless surprise you 
 by the accuracy with which they will often describe 
 the real character of the person. In the same way, 
 sing or play to them music of good character, written 
 by composers of merit, for specific words or specific 
 occasions, and let the pupils, without hint or clew, 
 tell you how the music sounds to them, — what feeling 
 it expresses, or for what occasion it seems adapted. 
 This will increase very much their appreciation of 
 music, and its usefulness to them. 
 
 I have spoken of the use of classics as reading 
 books ; Mrs. Barbauld and Miss Edgeworth for 
 younger scholars; Shakspeare and Wordsworth for 
 older classes. If you have not this privilege, but must 
 use the ordinary collections, let the class read two 
 pieces of very unequal literary merit, and then call 
 upon them, without hint of your own opinion, to give 
 their judgment as to the respective style and finish of 
 the two pieces. After they have given their opinion, 
 give them the benefit of yours. 
 
ETHICS. . - 139 
 
 CHAPTER XX. 
 
 ETHICS. 
 
 AS we approach the higher branches of the hier- 
 archy we come as I remarked concerning 
 Pohtical Economy, to disputed questions ; and are to 
 be careful not to arouse partisan feehngs, nor to give 
 doubtful opinions for settled truths. There are various 
 theories as to the logical foundation of ethics, but the 
 discussion of those theories is to come only in an ad- 
 vanced stage. 
 
 At the child's entrance into school he has learned 
 the meaning of the words "you must," and "you 
 ought." He has a dim sense of the difference be- 
 tween a mistake and a sin, between want of taste and 
 want of principle. The teacher who begins to reason 
 with him at once, and explain to him the fundamental 
 theories of ethics, will probably do him harm, and 
 make him doubt the reality of ethical distinctions. 
 The natural mode of procedure is to deepen, first of 
 all, as far as you are able, his sense of obligation, of 
 duty. Let him see that you feel it binding upon you ; 
 and that nothing earthly, or unearthly, could tempt 
 you to do what you are clearly convinced is wrong. 
 Feelings and sentiments are contagious ; the char- 
 acter of the teacher is, in spite of himself, reflected in 
 
140 TRUE ORDER OF STUDIES. 
 
 some degree in the character of his pupils. I once 
 asked a teacher, who succeeded, incomparably better 
 than any other teacher I ever knew, in keeping the 
 clothes and faces of her pupils clean, the school-house 
 and outbuildings perfectly undefaced, how she did it. 
 " I don't know, Mr. Hill," was her honest answer, " / 
 do not try to do Ur Then, after a pause, she added, 
 modestly, " there is perhaps one thing, I am always 
 scrupulously neat myself." That was doubtless the 
 secret ; her own person, her dress, her desk, and table, 
 her books, were always perfectly clean and in perfect 
 order. 
 
 " Thus also the teacher who has himself seen the 
 awful sanctity of the moral law, and felt that in spite 
 of all which utilitarians and sensationalists may say, a 
 man had better die, and be annihilated, than deliber- 
 ately to do what he clearly knows to be wrong, he 
 will without lectures, sermons, or twaddle, impart to 
 his pupils the same sentiment. If you would know 
 the reality and cursedness of sin, the nobility and 
 glory of virtue, said my Latin tutor to me, read the 
 " Agricola," of Tacitus. You can see it in the lives of 
 men, you cannot learn it from their lips. 
 
 Mary Wolstonecraft carried out that idea in her 
 " Elements of Morality " ; which was a series of por- 
 traitures of vices and of virtues, woven into a story of 
 Mr. Jones, a merchant in Bristol. The same thing was 
 well done for American schools by M. F. Cowdrey, 
 of Sandusky, Ohio ; his anecdotes were not, however, 
 interwoven in a story. The fascination of the modern 
 novel and tale is in the portraiture of characters which 
 
ETHICS. 141 
 
 they present, " holding the mirror up to nature " ; and 
 if it is truthfully done, giving the hideous aspects of 
 sin, and the attractive side of goodness, it is a good 
 work. A novel is thus a potent agency, for good, or 
 for evil. The same may be said, in its degree, of the 
 little stories which are told in a child's hearing, or 
 embodied in the books which it reads. Good morals 
 and good manners come first of all in the objects to 
 be sought in the public schools, but they are most 
 successfully taught by the teacher taking the greatest 
 pains first to be irreproachable himself. The art of 
 living well, like other arts, is learned by imitation of a 
 good model ; and a living object is the best model in 
 all cases, — if accessible. 
 
142 TRUE ORDER OF STUDIES. 
 
 CHAPTER XXI. 
 
 THEOLOGY. 
 
 IT is difficult to separate morality from religion ; 
 even the idolatrous, and semi-atheistic Chinaman 
 sanctions his moral precepts by religious doctrines ; 
 and a Chinaman who had thrown off his idolatry, and 
 for a time rested in pure atheism, told me that he felt 
 during that time no moral restraint ; and that his 
 sense of duty and obligation did not return, until two 
 or three years afterwards, when he was converted, by 
 the simple sublimity of the first chapter of Genesis, 
 to a faith in Theism, and then to Christianity. 
 
 Debates have arisen in America within a few years 
 concerning the use of the Bible in schools ; concern- 
 ing the introduction of the idea of God into the public 
 teaching ; concerning the separation of the public 
 school funds and the payment of a part of the income 
 to the support of Church-schools. The second of 
 these questions alone comes within the direct scope of 
 this volume ; but I am not unwilling to record my 
 opinion upon the other two. 
 
 It seems to me that public education is a necessity 
 in a republican government ; that the expenses there- 
 of should be met by a tax levied upon all ; and that 
 the proceeds of that tax should be expended pnly in 
 
. THEOLOGY. 1 43 
 
 the support of schools entirely within the control and 
 management of persons elected by the public vote. 
 
 It seems to me that while the reading of the Bible 
 is not a necessity in public education, it is highly fit 
 and proper that a portion of that book should be daily 
 used liturgically in the public schools of a Christian 
 community. The selections from the Bible by Joseph 
 T. Buckingham were used in Waltham, with happy 
 effect ; the selections by the Rev. D. G. Haskins 
 seem to me admirably made for school purposes. Our 
 rule in Waltham was that no child should be com- 
 pelled to read, if his parents objected, and we even 
 allowed those children,whose parents wished it, to enter 
 school after the morning reading. The promulgation 
 of this vote put an immediate stop to all complaints ; 
 and no parents ever availed themselves of the privilege. 
 " Sat erat potuisse videri." If my memory serves me, 
 the same thing took place at Antioch College ; a parent 
 objected to his son being obliged to attend morning 
 prayers. " If I had wanted him to study theology." 
 he wrote, " I could have done it cheaper at Oberlin." 
 I replied, that the young man was not obliged to 
 attend prayers, if either he, or his father had con- 
 scientious scruples. That closed the matter ; and the 
 young man attended, when he found that he was not 
 under constraint. 
 
 But in regard to the third question, the exclusion 
 of Theistic teaching, the case is different. We have 
 among us conscientious persons who demand the 
 entire secularization of the schools ; they would ex- 
 clude sectarianism by excluding Religion. I cannot 
 
144 TRUE ORDER OF STUDIES. 
 
 but regard this as a fundamentally erroneous position, 
 founded on radically defective postulates. 
 
 The education which the safety of the republic 
 demands, for every one of its children, is a liberal 
 education ; that is, an education becoming a freeman ; 
 an education fitting one for the duties of a citizen. 
 First of all, in the requisites of such an education, it 
 must impress upon the future citizen the inviolable 
 sanctity of law, the reality and eternal worth of 
 justice, the necessity of maintaining the rights of 
 others as well as your own. Now in my opinion, and 
 in the opinion of a vast majority of intelligent men, 
 this cannot be done, unless the child be led to recog- 
 nize reverently the being of God, the all seeing Wit- 
 ness and Judge, as the first and greatest of all truths ; 
 the widest and most firmly established of all induc- 
 tions ; the clearest and most certain of all intuitions. 
 Herbert Spencer, who is considered by most of his 
 readers as an anti-theistic writer, declares the being 
 of an Ultimate cause of the universe, to be avouched 
 to us by a strength of evidence, greater than that for any 
 other truth ; so that we are more sure of the existence 
 of such a cause, than we are of our own. Moreover 
 the same writer declares that there is no vice in the 
 constitution of things, but that every thing moves 
 forward towards better ends for the human race 
 Thus the leading opponent, in England, of theistic 
 views, virtually acknowledges that the existence of a 
 wise and beneficent origin and cause of the universe 
 is the most certain, and most comprehensive of all 
 truths. It is, I maintain, the simplest wisdom to give 
 
THEOLOGY. . I45 
 
 to this grandest and most certain of truths, a single 
 word, or name ; that is to teach the child to refer all 
 the wondrous harmonies of the universe, and its bene- 
 ficent laws of operation to God ; to teach him to re- 
 gard God as ever present, ever a witness even to his 
 thoughts, and ever being so wise, and so just, and so 
 merciful, that he will make it turn out well in the end 
 for those who adhere to the law of right, evil for those 
 who persist in doing evil. The child will, of course, 
 attach crude and false conceptions to this great name. 
 But they will be incomparably less crude, and less 
 false, than those which he will form for himself, if un- 
 taught. The superstition of a child brought up re- 
 ligiously may be lamentable, but that of a child brought 
 up atheistically is horrible. 
 
 The existence of sectarian disputes about religion, 
 and of partisan contests in politics, no more forbids 
 the introduction of religion, political economy, and 
 constitutional law, into schools, than the existence of 
 scientific differences of opinion forbids the introduc- 
 tion of science into schools. 
 
 Some believe that geometry deals with space, and 
 the ratio of circumference to diameter is about that 
 of 22 to 7 ; others believe that geometry deals with 
 dimensions, and that the ratio is that of 3 to i ; some 
 think it best, in subtraction, when the subtrahend 
 figure is smaller, to add ten mentally, first to the 
 minuend, then to the subtrahend ; others prefer to 
 transpose mentally one of the tens in the minuend. 
 In spite of these differences of opinion, geometry and 
 arithmetic continue to be the foundation of all human 
 
 7 
 
146 TRUE ORDER OF STUDIES. 
 
 learning and necessarily occupy the earliest place in 
 our course of education. The same may be said 
 (m. m.) of every branch of science. And above all, 
 unless political economy, constitutional law, ethics, and 
 theology, crown the education of the young man^ 
 then the whole course of his culture, so far as regards 
 the interests of the state and of the community, which 
 has borne the cost of his education, is concerned, is 
 worthless ; it has stopped short of the point for which 
 all the course is established. The Westminster 
 Assembly's first question, and answer, agree with the 
 saying of St. Paul, concerning the Creator, that of 
 Him, and Him, and for Him, are all things ; not a 
 step can be rightly taken but in explicit, or implicit, 
 obedience to that truth. The test of scientific theories 
 is their conformity to the Creative thought. In general- 
 ity, comprehensiveness, distinctness, and brevity of 
 statement Kepler's laws are equal to Newton's ; and the 
 great advantage of the latter is found in their intellec- 
 tual simplicity, and therefore presumed nearer accord- 
 ance with the way in which the Divine Mind sees the 
 planetary motion. The test of ethical and political 
 theories is their conformity to the will of .God. The 
 ethical judgments are drawn with such instinctive 
 rapidity that we are unconscious of their bases. But 
 when the reflective age comes, and the young man 
 begins to question why this action should be wrong, 
 and that right ; it will be a great danger to his in- 
 tegrity and virtue, if he has no faith in the being of 
 One all-seeing, all-holy, just, and righteous Judge, 
 guiding and controlling the destinies of men. 
 
THEOLOGY. I47 
 
 And,- as a merely intellectual idea, there is no 
 other fitting end of the study of the lower branches of 
 the hierarchy 1;han the recognition of the wisdom and 
 goodness of the Creator. Those modern European 
 writers who think that Theism is an inferior 
 system to Pantheism, because it is the system of 
 the Semitic races, who are inferior to the Japhetic, 
 are as mistaken in their intellectual conceptions of 
 science, as in their prejudice of race. Physical science 
 is the unfolding of the harmony of the creative 
 thoughts ; and Mathematical Science derives its value 
 from its furnishing means by which we demonstrate 
 that harmony. 
 
 I have been acquainted with two distinguished teach- 
 ers, who conscientiously abstained from giving to their 
 pupils their own opinions concerning religion ; they 
 seemed, in regard to theology, to value freedom above 
 truth ; and would rather have their pupils fall in error, 
 than to exert the slightest influence over them, to bias 
 them. It seemed to me a mistaken course, and I think 
 that in both cases, it had a disastrous effect on the pupils. 
 Irreligious and sceptical men, and sceptically inclined 
 young people, will interpret such silence as disbelief 
 in religion ; and the teachdr does thus bias the minds 
 of some of his pupils towards unbelief. I respect a 
 man who earnestly fights the principles of Newton as 
 erroneous, more than I can one who evades your 
 questions, and tells you that he does not wish to say 
 whether he believes or disbelieves the results of 
 science. I should prefer an outspoken atheistic, 
 materialistic opponent to Christianity, if I thought him 
 
148 TRUE ORDER OF STUDIES. 
 
 really honest, to a man who was unwilling to give 
 up the name of Christian, but even more unwilling 
 to let his pupils know his opinion concerning any point 
 of natural theology, or of revealed religion, or of the 
 evidences of Christianity. 
 
SCHOLIA. 
 
 149 
 
 CHAPTER XXII. 
 
 SCHOLIA. 
 
 I T^HE teacher must not forget that the education 
 -^ of the knowing faculties, is a very imperfect 
 and unimportant culture, unless we at the same time 
 time impart the power of expression and of action, and 
 awake sentiments and feelings worthy to be expressed 
 or embodied. In this Uttle volume we have been 
 chiefly occupied in showing in what manner we con- 
 ceive the circle of human sciences to be bound to- 
 gether in an ascending spire ; which is our best guide 
 in choosing subjects for intellectual instruction. But 
 the body also needs care ; the teacher and the parent 
 should see to it, that the child has fresh air, of proper 
 temperature : sufficient muscular exercise, and train- 
 ing of the muscles ; good and wholesome food, and 
 abstinence from what is hurtful; sunshine and 
 cheerful amusement. The heart needs training, and 
 the teacher and the parent must ever by the example 
 of reverence, kindness, good humor, patience, hope- 
 fulness, appreciation of the beautiful and the true, be 
 cultivating right affections. Above all the will needs 
 training, to prompt unhesitating action in obedience, 
 first to rightful authority on earth ; then to the will of 
 God, in heartfelt consecration to his service, and in 
 
150 TRUE ORDER OF STUDIES. 
 
 charity to men. The power of expression and action 
 is to be cultivated 'in every direction, pursuing every 
 scientific study, also, first of all as an art ; both for 
 its use as an art, and for the superiority of the mode 
 of approaching it as a science. 
 
 And we believe that the sequence of intellectual 
 studies which we have endeavored to show is con- 
 formed to the nature of things and to the nature of the 
 growing mind, will give also the best opportunity for 
 education in character and in executive ability. For 
 example, we place first in the scale of studies, the cul- 
 tivation of the powers of observation by the outward 
 senses ; before invention or reasoning. This intel- 
 lectual order gives the opportunity, in the case of the 
 child's body, for keeping him much out of doors, 
 rambling under the guidance of its teacher ; by the 
 roadside, or over the pastures, to the benefit of its 
 health, as much as of its mind. The same order gives 
 in moral education, the opportunity for developing 
 pure tastes, and a love of natural beauty ; it affords, 
 also, social pleasures of a higher character than the 
 ordinary plays of the school-yard. It gives, further- 
 more, the best opportunity for impressing the young 
 heart with a sense of the infinite wisdom and Ibve 
 manifested in the creation ; while the freedom of the 
 walk allows the child to manifest its character in its 
 treatment of its schoolmates ; and gives the skilful 
 teacher opportunities to influence it to active kind- 
 ness, thoughtfulness, and helpfulness. 
 
 The complaint, so urgently made by some, that an 
 intellectual education is a moral injury rather than a 
 
SCHOLIA. 151 
 
 moral benefit, has been abundantly shown by statistics 
 to be without adequate foundation. So far as it has 
 any foundation, it is grounded chiefly upon facts 
 arising out of the inverted order of our intellectual 
 drill ; teaching reasoning rather than observation • 
 taking the child's attention from God's book of nature 
 to fix it on books written by inferior men ; making 
 intellectual training so difficult and discouraging as to 
 interfere with the time and strength and heart for 
 moral training. 
 
 In like manner, the injury sometimes done to the 
 bodily health of students, by over exertion of the brain, 
 . comes in no small degree, from the unnatural order of 
 studies, giving the abstract before the concrete ; by 
 virtue of which the difficulties of each step are greatly 
 increased ; and it frequently becomes necessary for 
 the student to master, in a hurried manner, in a few 
 months, that which, under the natural order of studies, 
 he would have acquired leisurely and pleasurably, 
 years before. Whatever be the amount of knowledge 
 acquired in a given time, the ease of its acquisition, 
 and the case with which it can be applied to use, will 
 be partly proportional to the lucidness and naturalness 
 of the order in which its parts were arranged and pre- 
 sented to the student. This purely intellectual ques- 
 tions, therefore, of the true order of studies is inti- 
 mately connected, in more than one mode, with all 
 questions that involve the highest welfare of the indi- 
 vidual, and of the fam.ily, of the State and of the 
 Church. 
 
 Whether I have made any contribution toward 
 
152 TRUE ORDER OF STUDIES. 
 
 settling the question in what order the studies of the 
 curriculum ought to be placed, or not, the reader must 
 judge. August Comte classified the branches of 
 knowledge according to the degree of generality of 
 their ideas, placing mathematics first, because the 
 laws of form and number govern all matter in the 
 solar system ; and political economy last, because its 
 laws govern only about one million tons of matter, in 
 the form of human brains ; psychology and theology 
 he remanded to the realms of fable. Herbert Spencer 
 denies that the sciences can be arranged in any one 
 series ; but arranges them in two or more, making 
 the sequence in each series depend not upon the 
 generality, but upon the abstractness of the ideas in- 
 volved in the sciences. Thus he also places the 
 mathematics first because they are, in his view, the 
 most abstract. Other writers have classified the ob- 
 jects of study more or less thoroughly. But in what- 
 ever manner our philosophy leads us to classify the 
 branches of human knowledge ; and whether we do, 
 or do not, see a universal order and arrangement such 
 as I have given as the hierarchy of sciences ; this one 
 point I would press upon the reader as certainly true, 
 and of great practical moment, viz. : that in a great 
 many cases, notably in mathematics and physics, there 
 is a natural order in which they should be taken up, 
 and that the neglect of this order, so common in our 
 schools and colleges, involves a great waste of the 
 student's time and power, and cripples his usefulness 
 in after life. 
 
 While all the studies of the curriculum must be 
 
SCHOLIA. 153 
 
 used as means of guiding and developing the power of 
 action and expression, as well as of thought, it must 
 especially be remembered that the historical studies, 
 (trades, arts, language and law) are peculiarly adapted 
 to this function; and the teacher must be careful to 
 make them all conspire in giving the pupil freedom 
 and power in utterance ; by the lips, by the pen, by 
 the fine arts, by right action. Intellectual thought 
 finds utterance in words ; sentiment in art ; principle, 
 in acts. Action strengthens principle, gives depth to 
 sentiment, and clearness to the intellectual vision. 
 
 To recapitulate ; I see the objects of human 
 thought and knowledge arrange themselves in five 
 great groups. Under the first come Space and Time, 
 and the abstract idea of Number ; concerning these, 
 men build the sciences of Geometry, Arithmetic, 
 Algebra, and higher mathematics. Under the second 
 lies matter, the physical universe in all forms ; con- 
 cerning which we have sciences of mechanics, with 
 its remote branches of acoustics, thermotics, optics, &c., 
 chemistry, physiology, botany, zoology, geology, astron- 
 omy, &c. The third group is historical, and embraces 
 all that man has said or done on this planet ; his 
 manufactures, commerce, agriculture, government, 
 war, literature, fine arts, &c. The fourth group takes 
 in the mental, and spiritual powers of man ; and con- 
 siders his capacity for thought, for passion and senti- 
 ment, and for actions what the powers are, and how 
 limited and modified. The fifth group embraces all 
 the attempts which man has made to rise to a knowl- 
 edge of the ultimate causes of things, the origin of the 
 
 7* ■ ' 
 
154 TRUE ORDER OF STUDIES. 
 
 Universe, the mystery of the government of all the 
 phenomena by noumena, — the reign of law, which law 
 is thought. 
 
 These five great branches appear to be logically 
 dependent in the order in which I have placed them ; 
 geometry being the foundation of learning ; nor can 
 we conceive a man gaining a knowledge of anything 
 whatever, except geometry, until he has gained the 
 corresponding foundations of his knowledge in each 
 of the groups below, down until he reaches the knowl- 
 edge of relations in space. 
 
 The order of the hierarchy is the logical order in 
 which the sciences are developed one after the other, 
 but it by no means follows that mathematics can 
 be developed and followed to their highest sum- 
 mit without reference to any thing that succeeds. 
 There is such a mutual inter-dependence that the 
 lower branches are continually suggested by the 
 higher ; and in any one study, we not only require 
 a competent knowledge of the lower branches, to en- 
 able us to stand where we are, but we must attempt 
 to use our knowledge upon a higher branch, in order 
 to receive any impulse, to rise higher in the one upon 
 which we stand. Thus the mathematics were stimu- 
 lated and enlarged by the attempt to apply them to 
 mechanics and crystallography, and these again 
 stimulated by the attempt to apply them to chemistry. 
 Chemistry saw new fields when she sought to solve 
 the problems of physiology ; and thus on through the 
 whole of the sacred circle. 
 
 For a full harmonious development of a child's 
 
SCHOLIA. 
 
 155 
 
 mind we must daily recur to the five essential branches 
 of inquiry suggested by every sight of nature. The 
 youngest child brings in, for example, a dandelion. 
 Its circular form, its radiant lines, the number of its 
 rays, the bell shape of the involucre, the cylindrical 
 scape, and its cylindrical cavity, the close spiral into 
 which the split end of the scape curls itself, these 
 are mathematical points to which his attention may 
 easily be directed. Its yellow color, slightly bitter 
 taste, the use of its root in medicine, and in the 
 adulteration and imitation of coffee, its relationship to 
 asters, sunflowers, ox-eye daisies, fleabane, tansy, 
 yarrow, ragweed, — these matters belong to the great 
 group of natural history ; — in some of them the 
 youngest child can be interested, and in all of them 
 the older ones. The derivation of the name, 
 dandelion (dents de lion, dens leonis) from the 
 form of the green leaf ; and of the generic name, 
 taraxacum, from its medical effects ; the fact of its 
 introduction from Europe ; quotations from Lowell, 
 and other poets, referring to it ; these would be 
 historical instructions naturally flowing from the 
 incident of the dandelion being brought into the 
 schoolroom. If now the child is asked Avhy he likes 
 the flower so much ; whether it is because it is 
 prettier than others ; or whether because it comes so 
 early in the Spring ; or whether because it is so com- 
 mon, the poor man's flower, and the children's flower; 
 the questions will stimulate a healthy psychological 
 curiosity, not a morbid introversion, but held still to a 
 healthy attitude by its external hold upon the flower. 
 
156 TRUE ORDER OF STUDIES. 
 
 And finally this little flower may give theological 
 lessons of great value, if without parade or cant, but 
 in a simple and natural manner, you allude as from 
 your own fulness of heart, to the goodness of the 
 Heavenly Father, in spreading beauty with so un- 
 sparing a hand ; or simply bringing to the child's re- 
 membrance, by quotation, or by a child like para- 
 phrase, the Saviour's appeal to our consciences, drawn 
 from the lily of the field. 
 
 Now every lesson, in this school of life, will lead, 
 as naturally as this dandelion has done, to the five 
 great branches of intellectual studies ; and no lesson 
 has done its full work for our minds until it has been 
 thus linked into relation with all the main lines of de- 
 pendent truth. The simplest geometry has its appli- 
 cation to physics ; its history of discovery and appli- 
 cation ; its psychological questions of the foundations 
 of belief, and the nature of proof; its theological 
 aspect, in the query for example whether the relations 
 of space are dependent on the nature of our minds, and 
 thus upon the will of the Creator. The cycle of the 
 five branches must thus be daily recurring, and my 
 aim in these chapters has been to show in what order 
 the five branches are to be placed ; which must 
 always precede, and which follow ; which must always 
 be in a higher state of development ; and which, the 
 crown and glory of the whole, must always lie least 
 within the reach of our finite faculties. 
 
 The highest truths which man can possibly seek 
 are those which directly pertain to the unlimited 
 Power, the unfathomable Wisdom, the inexhaustible 
 
SCHOLIA. 157 
 
 Love, out of which the wondrous spectacle of the 
 Universe, and we, as spectators and actors therein, 
 ever flow ; the knowledge of these truths is Theology. 
 The next subject in dignity and importance is the 
 investigation of our own souls, whose thoughts and 
 emotions, and holiest sentiments, we see prefigured 
 and pre-embodied in nature ; and it is by that pre- 
 sence of a likeness within us to the creative energies, 
 that we are able partly to comprehend the created 
 universe. The study of the human mind, the greatest 
 work of God known to us is Psychology. Thirdly, in 
 our inquiries, we ask what our fellow men have 
 thought, and said, and done, on this theatre of the 
 earth ; and the answer to these inquiries we call 
 history. Fourthly, we ask concerning the other acts 
 of the Creator, known to us, beside the creation of 
 human spirits ; we inquire concerning this universe 
 of matter which He has made, — and trust that it is 
 not irreverent to call the answer to our inquiries 
 Natural History. Finally, our attention is directed to 
 the Universe of Space and Time, in which the realm 
 of matter floats, and to which our spirits are tied by 
 our material bodies ; but the relation of which either 
 to the finite or the Infinite Spirit, is beyond our grasp. 
 And the truths of space and time which we are 
 taught, we call mathematics. 
 
 In the following Curriculum, I lay out the plan of 
 studies for an ideal course of liberal education ; laid 
 out as within the reach of the majority of pupils, as I 
 have known them in a long acquaintance with public 
 
158 TRUE OEDER OF STUDIES. 
 
 schools in our country. But it must be borne in mind 
 by him who would examine and criticise that course 
 of studies, that it has a unity from beginning to end ; 
 and that the work of the later years will be impractic- 
 able for scholars who have not had the earlier training 
 here prescribed. 
 
A CURRICULUM. 
 
 159 
 
 CHAPTER XXIII. 
 
 A CURRICULUM. 
 
 . I. Alphabet, or Sub-primary School. 
 For children five to eight years old. 
 
 1. Mathematics. — Building with little bricks, and 
 blocks, playing with geometrical puzzles or tangrams, 
 drawing geometrical figures ; counting beans, and 
 grouping them ; keeping time in music, afterwards 
 learning the Arabic figures. 
 
 2. Natural Histoiy. — Equilibrium, and breaking 
 joints in their block buildings, gathering and naming 
 stones, plants and insects ; afterwards learning the 
 names of their own limbs and bones ; and the simp- 
 lest facts of geography illustrated by a globe, rectified 
 in the actual sunshine. 
 
 3. History. — Singing by rote, and afterwards by 
 note ; phonetic analysis of words, reading phonotype, 
 and in the last year common print. Drawing from 
 copies and natural objects. Careful subjection to the 
 rules of the school, and incidental instruction. 
 
 4. Psychology. — Very little and purely incidental. 
 
 5. Theology. — Incidental, from presence at devot- 
 ional exercises, &;c. 
 
l6o TRUE ORDER OF STUDIES. 
 
 11. Primary School. 
 
 For children front eight to eleven years old. 
 
 1. Mathematics. — Theorems of geometry as facts, 
 without reasons. Drawing. The four simple rules of 
 written arithmetic, in whole numbers and decimals, 
 practised as an art, not studied as a science. Keeping 
 time in music. 
 
 2. Natural History. — Incidental instruction on the 
 sensible properties of body, degrees and kinds of hard- 
 ness, elasticity, fluidity, etc. Afterwards on rust, com- 
 bustion, soap making, fermentation, etc. Examination 
 of minerals, plants and animals, and learning to recog- 
 nize them. Geography from the globe. 
 
 3. History. — Visits to shops, farms, factories, &c. 
 Draw, sing, and begin on the piano if convenient, at 
 home. Reading and writing, both common hand and 
 phonography ; keeping in short-hand a brief diary ; 
 and writing in long hand letters to other children 
 and little stories. Oral instruction in History of the 
 United States. 
 
 4. Psychology. — As before. 
 
 5. TJieology. — Incidental instruction directed chief- 
 ly to cultivation of a reverent and devout spirit, rather 
 than to any theological opinions. 
 
 III. Grammar School. 
 For children from eleven to fourteen years old, 
 I. Mathematics. — Plane geometry. Mental and 
 
A CURRICULUM. l6l 
 
 written arithmetic, except evolution. Use of log- 
 arithms. 
 
 2. Natural History. — Astronomy in simple form. 
 Physical geography, maps. Elementary mechanics. 
 Incidental chemistry. Botany, zoology, anatomy. 
 
 3. History. — Oral accounts of inventions, and dis- 
 coveries. Continue drawing and singing, introducing 
 landscape, and part-singing. Commit to memory 
 selections from the best poetry. Read French with- 
 out grammar or dictionary. Towards the close, learn 
 the parts of speech, and take the elements of grammar. 
 Continue the History of the United States, and begin 
 that of England and the Jews. 
 
 4 and 5. Psychology ajid Theology. — As before, the 
 incidental instruction being based partly now upon 
 the readings from the Bible. 
 
 IV. High School. 
 
 For scholars from fourteen to seventeen years old, 
 
 I. Mathematics. — Solid geometry, algebra, trigono- 
 metry and its applications. Brief review of arith- 
 metic, with evolution, and practice in logarithms. An- 
 alytic geometry. For scholars of higher ability, the 
 rudiments of calculus, and of quaternions, orally 
 imparted. 
 
 X 2. Natural History. — Elements of acoustics, op- 
 tics and thereotics. Physical geography. Geology. 
 Elements of Chemistry, electricity and magnetism. 
 Physiology, botany and zoology. 
 
1 62 TRUE ORDER OF STUDIES. 
 
 3. History. — History of agriculture, manufactures, 
 and commerce. Drawing and music. Continue to 
 read French as before, and take up the study of Latin. 
 Afterwards read German as you did the French, and 
 take up the rudiments of Greek. Take successively 
 histories of England and of Greece, and Rome. Con- 
 stitution of the United States, with oral instruction on 
 constitutional law. 
 
 4. Psychology. — Begin elements of intellectual 
 philosophy, criticism, and ethics. 
 
 5. Theology. — The incidental instruction, from the 
 Bible reading and from history, may become more 
 full and explicit. 
 
 V. College. 
 
 For scholars from seventeen to twenty-one years old. 
 
 1. Mathematics. — (Only for those of mathematical 
 ability). — Analytic geometry as affected by the calcu- 
 lus. Elements of more modern inventions, quaternions, 
 stis-matics, kinematics, etc. Lectures on the methods 
 of the mathematics. 
 
 2. Natural History. — (Reserved for those of 
 special taste for these studies). — Analytical mechanics, 
 applied to optics, thermotics, astronomy, etc., etc. 
 Chemistry, botany, zoology, geology. 
 
 3. History. — Political economy, rhetoric. Writing 
 on themes. Extemporaneous debate. Declamation of 
 the student's own writing. Constitutional law. His- 
 tory of the Greeks, Romans, Jews and EngUsh. For 
 
A CURRICULUM. I63 
 
 those of special tastes, Music and other arts ; or 
 languages, and philology. 
 
 4. Psychology. — Metaphysics, logic, aesthetics, 
 ethics. 
 
 5. Theology. — Natural theology, evidences of 
 Christianity. 
 
 THE END. 
 
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