150 



THE POPULAR EDUCATOR. 



different divisions of arithmetic may be placed before the 

 learner. In the earliest stages, then, the teacher should deal 

 almost entirely with concrete numbers, and these of the simplest 

 nature. After patiently giving the pupil the first ideas of 

 number, he may show how to add simple and easy numbers 

 together, in every case giving questions to be solved mentally, 

 before proceeding to the use of pen or pencil. When the pupil 

 becomes expert in the addition of units, easy sums of two 

 columns may be given, with a clear explanation, so far as is 

 needful at this stage, of the decimal system of notation. Sub- 

 traction of small numbers may now be very properly intro- 

 duced ; the columns should very gradually be extended to three, 

 then four, and so on up to millions. Assuming that during 

 these lessons frequent mental exercises have been given in 

 addition and subtraction, illustrated by reference to actual ob- 

 jects, as marbles, buttons, or nuts, whenever a difficulty occurs, 

 we would now introduce the multiplication table by short and 

 easy steps, occasionally proving the truth of the various pro- 

 ducts by reference to tangible objects, and showing that the 

 result is the same, in whatever order we use the factors e.g., 

 9x7=7x9. Multiplication and, after a time, division may 

 be explained to the pupil at first by very simple and easy 

 examples, the difficulties being increased as the pupil has cou- 

 rage and power to encounter them. The cnnection between 

 addition and multiplication, and that between subtraction and 

 division, may now conveniently and with great advantage be 

 demonstrated and illustrated by appropriate examples. Long 

 before this stage, however, the idea of a fraction should have 

 been imparted to the scholar, and very simple questions given 

 to exemplify the various fundamental operations which such an 

 idea involves : without this the pupil will be totally unprepared 

 to realise the nature of a remainder in an example in division. 

 Want of space entirely precludes us from noticing, even in 

 this very cursory manner, the compound rules, practice, bills of 

 parcels, proportion, vulgar and decimal fractions, and the rules 

 which ordinarily follow them ; but in every case the advance 

 should be gradual and easy, the examples very numerous, and 

 principles should precede the enunciation of rules. 



We have said that these three subjects reading, writing, and 

 arithmetic must form the basis of every rational and useful 

 education, and more especially so in our primary schools ; but 

 much more may with immense advantage be built upon them. 

 Daring the earlier months of the pupil's school life, such lessons 

 on familiar things as we indicated in a preceding paper may be 

 given. Lessons on geography, on outline drawing, and exercises 

 in vocal music set to simple and healthy school songs, may 

 next occupy some portion of the attention ; and the elder and 

 more advanced scholars may receive, in addition, elementary 

 instruction in grammar and English history, simple expositions 

 of the laws of health, and of the conditions of success in 

 social life. If to these we add a continuous attention to tho 

 inculcation of moral and religious duties, based on the teaching 

 of Holy Scripture, we shall have a programme of school work 

 at once useful and practicable for the great majority of our 

 people. 



We are compelled to compress our remarks on the sundry 

 studies suitable for the middle and higher schools, and for 

 evening classes, within scanty limits. They may for the most 

 part be included under three heads language, mathematics, 

 and science. The first of these heads includes the English 

 language, French, German, Italian, Latin, and Greek. Admir- 

 able courses on each of these subjects, as well as on many 

 others, are included in this series of the POPULAR EDU- 

 CATOR. Language, when studied in connection with the lite- 

 rature, geography, and manners of the country and people, is, 

 perhaps, the most efficient educational instrument which can 

 be found far superior, indeed, in its effects on the mind and 

 character, to either mathematics or science when used' alone. 

 It is valuable on account of the information which its study 

 affords : by its means we see into the mental life and the cha- 

 racter of those who use it, and cannot fail to profit by the 

 spectacle. The study of language affords an admirable disci- 

 pline for the mind by developing and sharpening the powers 

 of analysis, and by training to patient habits of investigation 

 and comparison. The parsing of words, the study and analysis 

 of sentences, the investigation of idioms and modes of expres- 

 sion, and of the meaning of -words in relation to their con- 

 text, form an unequalled mental training. Mathematics may 



be divided into three sections : 1, The science of number, in- 

 cluding arithmetic and its varied applications ; 2, the science 

 of magnitude, as geometry, trigonometry, geometrical analysis, 

 physical and nautical astronomy ; 3, the science of processes, 

 comprehending algebra, conic sections, the theory of equations, 

 the differential and integral calculus. The diligent study of 

 these branches of human knowledge tends to cultivate the 

 habit of continuous and close attention, fosters the power of 

 attending to details a habit invaluable to the student and to 

 the man of business strengthens the faculties of abstraction 

 and generalisation, trains the mind to synthetical as well as 

 analytical reasoning, and gives full scope to that resolute and 

 indomitable determination to encounter and conquer difficulties 

 which is the best pledge of success in the future battle with 

 the world. Our third head includes physical science, mechani- 

 cal science, astronomy, optics, chemistry, electricity, magnetism, 

 physiology, anatomy, zoology, botany, geology, and mental and 

 moral philosophy. The intelligent comprehension of one or more 

 of these subjects is not only attended by many pf the advan- 

 tages mentioned above, but also makes man acquainted with 

 the blessings of life as we now live it, and fills the devout 

 mind with unspeakable wonder and admiration of His power 

 who created all things, and of His infinite wisdom in whose 

 mind all this knowledge was stored before the work of creation 

 was begun. 



We mention Holy Scripture last among the subjects of edu- 

 cation because we look upon it as chief among them all. It 

 should be the source from which the principal part of our 

 moral and religious instruction is drawn. The biography and 

 precepts contained therein furnish abundant topics on which 

 may be founded a complete course of training for the moral 

 and religious parts of our nature, and is " profitable for doc- 

 trine, for reproof, for correction, for instruction in righteous- 

 ness," that we may be "throughly furnished unto all good 

 works." 



CORRESPONDENCE IN FRENCH. IX. 



39. LETTER WITH STATEMENT OF ASSETS AND LIABILITIES. 



Manchester, July nth, 18 . 



Messrs. Wybourne and Ashford, Liverpool. 



Gentlemen, You will doubtless be acquainted with the sad 

 position of trade in Germany, from the effects of the unsettled 

 state of political affairs in that country. 



Under these circumstances, it is quite impossible at present 

 for the manufacturers to effect any sales, or even to raise money 

 upon their stocks, which are considerable. 



As you are aware, our chief business is with Germany, espe- 

 cially with Saxony, the very centre of the war ; you will there- 

 fore easily understand that wo are affected to a considerable 

 extent by this unfortunate state of things. 



For the last twelve months we have very much restricted our 

 transactions, and endeavoured, but unhappily without much 

 success, to collect our outstanding debts. 



It is therefore with the deepest concern that we are under the 

 painful necessity of informing you that, for the present, we are 

 unable to meet all our engagements. 



We enclose an approximate statement of our assets and 

 liabilities, from which you will perceive that the former greatly 

 exceed the latter, so that even allowing 25 / for any had debts 

 there will still be sufficient to pay our creditors in full. 



Our debtors, as you will see by the same statement, were all 

 good houses, whose difficulties arose in consequence of the events 

 before mentioned, and we doubt not that they will be able to 

 resume their payments as soon as political affairs become a 

 little more settled, and they are able to dispose of their goods. 



We are preparing a balance-sheet, which we "^all lay before 

 our creditors at the meeting which we purpose holding on 

 Monday, the 22nd, and at which we hope you will be present, so 

 that we may submit to you the exact state of our affairs, and, 

 we hope, arrive at an arrangement. 



We are, Gentlemen, 



Yours most obediently, 



A. MORI & Co. 



Manchester, Ic 17 Juillet 18 . 

 Messieurs Wybourne & Ashford, a Liverpool. 



Messieurs, Vous aurez Bans doute connaissance de la triste 



