106 



KNOWLEDGE 



[Apiul 1, 1890. 



boy has to deal with only the minus and plus quantities. 

 A simple instance will illustrate this. " Seven times 

 ninety-nine and three-quarters ? " would be a puzzle to 

 an Eni^lish child, both on account of its lumbering 

 phraseology, and the defective arithmetical process he is 

 taught to employ. The Indian boy would be asked, 

 "Sir* paune-miu'? " three words meaning "seven minus- 

 hundreds'?" The very form of the question tells him 

 that he has only to deduct seven quarters from 700, and 

 he instantly answers 698^. Equal facility is found with 

 any similar question, such as " five times fourteen and 

 three-quarters." The Indian boy is asked, " panch 

 paune-pandrah •? " i.e. "five — 15's'?" As the words 

 are uttered he knows that he has only to deduct 5 

 quarters from 5 fifteens, and he answers at once " paime 

 ■chau-hattrah," i.e. "a quarter less four-and-seventy " 

 .(73f). 



So much for the machinery with which the Indian boy 

 works. The more it is understood, the more it will be 

 appreciated. It is, undoubtedly, strange to English pre- 

 conceptions ; but it would be a real blessing to our country 

 if corresponding suitable terms were invented, and this 

 admirable system were introduced into all our schools. 



Some Europeans have sought to account for the sur- 

 prising results attained by Indian children, by attributing 

 them to special mental development due to ages of oral 

 •construction. It is perfectly true that Indians rely more 

 on their memories than on artificial reminders, and no one 

 can come into contact with the people without being struck 

 by their capacity for remembering. It is well knowTi that 

 many of the ablest men the country has produced could 

 neither read nor write ; but they hardly missed those ac- 

 complishments, for their mmds were frequently stored with 

 more information, which was more ready to their com- 

 mand, than that possessed by the majority of book-students. 

 It is well known that Eanjit Singh could neither read nor 

 write, but he knew all that was going on in every part of a 

 kingdom as large as France. He was an able financier, 

 and knew at all times accurately the contents of all his 

 treasuries, the capacities of his large and varied provinces, 

 the natures of all tenures, the relative power of his neigh- 

 bours, the strength and weakness of the English, and was, 

 in all respects, a first-class administrator. We commit 

 the mistake of tliinking that the means to knowledge is 

 knowledge itself. This induces us to give all the honour 

 and prizes to reading and writing, and leads us to despise 

 people — whatever their real attainments may be — who 

 have not acquired the knack of putting their information 

 on paper. It ought to modify our opinion on this point to 

 reflect that the architectural triumphs of India were nearly 

 all built by men who could neither read nor write. 

 Another illustration of dependence upon memory in- 

 stead of paper can be found in the Indian druggist, 

 who ^^'ill have hundreds of jars, one above another, from 

 floor to ceiling, not one of them marked by label or ticket, 

 yet he never hesitates in placmg his hand on the right 

 vessel whenever a drug is required. The same, to us, 

 jjhenomenal power of memorj' is shown by the ordinary 

 washermen, who go round to houses with their donkeys, 

 and collect the clothes, some from one house, some from 

 another. These they convey to the river and wash, and 

 in returning with the huge pile, never fail to deliver each 

 particular article to its rightful owner. 



The Indian boy's first task is necessarily to commit to 

 memory the names of the figures from 1 to 100. He is 

 next taught that there are nineteen places for figures, 

 and their names. These correspond to our imits, tens, 

 hundreds, &c. ; but the monosyllabic curtness in the 

 names of the higher numbers is his distinct advantaire. 



What we call tin; multiplication table then begins. In 

 England the nniltiplier remains constant, and the multi- 

 plicand changes ; thus, children repeat "twice one two; 

 twice two four ; twice three sis," &c. &c. In India the 

 boy is taught to say "one two, two; two twos, four; 

 three twos, six," &c., his multiplier changing, while the 

 miUtiplicand remains fixed. Another peculiarity is this, 

 he begins at 1, not at 2; and this furnishes him with a 

 series of most useful collective numbers. Here, again, the 

 English language lacks terms to translate the first table, 

 but an idea may be gained from the following attempt : — 



One unity 

 One couplet . 

 One triplet . 

 One quadrat. 

 One pentad . 

 &c. 



one 



two 



three 



four 



five 



These names for aggregates, as distmguished from mere 

 numerals, are of much value to the boy in the subsequent 

 processes, and give him another distinct advantage over 

 the English lad. 



In learning these tables the boy is not carried beyond 

 10, that is, he goes no further than "two tens, twenty," 

 " three tens, thirty," kc. ; but to make up for that for- 

 bearance he is carried on in this process of multiplying 

 figure b}' figure not only to 12, or (as is sometimes done 

 in England) up to 20, but he goes on through the thu'ties, 

 and does not make his first halt until he gets to " ten 

 forties, fom'-hundred." In achieving this result something 

 more than mere memory is brought into play, for he is 

 taught to assist his memory by reference from one table 

 to another, thus the first half of the six table is contained 

 in the three table, &c. 



A short supplementary table is next taught beginning 

 at 11x11 to 20x11 and then proceeding to 11x12 to 

 20x12, and so on up to 20 x 20. This method reduces 

 considerably the tax on the memory ; for one half of the 

 table is obviously the same as the other half, and there- 

 fore only half calls for special effort. 



The boy has now committed to memory the multiplica- 

 tion of every figure fi-om 1x1 to 20 x 20, and in addition 

 he knows the multiplication of every figure up to 40 by 

 the ten " digits." It will be observed that both tables 

 end at 400(10x10 and 20x20); in fact, 4 is the most 

 important factor in Hindu arithmetic, all tigiu'es and 

 fi'actions bemg built upon multiples and fractions of it. 



At this point, instead of practising on imaginary sums 

 in the hope of learning arithmetic empirically, the Indian 

 lad immediately proceeds to tables of fractions, the first 

 being the multiplication of every figure from 1 to 100 by 

 |. Here, again, according to English ideas, | would be 

 the last fraction we should attempt ; but in India it is 

 the first, and, by the superior system of nomenclature 

 there in use, it is a very easy affair. The boy, knowing 

 the multiplication of the whole numbers, is taught to 

 deduct the half of the half (j), and the thing is done. 

 Memoi-y is assisted by obser\'ing that every multiple of 4 

 is a whole number, and that the number below it will 

 always be a .■,((/(■(; of the next lower figure, and the number 

 above it always a iiuune of the next higher figure. Thus in 

 answer to the question | x 36 the Indian boy says mentally, 

 18, 9, 27 ; he also Imows that 36 is the !Jth multiple of 4, 

 and by immediately deducting 9 can get his 27 that way 

 also. Knowing, also, that 86 is a multiple of a 4 yielding 

 27, he knows that 35 will yield suiva chlidlihis (20^) ; and 

 that 37 will yield iKtiuie <ith<i,is (-28=27f). In this 

 way three-fourths of the table is a matter of logical necessity, 

 resting on the elementary table previously acquired. 



In the next table the boy is taught to multiply every 



