April ii, 1890.] 



SCIENCE. 



2J5^ 



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 surprising re- 

 sults attained by Indian children, by attributing them to special 

 mental development due to ages of oral construction. It is per- 

 fectly 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 known that many of the ablest men the country has 

 produced could neither read nor write ; but they hardly missed 

 those accomplishments, for their minds were frequently stored 

 with more information, which was more ready to their command, 

 than that possessed tiy the majority of book-students. It is well 

 known that Ranjit 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 neighbors, the strength and weakness of the English, 

 and was in all respects a flrst-class administi'ator. We commit 

 the mistake of thinking that the means to knowledge is knowl- 

 edge itself. This induces us to give all the honor and prizes to 

 reading and writing, and leads us to de.spise people, whatever 

 their i-eal 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 triuifiphs of 

 India were nearly all built by men who could neither read nor 

 write. Another illustration of dependence upon memory instead 

 of paper can be found in the Indian druggist, who will have hun- 

 dreds of jars, one above another, from floor to ceiling, not one of 

 them marked by label or ticket, yet he never hesitates in placing 

 his hand on the right vessel whenever a drug is required. The 

 same, to us, phenomenal power of memory is shown by the ordi- 

 nary 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 units, tens, hundreds, etc.; but the monosyllabic 

 curtness in the names of the higher numbers is his distinct ad- 

 vantage. 



What we call the multiplication table then begins. In England 

 the multiplier remains constant, and the multiplicand changes: 

 thus children repeat, "twice one, two; twice two, four; twice 

 three, six;"' etc. In India the boy is taught to say, " one two, 

 two; two twos, four; three twos, six; "' etc.; his multiplier chan- 

 ging, while the multiplicand 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 Eng- 

 lish language lacks terms to translate the first table, but an idea 

 may be gained from the following attempt: one unity, one; one 

 couplet, two; one triplet, three; one quadrat, four; one pentad, 

 five; etc. 



These names for aggregates, as distinguished from mere nu- 

 merals, are of much value to the boy in the subsequent processes, 

 and give him another distinct advantage. 



In learning these tables the boy is not carried beyond 10; that 

 is, he goes no further than "two tens, twenty," "three tens, 

 thirty," etc.; but to make up for that forbearance he is carried on 

 in this process of multiplying figure by figure not only to 12, or 

 up to 20, but he goes on througli the thirties, and does not make 

 his first halt until he gets to "ten forties, four hundred." In 

 achieving this result something more than mere memory is 

 brought into play, for he is taught to assist his memory by refer- 

 ence from one table to another; thus the first half of the six table 

 is contained in the three table, etc. 



A short supplementary table is next taught, beginning at 11 x 

 11 to 20 X 11, and then proceeding to 11 x 12 to 20 x 12, 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 therefore only half calls for special effort. 



The boy has now committed to memory the multiplication of 

 every figure from 1 X 1 to 20 X 20, and in addition be knows 

 the multiplication of every figure up to 40 by the ten "digits." 

 It will be observed that both tables end at 400 (10 x 40 and 20 X 

 20); in fact. 4 is the most important factor in Hindu arithmetic, 

 all figures and fractions being 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 immedi- 

 ately proceeds to tables of fractions, the first being the multipli- 

 cation of every figure from 1 to 100 by }. Here, again, f 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 (i), and 

 the thing is done. Memory is assisted by observing that every 

 multiple of 4 is a whole number, and that the number below it 

 will always be a sawd of the next lower figure, and the number 

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

 answer to the question f x 36, the Indian boy says mentally, 18, 

 9, 27; he also knows that 36 is the ninth multiple of 4, and by im- 

 mediately deducting 9 can get his 27 that way also. Knowing, 

 also, that 36 is a multiple of a 4 yielding 27, he knows that 35 will 

 yield saifrJ cM«6&is (26J), and that 37 wUl yield paune athd, is 

 ( — 28 = 27i). In this way three-fourths of the table isa matter of 

 logical necessity, resting on the elementary table previously 

 acquired. 



In the next table the boy is taught to multiply every figure 

 from 1 to 100 by IJ. This, of course, is. precisely the reverse of 

 the last: the J is ascertained and added, iiistead of being deducted. 

 Here, again, the multiples of 4 are whole numbers; but the fig- 

 ures preceding result this time in a paune, and those next fol- 

 lowing in a sawa. This table also costs but little effort when: 

 thus taught. 



The next table leaches the boy to multiply from 1 to 100 by 1|, 

 and of course means simply adding half the multiplier to the fig- 

 ure itself. 



The next step, multiplying from 1 to 100 by If, is achieved by 

 simply adding three-quarters of the multiplier to the multiplier 

 itself. The "three-quarters" table has been already acquired by 

 the boy, and he has therefore only to add any given multiplier ta 

 it. Thus, if asked, "What is 27 times If?" he knows that 27 

 paunes are 20 J: he has therefore only to add this to the 27 itself 

 to get 47i as the instant answer. 



The boy is next exercised in multiplying 1 to 100 by 2|, and he 

 is taught to do this by adding half the multiplier to the " twice- 

 times" table. 



Then follow similar tables multiplying by Si, 4J, and 5i; and 

 the results are arrived at instantaneously by adding to the "three- 

 times," "four-times," and "five-times' tables half the multiplier 

 in every case. 



In all these tables the rapidity and simplicity is in great part 

 due to the terms employed. The boy is not asked to "multiply 

 seventeen by three and a half," or "What is three and a half 

 times seventeen?" or puzzled by any other form of clumsy ver- 

 bosity. The terms he uses allow him to be asked " sattrah 

 hmthe"' ("seventeen three-and-a-halfs"). His elementary table 

 has taught him that 17 x 8 = 51, and he knows that he has only 

 to add half 17 to that, and the sum is done. 



The final task of the Indian boy is a money table, which deals 

 with a coinage which may be thus sunmiarized : \Q damri = 1 

 taM; 16 take = 1 and; 16 dne = 1 rupi. 



There is a small coin called dam, three of which make 1 damri;-, 

 and therefore 48 make 1 taM, and 96 = ana, 4* being still the 

 unit. The table imparts a familiarity in combining these coins. 

 together. 



This completes an Indian boy's most elementary course of arith- 

 metic; and a little reflection on the great facility for computatior*. 

 which Indian children show, and the simplicity of the means by 

 which it is effected, ought to make us rather ashamed than boast- 

 ful of our own defective methods. 



