234 



SCIENCE. 



[Vol. XV. No. 375 



must be specially well fitted for one kird of work, and for no other 

 as well. 



That would spem to settle the question, but it does so only ap 

 parently. The child is a " soft and yielding being." Plant-like, 

 he accommodates himself to influences which play upon him. 

 His aptitudes grow exuberantly on the one side, and become 

 crippled on the other, as friend iv or hostile influences prevail. A 

 symmetrically shaped plant will become twi.sted and distorted if 

 placed against a wall. It depends upon the treatment of the 

 gardener, whether a tree will spend its energy in producing leases 

 or fruit. A. boy six years old may have a talent for art, his sense 

 of form and color may be very pronounced; yet after five years 

 he may be found to have apparently lost that faculty, and devel- 

 oped in a direction which makes the observer prophesy that the 

 boy will become a great lawyer. And, again, after some years 

 he may be found to have developed great skill in manual occupa- 

 tion, having apparently pressed into the background his liking of 

 art and literature. 



These are no hypothetical cases. Every observant educator 

 will have come to the conclusion ere this, that it is utterly un- 

 fruitful and perilous to fore ordain a pupil's future. This being 

 the case, it seeais to me wise to follow the advice of eminent men ; 

 to wit, develop harmoniously all the talents that manifest them- 

 selves in the child, and leave the choice of occupation or calling 

 to the developed and ripe judgment of the youth. Do not make 

 this choice irrevocable. Give every one the greatest possible 

 freedom for changing his profession, or occupation, or calling (or 

 give it whatever name you will), if he comes to the conclusion 

 that he missed it in his first choice. A human being who has had 

 the chance and manifold opportunities for testing his natural 

 gifts, and is permitted to exert himself in many directions, will 

 certainly find his natural calling, and achieve great success. Let 

 there be no arbitrary rules, no guild regulations, but let us main- 

 tain that liberty of action which has made this nation what it is, 

 the greatest, noblest, most talented, most energetic, most suc- 

 cessful, and therefore happiest, nation on the face of the earth. 



HINDU ARITHMETIC. 



Europeans who have resided in India have frequently expressed 

 astonishment at the rapidity with which arithmetical calculations 

 are mentally made by very small Indian boys. Some account, 

 therefore, of the Indian method of teaching arithmetic, w])ich is 

 believed to be superior to the English methods, is given by Fred- 

 eric Pincott, M.R.A.S., in the April number of Knowledge, and 

 will probably be interesting to our readers. 



The arithmetical system of Europe was revolutionized by India 

 when the so-called Arabic figures which we daily use were bor- 

 rowed by Arab traders to the Malabar coast, and by them intro- 

 duced into Europe. It was Indian intelligence which devised the 

 method of changing the values of the numeral symbols according 

 to their positions. This ingenious conception rapidly superseded 

 the older methods, and gave enormously increased facility to 

 arithmetical computations as compared with the Greek and 

 Roman and the older Arabic methods. 



In order to explain the present Indian system of arithmetic, it 

 is necessary to premise that the Pdndhes, or schoolmasters, em- 

 ploy a number of terms unknown to English teachers. These 

 terms have been invented for the purpose of facihtating calcula- 

 tion, and the astonishing results achieved cannot be understood 

 without comprehending the terms employed. The strangeness of 

 the names of the figures and fractions arrests the attention of 

 every student of Hindi Few attempt to master the fractions; 

 and there are some who, after many years' residence in India, 

 cannot repeat even the numbers from one to a hundred. 



Indians use monosyllables similar to ours, from 1 to 10; but 

 from that point the words are built on the model of " 1 and 10," 

 " 3 and 10," " 3 and 10," etc.,' up to " 8 and 10 ;" but the word 

 for 19 means " minus 20."' After 20 the same method is con- 

 tinued ; " 21 " being impossible, the form is invariably"! and 



1 This is also the original raeaningof the English words "eleven," "twelve," 

 etc., up to "nineteen." 



20," " 3 and 20," up to " minus 30," " 30," " 1 and 30," and so 

 on. This method of nomenclature goes back to remote antiquity, 

 for the old Sanscrit language presents the same peculiarity.' The 

 object of this nomenclature is to facilitate computation ; for, in 

 reckoning, the mind has to deal with the even tens, the simplest 

 of all figures to multiply. Thus the question, " 9 times 19," is 

 not a simple one to an English child ; but the Indian boy would 

 be asked, '■ 9 minus-twenties." In an instant he knows that he 

 has only to deduct 9 minus quantities from 9 twenties, and the 

 answer 171 comes before the English boy has fuUy realized the 

 question. The formidable difficulty of ibe 9 is thus completely 

 got rid of by a mere improvement in nomenclature. 



Another advantage that the Indian boy has is the use of short, 

 mostly monosyllabic, terms for every ascent in the decimal scale; 

 thus such lumbering expressions as '■ one hundred thousand " aire 

 unknown to him, the simple word Idkh conveying the idea fully 

 to his mind. So, also, "one thousand millions" is arb ; "one 

 hundred thousand millions "is kharb ; and so on. The advan- 

 tages of this terseness must be at once apparent. 



It is, however, with respect to fractional numbers that the ad- 

 vantage of the Indian system of nomenclature becomes most con- 

 spicuous, when once understood. They employ a large number 

 of terms, which are gi^en below, - 



These terms are prefixed when used in combination with whole 

 numbers, the object being to present the special modification to 

 the mind before the number itself is named. Complicated as this 

 nomeifclature appears at first sight;, its difficulties disappear when 

 brought to the test of practice. It is the outcome of centuries of 

 practical experience, and the thoughtful application of means to 

 an end. It will be sufficient to illustrate the use of these words, 

 and the extraordinary arithmetical facilities they afford, if the 

 use of panne is explained, that is, |, that being the fraction 

 which the English child has most trouble with. The Indian boy 

 knows no such expression as " two and three-quarters ; " in fact, 

 the term " three-quarters " in combination with whole numbers 

 has no existence in his language. His teacher resorts to the same 

 device as has been explained when speaking of the figur-e 9 : he 

 employs a term which implies " minus." By this process 2f be- 

 comes panne tin. that is, " minus 3,'" or "a quarter less 3 ; " and 

 in the same way 3f is paune char, that is, " minus 4 ; " and so on. 



Precisely the same plan is adopted with reference to the term 

 saud, which implies " one-quarter more :" thus 3J is saua. tin rs 

 " plus 3 ; " 4J is saiva char =" plus 4 ; ' etc. It will now be seen 

 that the vhole numbers form centres of triplets, having a minus 

 modification on one side, and a plus mr dification on the other. 

 This peculiar nomenclature will be clearly apprehended by the 

 following arrangement : — 



2% paune- tin — 3 1 



t paune-panch — 5 i 

 panch 5 >- 



a Tin Or a cnar 4t >- o paucn o > 



3^ sawa-tin 4-3 \ 4^ sawa-char -j-4 \ 5^ sawa-panch -f-5 ) 



In multiplying thefe fractions, therefore, the Indian boy has to 

 deal with only the minus and plus quantities. A simple instance 

 will illustrate this. " 7 times 99f " would be a puzzle to an Eng- 

 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, " Sat paune-saii ?" — three words meaning 

 "seven minus-hundreds?" The very form of the question tells. 

 him that he has only to deduct 7 quarters from 700, and he in- 

 stantly answers 698^. Equal facility is found with any similar 

 question, such as "5 times 14f ?" The Indian boy is asked, "Panoli 

 paune-pandrah ?" i.e., "5 minus-fifteens?" As the words are 

 uttered, he knows that he has only to deduct 5 quarters from 5, 

 fifteens; and he answers at once, "Paune chauhattrab," i.e.^ 

 " a quarter less four and-seventy " (73J). 



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 our preconceptions ; but it would be a 



1 In the ancient language there was also an optional form in conformity with 

 the English method. 



'^ Pa,o = J4 i adh = J^ ; paun = ^ ; paune = — J4 (M lessthanany number to 

 which it is prefixed) ; sawa = 1?4 (?4 more than any number to which it is pre- 

 fixed) ; sarhe = -|- J^ G^ more than any number to which it is prefixed) ; derh. 

 = 11^ (a number -f half itself) ; pawanna = 1%; arha.i = 2^ (twice and a halt 

 times any number); hCinth^ = 3^; dhauncha := 4^; pahuneha = 5J^, 



