Apbil 1, 1890.] 



KNOWLEDGE 



105 



themselves. The pads are, in fact, hollow and contain 

 protruding into their ca\-ity the nipple-shaped ends of a 

 sac which occupies more or less of the interior of the last 

 fom' tarsal joints. This sac secretes a j)erfectly clear, 

 viscid liquid, which exudes into the pad, and fi'om that 

 into the hairs which project from it. These hairs, which 

 are said to number about 1,200 on each pad, are hollow, 

 terminate in tubular orifices, and are kept full of the secre- 

 tion. Hence the entire surface of each pad is crowded 

 with a number of viscid points ; and as there are in all 

 twelve pads, two to each foot, these, when applied to the 

 surface over which the fly is walking produce an adhesion 

 sufficiently strong to support the slight weight of the 

 insect. The viscid liquid soon hardens on exposure to the 

 air, but no doubt remanis liquid while covered by the pad. 

 Thus the insect is, as it were, at every step, temporarily 

 glued to the surface over which it is travelling, and leaves 

 on a clean surface little rows of dots as its footprints. This 

 does not necessarily involve any violent strain in wrench- 

 ing the foot ofi' again, since the tarsus is raised obliquely 

 and each row of hairs is therefore successively detached, 

 somewhat in the same way as a piece of court plaster may 

 be easily removed from the hand by taking it up at one 

 end and raising it obliquely, though it might resist a con- 

 siderably greater strain if merely pulled at one end without 

 raising, all the points of contact then combining to resist 

 the strain. 



(T(i be continued, i 



HINDU ARITHMETIC. 



By Fredebic Pincott, M.R.A.S. 



El'ROPEANS who have resided in India have fi-e- 

 (juently expressed astonishment at the rajsidity 

 with which arithmetical calculations are mentally 

 made by very small Indian boys. Some account, 

 therefore, of the Indian method of teaching 

 arithmetic, which I believe to be superior to the English 

 methods, will probably be interesting to the readers of 

 Knowlkixje. 



The arithmetical system of I'hirope was revolutionized 

 by India, when the so-called Arabic figures which we daily 

 use were borrowed by Arab traders to the Malabar coast, 

 and by them introduced into Europe. It was Indian in- 

 telligence 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 arith- 

 metical computations as compared with the Greek and 

 Roman and the older Arabic methods. 



In order to explain the present Indian system of arith- 

 metic, it is necessary to premise that the J'dmlhex, or 

 schoolmasters, employ a number of terms unknown to 

 English teachers. These terms have been invented for 

 the purpose of facilitating calculation, and the astonishing 

 results achieved cannot be understood without compre- 

 hending the terms employed. The strangeness of the 

 names of the figures and fractions arrests the attention of 

 e\'ery student of Hindi. I'^cw Europeans 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," "2 and 10," "8 and 10," &c.,- up to 



* This is also tho orij{iiml meaniii]^' of the Eiifjlisli words elcrai, 

 iivelve, &c. , up to nineteen. 



" 8 and 10," but the word for 19 means " minus 20." 

 After 20 the same method is continued; "twenty-one" 

 being impossible, the form is invariably " 1 and 20, ' 

 " 2 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 Sanski-it language presents the same 

 peculiarity, t The object of this nomenclature is to facUi- 

 tate computation ; for, in reckoning, the mind has to deal 

 with the even tens, the simplest of all figures to multiply. 

 Thus the question " Nine times nineteen '? " is not a simple 

 one to an English child ; but the Indian boy would be 

 asked " Nine minus-twenties '? " In an instant he knows 

 that he has only to deduct 9 minus quantities fi'om 9 

 twenties, and the answer 171 comes before the English 

 boy has fully realized the question. The fonnidable diffi- 

 culty of the 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 " are unknown to him, the simple word 

 Idkli conveying the idea fuUy to his mind. So also " one 

 thousand mOlions " isarh; "one hundred thousand mil- 

 lions ' is kliarli, and so on. The advantages of this terse- 

 ness must be at once apparent. 



It is, however, with respect to fi'actional numbers that 

 the advantage of the Indian system of uomenclatm-e 

 becomes most conspicuous, when once understood. They 

 employ a large number of terms, which are given below.; 



These terms are preri-eed 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 nomenclature appears at first sight, 

 its difficulties disappear when brought to the test of prac- 

 tice. It is the outcome of centuries of practical expe- 

 rience ; and the thoughtful application of means to an 

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

 words, and the extraordinary arithmetical facOities they 

 afford, if I explain the use of paune, that is |, that being the 

 fi'action which the English cliild has most trouble with. 

 The Indian boy knows no such expression as " two and 

 three-quarters," in fact the term " three-quarters " in com- 

 bination \sith whole numbers, has no existence in his lan- 

 guage. His teacher resorts to the same device as has been 

 explained when speaking of the figure 9 ; he employs a 

 term which implies •' minus." By this process 2| becomes 

 panne tin, that is " minus 3," or " a quarter less 3," 

 and, in the same way, 3| is paune (7i(!)=" minus 4," and 

 so on. 



Precisely the same plan is adopted with reference to 

 the term saird, which implies " one quarter more " ; thus 

 3, 1, is saird «("«=:•' plus 3"; 4i is sand f/i>?r=" plus 4," 

 itc. etc. It will now be seen that the u/iole numbers form 

 centres of triplets, ha%'ing a minus modification on one 

 side, and a plus modification on the other. This peculiar 

 nomenclature will be clearly apprehended by the following 

 arrangement : — 



2J pauno-tin —3) 3J paune-chiir -4^ 4J pnune-panch -5'4 



3 tin 3,- 4 char 4!- 5 panch 5 >■ 



3J sawa-tiu -f 3) 4J sawa-char +i) 5J savr^-paQch +0) 



In multiplying these fractions, therefore, the Indian 



t In tlie ancient language thore was also an optional form in con- 

 formity with the English method. 



J PiijO = i ; adh =: i ; paun := J : panne = - i (J less than any 

 number to which it is pretixed) ; sawa ^ IJ (^ more than any 

 number to which it is pretixed) ; sarhe^ +h (J mi ro thjin ,iuy num- 

 ber to which it is pretixed); dorh=rlA (a number-!- half itself); 

 pawannfi = IJ ; ai'ha.i^: 2J (twice and a half times any number); 

 hiiiitha = 3J ; dhauncha = 4 J ; pahflnchiii^o.J. 



