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FEBRUARY, 1891.]
THE BURMESE SYSTEM OF ARITHMETIC.
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An application to a well known monastic calculator in Mandalay produced the following, written on black parabaik:
(1) Kogyaunglinga, multiplication verses. (2) Bølingá, astrological verses.
The enumeration of these books" is sufficient to shew the extent and nature of Burmese mathematical science. They do not, in fact, reduce their rales of thumb to writing as a general practice, but hand them down orally and by ocalar demonstration on the sand or in the dust about the monasteries.
It has been said above that the Burmese system of arithmetic is especially adapted to mental processes. Now, in adding 325 to 896, Europeans and Indians begin on paper with the units and work on to the tens and hundreds. This is the most convenient way, because each unit cipher of the calculation is discarded from the memory as it is jotted down. Thus 6 and 5 are 11, put down 1 and carry 1; 1 and 9 are 10, 10 and 2 are 12, put down 2 and carry 1; 1 and 8 are 9, 9 and 3 are 12, put down 12: result 1221. In each of the above processes the mind is not troubled with anything beyond the cipher to be carried forward. Bat the Bur. man reverses the process and commences by adding the hundreds, then the tens and lastly the units. He proceeds thus : 3 and 8 are 11, rub out 3 and 8 and put down 11:9 2 and 9 are 11, rab out 2 and 9 and put down 1 for 9, and the 1 carried forward under the unit of 11, thas 1116; then add the two 1 together, 1 and 1 are 2, rub them out and pat down 2 for the init
15 of 11, thus 1216: 5 and 6 are 11, rab oat 5 and 6, and substitute as before, thus 1211 ; then add
the two 1 as before and substitute, 1221. Q. E. D.
Now, for a paper process, this is awkward; but it requires less mental effort than the European method, and it is that in use in mental addition all the world over. Rapid mental calculations in Europe and Indian mental arithmetic are both done in this way. Thos a man in rapidly working out the above problem in his head will commence 300 and 80 ) = 1100; 20 and 90 = 110, total 1210 : 5 and 6 = 11, total 1221. The very rapid addition of account columns common in banks is really achieved in the same way: the pounds first, then the shillings, and lastly the penoe are calculated out. Thus to add mentally
319 241
678
14
1240 The operator will proceed thus: - £6 + 2 + 3=]1; 7+ 4+1=12, 122; 8+1+9= 18, 1238 : . J4 + 7 + 17 = 38, £ 1-18, £ 1239-18: d. 5 + 11 + 9 = 25, 28. 1 d., £ 1239 + £1 + 1 d., £ 1240-0-1. He then puts the result down, appearing to be able to calculate all three columns at once, but, of course, he does nothing of the kind in reality.
All the Burmese processes are worked in the same way. They begin with the large figures and go on to the units, rubbing out and substituting as they proceed.
. I have a small book of 86 pages printed at the Hanthawaddy (Hana vatt) Prosa, Rangoon, in 1889, and bearing the high-sounding title of Thumáhadibag. Bedinsigyd, which I take to mean "Astronomical Writings Iluminating the Maltitude," sigyd is Barmese meaning 'writings.' Bldin = Veda, which in Burma means an astronomical, or, more strictly, an astr slogical, work. The rest of the title represents the PAli Samdhadipaka. This book contains a large number of rules and methods for many sorta of caloulations, including the K88gyaung 2. Mlaga, &o., Dotioed above. It would probably be well worth a detailed examination.
• It being remembered that he always works by a process of erasing the steps of his onloulation as be proceede.
